# AlgEquiv: Answer test results

This page exposes the results of running answer tests on STACK test cases.  This page is automatically generated from the STACK unit tests and is designed to show question authors what answer tests actually do.  This includes cases where answer tests currentl fail, which gives a negative expected mark.  Comments and further test cases are very welcome.



<h2>AlgEquiv</h2><div class="no-overflow"><table class="flexible table table-striped table-hover generaltable generalbox stacktestsuite"><thead><tr><th class="header c0" scope="col">Test<div class="commands"></div></th><th class="header c1" scope="col">?<div class="commands"></div></th><th class="header c2" scope="col">Student response<div class="commands"></div></th><th class="header c3" scope="col">Teacher answer<div class="commands"></div></th><th class="header c4" scope="col">Opt<div class="commands"></div></th><th class="header c5" scope="col">Mark<div class="commands"></div></th><th class="header c6" scope="col">Answer note<div class="commands"></div></th>
</tr></thead><tbody>
<tr class="expectedfail">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:orange;"><i class="fa fa-adjust"></i></span></td>
  <td class="cell c2"><pre>1/0</pre></td>
  <td class="cell c3"><pre>1</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">-1</td>
  <td class="cell c6">ATAlgEquiv_STACKERROR_SAns.</td>
</tr>
<tr class="expectedfail">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">TEST_FAILED</td></td>
</tr>
<tr class="expectedfail">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">The answer test failed to execute correctly: please alert your teacher. Division by zero.</td></td>
</tr>
<tr class="expectedfail">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:orange;"><i class="fa fa-adjust"></i></span></td>
  <td class="cell c2"><pre>1</pre></td>
  <td class="cell c3"><pre>1/0</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">-1</td>
  <td class="cell c6">ATAlgEquiv_STACKERROR_TAns.</td>
</tr>
<tr class="expectedfail">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">TEST_FAILED</td></td>
</tr>
<tr class="expectedfail">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">The answer test failed to execute correctly: please alert your teacher. Division by zero.</td></td>
</tr>
<tr class="expectedfail">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:orange;"><i class="fa fa-adjust"></i></span></td>
  <td class="cell c2"><pre></pre></td>
  <td class="cell c3"><pre>(x-1)^2</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">-1</td>
  <td class="cell c6">ATAlgEquivTEST_FAILED-Empty SA.</td>
</tr>
<tr class="expectedfail">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">The answer test failed to execute correctly: please alert your teacher. Attempted to execute an answer test with an empty student answer, probably a CAS validation problem when authoring the question.</td></td>
</tr>
<tr class="expectedfail">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:orange;"><i class="fa fa-adjust"></i></span></td>
  <td class="cell c2"><pre>x^2</pre></td>
  <td class="cell c3"><pre></pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">-1</td>
  <td class="cell c6">ATAlgEquivTEST_FAILED-Empty TA.</td>
</tr>
<tr class="expectedfail">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">The answer test failed to execute correctly: please alert your teacher. Attempted to execute an answer test with an empty teacher answer, probably a CAS validation problem when authoring the question.</td></td>
</tr>
<tr class="expectedfail">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:orange;"><i class="fa fa-adjust"></i></span></td>
  <td class="cell c2"><pre>x-1)^2</pre></td>
  <td class="cell c3"><pre>(x-1)^2</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">-1</td>
  <td class="cell c6">ATAlgEquivTEST_FAILED-Empty SA.</td>
</tr>
<tr class="expectedfail">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">The answer test failed to execute correctly: please alert your teacher. Attempted to execute an answer test with an empty student answer, probably a CAS validation problem when authoring the question.</td></td>
</tr>
<tr class="notes">
  <td class="cell c0"><td colspan="6">See docs on subscripts and different atoms.</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x1</pre></td>
  <td class="cell c3"><pre>x_1</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x_1</pre></td>
  <td class="cell c3"><pre>x[1]</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x[1]</pre></td>
  <td class="cell c3"><pre>x1</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="notes">
  <td class="cell c0"><td colspan="6">Logic</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>true</pre></td>
  <td class="cell c3"><pre>true</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATLogic_True.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>false</pre></td>
  <td class="cell c3"><pre>false</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATLogic_True.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>true</pre></td>
  <td class="cell c3"><pre>false</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>false</pre></td>
  <td class="cell c3"><pre>true</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="notes">
  <td class="cell c0"><td colspan="6">Predicates</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>integerp(3)</pre></td>
  <td class="cell c3"><pre>true</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATLogic_True.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>integerp(3.1)</pre></td>
  <td class="cell c3"><pre>true</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>integerp(3)</pre></td>
  <td class="cell c3"><pre>false</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>integerp(3)</pre></td>
  <td class="cell c3"><pre>true</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATLogic_True.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>lowesttermsp(x^2/x)</pre></td>
  <td class="cell c3"><pre>true</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATLogic_True.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>lowesttermsp(-y/-x)</pre></td>
  <td class="cell c3"><pre>true</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATLogic_True.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>lowesttermsp((x^2-1)/(x-1))</pre></td>
  <td class="cell c3"><pre>true</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>lowesttermsp((x^2-1)/(x+2))</pre></td>
  <td class="cell c3"><pre>true</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATLogic_True.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>scientific_notationp(4.1561*10
^16)</pre></td>
  <td class="cell c3"><pre>true</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="notes">
  <td class="cell c0"><td colspan="6">Case sensitivity</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>X</pre></td>
  <td class="cell c3"><pre>x</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATAlgEquiv_WrongCase.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>1/(R-r)</pre></td>
  <td class="cell c3"><pre>1</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>exdowncase(X)</pre></td>
  <td class="cell c3"><pre>x</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>exdowncase((X-1)^2)</pre></td>
  <td class="cell c3"><pre>x^2-2*x+1</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="notes">
  <td class="cell c0"><td colspan="6">Permutations of variables (To do: a dedicated answer test with feedback)</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>Y=1+X</pre></td>
  <td class="cell c3"><pre>y=1+x</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATEquation_default</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>v+w+x+y+z</pre></td>
  <td class="cell c3"><pre>a+b+c+A+B</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="notes">
  <td class="cell c0"><td colspan="6">Numbers</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>4^(-1/2)</pre></td>
  <td class="cell c3"><pre>1/2</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>4^(1/2)</pre></td>
  <td class="cell c3"><pre>sqrt(4)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="notes">
  <td class="cell c0"><td colspan="6">Mix of floats and rational numbers</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>0.5</pre></td>
  <td class="cell c3"><pre>1/2</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>0.33</pre></td>
  <td class="cell c3"><pre>1/3</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>452</pre></td>
  <td class="cell c3"><pre>4.52*10^2</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>5.1e-2</pre></td>
  <td class="cell c3"><pre>51/1000</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>0.333333333333333</pre></td>
  <td class="cell c3"><pre>1/3</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>0.99999999</pre></td>
  <td class="cell c3"><pre>1</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>0.99999999</pre></td>
  <td class="cell c3"><pre>99999999/10^8</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>0.99999999</pre></td>
  <td class="cell c3"><pre>99999998/99999999</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>99999999/10^8</pre></td>
  <td class="cell c3"><pre>99999998/99999999</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>(0.5+x)*2</pre></td>
  <td class="cell c3"><pre>2*x+1</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>0.333333333333333*x^2</pre></td>
  <td class="cell c3"><pre>x^2/3</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>0.1*(2.0*s^2+6.0*s-25.0)/s</pre></td>
  <td class="cell c3"><pre>(2*s^2+6*s-25)/(10*s)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>0.1*(2.0*s^2+6.0*s-25.00001)/s</pre></td>
  <td class="cell c3"><pre>(2*s^2+6*s-25)/(10*s)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>100.4-80.0</pre></td>
  <td class="cell c3"><pre>20.4</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="notes">
  <td class="cell c0"><td colspan="6">Complex numbers</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>sqrt(-1)</pre></td>
  <td class="cell c3"><pre>%i</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>%i</pre></td>
  <td class="cell c3"><pre>e^(i*pi/2)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>(4*sqrt(3)*%i+4)^(1/5)</pre></td>
  <td class="cell c3"><pre>8^(1/5)*(cos(%pi/15)+%i*sin(%p
i/15))</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>(4*sqrt(3)*%i+4)^(1/5)</pre></td>
  <td class="cell c3"><pre>rectform((4*sqrt(3)*%i+4)^(1/5
))</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>(4*sqrt(3)*%i+4)^(1/5)</pre></td>
  <td class="cell c3"><pre>polarform((4*sqrt(3)*%i+4)^(1/
5))</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>5/4*%e^(%i*%pi/6)</pre></td>
  <td class="cell c3"><pre>5*sqrt(3)/8+5/8*%i</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>%i/sqrt(x)</pre></td>
  <td class="cell c3"><pre>sqrt(-1/x)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>%e^(%i*t)</pre></td>
  <td class="cell c3"><pre>cos(t)+%i*sin(t)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>%e^(%i*t)</pre></td>
  <td class="cell c3"><pre>%i*sin(t)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>%e^(%i*200*t)</pre></td>
  <td class="cell c3"><pre>%e^(%i*199*t)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>%i*sin(3*k)+cos(3*k)</pre></td>
  <td class="cell c3"><pre>%e^(3*%i*k)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>%i*(3*cos(k)^2*sin(k)-sin(k)^3
)-3*cos(k)*sin(k)^2+cos(k)^3</pre></td>
  <td class="cell c3"><pre>%e^(3*%i*k)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>%i*(3*cos(k)^2*sin(k)-sin(k)^3
)-3*cos(k)*sin(k)^2+cos(k)^3</pre></td>
  <td class="cell c3"><pre>%e^(7*%i*k)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>F(k-3)*%e^(31*%i*k)</pre></td>
  <td class="cell c3"><pre>F(k-3)*%e^(30*%i*k)+F(k+3)*%e^
(30*%i*k)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>F(k-3)*%e^(31*%i*k)</pre></td>
  <td class="cell c3"><pre>(algebraic_equivalence_trigexp
andp:false,F(k-3)*%e^(300*%i*k
)+F(k+3)*%e^(300*%i*k))</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>F(k)*sin(1000*k)</pre></td>
  <td class="cell c3"><pre>(algebraic_equivalence_trigexp
andp:false,F(k)*cos(1000*x))</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>(-%i*k^3*%e^(800*%i*k)*F(k+3)-
%i*F(k-3)*k^3*%e^(800*%i*k))/2</pre></td>
  <td class="cell c3"><pre>(algebraic_equivalence_trigexp
andp:false,-(%i*F(k-3)*k^3*%e^
(800*%i*k))/2)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>F(k)*%e^(1000*k)</pre></td>
  <td class="cell c3"><pre>(algebraic_equivalence_factorp
:false,F(k)*%e^(1000*x))</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>F(k)*%e^(1000*k)</pre></td>
  <td class="cell c3"><pre>F(k)*%e^(1000*k)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>sum(sin(n*x/6)*exp(-7*n^2*t/36
),n,1,inf)</pre></td>
  <td class="cell c3"><pre>%e^-(112*t)*sin(4*x)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>F(xi)</pre></td>
  <td class="cell c3"><pre>int(f(x)*%e^(-i*x*xi), x, -inf
, inf)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="notes">
  <td class="cell c0"><td colspan="6">Infinity</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>inf</pre></td>
  <td class="cell c3"><pre>inf</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>inf</pre></td>
