<?php
// This file is part of Stack - http://stack.maths.ed.ac.uk/
//
// Stack is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// Stack is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU General Public License
// along with Stack.  If not, see <http://www.gnu.org/licenses/>.

/**
 * Add description here!
 * @package    qtype_stack
 * @copyright  2024 University of Edinburgh.
 * @license    http://www.gnu.org/copyleft/gpl.html GNU GPL v3 or later.
 */

namespace qtype_stack;

use qtype_stack_testcase;
use stack_ast_container;
use stack_ast_container_silent;
use stack_cas_keyval;
use stack_cas_security;
use stack_cas_session2;
use stack_numbers_test_data;
use stack_options;
use function stack_utils\get_config;

defined('MOODLE_INTERNAL') || die();

require_once(__DIR__ . '/../locallib.php');
require_once(__DIR__ . '/fixtures/test_base.php');
require_once(__DIR__ . '/fixtures/numbersfixtures.class.php');
require_once(__DIR__ . '/../stack/cas/cassession2.class.php');
require_once(__DIR__ . '/../stack/cas/keyval.class.php');
require_once(__DIR__ . '/../stack/cas/ast.container.class.php');

/**
 * Add description
 * @group qtype_stack
 * @covers \stack_cas_session2
 */
final class cassession2_test extends qtype_stack_testcase {

    public function test_internal_config(): void {

        // This test checks if the version number returned by Maxima matches our internal config.
        $cs = ['m:MAXIMA_VERSION_NUM'];
        foreach ($cs as $s) {
            $s1[] = stack_ast_container::make_from_teacher_source($s, '', new stack_cas_security(), []);
        }
        $at1 = new stack_cas_session2($s1, null, 0);
        $at1->instantiate();

        $ast = $at1->get_by_key('m');
        $maximaversion = '5.' . $ast->get_value();
        $maximaconfig = \get_config('qtype_stack', 'maximaversion');
        $this->assertEquals($maximaconfig, $maximaversion);
    }

    public function test_get_valid(): void {

        $strings = ['foo', 'bar', 'sqrt(4)'];

        $casstrings = [];

        foreach ($strings as $string) {
            $casstrings[] = stack_ast_container::make_from_teacher_source($string, 'test_get_valid()',
                    new stack_cas_security());
        }

        $session = new stack_cas_session2($casstrings);

        $this->assertTrue($session->get_valid());
    }

    public function test_get_valid_false(): void {

        $strings = ['foo', 'bar', 'system(4)'];

        $casstrings = [];

        foreach ($strings as $string) {
            $casstrings[] = stack_ast_container::make_from_teacher_source($string, 'test_get_valid_false()',
                    new stack_cas_security());
        }

        $session = new stack_cas_session2($casstrings);

        $this->assertFalse($session->get_valid());
    }

    public function test_instantiation_and_return_values(): void {

        $strings = [
            '1+2' => '3',
            'sqrt(4)' => '2',
            'diff(x^2,x)' => '2*x',
        ];

        $casstrings = [];

        foreach ($strings as $string => $result) {
            $casstrings[] = stack_ast_container::make_from_teacher_source($string,
                    'test_instantiation_and_return_values()', new stack_cas_security());
        }

        $session = new stack_cas_session2($casstrings);

        $this->assertTrue($session->get_valid());
        $this->assertFalse($session->is_instantiated());
        $session->instantiate();
        $this->assertTrue($session->is_instantiated());

        $i = 0;
        foreach ($strings as $string => $result) {
            $this->assertEquals($result, $casstrings[$i]->get_evaluated()->toString());
            $i = $i + 1;
        }
    }

    public function test_keys_or_not(): void {

        // Keys are optional in the new cassession, we can extract the values
        // if need be even if keys do not exist, and if you do an assignement
        // it wont be visible in the return values anyway.
        $strings = [
            'foo:1+2' => ['3', '3'],
            '1+2' => ['3', '3'],
            'bar:diff(x^2,x)' => ['2*x', '2\\cdot x'],
            'diff(x^2,x)' => ['2*x', '2\\cdot x'],
        ];
        $casstrings = [];

        foreach ($strings as $string => $result) {
            $casstrings[] = stack_ast_container::make_from_teacher_source($string, 'test_keys_or_not()', new stack_cas_security());
        }

        $session = new stack_cas_session2($casstrings);

        $this->assertTrue($session->get_valid());
        $this->assertFalse($session->is_instantiated());
        $session->instantiate();
        $this->assertTrue($session->is_instantiated());

        $i = 0;
        foreach ($strings as $string => $result) {
            $this->assertEquals($result[0], $casstrings[$i]->get_evaluated()->toString());
            $this->assertEquals($result[1], $casstrings[$i]->get_latex());
            $i = $i + 1;
        }
    }

    public function test_error(): void {

        $simpon = stack_ast_container::make_from_teacher_source('simp:true', 'test_error()', new stack_cas_security());
        $divzero = stack_ast_container::make_from_teacher_source('1/0', 'test_error()', new stack_cas_security());
        $foo = stack_ast_container::make_from_teacher_source('sconcat("f","o","o")', 'test_error()', new stack_cas_security());
        $bar = stack_ast_container::make_from_teacher_source('simplode(["f","o","o"], "-");', '', new stack_cas_security());

        $session = new stack_cas_session2([$simpon, $divzero, $foo, $bar]);

        $this->assertTrue($session->get_valid());
        $this->assertFalse($session->is_instantiated());
        $session->instantiate();
        $this->assertTrue($session->is_instantiated());

        $this->assertEquals('', $simpon->get_errors());
        $this->assertEquals('', $foo->get_errors());
        $this->assertEquals('"foo"', $foo->get_value());
        $this->assertEquals('"f-o-o"', $bar->get_value());
        $this->assertTrue(count($divzero->get_errors(true)) > 0);
        $this->assertEquals(['Division by zero.'], $divzero->get_errors(true));
    }

    public function test_feedback(): void {

        $simpoff = stack_ast_container::make_from_teacher_source('simp:false', 'test_answernote()', new stack_cas_security());
        $validation = stack_ast_container::make_from_teacher_source('stack_validate_typeless([2/4], true, 1/2, 0, true)',
                'test_answernote()', new stack_cas_security());

        $session = new stack_cas_session2([$simpoff, $validation]);
        $this->assertEquals('', $validation->get_answernote());

        $this->assertTrue($session->get_valid());
        $this->assertFalse($session->is_instantiated());
        $session->instantiate();
        $this->assertTrue($session->is_instantiated());

        $this->assertStringContainsString('lowest terms', $validation->get_feedback());
    }

    public function test_answertest_usage(): void {

        $qv = 'ta:diff(sin(x),x);';
        $qv = new stack_cas_keyval($qv, null, 123);

        $basesession = $qv->get_session();
        $security = new stack_cas_security();
        $security->set_forbiddenkeys($qv->get_variable_usage()['write']);
        // Skip the allowed/forbidden words thing but the input could play with them if need be.