  <td class="cell c3"><pre>-inf</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>2*inf</pre></td>
  <td class="cell c3"><pre>inf</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>0*inf</pre></td>
  <td class="cell c3"><pre>0</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>exp(-%i)</pre></td>
  <td class="cell c3"><pre>inf</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="notes">
  <td class="cell c0"><td colspan="6">Powers and roots</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x^(1/2)</pre></td>
  <td class="cell c3"><pre>sqrt(x)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x</pre></td>
  <td class="cell c3"><pre>sqrt(x^2)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>&#039;root(x)</pre></td>
  <td class="cell c3"><pre>x^(1/2)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>&#039;root(x)</pre></td>
  <td class="cell c3"><pre>sqrt(x)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>&#039;root(x,m)</pre></td>
  <td class="cell c3"><pre>x^(1/m)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x</pre></td>
  <td class="cell c3"><pre>&#039;root(x^2)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>abs(x)</pre></td>
  <td class="cell c3"><pre>sqrt(x^2)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>(assume(a&gt;0),a*sqrt(5))</pre></td>
  <td class="cell c3"><pre>sqrt(5*a^2)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>1/abs(x)^(1/3)</pre></td>
  <td class="cell c3"><pre>(abs(x)^(1/3)/abs(x))^(1/2)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>sqrt((x-3)*(x-5))</pre></td>
  <td class="cell c3"><pre>sqrt(x-3)*sqrt(x-5)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>1/sqrt(x)</pre></td>
  <td class="cell c3"><pre>sqrt(1/x)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x-1</pre></td>
  <td class="cell c3"><pre>(x^2-1)/(x+1)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>2^((1/5.1)*t)</pre></td>
  <td class="cell c3"><pre>2^((1/5.1)*t)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>2^((1/5.1)*t)</pre></td>
  <td class="cell c3"><pre>2^(0.196078431373*t)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>1-root(2)</pre></td>
  <td class="cell c3"><pre>1-2^(1/2)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>1-root(2)</pre></td>
  <td class="cell c3"><pre>1-sqrt(2)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>root(2,2)+1</pre></td>
  <td class="cell c3"><pre>1+sqrt(2)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>a^b*a^c</pre></td>
  <td class="cell c3"><pre>a^(b+c)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>(a^b)^c</pre></td>
  <td class="cell c3"><pre>a^(b*c)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>(assume(a&gt;0),(a^b)^c)</pre></td>
  <td class="cell c3"><pre>a^(b*c)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>(assume(x&gt;2),6*((x-2)^2)^k)</pre></td>
  <td class="cell c3"><pre>6*(x-2)^(2*k)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>signum(-3)</pre></td>
  <td class="cell c3"><pre>-1</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>6*((x-2)^3)^k</pre></td>
  <td class="cell c3"><pre>6*(x-2)^(3*k)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>(4*sqrt(3)*%i+4)^(1/5)</pre></td>
  <td class="cell c3"><pre>6^(1/5)*cos(%pi/15)-6^(1/5)*%i
*sin(%pi/15)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>2+2*sqrt(3+x)</pre></td>
  <td class="cell c3"><pre>2+sqrt(12+4*x)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>6*e^(6*(y^2+x^2))+72*x^2*e^(6*
(y^2+x^2))</pre></td>
  <td class="cell c3"><pre>(72*x^2+6)*e^(6*(y^2+x^2))</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="notes">
  <td class="cell c0"><td colspan="6">Expressions with subscripts</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>a1</pre></td>
  <td class="cell c3"><pre>a_1</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>rho*z*V/(4*pi*epsilon[0]*(R^2+
z^2)^(3/2))</pre></td>
  <td class="cell c3"><pre>rho*z*V/(4*pi*epsilon[0]*(R^2+
z^2)^(3/2))</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>rho*z*V/(4*pi*epsilon[1]*(R^2+
z^2)^(3/2))</pre></td>
  <td class="cell c3"><pre>rho*z*V/(4*pi*epsilon[0]*(R^2+
z^2)^(3/2))</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>sqrt(k/m)*sqrt(m/k)</pre></td>
  <td class="cell c3"><pre>1</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>(2*pi)/(k/m)^(1/2)</pre></td>
  <td class="cell c3"><pre>(2*pi)/(k/m)^(1/2)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>(2*pi)*(m/k)^(1/2)</pre></td>
  <td class="cell c3"><pre>(2*pi)/(k/m)^(1/2)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>sqrt(2*x/10+1)</pre></td>
  <td class="cell c3"><pre>sqrt((2*x+10)/10)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>&#039;root(2*x/10+1)</pre></td>
  <td class="cell c3"><pre>sqrt((2*x+10)/10)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>((x+3)^2*(x+3))^(1/3)</pre></td>
  <td class="cell c3"><pre>((x+3)*(x^2+6*x+9))^(1/3)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="notes">
  <td class="cell c0"><td colspan="6">Need to factor internally.</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>((x+3)^2*(x+3))^(1/3)</pre></td>
  <td class="cell c3"><pre>((x+3)*(x^2+6*x+9))^(1/3)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="notes">
  <td class="cell c0"><td colspan="6">Polynomials and rational function</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>(x-1)^2</pre></td>
  <td class="cell c3"><pre>x^2-2*x+1</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>(x-1)*(x^2+x+1)</pre></td>
  <td class="cell c3"><pre>x^3-1</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>(x-1)^(-2)</pre></td>
  <td class="cell c3"><pre>1/(x^2-2*x+1)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>1/(4*x-(%pi+sqrt(2)))</pre></td>
  <td class="cell c3"><pre>1/(x+1)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>(x-a)^6000</pre></td>
  <td class="cell c3"><pre>(x-a)^6000</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>(a-x)^6000</pre></td>
  <td class="cell c3"><pre>(x-a)^6000</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>(4*a-x)^6000</pre></td>
  <td class="cell c3"><pre>(x-4*a)^6000</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>(x-a)^6000</pre></td>
  <td class="cell c3"><pre>(x-a)^5999</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>(k+8)/(k^2+4*k-12)</pre></td>
  <td class="cell c3"><pre>(k+8)/(k^2+4*k-12)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>(k+7)/(k^2+4*k-12)</pre></td>
  <td class="cell c3"><pre>(k+8)/(k^2+4*k-12)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>-(2*k+6)/(k^2+4*k-12)</pre></td>
  <td class="cell c3"><pre>-(2*k+6)/(k^2+4*k-12)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>1/n-1/(n+1)</pre></td>
  <td class="cell c3"><pre>1/(n*(n+1))</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>1/(a-b)-1/(b-a)</pre></td>
  <td class="cell c3"><pre>1/(a-b)+1/(b-a)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>0.5*x^2+3*x-1</pre></td>
  <td class="cell c3"><pre>x^2/2+3*x-1</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>14336000000*x^13+250265600000*
x^12+1862860800000*x^11+762392
5760000*x^10+18290677760000*x^
9+24744757985280*x^8+145672123
51488*x^7-3267871272960*x^6-64
08053107200*x^5+670406720000*x
^4+1179708800000*x^3-429244800
000*x^2+56696000000*x-26800000
00</pre></td>
  <td class="cell c3"><pre>512*(2*x+5)^7*(5*x-1)^5*(70*x+
67)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>14336000000*x^13+250265600000*
x^12+1862860800000*x^11+762392
5760000*x^10+18290677760000*x^
9+24744757985280*x^8+145672123
51488*x^7-3267871272960*x^6-64
08053107200*x^5+670406720000*x
^4+1179708800000*x^3-429244800
000*x^2+56696000000*x-26800000
01</pre></td>
  <td class="cell c3"><pre>512*(2*x+5)^7*(5*x-1)^5*(70*x+
67)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>14336000000*x^13</pre></td>
  <td class="cell c3"><pre>512*(2*x+5)^7*(5*x-1)^5*(70*x+
67)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="notes">
  <td class="cell c0"><td colspan="6">Trig functions</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>cos(x)</pre></td>
  <td class="cell c3"><pre>cos(-x)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>cos(x)^2+sin(x)^2</pre></td>
  <td class="cell c3"><pre>1</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>cos(x+y)</pre></td>
  <td class="cell c3"><pre>cos(x)*cos(y)-sin(x)*sin(y)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>cos(x+y)</pre></td>
  <td class="cell c3"><pre>cos(x)*cos(y)+sin(x)*sin(y)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>(-1)^n*cos(x)^n</pre></td>
  <td class="cell c3"><pre>(-cos(x))^n</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>cos(x#pm#y)</pre></td>
  <td class="cell c3"><pre>cos(x)*cos(y)-(#pm#sin(x)*sin(
y))</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATLogic_True.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>sin(x#pm#y)</pre></td>
  <td class="cell c3"><pre>sin(x)*cos(y)#pm#cos(x)*sin(y)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATLogic_True.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>sin(x#pm#y)</pre></td>
  <td class="cell c3"><pre>cos(x)*sin(y)#pm#sin(x)*cos(y)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>2*cos(x)^2-1</pre></td>
  <td class="cell c3"><pre>cos(2*x)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>1.0*cos(1200*%pi*x)</pre></td>
  <td class="cell c3"><pre>cos(1200*%pi*x)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>diff(tan(10*x)^2,x)</pre></td>
  <td class="cell c3"><pre>cos(6*x)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>exp(%i*%pi)</pre></td>
  <td class="cell c3"><pre>-1</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>2*cos(2*x)+x+1</pre></td>
  <td class="cell c3"><pre>-sin(x)^2+3*cos(x)^2+x</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>4*x*cos(x^12/%pi)</pre></td>
  <td class="cell c3"><pre>x*cos(x^12/%pi)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>(2*sec(2*t)^2-2)/2</pre></td>
  <td class="cell c3"><pre>-(sin(4*t)^2-2*sin(4*t)+cos(4*
t)^2-1)*(sin(4*t)^2+2*sin(4*t)
+cos(4*t)^2-1)/(sin(4*t)^2+cos
(4*t)^2+2*cos(4*t)+1)^2</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>1+cosec(3*x)</pre></td>
  <td class="cell c3"><pre>1+csc(3*x)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>1/(1+exp(-2*x))</pre></td>
  <td class="cell c3"><pre>tanh(x)/2+1/2</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>1+cosech(3*x)</pre></td>
  <td class="cell c3"><pre>1+csch(3*x)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>-4*sec(4*z)^2*sin(6*z)-6*tan(4
*z)*cos(6*z)</pre></td>
  <td class="cell c3"><pre>-4*sec(4*z)^2*sin(6*z)-6*tan(4
*z)*cos(6*z)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>-4*sec(4*z)^2*sin(6*z)-6*tan(4
*z)*cos(6*z)</pre></td>
  <td class="cell c3"><pre>4*sec(4*z)^2*sin(6*z)+6*tan(4*
z)*cos(6*z)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>csc(6*x)^2*(7*sin(6*x)*cos(7*x
)-6*cos(6*x)*sin(7*x))</pre></td>
  <td class="cell c3"><pre>-(6*cos(6*x)*sin(7*x)-7*sin(6*
x)*cos(7*x))/sin(6*x)^2</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>csc(6*x)^2*(7*sin(6*x)*cos(7*x
)-6*cos(6*x)*sin(7*x))</pre></td>
  <td class="cell c3"><pre>(6*cos(6*x)*sin(7*x)-7*sin(6*x
)*cos(7*x))/sin(6*x)^2</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>-(7*x^6+4*x^3)/sin(7*y+x^7+x^4
+1)^2</pre></td>
  <td class="cell c3"><pre>-(7*x^6+4*x^3)*csc(7*y+x^7+x^4
+1)^2</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>sin((2*%pi*n-%pi)/2)</pre></td>
  <td class="cell c3"><pre>-cos(n*%pi)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>sin(x/2)/(1+tan(x)*tan(x/2))</pre></td>
  <td class="cell c3"><pre>sin(x/2)*cos(x)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>(declare(n,integer),trigrat(si
n((2*%pi*n-%pi)/2)))</pre></td>
  <td class="cell c3"><pre>-(-1)^n</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="expectedfail">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:orange;"><i class="fa fa-adjust"></i>!</span></td>
  <td class="cell c2"><pre>cot(%pi/20)+cot(%pi/24)-cot(%p
i/10)</pre></td>
  <td class="cell c3"><pre>sqrt(1)+sqrt(2)+sqrt(3)+sqrt(4
)+sqrt(5)+sqrt(6)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">-3</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>trigeval(cot(%pi/20)+cot(%pi/2
4)-cot(%pi/10))</pre></td>
  <td class="cell c3"><pre>sqrt(1)+sqrt(2)+sqrt(3)+sqrt(4
)+sqrt(5)+sqrt(6)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="expectedfail">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:orange;"><i class="fa fa-adjust"></i>!</span></td>
  <td class="cell c2"><pre>sin([1/8,1/6, 1/4, 1/3, 1/2, 1
]*%pi)</pre></td>
  <td class="cell c3"><pre>[sqrt(2-sqrt(2))/2,1/2,1/sqrt(
2),sqrt(3)/2,1,0]</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">-3</td>
  <td class="cell c6">(ATList_wrongentries 1).</td>
</tr>
<tr class="expectedfail">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">The entries underlined in red below are those that are incorrect. <span class="filter_mathjaxloader_equation"><span class="nolink">\[\left[ {\color{red}{\underline{\sin \left( \frac{\pi}{8} \right)}}} , \frac{1}{2} , \frac{1}{\sqrt{2}} , \frac{\sqrt{3}}{2} , 1 , 0 \right] \]</span></span></td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>trigeval(sin([1/8,1/6, 1/4, 1/
3, 1/2, 1]*%pi))</pre></td>
  <td class="cell c3"><pre>[sqrt(2-sqrt(2))/2,1/2,1/sqrt(
2),sqrt(3)/2,1,0]</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>1+x</pre></td>
  <td class="cell c3"><pre>taylor(1/(1-x),x,0,1)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>1</pre></td>
  <td class="cell c3"><pre>taylor(1/(1-x),x,0,1)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="notes">
  <td class="cell c0"><td colspan="6">Logarithms</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>log(a^2*b)</pre></td>
  <td class="cell c3"><pre>2*log(a)+log(b)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>(2*log(2*x)+x)/(2*x)</pre></td>
  <td class="cell c3"><pre>(log(2*x)+2)/(2*sqrt(x))</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>log(abs((x^2-9)))</pre></td>
  <td class="cell c3"><pre>log(abs(x-3))+log(abs(x+3))</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>lg(10^x)</pre></td>
  <td class="cell c3"><pre>x</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>lg(3^x,3)</pre></td>
  <td class="cell c3"><pre>x</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>lg(a^x,a)</pre></td>
  <td class="cell c3"><pre>x</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>1+lg(27,3)</pre></td>
  <td class="cell c3"><pre>4</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>1+lg(27,3)</pre></td>
  <td class="cell c3"><pre>3</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>lg(1/8,2)</pre></td>
  <td class="cell c3"><pre>-3</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>lg(root(x,n))</pre></td>
  <td class="cell c3"><pre>lg(x,10)/n</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>log(root(x,n))</pre></td>
  <td class="cell c3"><pre>lg(x,10)/n</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x^log(y)</pre></td>
  <td class="cell c3"><pre>y^log(x)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>log((x+1)/(1-x))</pre></td>
  <td class="cell c3"><pre>-log((1-x)/(x+1))</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>ratsimp(logcontract(log((x+1)/
(1-x))))</pre></td>
  <td class="cell c3"><pre>ratsimp(logcontract(-log((1-x)
/(x+1))))</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>log((x+1)/(1-x))</pre></td>
  <td class="cell c3"><pre>-log((1-x)/(x+2))</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="notes">
  <td class="cell c0"><td colspan="6">Hyperbolic trig</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>e^1-e^(-1)</pre></td>
  <td class="cell c3"><pre>2*sinh(1)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="notes">
  <td class="cell c0"><td colspan="6">Lists</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x</pre></td>
  <td class="cell c3"><pre>[1,2,3]</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATAlgEquiv_SA_not_list.</td>
</tr>
<tr class="pass">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">Your answer should be a list, but is not. Note that the syntax to enter a list is to enclose the comma separated values with square brackets.</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>[1,2]</pre></td>
  <td class="cell c3"><pre>[1,2,3]</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATList_wronglen.</td>
</tr>
<tr class="pass">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">Your list should have <span class="filter_mathjaxloader_equation"><span class="nolink">\(3\)</span></span> elements, but it actually has <span class="filter_mathjaxloader_equation"><span class="nolink">\(2\)</span></span>.</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>[1,2,4]</pre></td>
  <td class="cell c3"><pre>[1,2,3]</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">(ATList_wrongentries 3).</td>
</tr>
<tr class="pass">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">The entries underlined in red below are those that are incorrect. <span class="filter_mathjaxloader_equation"><span class="nolink">\[\left[ 1 , 2 , {\color{red}{\underline{4}}} \right] \]</span></span></td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>[1,x&gt;2]</pre></td>
  <td class="cell c3"><pre>[1,2&lt;x]</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>[1,2,[2-x&lt;0,{1,2,2,2, 1,3}]
]</pre></td>
  <td class="cell c3"><pre>[1,2,[2-x&lt;0,{1,2}]]</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">(ATList_wrongentries 3: (ATList_wrongentries 2: ATSet_wrongsz)).</td>
</tr>
<tr class="pass">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">The entries underlined in red below are those that are incorrect. <span class="filter_mathjaxloader_equation"><span class="nolink">\[\left[ 1 , 2 , \left[ 2-x < 0 , \left \{1 , 2 , 3 \right \} \right] \right] \]</span></span></td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>[(k+8)/(k^2+4*k-12),-(2*k+6)/(
k^2+4*k-12)]</pre></td>
  <td class="cell c3"><pre>[(k+8)/(k^2+4*k-12),-(2*k+6)/(
k^2+4*k-12)]</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>[1,2]</pre></td>
  <td class="cell c3"><pre>ntuple(1,2)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATAlgEquiv_SA_not_expression.</td>
</tr>
<tr class="pass">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">Your answer should be an expression, not an equation, inequality, list, set or matrix.</td></td>
</tr>
<tr class="notes">
  <td class="cell c0"><td colspan="6">Rounding of floats</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>round(0.5)</pre></td>
  <td class="cell c3"><pre>0.0</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>round(1.5)</pre></td>
  <td class="cell c3"><pre>2.0</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>round(2.5)</pre></td>
  <td class="cell c3"><pre>2.0</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>round(12.5)</pre></td>
  <td class="cell c3"><pre>12.0</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>significantfigures(0.5,1)</pre></td>
  <td class="cell c3"><pre>0.5</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>significantfigures(1.5,1)</pre></td>
  <td class="cell c3"><pre>2.0</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>significantfigures(2.5,1)</pre></td>
  <td class="cell c3"><pre>3.0</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>significantfigures(3.5,1)</pre></td>
  <td class="cell c3"><pre>4.0</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>significantfigures(11.5,2)</pre></td>
  <td class="cell c3"><pre>12.0</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>1500</pre></td>
  <td class="cell c3"><pre>scientific_notation(1500,3)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>1500</pre></td>
  <td class="cell c3"><pre>displaysci(1.5,2,3)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>[3,3.1,3.14,3.142,3.1416,3.141
59,3.141593,3.1415927]</pre></td>
  <td class="cell c3"><pre>makelist(significantfigures(%p
i,i),i,8)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="notes">
  <td class="cell c0"><td colspan="6">Sets</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x</pre></td>
  <td class="cell c3"><pre>{1,2,3}</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATAlgEquiv_SA_not_set.</td>
</tr>
<tr class="pass">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">Your answer should be a set, but is not. Note that the syntax to enter a set is to enclose the comma separated values with curly brackets.</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>co(1,2)</pre></td>
  <td class="cell c3"><pre>{1,2,3}</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATAlgEquiv_SA_not_set.</td>
</tr>
<tr class="pass">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">Your answer should be a set, but is not. Note that the syntax to enter a set is to enclose the comma separated values with curly brackets.</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>{1,2}</pre></td>
  <td class="cell c3"><pre>{1,2,3}</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATSet_wrongsz.</td>
</tr>
<tr class="pass">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">Your set should have <span class="filter_mathjaxloader_equation"><span class="nolink">\(3\)</span></span> different elements, but it actually has <span class="filter_mathjaxloader_equation"><span class="nolink">\(2\)</span></span>.</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>{2/4, 1/3}</pre></td>
  <td class="cell c3"><pre>{1/2, 1/3}</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>{A[1],A[2],A[4]}</pre></td>
  <td class="cell c3"><pre>{A[1],A[2],A[3]}</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATSet_wrongentries.</td>
</tr>
<tr class="pass">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">The following entries are incorrect, although they may appear in a simplified form from that which you actually entered. <span class="filter_mathjaxloader_equation"><span class="nolink">\[\left \{A_{4} \right \}\]</span></span></td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>{A[1],A[2],A[3]}</pre></td>
  <td class="cell c3"><pre>{A[1],A[2],A[3]}</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>{1,2,4}</pre></td>
  <td class="cell c3"><pre>{1,2,3}</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATSet_wrongentries.</td>
</tr>
<tr class="pass">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">The following entries are incorrect, although they may appear in a simplified form from that which you actually entered. <span class="filter_mathjaxloader_equation"><span class="nolink">\[\left \{4 \right \}\]</span></span></td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>{1,x&gt;4}</pre></td>
  <td class="cell c3"><pre>{4&lt;x, 1}</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>{x-1=0,x&gt;1 and 5&gt;x}</pre></td>
  <td class="cell c3"><pre>{x&gt;1 and x&lt;5,x=1}</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>{x-1=0,x&gt;1 and 5&gt;x}</pre></td>
  <td class="cell c3"><pre>{x&gt;1 and x&lt;5,x=2}</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATSet_wrongentries.</td>
</tr>
<tr class="pass">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">The following entries are incorrect, although they may appear in a simplified form from that which you actually entered. <span class="filter_mathjaxloader_equation"><span class="nolink">\[\left \{x-1=0 \right \}\]</span></span></td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>{x-1=0,x&gt;1 and 5&gt;x}</pre></td>
  <td class="cell c3"><pre>{x&gt;1 and x&lt;3,x=1}</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATSet_wrongentries.</td>
</tr>
<tr class="pass">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">The following entries are incorrect, although they may appear in a simplified form from that which you actually entered. <span class="filter_mathjaxloader_equation"><span class="nolink">\[\left \{5-x &gt; 0\,{\text{ and }}\, x-1 > 0 \right \}\]</span></span></td></td>
</tr>
<tr class="notes">
  <td class="cell c0"><td colspan="6">Equivalence for elements of sets is different from expressions: see docs.</td></td>
</tr>
<tr class="expectedfail">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:orange;"><i class="fa fa-adjust"></i>!</span></td>
  <td class="cell c2"><pre>{-sqrt(2)/sqrt(3)}</pre></td>
  <td class="cell c3"><pre>{-2/sqrt(6)}</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">-3</td>
  <td class="cell c6">ATSet_wrongentries.</td>
</tr>
<tr class="expectedfail">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">The following entries are incorrect, although they may appear in a simplified form from that which you actually entered. <span class="filter_mathjaxloader_equation"><span class="nolink">\[\left \{-\frac{\sqrt{2}}{\sqrt{3}} \right \}\]</span></span></td></td>
</tr>
<tr class="expectedfail">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:orange;"><i class="fa fa-adjust"></i>!</span></td>
  <td class="cell c2"><pre>{[-sqrt(2)/sqrt(3),0],[2/sqrt(
6),0]}</pre></td>
  <td class="cell c3"><pre>{[2/sqrt(6),0],[-2/sqrt(6),0]}</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">-3</td>
  <td class="cell c6">ATSet_wrongentries.</td>
</tr>
<tr class="expectedfail">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">The following entries are incorrect, although they may appear in a simplified form from that which you actually entered. <span class="filter_mathjaxloader_equation"><span class="nolink">\[\left \{\left[ -\frac{\sqrt{2}}{\sqrt{3}} , 0 \right] \right \}\]</span></span></td></td>
</tr>
<tr class="expectedfail">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:orange;"><i class="fa fa-adjust"></i>!</span></td>
  <td class="cell c2"><pre>{5/4*%e^(%i*%pi/6)}</pre></td>
  <td class="cell c3"><pre>{5*sqrt(3)/8+5/8*%i}</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">-3</td>
  <td class="cell c6">ATSet_wrongentries.</td>
</tr>
<tr class="expectedfail">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">The following entries are incorrect, although they may appear in a simplified form from that which you actually entered. <span class="filter_mathjaxloader_equation"><span class="nolink">\[\left \{\frac{5\cdot \mathrm{i}+5\cdot \sqrt{3}}{8} \right \}\]</span></span></td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>map(expand,{5/4*%e^(%i*%pi/6)}
)</pre></td>
  <td class="cell c3"><pre>{5*sqrt(3)/8+5/8*%i}</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>ratsimp({5/4*%e^(%i*%pi/6)})</pre></td>
  <td class="cell c3"><pre>ratsimp({5*sqrt(3)/8+5/8*%i})</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>ev(radcan({-sqrt(2)/sqrt(3)}),
simp)</pre></td>