        $input = '-cos(0-x)';
        $input = stack_ast_container::make_from_student_source($input, 'ans1:raw-input', $security);
        // First needs to have a key. As we probably are not adding that at the input side
        // we probably should do that there.
        $input->set_key('ans1');

        $basesession->add_statement($input);
        // We now have a session with the $input and the question variables.

        // If our PRT requires simplification.
        $simpon = stack_ast_container_silent::make_from_teacher_source('simp:true', 'PRT1:simpon', $security);

        // If we have feedbackvariables.
        $fv = '';
        $fv = new stack_cas_keyval($fv, null, 123);

        $prtsession = $fv->get_session();

        // Maybe set the simp before those?
        $prtsession->add_statement($simpon, false);

        // Add the shared stuff there naturelly before those...
        $basesession->prepend_to_session($prtsession);

        // Now then let's make some statements. No options now.
        $sans = 'ans1';
        $tans = 'ta';

        $sans = stack_ast_container::make_from_teacher_source($sans, 'node1:sans', $security);
        $tans = stack_ast_container::make_from_teacher_source($tans, 'node1:tans', $security);
        $sans->set_key('STACKSA');
        $tans->set_key('STACKTA');

        $result = stack_ast_container::make_from_teacher_source('ATAlgEquiv(STACKSA,STACKTA)', 'node1:test', $security);

        // Add those to the session.
        $prtsession->add_statement($sans);
        $prtsession->add_statement($tans);
        $prtsession->add_statement($result);

        // Instantiate.
        $prtsession->instantiate();

        // Check parameters.
        $this->assertEquals('', $sans->get_errors());
        $this->assertEquals('', $tans->get_errors());
        $this->assertEquals('', $result->get_errors());
        $this->assertEquals('cos(x)', $tans->get_value());

        // Note that the value is available as an AST and there is already
        // an unpacking function to pick it apart.
        $this->assertEquals('[true,false,"",""]', $result->get_value());

    }

    public function test_get_display(): void {

        $cs = ['a:x^2', 'b:1/(1+x^2)', 'c:e^(i*pi)'];
        foreach ($cs as $s) {
            $s1[] = stack_ast_container::make_from_student_source($s, '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $options->set_option('simplify', false);

        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();
        $this->assertEquals('x^2', $s1[0]->get_display());
        $this->assertEquals('\frac{1}{1+x^2}', $s1[1]->get_display());
        $this->assertEquals('e^{\mathrm{i}\cdot \pi}', $s1[2]->get_display());

    }

    public function test_polarform_simp(): void {

        $cs = ['p0:polarform_simp(%i+1)'];
        $cs[] = 'p1:polarform_simp(2)';
        $cs[] = 'p2:polarform_simp(-2)';
        $cs[] = 'p3:polarform_simp(%i)';
        foreach ($cs as $s) {
            $s1[] = stack_ast_container::make_from_student_source($s, '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $options->set_option('simplify', false);

        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();
        $this->assertEquals('sqrt(2)*%e^((%i*%pi)/4)', $s1[0]->get_value());
        $this->assertEquals('\sqrt{2}\cdot e^{\frac{\mathrm{i}\cdot \pi}{4}}', $s1[0]->get_display());

        $this->assertEquals('2', $s1[1]->get_value());
        $this->assertEquals('2*%e^(%i*%pi)', $s1[2]->get_value());
        $this->assertEquals('%e^((%i*%pi)/2)', $s1[3]->get_value());
    }

    public function test_multiplication_option_complexno_i(): void {

        $cs = ['p:a+b*%i', 'q:a+b*i', 'r:a+b*j'];
        foreach ($cs as $s) {
            $s1[] = stack_ast_container::make_from_student_source($s, '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $options->set_option('simplify', false);
        $options->set_option('complexno', 'i');

        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();
        $p = $at1->get_by_key('p');
        $this->assertEquals('a+b\cdot \mathrm{i}', $p->get_display());
        $q = $at1->get_by_key('q');
        $this->assertEquals('a+b\cdot \mathrm{i}', $q->get_display());
        $r = $at1->get_by_key('r');
        $this->assertEquals('a+b\cdot j', $r->get_display());
    }

    public function test_multiplication_option_complexno_j(): void {

        $cs = ['p:a+b*%i', 'q:a+b*i', 'r:a+b*j'];
        foreach ($cs as $s) {
            $s1[] = stack_ast_container::make_from_student_source($s, '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $options->set_option('simplify', false);
        $options->set_option('complexno', 'j');

        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();
        $p = $at1->get_by_key('p');
        $this->assertEquals('a+b\cdot \mathrm{j}', $p->get_display());
        $q = $at1->get_by_key('q');
        $this->assertEquals('a+b\cdot i', $q->get_display());
        $r = $at1->get_by_key('r');
        $this->assertEquals('a+b\cdot \mathrm{j}', $r->get_display());
    }

    public function test_multiplication_option_complexno_symi(): void {

        $cs = ['p:a+b*%i', 'q:a+b*i', 'r:a+b*j'];
        foreach ($cs as $s) {
            $s1[] = stack_ast_container::make_from_student_source($s, '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $options->set_option('simplify', false);
        $options->set_option('complexno', 'symi');

        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();
        $p = $at1->get_by_key('p');
        $this->assertEquals('a+b\cdot \mathrm{i}', $p->get_display());
        $q = $at1->get_by_key('q');
        $this->assertEquals('a+b\cdot i', $q->get_display());
        $r = $at1->get_by_key('r');
        $this->assertEquals('a+b\cdot j', $r->get_display());
    }

    public function test_multiplication_option_complexno_vector_order(): void {

        $cs = ['ordergreat(i,j,k)', 'texput(i,"\\\\vec{i}")', 'texput(j,"\\\\vec{j}")', 'texput(k,"\\\\vec{k}")',
            'p:j*4+3*i+5*k', 'q:j*b+a*i+c*k', ];
        foreach ($cs as $s) {
            $s1[] = stack_ast_container::make_from_teacher_source($s, '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $options->set_option('simplify', true);
        $options->set_option('complexno', 'symi');