  <td class="cell c3"><pre>ev(radcan({-2/sqrt(6)}),simp)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>ev(radcan(ratsimp({(-sqrt(10)/
2)-2,sqrt(10)/2-2},algebraic:t
rue)),simp)</pre></td>
  <td class="cell c3"><pre>ev(radcan(ratsimp({(-sqrt(5)/s
qrt(2))-2,sqrt(5)/sqrt(2)-2},a
lgebraic:true)),simp)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>(a^b)^c</pre></td>
  <td class="cell c3"><pre>a^(b*c)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>ev(radcan((a^b)^c),radexpand:a
ll,simp)</pre></td>
  <td class="cell c3"><pre>a^(b*c)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>(n+1)^((n+2)/(n+1))/(n+2)</pre></td>
  <td class="cell c3"><pre>1/(n+2)*((n+1)^(1/(n+1)))^(n+2
)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>ev(radcan((n+1)^((n+2)/(n+1))/
(n+2)),radexpand:all,simp)</pre></td>
  <td class="cell c3"><pre>ev(radcan(1/(n+2)*((n+1)^(1/(n
+1)))^(n+2)),radexpand:all,sim
p)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>{(2-2^(5/2))/2,(2^(5/2)+2)/2}</pre></td>
  <td class="cell c3"><pre>{1-2^(3/2),2^(3/2)+1}</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATSet_wrongentries.</td>
</tr>
<tr class="pass">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">The following entries are incorrect, although they may appear in a simplified form from that which you actually entered. <span class="filter_mathjaxloader_equation"><span class="nolink">\[\left \{\frac{2-2^{\frac{5}{2}}}{2} , \frac{2^{\frac{5}{2}}+2}{2} \right \}\]</span></span></td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>ev(radcan({(2-2^(5/2))/2,(2^(5
/2)+2)/2}),simp)</pre></td>
  <td class="cell c3"><pre>{1-2^(3/2),2^(3/2)+1}</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>{(x-a)^6000}</pre></td>
  <td class="cell c3"><pre>{(a-x)^6000}</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATSet_wrongentries.</td>
</tr>
<tr class="pass">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">The following entries are incorrect, although they may appear in a simplified form from that which you actually entered. <span class="filter_mathjaxloader_equation"><span class="nolink">\[\left \{{\left(x-a\right)}^{6000} \right \}\]</span></span></td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>{(k+8)/(k^2+4*k-12),-(2*k+6)/(
k^2+4*k-12)}</pre></td>
  <td class="cell c3"><pre>{(k+8)/(k^2+4*k-12),-(2*k+6)/(
k^2+4*k-12)}</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="notes">
  <td class="cell c0"><td colspan="6">Matrices</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>matrix([1,2],[2,3])</pre></td>
  <td class="cell c3"><pre>matrix([1,2],[2,3])</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>matrix([1,2],[2,3])</pre></td>
  <td class="cell c3"><pre>matrix([1,2,3],[2,3,3])</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATMatrix_wrongsz_columns.</td>
</tr>
<tr class="pass">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">Your matrix should be <span class="filter_mathjaxloader_equation"><span class="nolink">\(2\)</span></span> by <span class="filter_mathjaxloader_equation"><span class="nolink">\(3\)</span></span>, but it is actually <span class="filter_mathjaxloader_equation"><span class="nolink">\(2\)</span></span> by <span class="filter_mathjaxloader_equation"><span class="nolink">\(2\)</span></span>.</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>matrix([1,2],[2,3])</pre></td>
  <td class="cell c3"><pre>matrix([1,2],[2,5])</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATMatrix_wrongentries.</td>
</tr>
<tr class="pass">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">The entries underlined in red below are those that are incorrect. <span class="filter_mathjaxloader_equation"><span class="nolink">\[ \left[\begin{array}{cc} 1 & 2 \\ 2 & {\color{red}{\underline{3}}} \end{array}\right]\]</span></span></td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>matrix([0.33,1],[1,1])</pre></td>
  <td class="cell c3"><pre>matrix([0.333,1],[1,1])</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATMatrix_wrongentries.</td>
</tr>
<tr class="pass">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">The entries underlined in red below are those that are incorrect. <span class="filter_mathjaxloader_equation"><span class="nolink">\[ \left[\begin{array}{cc} {\color{red}{\underline{0.33}}} & 1 \\ 1 & 1 \end{array}\right]\]</span></span></td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>matrix([x+x,2],[2,x*x])</pre></td>
  <td class="cell c3"><pre>matrix([2*x,2],[2,x^2])</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>matrix([epsilon[0],2],[2,x^2])</pre></td>
  <td class="cell c3"><pre>matrix([epsilon[0],2],[2,x^2])</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>matrix([epsilon[2],2],[2,x^2])</pre></td>
  <td class="cell c3"><pre>matrix([epsilon[0],2],[2,x^3])</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATMatrix_wrongentries.</td>
</tr>
<tr class="pass">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">The entries underlined in red below are those that are incorrect. <span class="filter_mathjaxloader_equation"><span class="nolink">\[ \left[\begin{array}{cc} {\color{red}{\underline{\varepsilon_{2}}}} & 2 \\ 2 & {\color{red}{\underline{x^2}}} \end{array}\right]\]</span></span></td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>matrix([x&gt;4,{1,x^2}],[[1,2]
,[1,3]])</pre></td>
  <td class="cell c3"><pre>matrix([4-x&lt;0,{x^2, 1}],[[1
,2],[1,3]])</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>matrix([x&gt;4,{1,x^2}],[[1,2]
,[1,3]])</pre></td>
  <td class="cell c3"><pre>matrix([4-x&lt;0,{x^2, 1}],[[1
,2],[1,4]])</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATMatrix_wrongentries.</td>
</tr>
<tr class="pass">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">The entries underlined in red below are those that are incorrect. <span class="filter_mathjaxloader_equation"><span class="nolink">\[ \left[\begin{array}{cc} x > 4 & \left \{1 , x^2 \right \} \\ \left[ 1 , 2 \right] & \left[ 1 , {\color{red}{\underline{3}}} \right] \end{array}\right]\]</span></span></td></td>
</tr>
<tr class="notes">
  <td class="cell c0"><td colspan="6">Vectors</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>a</pre></td>
  <td class="cell c3"><pre>stackvector(a)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="notes">
  <td class="cell c0"><td colspan="6">Equations</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>1</pre></td>
  <td class="cell c3"><pre>x=1</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATAlgEquiv_SA_not_equation.</td>
</tr>
<tr class="pass">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">Your answer should be an equation, but is not.</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x=1</pre></td>
  <td class="cell c3"><pre>x=1</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATEquation_sides</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>1=x</pre></td>
  <td class="cell c3"><pre>1=x</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATEquation_sides</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>1=x</pre></td>
  <td class="cell c3"><pre>x=1</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATEquation_sides_op</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>1=1</pre></td>
  <td class="cell c3"><pre>1=x</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATEquation_default</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>1=1</pre></td>
  <td class="cell c3"><pre>x=1</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATEquation_default</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x=2</pre></td>
  <td class="cell c3"><pre>x=1</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATEquation_lhs_notrhs</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>2=x</pre></td>
  <td class="cell c3"><pre>x=1</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATEquation_default</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x=x</pre></td>
  <td class="cell c3"><pre>y=y</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATEquation_zero</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x+y=1</pre></td>
  <td class="cell c3"><pre>y=1-x</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>2*x+2*y=1</pre></td>
  <td class="cell c3"><pre>y=0.5-x</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATEquation_ratio</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>1/x+1/y=2</pre></td>
  <td class="cell c3"><pre>y = x/(2*x-1)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATEquation_ratio</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>y=sin(2*x)</pre></td>
  <td class="cell c3"><pre>y/2=cos(x)*sin(x)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATEquation_ratio</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>y=(x-a)^6000</pre></td>
  <td class="cell c3"><pre>y=(x-a)^6000</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATEquation_sides</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>y=(x-a)^5999</pre></td>
  <td class="cell c3"><pre>y=(x-a)^6000</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATEquation_lhs_notrhs</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>y=(a-x)^6000</pre></td>
  <td class="cell c3"><pre>y=(x-a)^6000</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATEquation_sides</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>y=(a-x)^5999</pre></td>
  <td class="cell c3"><pre>y=(x-a)^5999</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATEquation_lhs_notrhs</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>y=(a-x)^59999</pre></td>
  <td class="cell c3"><pre>y=(x-a)^5999</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATEquation_lhs_notrhs</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x+y=i</pre></td>
  <td class="cell c3"><pre>y=i-x</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>(1+%i)*(x+y)=0</pre></td>
  <td class="cell c3"><pre>y=-x</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>s^2*%e^(s*t)=0</pre></td>
  <td class="cell c3"><pre>s^2=0</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATEquation_default</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>0=-x+y/A+(y-z)/B</pre></td>
  <td class="cell c3"><pre>0=x-y/A-(y-z)/B</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x^6000-x^6001=x^5999</pre></td>
  <td class="cell c3"><pre>x^5999*(1-x+x^2)=0</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATEquation_ratio</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x^6000-x^6001=x^5999</pre></td>
  <td class="cell c3"><pre>x^5999*(1-x+x^3)=0</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATEquation_default</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>258552*x^7*(81*x^8+1)^398</pre></td>
  <td class="cell c3"><pre>x^3*(x^4+1)^399</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>Ia*(R1+R2+R3)-Ib*R3=0</pre></td>
  <td class="cell c3"><pre>-Ia*(R1+R2+R3)+Ib*R3=0</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>a=0 or b=0</pre></td>
  <td class="cell c3"><pre>a*b=0</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATEquation_sides</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>a*b=0</pre></td>
  <td class="cell c3"><pre>a=0 or b=0</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATEquation_sides</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>a*x=a*y</pre></td>
  <td class="cell c3"><pre>x=y</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATEquation_default</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>a*x=a*y</pre></td>
  <td class="cell c3"><pre>a=0 or x=y</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATEquation_ratio</td>
</tr>
<tr class="notes">
  <td class="cell c0"><td colspan="6">Unary Equations</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>1</pre></td>
  <td class="cell c3"><pre>stackeq(1)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>stackeq(1)</pre></td>
  <td class="cell c3"><pre>1</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>stackeq(1)</pre></td>
  <td class="cell c3"><pre>0</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="notes">
  <td class="cell c0"><td colspan="6">Equations: Loose/gain roots with nth powers of each side.</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x=y</pre></td>
  <td class="cell c3"><pre>x^2=y^2</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATEquation_default</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>(x-2)^2=0</pre></td>
  <td class="cell c3"><pre>x=2</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATEquation_default</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>4*x^2-71*x+220 = 0 or 14*x^2-9
1*x+140 = 0</pre></td>
  <td class="cell c3"><pre>x = 5/2 or x = 4 or x = 55/4</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATEquation_default</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>4*x^2-71*x+220 = 0 or 14*x^2-9
1*x+140 = 0</pre></td>
  <td class="cell c3"><pre>x = 5/2 or x = 4 or x=4 or x =
 55/4</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATEquation_sides</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x^2=4</pre></td>
  <td class="cell c3"><pre>x=2 or x=-2</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATEquation_ratio</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x^2=4</pre></td>