        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();
        $p = $at1->get_by_key('p');
        $this->assertEquals('3\cdot \vec{i}+4\cdot \vec{j}+5\cdot \vec{k}', $p->get_display());
        $q = $at1->get_by_key('q');
        $this->assertEquals('a\cdot \vec{i}+b\cdot \vec{j}+c\cdot \vec{k}', $q->get_display());
    }

    public function test_multiplication_option_complexno_symj(): void {

        $cs = ['p:a+b*%i', 'q:a+b*i', 'r:a+b*j'];
        foreach ($cs as $s) {
            $s1[] = stack_ast_container::make_from_student_source($s, '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $options->set_option('simplify', false);
        $options->set_option('complexno', 'symj');

        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();
        $p = $at1->get_by_key('p');
        $this->assertEquals('a+b\cdot \mathrm{j}', $p->get_display());
        $q = $at1->get_by_key('q');
        $this->assertEquals('a+b\cdot i', $q->get_display());
        $r = $at1->get_by_key('r');
        $this->assertEquals('a+b\cdot j', $r->get_display());
    }

    public function test_multiplication_option_dot(): void {

        $cs = ['a:x*y', 'b:x*y*z', 'c:x*(y*z)', 'd:(x*y)*z'];
        foreach ($cs as $s) {
            $s1[] = stack_ast_container::make_from_student_source($s, '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $options->set_option('multiplicationsign', 'dot');
        $options->set_option('simplify', false);

        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();
        $this->assertEquals('x\cdot y', $s1[0]->get_display());
        $this->assertEquals('x\cdot y\cdot z', $s1[1]->get_display());
        $this->assertEquals('x\cdot \left(y\cdot z\right)', $s1[2]->get_display());
        // Notice the associativity of Maxima suppresses the extra explicit brackets here.
        $this->assertEquals('x\cdot y\cdot z', $s1[3]->get_display());
    }

    public function test_multiplication_option_none(): void {

        $cs = ['a:x*y', 'b:x*y*z', 'c:x*(y*z)', 'd:(x*y)*z'];
        foreach ($cs as $s) {
            $s1[] = stack_ast_container::make_from_student_source($s, '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $options->set_option('multiplicationsign', 'none');
        $options->set_option('simplify', false);

        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();
        $this->assertEquals('x y', $s1[0]->get_display());
        $this->assertEquals('x y z', $s1[1]->get_display());
        $this->assertEquals('x \left(y z\right)', $s1[2]->get_display());
        // Notice the associativity of Maxima suppresses the extra explicit brackets here.
        $this->assertEquals('x y z', $s1[3]->get_display());
    }

    public function test_multiplication_option_cross(): void {

        $cs = ['a:x*y', 'b:x*y*z', 'c:x*(y*z)', 'd:(x*y)*z'];
        foreach ($cs as $s) {
            $s1[] = stack_ast_container::make_from_student_source($s, '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $options->set_option('multiplicationsign', 'cross');
        $options->set_option('simplify', false);

        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();
        $this->assertEquals('x\times y', $s1[0]->get_display());
        $this->assertEquals('x\times y\times z', $s1[1]->get_display());
        $this->assertEquals('x\times \left(y\times z\right)', $s1[2]->get_display());
        // Notice the associativity of Maxima suppresses the extra explicit brackets here.
        $this->assertEquals('x\times y\times z', $s1[3]->get_display());

    }

    public function test_multiplication_option_onum(): void {

        $s1 = [];
        $cs = ['a:2*x', 'b:2*3*x', 'c:3*5^2', 'd:3*x^2', 's1:x*(-y)', 's2:3*(-4)*x*(-y)'];
        foreach ($cs as $s) {
            $s1[] = stack_ast_container::make_from_student_source($s, '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $options->set_option('multiplicationsign', 'onum');
        $options->set_option('simplify', false);

        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();
        $this->assertEquals('2\, x', $s1[0]->get_display());
        $this->assertEquals('2\times 3\, x', $s1[1]->get_display());
        $this->assertEquals('3\, 5^2', $s1[2]->get_display());
        $this->assertEquals('3\, x^2', $s1[3]->get_display());
        $this->assertEquals('x\, \left(-y\right)', $s1[4]->get_display());
        $this->assertEquals('3\times \left(-4\right)\, x\, \left(-y\right)', $s1[5]->get_display());

        $s1 = [];
        $cs = [
            'texput(multsgnonlyfornumberssym, "\\\\cdot")',
            'a:9*x', 'b:5*7*x', 'c:3*5^2', 'd:3*x^2', 'z:3*(5/2)',
        ];
        foreach ($cs as $s) {
            $s1[] = stack_ast_container::make_from_teacher_source($s, '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $options->set_option('multiplicationsign', 'onum');
        $options->set_option('simplify', false);

        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();
        $this->assertEquals('9\, x', $s1[1]->get_display());
        $this->assertEquals('5\cdot 7\, x', $s1[2]->get_display());
        $this->assertEquals('3\, 5^2', $s1[3]->get_display());
        $this->assertEquals('3\, x^2', $s1[4]->get_display());
        $this->assertEquals('3\, x^2', $s1[4]->get_display());
        $this->assertEquals('3\, \left(\frac{5}{2}\right)', $s1[5]->get_display());
    }

    public function test_multiplication_option_space(): void {
        $s1 = [];
        $cs = ['a:2*x', 'b:2*3*x', 'c:3*5^2', 'd:3*x^2', 's1:x*(-y)', 's2:3*(-4)*x*(-y)'];
        foreach ($cs as $s) {
            $s1[] = stack_ast_container::make_from_student_source($s, '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $options->set_option('multiplicationsign', 'space');
        $options->set_option('simplify', false);

        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();
        $this->assertEquals('2\,x', $s1[0]->get_display());
        $this->assertEquals('2\,3\,x', $s1[1]->get_display());
        $this->assertEquals('3\,5^2', $s1[2]->get_display());
        $this->assertEquals('3\,x^2', $s1[3]->get_display());
        $this->assertEquals('x\,\left(-y\right)', $s1[4]->get_display());
        $this->assertEquals('3\,\left(-4\right)\,x\,\left(-y\right)', $s1[5]->get_display());
    }

    public function test_function_power_display(): void {

        $cs = ['A:f(0)', 'B:f(0)^5', 'C:f(x)', 'D:f(x)^3', 'E:f(x+1)', 'F:f(x+1)^30'];
        $s1 = [];
        foreach ($cs as $s) {
            $s1[] = stack_ast_container::make_from_teacher_source($s, '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();