  <td class="cell c3"><pre>x=2 nounor x=-2</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATEquation_ratio</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x^2-5*x+6=0</pre></td>
  <td class="cell c3"><pre>x=2 nounor x=3</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATEquation_sides</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x^2-5*x+6=0</pre></td>
  <td class="cell c3"><pre>x=(5 #pm# sqrt(25-24))/2</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATEquation_sides</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x^2-5*x+6=0</pre></td>
  <td class="cell c3"><pre>x=(5 #pm# sqrt(25-23))/2</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATEquation_default</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>a^3*b^3=0</pre></td>
  <td class="cell c3"><pre>a=0 or b=0</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATEquation_default</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>a^3*b^3=0</pre></td>
  <td class="cell c3"><pre>a*b=0</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATEquation_default</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>(x-y)*(x+y)=0</pre></td>
  <td class="cell c3"><pre>x^2=y^2</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATEquation_ratio</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x=1</pre></td>
  <td class="cell c3"><pre>(x-1)^3=0</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATEquation_default</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>sqrt(x)=sqrt(y)</pre></td>
  <td class="cell c3"><pre>x=y</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATEquation_default</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x=sqrt(a)</pre></td>
  <td class="cell c3"><pre>x^2=a</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATEquation_default</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>(x-sqrt(a))*(x+sqrt(a))=0</pre></td>
  <td class="cell c3"><pre>x^2=a</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATEquation_ratio</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>(x-%i*sqrt(a))*(x+%i*sqrt(a))=
0</pre></td>
  <td class="cell c3"><pre>x^2=-a</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATEquation_ratio</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>(x-%i*sqrt(abs(a)))*(x+%i*sqrt
(abs(a)))=0</pre></td>
  <td class="cell c3"><pre>x^2=-abs(a)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATEquation_ratio</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>y=sqrt(1-x^2)</pre></td>
  <td class="cell c3"><pre>x^2+y^2=1</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATEquation_default</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>(y-sqrt(1-x^2))*(y+sqrt(1-x^2)
)=0</pre></td>
  <td class="cell c3"><pre>x^2+y^2=1</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATEquation_ratio</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>(y-sqrt((1-x)*(1+x)))*(y+sqrt(
(1-x)*(1+x)))=0</pre></td>
  <td class="cell c3"><pre>x^2+y^2=1</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATEquation_ratio</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>(x-1)*(x+1)*(y-1)*(y+1)=0</pre></td>
  <td class="cell c3"><pre>y^2+x^2=1+x^2*y^2</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATEquation_ratio</td>
</tr>
<tr class="notes">
  <td class="cell c0"><td colspan="6">Equations: edge cases. Teacher must enter an equation, all or none here.</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>all</pre></td>
  <td class="cell c3"><pre>x=x</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATEquation_zero</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>true</pre></td>
  <td class="cell c3"><pre>x=x</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATEquation_zero</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x=x</pre></td>
  <td class="cell c3"><pre>all</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATEquation_zero</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>all</pre></td>
  <td class="cell c3"><pre>all</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATEquation_zero</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>true</pre></td>
  <td class="cell c3"><pre>all</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATEquation_zero</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>a=a</pre></td>
  <td class="cell c3"><pre>x=x</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATEquation_zero</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>false</pre></td>
  <td class="cell c3"><pre>x=x</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATEquation_zero_fail</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>false</pre></td>
  <td class="cell c3"><pre>all</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATEquation_zero_fail</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>none</pre></td>
  <td class="cell c3"><pre>all</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATEquation_zero_fail</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>all</pre></td>
  <td class="cell c3"><pre>none</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATEquation_empty_fail</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>2=3</pre></td>
  <td class="cell c3"><pre>1=4</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATEquation_empty</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>2=3</pre></td>
  <td class="cell c3"><pre>2=4</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATEquation_empty</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>none</pre></td>
  <td class="cell c3"><pre>1=2</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATEquation_empty</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>false</pre></td>
  <td class="cell c3"><pre>1=2</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATEquation_empty</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>none</pre></td>
  <td class="cell c3"><pre>none</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATEquation_empty</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>false</pre></td>
  <td class="cell c3"><pre>none</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATEquation_empty</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>3=0</pre></td>
  <td class="cell c3"><pre>none</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATEquation_empty</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>0=3</pre></td>
  <td class="cell c3"><pre>none</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATEquation_empty</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>all</pre></td>
  <td class="cell c3"><pre>1=2</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATEquation_empty_fail</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>true</pre></td>
  <td class="cell c3"><pre>1=2</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATEquation_empty_fail</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>{}</pre></td>
  <td class="cell c3"><pre>1=2</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATAlgEquiv_SA_not_equation.</td>
</tr>
<tr class="pass">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">Your answer should be an equation, but is not.</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>[]</pre></td>
  <td class="cell c3"><pre>1=2</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATAlgEquiv_SA_not_equation.</td>
</tr>
<tr class="pass">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">Your answer should be an equation, but is not.</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>{}</pre></td>
  <td class="cell c3"><pre>none</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATAlgEquiv_SA_not_logic.</td>
</tr>
<tr class="pass">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">Your answer should be an equation, inequality or a logical combination of many of these, but is not.</td></td>
</tr>
<tr class="notes">
  <td class="cell c0"><td colspan="6">Sets of real numbers</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x^2</pre></td>
  <td class="cell c3"><pre>cc(1,3)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATAlgEquiv_SA_not_realset.</td>
</tr>
<tr class="pass">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">Your answer should be a subset of the real numbers. This could be a set of numbers, or a collection of intervals.</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>%union(oo(1,2),oo(3,4))</pre></td>
  <td class="cell c3"><pre>%union(oo(1,2),oo(3,4))</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATRealSet_true.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>%union(oc(1,2),co(2,3))</pre></td>
  <td class="cell c3"><pre>oo(1,3)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATRealSet_true.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>%union(oc(1,2),co(2,3))</pre></td>
  <td class="cell c3"><pre>cc(1,3)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATRealSet_false.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>{-1,1}</pre></td>
  <td class="cell c3"><pre>%union({-1,1})</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATRealSet_true.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>{1,3}</pre></td>
  <td class="cell c3"><pre>cc(1,3)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATRealSet_false.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>%intersection(oc(-1,1),co(1,2)
)</pre></td>
  <td class="cell c3"><pre>%union({1})</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATRealSet_true.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>oo(-inf,1)</pre></td>
  <td class="cell c3"><pre>oo(-inf,1)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATRealSet_true.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>oo(-1,inf)</pre></td>
  <td class="cell c3"><pre>oo(0,inf)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATRealSet_false.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>%union(oc(-inf,0),oo(-1,4))</pre></td>
  <td class="cell c3"><pre>oo(-inf,4)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATRealSet_true.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>%union(oo(-inf,1),oo(-1,inf))</pre></td>
  <td class="cell c3"><pre>oo(-inf,inf)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATRealSet_true.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>all</pre></td>
  <td class="cell c3"><pre>oo(-inf,inf)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATRealSet_true.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>co(1,2)</pre></td>
  <td class="cell c3"><pre>1 &lt;= x nounand x&lt;2</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATAlgEquiv_SA_not_logic.</td>
</tr>
<tr class="pass">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">Your answer should be an equation, inequality or a logical combination of many of these, but is not.</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>1 &lt;= x nounand x&lt;2</pre></td>
  <td class="cell c3"><pre>co(1,2)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATAlgEquiv_SA_not_realset.</td>
</tr>
<tr class="pass">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">Your answer should be a subset of the real numbers. This could be a set of numbers, or a collection of intervals.</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>minf &lt;= x</pre></td>
  <td class="cell c3"><pre>co(minf,inf)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATAlgEquiv_SA_not_realset.</td>
</tr>
<tr class="pass">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">Your answer should be a subset of the real numbers. This could be a set of numbers, or a collection of intervals.</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>-inf &lt;= x</pre></td>
  <td class="cell c3"><pre>co(minf,inf)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATAlgEquiv_SA_not_realset.</td>
</tr>
<tr class="pass">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">Your answer should be a subset of the real numbers. This could be a set of numbers, or a collection of intervals.</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x &lt;= inf</pre></td>
  <td class="cell c3"><pre>oc(minf,inf)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATAlgEquiv_SA_not_realset.</td>
</tr>
<tr class="pass">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">Your answer should be a subset of the real numbers. This could be a set of numbers, or a collection of intervals.</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>minf &lt;= x</pre></td>
  <td class="cell c3"><pre>oo(minf,inf)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATAlgEquiv_SA_not_realset.</td>
</tr>
<tr class="pass">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">Your answer should be a subset of the real numbers. This could be a set of numbers, or a collection of intervals.</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>stack_single_variable_solver(m
inf &lt;= x)</pre></td>
  <td class="cell c3"><pre>co(minf,inf)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATRealSet_true.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>stack_single_variable_solver(-
inf &lt;= x)</pre></td>
  <td class="cell c3"><pre>co(minf,inf)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATRealSet_true.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>stack_single_variable_solver(x
 &lt;= inf)</pre></td>
  <td class="cell c3"><pre>oc(minf,inf)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATRealSet_true.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>stack_single_variable_solver(m
inf &lt;= x)</pre></td>
  <td class="cell c3"><pre>oo(minf,inf)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATRealSet_false.</td>
</tr>
<tr class="notes">
  <td class="cell c0"><td colspan="6">Complex numbers</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>a=b/%i</pre></td>
  <td class="cell c3"><pre>%i*a=b</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATEquation_num_i</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>b/%i=a</pre></td>
  <td class="cell c3"><pre>%i*a=b</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATEquation_num_i</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>b=a/%i</pre></td>
  <td class="cell c3"><pre>%i*a=b</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATEquation_lhs_notrhs_op</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>a*(2+%i)=b</pre></td>
  <td class="cell c3"><pre>a=b/(2+%i)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATEquation_ratio</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>a*(2+%i)=b</pre></td>
  <td class="cell c3"><pre>a=b*(2-%i)/5</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATEquation_num_i</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>a*(2+%i)=b</pre></td>
  <td class="cell c3"><pre>a=b*(2-%i)/4</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATEquation_default</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>i</pre></td>
  <td class="cell c3"><pre>disp_complex(0,1)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="notes">
  <td class="cell c0"><td colspan="6">Absolute value in equations</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>abs(x)=abs(y)</pre></td>
  <td class="cell c3"><pre>x=y</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATEquation_default</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>abs(x)=abs(y)</pre></td>
  <td class="cell c3"><pre>x=y or x=-y</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>abs(x)=abs(y)</pre></td>
  <td class="cell c3"><pre>(x-y)*(x+y)=0</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="notes">
  <td class="cell c0"><td colspan="6">Functions</td></td>
</tr>
<tr class="expectedfail">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:orange;"><i class="fa fa-adjust"></i></span></td>
  <td class="cell c2"><pre>f(x):=1/0</pre></td>
  <td class="cell c3"><pre>f(x):=x^2</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">-1</td>
  <td class="cell c6">TEST_FAILED</td>
</tr>
<tr class="expectedfail">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">TEST_FAILED</td></td>
</tr>
<tr class="expectedfail">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">The answer test failed to execute correctly: please alert your teacher. Division by zero.</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>1</pre></td>
  <td class="cell c3"><pre>f(x):=x^2</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATAlgEquiv_SA_not_function.</td>
</tr>
<tr class="pass">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">Your answer should be a function, defined using the operator <tt>:=</tt>, but is not.</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>f(x)=x^2</pre></td>
  <td class="cell c3"><pre>f(x):=x^2</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATAlgEquiv_SA_not_function.</td>
</tr>
<tr class="pass">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">Your answer should be a function, defined using the operator <tt>:=</tt>, but is not.</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>f(x):=x^2</pre></td>
  <td class="cell c3"><pre>f(x,y):=x^2+y^2</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATFunction_length_args. ATFunction_false.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>f(x):=x^2</pre></td>
  <td class="cell c3"><pre>f(x)=x^2</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATAlgEquiv_SA_not_equation.</td>
</tr>
<tr class="pass">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">Your answer should be an equation, but is not.</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>f(x):=x^2</pre></td>
  <td class="cell c3"><pre>f(x):=x^2</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATFunction_true.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>f(x):=x^2</pre></td>
  <td class="cell c3"><pre>f(x):=sin(x)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATFunction_false.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>g(x):=x^2</pre></td>
  <td class="cell c3"><pre>f(x):=x^2</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATFunction_wrongname. ATFunction_true.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>f(y):=y^2</pre></td>
  <td class="cell c3"><pre>f(x):=x^2</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATFunction_arguments_different. ATFunction_true.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>f(a,b):=a^2+b^2</pre></td>
  <td class="cell c3"><pre>f(x,y):=x^2+y^2</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATFunction_arguments_different. ATFunction_true.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>-30*F</pre></td>
  <td class="cell c3"><pre>6*F(l-5*x)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="notes">
  <td class="cell c0"><td colspan="6">Inequalities</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>1</pre></td>
  <td class="cell c3"><pre>x&gt;1</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATAlgEquiv_SA_not_inequality.</td>
</tr>
<tr class="pass">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">Your answer should be an inequality, but is not.</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x=1</pre></td>
  <td class="cell c3"><pre>x&gt;1 and x&lt;5</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATAlgEquiv_TA_not_equation.</td>
</tr>
<tr class="pass">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">You have entered an equation, but an equation is not expected here. You may have typed something like "y=2*x+1" when you only needed to type "2*x+1".</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x&lt;1</pre></td>
  <td class="cell c3"><pre>x&gt;1</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATInequality_backwards.</td>
</tr>
<tr class="pass">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">Your inequality appears to be backwards.</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>1&lt;x</pre></td>
  <td class="cell c3"><pre>x&gt;1</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>a&lt;b</pre></td>
  <td class="cell c3"><pre>b&gt;a</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>2&lt;2*x</pre></td>
  <td class="cell c3"><pre>x&gt;1</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>-2&gt;-2*x</pre></td>
  <td class="cell c3"><pre>x&gt;1</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x&gt;1</pre></td>
  <td class="cell c3"><pre>x&lt;=1</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATInequality_strict. ATInequality_backwards.</td>
</tr>
<tr class="pass">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">Your inequality should not be strict! Your inequality appears to be backwards.</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x&gt;=2</pre></td>
  <td class="cell c3"><pre>x&lt;2</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATInequality_nonstrict. ATInequality_backwards.</td>
</tr>
<tr class="pass">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">Your inequality should be strict, but is not! Your inequality appears to be backwards.</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x&gt;=1</pre></td>
  <td class="cell c3"><pre>x&gt;2</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATInequality_nonstrict.</td>
</tr>
<tr class="pass">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">Your inequality should be strict, but is not!</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x&gt;1</pre></td>
  <td class="cell c3"><pre>x&gt;1</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x&gt;=1</pre></td>
  <td class="cell c3"><pre>x&gt;=1</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x&gt;2</pre></td>
  <td class="cell c3"><pre>x&gt;1</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>1&lt;x</pre></td>
  <td class="cell c3"><pre>x&gt;1</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>2*x&gt;=x^2</pre></td>
  <td class="cell c3"><pre>x^2&lt;=2*x</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>2*x&gt;=x^2</pre></td>
  <td class="cell c3"><pre>x^2&lt;=2*x</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>3*x^2&lt;9*a</pre></td>
  <td class="cell c3"><pre>x^2-3*a&lt;0</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x^2&gt;4</pre></td>
  <td class="cell c3"><pre>x&gt;2 or x&lt;-2</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATLogic_True.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>1&lt;x or x&lt;-3</pre></td>
  <td class="cell c3"><pre>x&lt;-3 or 1&lt;x</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATLogic_True.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>1&lt;x or x&lt;-3</pre></td>
  <td class="cell c3"><pre>x&lt;-1 or 3&lt;x</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x&gt;1 and x&lt;5</pre></td>
  <td class="cell c3"><pre>x&gt;1 and x&lt;5</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATLogic_True.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x&gt;1 and x&lt;5</pre></td>
  <td class="cell c3"><pre>5&gt;x and 1&lt;x</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATLogic_True.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>not (x&lt;=2 and -2&lt;=x)</pre></td>
  <td class="cell c3"><pre>x&gt;2 or -2&gt;x</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATLogic_True.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>sigma&gt;1</pre></td>
  <td class="cell c3"><pre>x&gt;1</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATInequality_solver.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>a&gt;1</pre></td>
  <td class="cell c3"><pre>x&gt;1</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATInequality_solver.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>sigma&gt;1</pre></td>
  <td class="cell c3"><pre>x&gt;2</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x&gt;2 or -2&gt;x</pre></td>
  <td class="cell c3"><pre>not (x&lt;=2 and -2&lt;=x)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATLogic_True.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x&gt;=1 or 1&lt;=x</pre></td>
  <td class="cell c3"><pre>x&gt;=1</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x&gt;=1 and x&lt;=1</pre></td>
  <td class="cell c3"><pre>x=1</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATInequality_solver.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>(x&gt;4 and x&lt;5) or (x&lt;-
4 and x&gt;-5) or (x+5&gt;0 an
d x&lt;-4)</pre></td>
  <td class="cell c3"><pre>(x&gt;-5 and x&lt;-4) or (x&gt
;4 and x&lt;5)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATLogic_True.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>(x&gt;4 and x&lt;5) or (x&lt;-
4 and x&gt;-5) or (x+5&gt;0 an
d x&lt;-4)</pre></td>
  <td class="cell c3"><pre>(x&gt;-5 and x&lt;-4) or (x&gt
;8 and x&lt;5)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>(x &lt; 0 nounor x &gt;= 1) no
unand x &lt;= 3</pre></td>
  <td class="cell c3"><pre>x &lt; 0 or (x &gt;= 1 and x &
lt;= 3)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATLogic_True.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>(x &lt; 0 nounor x &gt;= 1) no
unand x &lt;= 3</pre></td>
  <td class="cell c3"><pre>x &lt; 0 or x &gt;= 1 and x &l
t;= 3</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATLogic_True.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>(x &lt; 0 nounor x &gt;= 1) no
unand x &lt;= 3</pre></td>
  <td class="cell c3"><pre>x &lt; 0 or (x &gt;= 1 and x &
lt;= 3)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATLogic_True.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>(x &lt; 0 nounor x &gt;= 1) no
unand x &lt;= 3</pre></td>
  <td class="cell c3"><pre>(x &lt; 0 or x &gt;= 1) and x 
&lt;= 3</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATLogic_True.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>(x &lt; 0 nounor x &gt;= 1) no
unand x &lt;= 3</pre></td>
  <td class="cell c3"><pre>x &lt; 0 or (x &gt;= 1 and x &
lt;= 3)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATLogic_True.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>natural_domain(1/x^2)</pre></td>
  <td class="cell c3"><pre>natural_domain(1/x)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATRealSet_true.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x^4&gt;=0</pre></td>
  <td class="cell c3"><pre>x^2&gt;=0</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x^4&gt;=16</pre></td>
  <td class="cell c3"><pre>x^2&gt;=4</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x^4&gt;=16</pre></td>
  <td class="cell c3"><pre>x^2&gt;=4</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>-3&lt;=x</pre></td>
  <td class="cell c3"><pre>-3&lt;=x nounand x&lt;=3</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>{2,-2}</pre></td>
  <td class="cell c3"><pre>x&gt;2 nounor -2&gt;x</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATAlgEquiv_SA_not_logic.</td>
</tr>