        $this->assertEquals('f\left(0\right)', $s1[0]->get_display());
        $this->assertEquals('f^5\left(0\right)', $s1[1]->get_display());
        $this->assertEquals('f\left(x\right)', $s1[2]->get_display());
        $this->assertEquals('f^3\left(x\right)', $s1[3]->get_display());
        $this->assertEquals('f\left(x+1\right)', $s1[4]->get_display());
        $this->assertEquals('f^{30}\left(x+1\right)', $s1[5]->get_display());

        $cs = ['A:sin(1)', 'B:sin(1)^5', 'C:sin(x)', 'D:sin(x)^3', 'E:sin(x+1)', 'F:sin(x+1)^30', 'G:sin^50'];
        $s1 = [];
        foreach ($cs as $s) {
            $s1[] = stack_ast_container::make_from_teacher_source($s, '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();

        $this->assertEquals('\sin \left( 1 \right)', $s1[0]->get_display());
        $this->assertEquals('\sin ^5\left(1\right)', $s1[1]->get_display());
        // The test below is the odd one out, and required attention June 2021.
        $this->assertEquals('\sin \left( x \right)', $s1[2]->get_display());
        $this->assertEquals('\sin ^3\left(x\right)', $s1[3]->get_display());
        $this->assertEquals('\sin \left( x+1 \right)', $s1[4]->get_display());
        $this->assertEquals('\sin ^{30}\left(x+1\right)', $s1[5]->get_display());
        $this->assertEquals('\sin ^{50}', $s1[6]->get_display());
    }

    public function test_acos_option_cosmone(): void {

        $cs = ['a:acos(x)', 'b:asin(x)', 'c:asinh(x)', 'd:asin(x)^3', 'e:asin(x^2+1)^30'];
        foreach ($cs as $s) {
            $s1[] = stack_ast_container::make_from_student_source($s, '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $options->set_option('inversetrig', 'cos-1');

        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();
        $this->assertEquals('\cos^{-1}\left( x \right)', $s1[0]->get_display());
        $this->assertEquals('\sin^{-1}\left( x \right)', $s1[1]->get_display());
        $this->assertEquals('{\rm sinh}^{-1}\left( x \right)', $s1[2]->get_display());
        $this->assertEquals('\sin^{-1}^3\left(x\right)', $s1[3]->get_display());
        // Note, the LaTeX below will break MathJax.
        // But if you are willing to have inverses and powers with the same notation then you deserve to break things!
        $this->assertEquals('\sin^{-1}^{30}\left(x^2+1\right)', $s1[4]->get_display());
        // Babbage comlained around 1820 about people using this notation and people still use this notation!
    }

    public function test_acos_option_acos(): void {

        $cs = ['a:acos(x)', 'b:asin(x)', 'c:asinh(x)', 'd:asin(x)^3', 'e:asin(x^2+1)^30'];
        foreach ($cs as $s) {
            $s1[] = stack_ast_container::make_from_student_source($s, '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $options->set_option('inversetrig', 'acos');

        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();
        $this->assertEquals('{\rm acos}\left( x \right)', $s1[0]->get_display());
        $this->assertEquals('{\rm asin}\left( x \right)', $s1[1]->get_display());
        $this->assertEquals('{\rm asinh}\left( x \right)', $s1[2]->get_display());
        $this->assertEquals('{\rm asin}^3\left(x\right)', $s1[3]->get_display());
        $this->assertEquals('{\rm asin}^{30}\left(x^2+1\right)', $s1[4]->get_display());
    }

    public function test_acos_option_arccos(): void {

        $cs = ['a:acos(x)', 'b:asin(x)', 'c:asinh(x)', 'd:asin(x)^3', 'e:asin(x^2+1)^30'];
        foreach ($cs as $s) {
            $s1[] = stack_ast_container::make_from_student_source($s, '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $options->set_option('inversetrig', 'arccos');

        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();
        $this->assertEquals('\arccos \left( x \right)', $s1[0]->get_display());
        $this->assertEquals('\arcsin \left( x \right)', $s1[1]->get_display());
        $this->assertEquals('{\rm arcsinh}\left( x \right)', $s1[2]->get_display());
        $this->assertEquals('\arcsin ^3\left(x\right)', $s1[3]->get_display());
        $this->assertEquals('\arcsin ^{30}\left(x^2+1\right)', $s1[4]->get_display());
    }

    public function test_acos_option_arcosh(): void {

        $cs = [
            'a:acos(x)', 'b:asin(x)', 'c:asinh(x)', 'd:asin(x)^3', 'e:asin(x^2+1)^30',
            'f:asinh(x)^7', 'g:asinh(x)^70',
        ];
        foreach ($cs as $s) {
            $s1[] = stack_ast_container::make_from_student_source($s, '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $options->set_option('inversetrig', 'arsinh');

        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();
        $this->assertEquals('\arccos \left( x \right)', $s1[0]->get_display());
        $this->assertEquals('\arcsin \left( x \right)', $s1[1]->get_display());
        $this->assertEquals('{\rm arsinh}\left( x \right)', $s1[2]->get_display());
        $this->assertEquals('\arcsin ^3\left(x\right)', $s1[3]->get_display());
        $this->assertEquals('\arcsin ^{30}\left(x^2+1\right)', $s1[4]->get_display());
        $this->assertEquals('{\rm arsinh}^7\left(x\right)', $s1[5]->get_display());
        $this->assertEquals('{\rm arsinh}^{70}\left(x\right)', $s1[6]->get_display());
    }

    public function test_logicsymbol_option_lang(): void {

        $cs = ['a:A and B', 'b:A nounand B', 'c:A and (B or C)', 'd:A nounand (B nounor C)'];
        foreach ($cs as $s) {
            $s1[] = stack_ast_container::make_from_student_source($s, '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $options->set_option('logicsymbol', 'lang');

        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();
        $this->assertEquals('A\,{\text{ and }}\, B', $s1[0]->get_display());
        $this->assertEquals('A\,{\text{ and }}\, B', $s1[1]->get_display());
        $this->assertEquals('A\,{\text{ and }}\, \left(B\,{\text{ or }}\, C\right)', $s1[2]->get_display());
        $this->assertEquals('A\,{\text{ and }}\, \left(B\,{\text{ or }}\, C\right)', $s1[3]->get_display());
    }

    public function test_logicsymbol_option_symbol(): void {

        $cs = ['a:A and B', 'b:A nounand B', 'c:A and (B or C)', 'd:A nounand (B nounor C)'];
        foreach ($cs as $s) {
            $s1[] = stack_ast_container::make_from_student_source($s, '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $options->set_option('logicsymbol', 'symbol');