<tr class="pass">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">Your answer should be an equation, inequality or a logical combination of many of these, but is not.</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x^2&lt;4</pre></td>
  <td class="cell c3"><pre>x&lt;2 nounand x&gt;-2</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATLogic_Solver_True.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x^2&lt;6</pre></td>
  <td class="cell c3"><pre>x&lt;2 nounand x&gt;-2</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x&gt;1 nounand x&lt;-1</pre></td>
  <td class="cell c3"><pre>false</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATLogic_Solver_True.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x&gt;1 nounand x&lt;3</pre></td>
  <td class="cell c3"><pre>true</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x&gt;1 nounor x&lt;3</pre></td>
  <td class="cell c3"><pre>true</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATLogic_Solver_True.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x&gt;1 nounor x&lt;3</pre></td>
  <td class="cell c3"><pre>all</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATLogic_Solver_True.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>abs(x)&lt;1</pre></td>
  <td class="cell c3"><pre>abs(x)&lt;1</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>abs(x)&lt;1</pre></td>
  <td class="cell c3"><pre>abs(x)&lt;2</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>abs(x)&lt;1</pre></td>
  <td class="cell c3"><pre>abs(x)&gt;1</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATInequality_backwards.</td>
</tr>
<tr class="pass">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">Your inequality appears to be backwards.</td></td>
</tr>
<tr class="expectedfail">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:orange;"><i class="fa fa-adjust"></i>!</span></td>
  <td class="cell c2"><pre>abs(x)&lt;2</pre></td>
  <td class="cell c3"><pre>-2&lt;x and x&lt;2</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">-3</td>
  <td class="cell c6"></td>
</tr>
<tr class="expectedfail">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:orange;"><i class="fa fa-adjust"></i>!</span></td>
  <td class="cell c2"><pre>-2&lt;x and x&lt;2</pre></td>
  <td class="cell c3"><pre>abs(x)&lt;2</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">-3</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>abs(x)&lt;2</pre></td>
  <td class="cell c3"><pre>-1&lt;x and x&lt;1</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x^2&lt;=9</pre></td>
  <td class="cell c3"><pre>abs(x)&lt;3</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="expectedfail">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:orange;"><i class="fa fa-adjust"></i>!</span></td>
  <td class="cell c2"><pre>x^2&lt;=9</pre></td>
  <td class="cell c3"><pre>abs(x)&lt;=3</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">-3</td>
  <td class="cell c6"></td>
</tr>
<tr class="expectedfail">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:orange;"><i class="fa fa-adjust"></i>!</span></td>
  <td class="cell c2"><pre>x^6&lt;1</pre></td>
  <td class="cell c3"><pre>abs(x)&lt;1</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">-3</td>
  <td class="cell c6"></td>
</tr>
<tr class="expectedfail">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:orange;"><i class="fa fa-adjust"></i>!</span></td>
  <td class="cell c2"><pre>abs(x)&gt;1</pre></td>
  <td class="cell c3"><pre>x&lt;-1 or x&gt;1</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">-3</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>minf &lt; x</pre></td>
  <td class="cell c3"><pre>minf &lt;= x</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATInequality_strict.</td>
</tr>
<tr class="pass">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">Your inequality should not be strict!</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x&gt;minf</pre></td>
  <td class="cell c3"><pre>minf &lt; x</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x&gt;-inf</pre></td>
  <td class="cell c3"><pre>minf &lt; x</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x&lt;2*inf</pre></td>
  <td class="cell c3"><pre>x&lt;inf</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>minf &lt; x nounand x &lt;1</pre></td>
  <td class="cell c3"><pre>x&lt;1</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>minf &lt; x nounand x &lt;1</pre></td>
  <td class="cell c3"><pre>x&lt;2</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="notes">
  <td class="cell c0"><td colspan="6">Maxima and infinity</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>2*inf</pre></td>
  <td class="cell c3"><pre>inf</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>-inf</pre></td>
  <td class="cell c3"><pre>minf</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="notes">
  <td class="cell c0"><td colspan="6">Not equal to</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x#1</pre></td>
  <td class="cell c3"><pre>x#1</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATLogic_True.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x#(1+1)</pre></td>
  <td class="cell c3"><pre>x#2</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATLogic_True.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>1#x</pre></td>
  <td class="cell c3"><pre>x#1</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATLogic_True.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>a#b</pre></td>
  <td class="cell c3"><pre>b#a</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x#2</pre></td>
  <td class="cell c3"><pre>x-2#0</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATLogic_True.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>[x#2]</pre></td>
  <td class="cell c3"><pre>[x-2#0]</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x-3#0</pre></td>
  <td class="cell c3"><pre>x#2</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x#2</pre></td>
  <td class="cell c3"><pre>x&lt;2 nounor x&gt;2</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATLogic_Solver_True.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x^2-3#1</pre></td>
  <td class="cell c3"><pre>x&lt;-2 nounor (x&lt;-2 and x&
lt;2) nounor 2&lt;x</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x^2-3#1</pre></td>
  <td class="cell c3"><pre>x&lt;-2 nounor (-2&lt;x and x&
lt;2) nounor 2&lt;x</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATLogic_Solver_True.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x#1</pre></td>
  <td class="cell c3"><pre>x#0</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="notes">
  <td class="cell c0"><td colspan="6">Surds</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>sqrt(12)</pre></td>
  <td class="cell c3"><pre>2*sqrt(3)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>sqrt(11+6*sqrt(2))</pre></td>
  <td class="cell c3"><pre>3+sqrt(2)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>(19601-13860*sqrt(2))^(7/4)</pre></td>
  <td class="cell c3"><pre>(5*sqrt(2)-7)^7</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>(19601-13861*sqrt(2))^(7/4)</pre></td>
  <td class="cell c3"><pre>(5*sqrt(2)-7)^7</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>(19601-13861*sqrt(2))^(7/4)</pre></td>
  <td class="cell c3"><pre>(5*sqrt(2)-7)^7</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>sqrt(2*log(26)+4-2*log(2))</pre></td>
  <td class="cell c3"><pre>sqrt(2*log(13)+4)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>sqrt(2)*sqrt(3)+2*(sqrt(2/3))*
x-(2/3)*(sqrt(2/3))*x^2+(4/9)*
(sqrt(2/3))*x^3</pre></td>
  <td class="cell c3"><pre>4*sqrt(6)*x^3/27-(2*sqrt(6)*x^
2)/9+(2*sqrt(6)*x)/3+sqrt(6)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x = -1/2 + sqrt(1/4 + 4/3)</pre></td>
  <td class="cell c3"><pre>x = (-3 + sqrt(9 + 48))/6</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATEquation_sides</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>{x = -1/2 + sqrt(1/4 + 4/3), x
 = (-1/2 - sqrt(1/4 + 4/3))}</pre></td>
  <td class="cell c3"><pre>{x = (-3 + sqrt(9 + 48))/6, x 
= (-3 - sqrt(9 + 48))/6}</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATSet_wrongentries.</td>
</tr>
<tr class="pass">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">The following entries are incorrect, although they may appear in a simplified form from that which you actually entered. <span class="filter_mathjaxloader_equation"><span class="nolink">\[\left \{x-\frac{\sqrt{19}-\sqrt{3}}{2\cdot \sqrt{3}}=0 , x+\frac{ \sqrt{19}+\sqrt{3}}{2\cdot \sqrt{3}}=0 \right \}\]</span></span></td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>radcan(trigrat({x = -1/2 + sqr
t(1/4 + 4/3), x = (-1/2 - sqrt
(1/4 + 4/3))}))</pre></td>
  <td class="cell c3"><pre>radcan(trigrat({x = (-3 + sqrt
(9 + 48))/6, x = (-3 - sqrt(9 
+ 48))/6}))</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="notes">
  <td class="cell c0"><td colspan="6">Factorials and binomials</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>(n+1)*n!</pre></td>
  <td class="cell c3"><pre>(n+1)!</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>n/n!</pre></td>
  <td class="cell c3"><pre>1/(n-1)!</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>n/n!</pre></td>
  <td class="cell c3"><pre>1/(n+1)!</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>n!/((k-1)!*(n-k+1)!)</pre></td>
  <td class="cell c3"><pre>n!*k/(k!*(n-k+1)!)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>n!/(k!*(n-k)!)</pre></td>
  <td class="cell c3"><pre>n!*(n-k+1)/(k!*(n-k+1)!)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>n!/(k!*(n-k)!)</pre></td>
  <td class="cell c3"><pre>binomial(n,k)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>binomial(n,k)+binomial(n,k+1)</pre></td>
  <td class="cell c3"><pre>binomial(n+1,k+1)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>n!/((k-1)!*(n-k+1)!)+n!/(k!*(n
-k)!)</pre></td>
  <td class="cell c3"><pre>n!*k/(k!*(n-k+1)!)+n!*(n-k+1)/
(k!*(n-k+1)!)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>binomial(n,k)+binomial(n,k+1)</pre></td>
  <td class="cell c3"><pre>binomial(n+1,k)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>binomial(n,k)</pre></td>
  <td class="cell c3"><pre>binomial(n,n-k)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>175!*56!/(55!*176!)</pre></td>
  <td class="cell c3"><pre>17556/55176</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>binomial(58,[9,15,20,14])</pre></td>
  <td class="cell c3"><pre>binomial(58,[15,9,20,14])</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>binomial(x,[a,b,c])</pre></td>
  <td class="cell c3"><pre>binomial(x,[b,c,a])</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="notes">
  <td class="cell c0"><td colspan="6">Unevaluated derviatives</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>3*s*diff(q(s),s)</pre></td>
  <td class="cell c3"><pre>3*s*diff(q(s),s)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>3*t*diff(q(s),s)</pre></td>
  <td class="cell c3"><pre>3*diff(t*q(s),s)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>diff(diff(q(s),s),s)</pre></td>
  <td class="cell c3"><pre>diff(q(s),s,2)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="notes">
  <td class="cell c0"><td colspan="6">Sums and products</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>sum(k^n,n,0,3)</pre></td>
  <td class="cell c3"><pre>sum(k^n,n,0,3)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>1+k+k^2+k^3</pre></td>
  <td class="cell c3"><pre>sum(k^n,n,0,3)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>1+k+k^2</pre></td>
  <td class="cell c3"><pre>sum(k^n,n,0,3)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>n*(n+1)*(2*n+1)/6</pre></td>
  <td class="cell c3"><pre>sum(k^2,k,1,n)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>sum((k+1)^2,k,0,n-1)</pre></td>
  <td class="cell c3"><pre>sum(k^2,k,1,n)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>product(cos(k*x),k,1,3)</pre></td>
  <td class="cell c3"><pre>product(cos(k*x),k,1,3)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>cos(x)*cos(2*x)*cos(3*x)</pre></td>
  <td class="cell c3"><pre>product(cos(k*x),k,1,3)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>cos(x)*cos(2*x)</pre></td>
  <td class="cell c3"><pre>product(cos(k*x),k,1,3)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="notes">
  <td class="cell c0"><td colspan="6">Scientific units are ignored</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>9.81*m/s^2</pre></td>
  <td class="cell c3"><pre>stackunits(9.81,m/s^2)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>6*stackunits(1,m)</pre></td>
  <td class="cell c3"><pre>stackunits(6,m)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>stackunits(2,m)^2</pre></td>
  <td class="cell c3"><pre>stackunits(4,m^2)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>stackunits(2,s)^2</pre></td>
  <td class="cell c3"><pre>stackunits(4,m^2)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>stack_units_nums(stackunits_ma
ke(m/s))</pre></td>
  <td class="cell c3"><pre>1</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>stack_units_nums(stackunits_ma
ke(m/s))</pre></td>
  <td class="cell c3"><pre>NULLNUM</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>ev(stack_units_nums(stackunits
_make(m/s)),NULLNUM=1)</pre></td>
  <td class="cell c3"><pre>1</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="notes">
  <td class="cell c0"><td colspan="6">Maxima does not simplify -inf (I agree!)</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>-inf</pre></td>