        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();
        $this->assertEquals('A\land B', $s1[0]->get_display());
        $this->assertEquals('A\land B', $s1[1]->get_display());
        $this->assertEquals('A\land \left(B\lor C\right)', $s1[2]->get_display());
        $this->assertEquals('A\land \left(B\lor C\right)', $s1[3]->get_display());
    }

    public function test_keyval_representation_1(): void {

        $cs = ['a:x^2', 'b:1/(1+x^2)', 'c:e^(i*pi)'];
        foreach ($cs as $s) {
            $s1[] = stack_ast_container::make_from_student_source($s, '', new stack_cas_security(), []);
        }

        $at1 = new stack_cas_session2($s1, null, 0);
        $at1->instantiate();
        $this->assertEquals("a:x^2;\nb:1/(1+x^2);\nc:e^(i*%pi);", $at1->get_keyval_representation());
    }

    public function test_keyval_representation_2(): void {

        $cs = ['a:(-1)^2'];
        foreach ($cs as $s) {
            $s1[] = stack_ast_container::make_from_student_source($s, '', new stack_cas_security(), []);
        }

        $at1 = new stack_cas_session2($s1, null, 0);
        $at1->instantiate();
        $this->assertEquals("a:(-1)^2;", $at1->get_keyval_representation());
        $this->assertEquals('a:1;', $at1->get_keyval_representation(true));
    }

    public function test_get_display_unary_minus(): void {

        $cs = ['p1:y^3-2*y^2-8*y', 'p2:y^2-2*y-8', 'p3:y^2-2*y-0.5', 'p4:x#pm#3+y', 'p5:x+(-5+y)'];
        // Notice the subtle difference in p4 & p5.
        // Where extra brackets are put in they should stay.
        foreach ($cs as $s) {
            $s1[] = stack_ast_container::make_from_student_source($s, '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $options->set_option('simplify', false);

        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();
        $this->assertEquals('y^3-2\\cdot y^2-8\\cdot y', $s1[0]->get_display());
        $this->assertEquals('y^2-2\\cdot y-8', $s1[1]->get_display());
        $this->assertEquals('y^2-2\\cdot y-0.5', $s1[2]->get_display());
        // Since we introduced a +- operator, changes from Maxima's x-3+y.
        $this->assertEquals('{x \pm 3}+y', $s1[3]->get_display());
        $this->assertEquals('x+\\left(-5+y\\right)', $s1[4]->get_display());
    }

    public function test_string1(): void {

        $cs = ['s:"This is a string"'];
        foreach ($cs as $s) {
            $s1[] = stack_ast_container::make_from_teacher_source($s, '', new stack_cas_security(), []);
        }
        $at1 = new stack_cas_session2($s1, null, 0);
        $at1->instantiate();
        $this->assertEquals('"This is a string"', $s1[0]->get_value());
    }

    public function test_qmchar(): void {

        $cs = ['s:5*?+6*?', 'A:matrix([?,1],[1,?])'];
        foreach ($cs as $s) {
            $s1[] = stack_ast_container::make_from_teacher_source($s, '', new stack_cas_security(), []);
        }
        $at1 = new stack_cas_session2($s1, null, 0);
        $at1->instantiate();

        $this->assertEquals('11*QMCHAR', $s1[0]->get_value());
        $this->assertEquals('11\cdot \color{red}{?}', $s1[0]->get_display());

        $this->assertEquals('matrix([QMCHAR,1],[1,QMCHAR])', $s1[1]->get_value());
    }

    public function test_subscript_disp(): void {

        // Fails with actual display output like '{\it pi_{025}}'.
        $this->skip_if_old_maxima('5.23.2');

        $cs = ['a:pi_25', 'b:1+x_3', 'c:f(x):=x^3', 'd:gamma_7^3', 'a2:pi_4^5'];
        foreach ($cs as $s) {
            $s1[] = stack_ast_container::make_from_teacher_source($s, '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $options->set_option('simplify', false);
        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();

        $this->assertEquals($s1[0]->get_value(), 'pi_25');
        $this->assertEquals($s1[0]->get_display(), '{\pi}_{25}');

        $this->assertEquals($s1[1]->get_value(), '1+x_3');
        $this->assertEquals($s1[1]->get_display(), '1+{x}_{3}');

        $this->assertEquals($s1[2]->get_value(), 'f(x):=x^3');
        $this->assertEquals($s1[2]->get_display(), 'f(x):=x^3');

        $this->assertEquals($s1[3]->get_value(), 'gamma_7^3');
        $this->assertEquals($s1[3]->get_display(), '{{\gamma}_{7}}^3');

        $this->assertEquals($s1[4]->get_value(), 'pi_4^5');
        $this->assertEquals($s1[4]->get_display(), '{{\pi}_{4}}^5');
    }

    public function test_matrix_eigenvalues(): void {

        $cs = ['A:matrix([7,1,3],[5,-3,4],[5,3,-4])', 'E:first(eigenvalues(A))', 'dt:determinant(A)'];
        foreach ($cs as $s) {
            $s1[] = stack_ast_container::make_from_teacher_source($s, '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $options->set_option('matrixparens', '(');

        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();

        $this->assertEquals('[1-sqrt(66),sqrt(66)+1,-2]', $s1[1]->get_value());
        $this->assertEquals('130', $s1[2]->get_value());
        $this->assertEquals('\left(\begin{array}{ccc} 7 & 1 & 3 \\\\ 5 & -3 & 4 \\\\ 5 & 3 & -4 \end{array}\right)',
                $s1[0]->get_display());

    }

    public function test_assignmatrixelements(): void {

        // Assign a value to matrix entries.
        $cs = ['A:matrix([1,2],[1,1])', 'A[1,2]:3', 'B:A'];
        foreach ($cs as $s) {
            $s1[] = stack_ast_container::make_from_teacher_source($s, '', new stack_cas_security(), []);
        }
        $at1 = new stack_cas_session2($s1, null, 0);
        $at1->instantiate();

        $this->assertEquals('matrix([1,3],[1,1])', $s1[0]->get_value());
        $this->assertEquals('matrix([1,3],[1,1])', $s1[2]->get_value());
    }

    public function test_simplify_false(): void {

        $cs = ['a:2+3', 'b:ev(a,simp)'];

        foreach ($cs as $s) {
            $s1[] = stack_ast_container::make_from_teacher_source($s, '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $options->set_option('simplify', false);
        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();

        $this->assertEquals('2+3', $s1[0]->get_value());
        $this->assertEquals('5', $s1[1]->get_value());
    }

    public function test_disp_control_structures(): void {

        $csl = [
            'p:if a>b then setelmx(0,m[k],m[j],A)',
            'addto1(ex):=thru ex do x:0.5*(x+5.0/x)',
            'addto2(ex):=for a from -3 step 7 thru ex do a^2',
            'addto3(ex):=for i from 2 while ex <= 10 do s:s+i',
            'addto4(ex):=block([l],l:ex,for f in [log,rho,atan] do l:append(l,[f]),l)',
            'l:addto4([sin,cos])',
        ];

        foreach ($csl as $s) {
            $s1[] = stack_ast_container::make_from_teacher_source($s, '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $options->set_option('simplify', false);
        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();

        $this->assertEquals([], $at1->get_errors(false));

        $this->assertEquals('if a > b then setelmx(0,m[k],m[j],A)', $s1[0]->get_value());
        $this->assertEquals('\mathbf{if}\;a > b\;\mathbf{then}\;{\it setelmx}\left(0 , m_{k} , m_{j} , A\right)',
                $s1[0]->get_display());

        // Confirm these expressions are unchanged by the CAS.
        $atsession = $at1->get_session();
        $at1->instantiate();
        for ($i = 1; $i <= 4; $i++) {
            $cs = $atsession[$i];
            $this->assertEquals($csl[$i], $cs->get_value());
        }

        $this->assertEquals('[sin,cos,log,rho,atan]', $s1[5]->get_value());
    }

    public function test_redefine_variable(): void {

        // This example redefines the value of n.
        // It should return the last value.
        $cs = ['n:3', 'n:n+3', 'n:n^2'];

        foreach ($cs as $s) {
            $s1[] = stack_ast_container::make_from_teacher_source($s, '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $options->set_option('simplify', true);
        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();

        // In the new logic we only return the value at the end of execution for
        // statements that have keys, and in this case you have three statements
        // with the same-key and only one will will receive that value. The session
        // could bring that value to every one of them but there is very little
        // need for that. This ties heavily to the concept of keys.
        // Try setting with "set_keyless()" and the value is not collected by the key but
        // instead by statement and it will then return you the values for each
        // statement separately. Keyless behaviour is present in CASText but
        // otherwise one does not really need it beyond some old unit-tests. Once
        // CASText2 appears, keyless behaviour becomes pointless beyond some debug
        // use-cases and unit-tests.
        // So we don't ecpect $s1[0]->get_value()) to return a value.

        $this->assertEquals('36', $s1[2]->get_value());
        $this->assertEquals('36', $s1[2]->get_display());
    }

    public function test_indirect_redefinition_of_variable(): void {

        // This example uses a loop to change the values of elements of C.
        // However the loop returns "done", and the values of C are changed.
        $cs = [
            'A:matrix([5,2],[4,3])', 'B:matrix([4,5],[6,5])',
            'C:zeromatrix (first(matrix_size(A)), second(matrix_size(A)))',
        ];
        $cs[] = 'BT:transpose(B)';
        $cs[] = 'S:for a:1 thru first(matrix_size(A)) do for b:1 thru second(matrix_size(A)) do ' .
                'C[ev(a,simp),ev(b,simp)]:apply("+",zip_with("*",A[ev(a,simp)],BT[ev(b,simp)]))';
        $cs[] = 'D:ev(C,simp)';
        // We need this last assignment to re-evaluate C, and then we can grab the results.....
        $cs[] = 'C:C';

        foreach ($cs as $s) {
            $s1[] = stack_ast_container::make_from_teacher_source($s, '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $options->set_option('simplify', false);
        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();

        $this->assertEquals('matrix([5,2],[4,3])', $s1[0]->get_value());
        $this->assertEquals('matrix([5*4+2*6,5*5+2*5],[4*4+3*6,4*5+3*5])', $s1[6]->get_value());
    }

    public function test_zip_with_matrix(): void {

        $cs = ['A:matrix([5,2],[4,5])', 'B:matrix([4,5],[6,5])'];
        $cs[] = 'M1:zip_with_matrix("+",A,B)';
        $cs[] = 'M2:zip_with_matrix(algebraic_equivalence,A,B)';
        foreach ($cs as $s) {
            $s1[] = stack_ast_container::make_from_teacher_source($s, '', new stack_cas_security(), []);
        }
        $options = new stack_options();
        $options->set_option('simplify', false);
        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();
        // Note, we have simp false here.
        $this->assertEquals('matrix([5+4,2+5],[4+6,5+5])', $s1[2]->get_value());
        $this->assertEquals('matrix([false,false],[false,true])', $s1[3]->get_value());
    }

    public function test_zip_with_matrix_at(): void {
        $cs = ['M1:matrix([3.1415,10.0])', 'M2:matrix([%pi,%pi^2])'];
        $cs[] = 'M:matrixmap(second,zip_with_matrix(lambda([ex1,ex2], ATNumAbsolute(ex1,ex2,0.01)), M1, M2))';
        foreach ($cs as $s) {
            $s1[] = stack_ast_container::make_from_teacher_source($s, '', new stack_cas_security(), []);
        }
        $options = new stack_options();
        $options->set_option('simplify', false);
        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();
        $this->assertEquals('matrix([true,false])', $s1[2]->get_value());
    }

    public function test_numerical_precision(): void {

        $cs = ['a:1385715.257'];
        foreach ($cs as $s) {
            $s1[] = stack_ast_container::make_from_teacher_source($s, '', new stack_cas_security(), []);
        }
        $at1 = new stack_cas_session2($s1, null, 0);
        $at1->instantiate();
        $this->assertEquals('1385715.257', $s1[0]->get_value());
    }

    public function test_rat(): void {

        $cs = ['a:ratsimp(sqrt(27))', 'b:rat(sqrt(27))', 'm:MAXIMA_VERSION_NUM'];
        foreach ($cs as $s) {
            $s1[] = stack_ast_container::make_from_teacher_source($s, '', new stack_cas_security(), []);
        }
        $at1 = new stack_cas_session2($s1, null, 0);
        $at1->instantiate();
        $this->assertEquals('3^(3/2)', $s1[0]->get_value());