  <td class="cell c3"><pre>minf</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="notes">
  <td class="cell c0"><td colspan="6">These currently fail</td></td>
</tr>
<tr class="expectedfail">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:orange;"><i class="fa fa-adjust"></i>!</span></td>
  <td class="cell c2"><pre>2/%i*ln(sqrt((1+z)/2)+%i*sqrt(
(1-z)/2))</pre></td>
  <td class="cell c3"><pre>-%i*ln(z+%i*sqrt(1-z^2))</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">-3</td>
  <td class="cell c6"></td>
</tr>
<tr class="expectedfail">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:orange;"><i class="fa fa-adjust"></i>!</span></td>
  <td class="cell c2"><pre>abs(x^2-4)/(abs(x-2)*abs(x+2))</pre></td>
  <td class="cell c3"><pre>1</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">-3</td>
  <td class="cell c6"></td>
</tr>
<tr class="expectedfail">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:orange;"><i class="fa fa-adjust"></i>!</span></td>
  <td class="cell c2"><pre>abs(x^2-4)</pre></td>
  <td class="cell c3"><pre>abs(x-2)*abs(x+2)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">-3</td>
  <td class="cell c6"></td>
</tr>
<tr class="expectedfail">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:orange;"><i class="fa fa-adjust"></i>!</span></td>
  <td class="cell c2"><pre>(sqrt(108)+10)^(1/3)-(sqrt(108
)-10)^(1/3)</pre></td>
  <td class="cell c3"><pre>2</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">-3</td>
  <td class="cell c6"></td>
</tr>
<tr class="expectedfail">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:orange;"><i class="fa fa-adjust"></i>!</span></td>
  <td class="cell c2"><pre>(sqrt(2+sqrt(2))+sqrt(2-sqrt(2
)))/(2*sqrt(2))</pre></td>
  <td class="cell c3"><pre>sqrt(sqrt(2)+2)/2</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">-3</td>
  <td class="cell c6"></td>
</tr>
<tr class="expectedfail">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:orange;"><i class="fa fa-adjust"></i>!</span></td>
  <td class="cell c2"><pre>sqrt(2*x*sqrt(x^2+1)+2*x^2+1)-
sqrt(x^2+1)-x</pre></td>
  <td class="cell c3"><pre>0</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">-3</td>
  <td class="cell c6"></td>
</tr>
<tr class="expectedfail">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:orange;"><i class="fa fa-adjust"></i>!</span></td>
  <td class="cell c2"><pre>(77+20*sqrt(13))^(1/6)-(77-20*
sqrt(13))^(1/6)</pre></td>
  <td class="cell c3"><pre>1</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">-3</td>
  <td class="cell c6"></td>
</tr>
<tr class="expectedfail">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:orange;"><i class="fa fa-adjust"></i>!</span></td>
  <td class="cell c2"><pre>(930249+416020*sqrt(5))^(1/30)
-(930249-416020*sqrt(5))^(1/30
)</pre></td>
  <td class="cell c3"><pre>1</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">-3</td>
  <td class="cell c6"></td>
</tr>
<tr class="expectedfail">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:orange;"><i class="fa fa-adjust"></i>!</span></td>
  <td class="cell c2"><pre>cos(2*%pi/17)</pre></td>
  <td class="cell c3"><pre>(-1+sqrt(17)+sqrt(34-2*sqrt(17
)))/16+(2*sqrt(17+3*sqrt(17)-s
qrt(34-2*sqrt(17))-2*sqrt(34+2
*sqrt(17))))/16</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">-3</td>
  <td class="cell c6"></td>
</tr>
<tr class="expectedfail">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:orange;"><i class="fa fa-adjust"></i>!</span></td>
  <td class="cell c2"><pre>(41-sqrt(511))/2</pre></td>
  <td class="cell c3"><pre>(sqrt((4*(cos((1/2*(acos((61/1
040*sqrt(130)))-atan(11/3)))))
^(2))+21)-(2*cos((1/2*(acos((6
1/1040*sqrt(130)))-atan(11 / 3
))))))^(2)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">-3</td>
  <td class="cell c6"></td>
</tr>
<tr class="expectedfail">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:orange;"><i class="fa fa-adjust"></i>!</span></td>
  <td class="cell c2"><pre>a*(1+sqrt(2))=b</pre></td>
  <td class="cell c3"><pre>a=b*(sqrt(2)-1)/3</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">-3</td>
  <td class="cell c6">ATEquation_default</td>
</tr>
<tr class="notes">
  <td class="cell c0"><td colspan="6">This is only equivalent for x>=0...</td></td>
</tr>
<tr class="expectedfail">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:orange;"><i class="fa fa-adjust"></i>!</span></td>
  <td class="cell c2"><pre>atan(1/2)</pre></td>
  <td class="cell c3"><pre>%pi/2-atan(2)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">-3</td>
  <td class="cell c6"></td>
</tr>
<tr class="notes">
  <td class="cell c0"><td colspan="6">This is true for all x...</td></td>
</tr>
<tr class="expectedfail">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:orange;"><i class="fa fa-adjust"></i>!</span></td>
  <td class="cell c2"><pre>asinh(x)</pre></td>
  <td class="cell c3"><pre>ln(x+sqrt(x^2+1))</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">-3</td>
  <td class="cell c6"></td>
</tr>
<tr class="notes">
  <td class="cell c0"><td colspan="6">Logical expressions</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>true and false</pre></td>
  <td class="cell c3"><pre>false</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATLogic_True.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>true or false</pre></td>
  <td class="cell c3"><pre>false</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>A and B</pre></td>
  <td class="cell c3"><pre>B and A</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATLogic_True.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>A and B</pre></td>
  <td class="cell c3"><pre>C and A</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>A and B=C</pre></td>
  <td class="cell c3"><pre>C=B and A</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATLogic_True.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>A and (B and C)</pre></td>
  <td class="cell c3"><pre>A and B and C</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATLogic_True.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>A and (B or C)</pre></td>
  <td class="cell c3"><pre>A and (B or C)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATLogic_True.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>(A and B) or (A and C)</pre></td>
  <td class="cell c3"><pre>A and (B or C)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATLogic_True.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>-(b#pm#sqrt(b^2-4*a*c))</pre></td>
  <td class="cell c3"><pre>-b#pm#sqrt(b^2-4*a*c)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATLogic_True.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x=-b#pm#c^2</pre></td>
  <td class="cell c3"><pre>x=c^2-b or x=-c^2-b</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATEquation_sides</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x=b#pm#c^2</pre></td>
  <td class="cell c3"><pre>x=c^2-b or x=-c^2-b</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATEquation_default</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x#pm#a = y#pm#b</pre></td>
  <td class="cell c3"><pre>x#pm#a = y#pm#b</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATEquation_sides</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>x#pm#a = y#pm#b</pre></td>
  <td class="cell c3"><pre>x#pm#a = y#pm#c</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATEquation_lhs_notrhs</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>not(A) and not(B)</pre></td>
  <td class="cell c3"><pre>not(A or B)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATLogic_True.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>not(A) and not(B)</pre></td>
  <td class="cell c3"><pre>not(A and B)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>not(A) or B</pre></td>
  <td class="cell c3"><pre>boolean_form(A implies B)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>not(A) or B</pre></td>
  <td class="cell c3"><pre>A implies B</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATLogic_True.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>not(A) and B</pre></td>
  <td class="cell c3"><pre>A implies B</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>(not A and B) or (not B and A)</pre></td>
  <td class="cell c3"><pre>A xor B</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATLogic_True.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>(A and B) or (not A and not B)</pre></td>
  <td class="cell c3"><pre>A xnor B</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATLogic_True.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>((not A) and (not B)) or ((not
 A) and B)</pre></td>
  <td class="cell c3"><pre>not A</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATLogic_True.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>(A xor B) nounand (A xnor B)</pre></td>
  <td class="cell c3"><pre>false</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATLogic_True.</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>{not(A) or B,A and B}</pre></td>
  <td class="cell c3"><pre>{A implies B,A and B}</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATSet_wrongentries.</td>
</tr>
<tr class="pass">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">The following entries are incorrect, although they may appear in a simplified form from that which you actually entered. <span class="filter_mathjaxloader_equation"><span class="nolink">\[\left \{{\rm not}\left( A \right)\,{\text{ or }}\, B \right \}\]</span></span></td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>{A implies B,A and B}</pre></td>
  <td class="cell c3"><pre>{not(A) and B,A and B}</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATSet_wrongentries.</td>
</tr>
<tr class="pass">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">The following entries are incorrect, although they may appear in a simplified form from that which you actually entered. <span class="filter_mathjaxloader_equation"><span class="nolink">\[\left \{A\,{\text{ implies }}\, B \right \}\]</span></span></td></td>
</tr>
<tr class="notes">
  <td class="cell c0"><td colspan="6">Differential equations</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>diff(x^2,x)</pre></td>
  <td class="cell c3"><pre>2*x</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>diff(x^2,x)</pre></td>
  <td class="cell c3"><pre>&#039;diff(x^2,x)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>noundiff(x^2,x)</pre></td>
  <td class="cell c3"><pre>2*x</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>diff(y,x)</pre></td>
  <td class="cell c3"><pre>0</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>noundiff(y,x)</pre></td>
  <td class="cell c3"><pre>0</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>diff(y(x),x)</pre></td>
  <td class="cell c3"><pre>0</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>diff(y(x),x)</pre></td>
  <td class="cell c3"><pre>diff(y,x)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>diff(y,x)</pre></td>
  <td class="cell c3"><pre>diff(y,x,2)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>int(f(x)*%e^(-i*x*xi), x, -inf
, inf)</pre></td>
  <td class="cell c3"><pre>int(f(x)*%e^(-i*x*xi), x, -inf
, inf)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6"></td>
</tr>
<tr class="expectedfail">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:orange;"><i class="fa fa-adjust"></i>!</span></td>
  <td class="cell c2"><pre>int(f(t)*%e^(-i*t*xi), t, -inf
, inf)</pre></td>
  <td class="cell c3"><pre>int(f(x)*%e^(-i*x*xi), x, -inf
, inf)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">-3</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>F(xi)</pre></td>
  <td class="cell c3"><pre>int(f(x)*%e^(-i*x*xi), x, -inf
, inf)</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>F(xi)^(-25*xi^2*t)</pre></td>
  <td class="cell c3"><pre>t</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6"></td>
</tr>
<tr class="notes">
  <td class="cell c0"><td colspan="6">Basic support for strings</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>&quot;Hello&quot;</pre></td>
  <td class="cell c3"><pre>&quot;Hello&quot;</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">1</td>
  <td class="cell c6">ATAlgEquiv_String</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>&quot;hello&quot;</pre></td>
  <td class="cell c3"><pre>&quot;Hello&quot;</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATAlgEquiv_String</td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>W</pre></td>
  <td class="cell c3"><pre>&quot;Hello&quot;</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATAlgEquiv_SA_not_string.</td>
</tr>
<tr class="pass">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">Your answer should be a string, but is not.</td></td>
</tr>
<tr class="pass">
  <td class="cell c0">AlgEquiv</td>
  <td class="cell c1"><span style="color:green;"><i class="fa fa-check"></i></span></td>
  <td class="cell c2"><pre>&quot;Hello&quot;</pre></td>
  <td class="cell c3"><pre>x^2</pre></td>
  <td class="cell c4"></td>
  <td class="cell c5">0</td>
  <td class="cell c6">ATAlgEquiv_SA_not_expression.</td>
</tr>
<tr class="pass">
  <td class="cell c0"><td colspan="2"></td></td>
  <td class="cell c1"><td colspan="4">Your answer should be an expression, not an equation, inequality, list, set or matrix.</td></td>
</tr></tbody></table></div>