        // @codingStandardsIgnoreStart
        // Warning to developers.   The behaviour of rat is not stable accross versions of Maxima.
        // In Maxima 5.25.1: rat(sqrt(27)) gives sqrt(3)^3.
        // In Maxima 5.36.1: rat(sqrt(27)) gives (3^(1/2)^3).
        // In Maxima 5.37.1: rat(sqrt(27)) gives sqrt(3)^3.
        // @codingStandardsIgnoreEnd
        $maximaversion = $s1[2]->get_value();
        if ($maximaversion == '36.1') {
            // Developers should add other versions of Maxima here as needed.
            $this->assertEquals('(3^(1/2))^3', $s1[1]->get_value());
        } else {
            $this->assertEquals('sqrt(3)^3', $s1[1]->get_value());
        }
    }

    public function test_ordergreat(): void {

        $cs = [
            'stack_reset_vars(true)', 'ordergreat(i,j,k)', 'p:matrix([-7],[2],[-3])',
            'q:matrix([i],[j],[k])', 'v:dotproduct(p,q)',
        ];
        foreach ($cs as $s) {
            $s1[] = stack_ast_container::make_from_teacher_source($s, '', new stack_cas_security(), []);
        }
        $at1 = new stack_cas_session2($s1, null, 0);
        $at1->instantiate();
        // There has been a subtle change to associativity in Maxima 5.37.0.
        $this->assertEquals('-7\cdot i+2\cdot j-3\cdot k', $s1[4]->get_display());
    }

    public function test_ordergreat_2(): void {

        $cs = ['ordergreat(a,b,c)', 'p:matrix([-7],[2],[-3])', 'q:matrix([a],[b],[c])', 'v:dotproduct(p,q)'];
        foreach ($cs as $s) {
            $s1[] = stack_ast_container::make_from_teacher_source($s, '', new stack_cas_security(), []);
        }
        $at1 = new stack_cas_session2($s1, null, 0);
        $at1->instantiate();
        // There has been a subtle change to associativity in Maxima 5.37.0.
        $this->assertEquals('-7\cdot a+2\cdot b-3\cdot c', $s1[3]->get_display());
    }

    public function test_plot_constant_function(): void {

        $cs = ['a:0', 'p:plot(a*x,[x,-2,2],[y,-2,2])'];
        foreach ($cs as $s) {
            $s1[] = stack_ast_container::make_from_teacher_source($s, '', new stack_cas_security(), []);
        }
        $at1 = new stack_cas_session2($s1, null, 0);
        $at1->instantiate();
        $this->assertEquals('0', $s1[0]->get_value());
        $this->assertTrue(is_numeric(strpos($s1[1]->get_value(), 'STACK auto-generated plot of 0 with parameters')));
        $this->assertEquals('', trim($s1[0]->get_errors()));
    }

    public function test_plot_fail(): void {

        $cs = ['a:0', 'p:plot(a*x/0,[x,-2,2],[y,-2,2])'];
        foreach ($cs as $s) {
            $s1[] = stack_ast_container::make_from_teacher_source($s, '', new stack_cas_security(), []);
        }
        $at1 = new stack_cas_session2($s1, null, 0);
        $at1->instantiate();
        $this->assertEquals('0', $s1[0]->get_value());
        $this->assertMatchesRegularExpression('/Division by (zero|0)/', trim($s1[1]->get_errors()));
        $this->assertFalse(strpos($s1[1]->get_value(), 'STACK auto-generated plot of 0 with parameters'));
    }

    public function test_rand_selection_err_1(): void {

        $cs = ['a:rand_selection(1,1)'];
        foreach ($cs as $s) {
            $s1[] = stack_ast_container::make_from_teacher_source($s, '', new stack_cas_security(), []);
        }
        $at1 = new stack_cas_session2($s1, null, 0);
        $at1->instantiate();
        $this->assertEquals('a', $s1[0]->get_value());
        $this->assertEquals('rand_selection error: first argument must be a list or set.', $s1[0]->get_errors());
    }

    public function test_rand_selection_err_2(): void {

        $cs = ['a:rand_selection([a,b,c,d], 7)'];
        foreach ($cs as $s) {
            $s1[] = stack_ast_container::make_from_teacher_source($s, '', new stack_cas_security(), []);
        }
        $at1 = new stack_cas_session2($s1, null, 0);
        $at1->instantiate();
        $this->assertEquals('a', $s1[0]->get_value());
        $this->assertEquals('rand_selection error: insuffient elements in the list/set.', $s1[0]->get_errors());
    }

    public function test_rand_selection(): void {

        $cs = ['a:rand_selection([a,b,c,d], 4)', 'b:sort(a)'];
        foreach ($cs as $s) {
            $s1[] = stack_ast_container::make_from_teacher_source($s, '', new stack_cas_security(), []);
        }
        $at1 = new stack_cas_session2($s1, null, 0);
        $at1->instantiate();
        $this->assertEquals('[a,b,c,d]', $s1[1]->get_value());
    }

    public function test_rand_selection_set(): void {

        $cs = ['a:rand_selection({a,b,c,d}, 4)', 'b:sort(a)'];
        foreach ($cs as $s) {
            $s1[] = stack_ast_container::make_from_teacher_source($s, '', new stack_cas_security(), []);
        }
        $at1 = new stack_cas_session2($s1, null, 0);
        $at1->instantiate();
        $this->assertEquals('[a,b,c,d]', $s1[1]->get_value());
    }

    public function test_trivial_rand_range(): void {

        // Cases should be in the form array('input', 'value', 'display').
        $cases = [];
        $cmds = [];

        $cases[] = ['rand_zero(0)', '0', '0'];
        $cases[] = ['rand_range(5,5)', '5', '5'];
        $cases[] = ['rand_range(6,6,5)', '6', '6'];

        $i = 0;
        foreach ($cases as $case) {
            $cmds[$i] = 'd'.$i.':' . $case[0];
            $i++;
        }

        $options = new stack_options();
        $kv = new stack_cas_keyval(implode(';', $cmds), $options, 0);
        $s = $kv->get_session(); // This does a validation on the side.

        $s->instantiate();
        $s1 = $s->get_session();

        $i = 0;
        foreach ($cases as $case) {
            $this->assertEquals($case[1], $s1[$i]->get_value());
            $this->assertEquals($case[2], $s1[$i]->get_display());
            $i++;
        }
    }

    public function test_greek_lower(): void {

        // The case gamma is separated out below, so we can skip it on old Maxima where it is a known fail.
        $cs = [
            'greek1:[alpha,beta,delta,epsilon]',
            'greek2:[zeta,eta,theta,iota,kappa]',
            'greek3:[lambda,mu,nu,xi,omicron,pi,rho]',
            'greek4:[sigma,tau,upsilon,phi,psi,chi,omega]',
        ];
        foreach ($cs as $s) {
            $s1[] = stack_ast_container::make_from_student_source($s, '', new stack_cas_security(), []);
        }
        $at1 = new stack_cas_session2($s1, null, 0);
        $at1->instantiate();
        $this->assertEquals('[alpha,beta,delta,epsilon]', $s1[0]->get_value());
        $this->assertEquals('\left[ \alpha , \beta , \delta , \varepsilon \right]',
                $s1[0]->get_display());
        $this->assertEquals('[zeta,eta,theta,iota,kappa]', $s1[1]->get_value());
        $this->assertEquals('\left[ \zeta , \eta , \theta , \iota , \kappa \right]',
                $s1[1]->get_display());
        // Note here that pi is returned as the constant %pi.
        $this->assertEquals('[lambda,mu,nu,xi,omicron,%pi,rho]', $s1[2]->get_value());
        $this->assertEquals('\left[ \lambda , \mu , \nu , \xi , o , \pi , \rho \right]',
                $s1[2]->get_display());
        $this->assertEquals('[sigma,tau,upsilon,phi,psi,chi,omega]', $s1[3]->get_value());
        $this->assertEquals('\left[ \sigma , \tau , \upsilon , \varphi , \psi , \chi , \omega \right]',
                $s1[3]->get_display());
    }

    public function test_greek_lower_gamma(): void {

        // In old maxima, you get '\Gamma' for the display output.
        $this->skip_if_old_maxima('5.23.2');
        $cs = stack_ast_container::make_from_student_source('greek1:gamma', '', new stack_cas_security(), []);

        $at1 = new stack_cas_session2([$cs], null, 0);
        $at1->instantiate();
        $this->assertEquals('gamma', $cs->get_value());
        $this->assertEquals('\gamma', $cs->get_display());
    }

    public function test_greek_upper(): void {

        $cs = [
            'greek1:[Alpha,Beta,Gamma,Delta,Epsilon]',
            'greek2:[Zeta,Eta,Theta,Iota,Kappa]',
            'greek3:[Lambda,Mu,Nu,Xi,Omicron,Pi,Rho]',
            'greek4:[Sigma,Tau,Upsilon,Phi,Chi,Psi,Omega]',
            'v:round(float(Pi))',
        ];
        foreach ($cs as $s) {
            $s1[] = stack_ast_container::make_from_student_source($s, '', new stack_cas_security(), []);
        }
        $at1 = new stack_cas_session2($s1, null, 0);
        $at1->instantiate();
        $this->assertEquals('[Alpha,Beta,Gamma,Delta,Epsilon]', $s1[0]->get_value());
        $this->assertEquals('\left[ {\rm A} , {\rm B} , \Gamma , \Delta , {\rm E} \right]',
                $s1[0]->get_display());
        $this->assertEquals('[Zeta,Eta,Theta,Iota,Kappa]', $s1[1]->get_value());
        $this->assertEquals('\left[ {\rm Z} , {\rm H} , \Theta , {\rm I} , {\rm K} \right]',
                $s1[1]->get_display());
        // Note here that pi is returned as the constant %pi.
        $this->assertEquals('[Lambda,Mu,Nu,Xi,Omicron,%pi,Rho]', $s1[2]->get_value());
        $this->assertEquals('\left[ \Lambda , {\rm M} , {\rm N} , \Xi , {\rm O} , \pi , {\rm P} \right]',
                $s1[2]->get_display());
        $this->assertEquals('[Sigma,Tau,Upsilon,Phi,Chi,Psi,Omega]', $s1[3]->get_value());
        $this->assertEquals('\left[ \Sigma , {\rm T} , \Upsilon , \Phi , {\rm X} , \Psi , \Omega \right]',
                $s1[3]->get_display());
        $this->assertEquals('3', $s1[4]->get_value());
    }

    public function test_taylor_cos_simp(): void {

        $cs = [
            'c1:taylor(cos(x),x,0,1)',
            'c3:taylor(cos(x),x,0,3)',
        ];
        foreach ($cs as $s) {
            $s1[] = stack_ast_container::make_from_student_source($s, '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $options->set_option('simplify', true);

        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();
        // For some reason Maxima's taylor function doesn't always put \cdots at the end.
        $this->assertEquals('+1', $s1[0]->get_value());
        $this->assertEquals('+1+\cdots', $s1[0]->get_display());
        $this->assertEquals('1-x^2/2', $s1[1]->get_value());
        $this->assertEquals('1-\frac{x^2}{2}+\cdots', $s1[1]->get_display());
    }

    public function test_taylor_cos_nosimp(): void {

        $cs = [
            'c1:taylor(cos(x),x,0,1)',
            'c3:taylor(cos(x),x,0,3)',
        ];
        foreach ($cs as $s) {
            $s1[] = stack_ast_container::make_from_student_source($s, '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $options->set_option('simplify', true);

        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();
        // For some reason Maxima's taylor function doesn't always put \cdots at the end.
        $this->assertEquals('+1', $s1[0]->get_value());
        $this->assertEquals('+1+\cdots', $s1[0]->get_display());
        $this->assertEquals('1-x^2/2', $s1[1]->get_value());
        $this->assertEquals('1-\frac{x^2}{2}+\cdots', $s1[1]->get_display());
    }

    public function test_lambda(): void {

        $cs = [
            'l1:lambda([ex], ex^3)',
            'l2:[1,2,3]',
            'l3:maplist(l1, l2)',
        ];
        foreach ($cs as $s) {
            $s1[] = stack_ast_container::make_from_student_source($s, '', new stack_cas_security(), []);
        }
        $at1 = new stack_cas_session2($s1, null, 0);
        $at1->instantiate();
        // For some reason Maxima's taylor function doesn't always put \cdots at the end.
        $this->assertEquals('lambda([ex],ex^3)', $s1[0]->get_value());
        $this->assertEquals('[1,8,27]', $s1[2]->get_value());
    }

    public function test_sets_simp(): void {

        $cs = ['c1:{}', 'c2:{b,a,c}'];
        foreach ($cs as $s) {
            $s1[] = stack_ast_container::make_from_student_source($s, '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $options->set_option('simplify', true);
        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();

        $this->assertEquals('{}', $s1[0]->get_value());
        $this->assertEquals('\left \{ \right \}', $s1[0]->get_display());
        $this->assertEquals('{a,b,c}', $s1[1]->get_value());
        $this->assertEquals('\left \{a , b , c \right \}', $s1[1]->get_display());
    }

    public function test_sets_simp_false(): void {

        $cs = ['c1:{}', 'c2:{b,a,c}'];
        foreach ($cs as $s) {
            $s1[] = stack_ast_container::make_from_student_source($s, '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $options->set_option('simplify', false);

        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();
        $this->assertEquals('{}', $s1[0]->get_value());
        $this->assertEquals('\left \{ \right \}', $s1[0]->get_display());
        $this->assertEquals('{b,a,c}', $s1[1]->get_value());
        $this->assertEquals('\left \{b , a , c \right \}', $s1[1]->get_display());
    }

    public function test_numerical_rounding(): void {

        $tests = stack_numbers_test_data::get_raw_test_data();
        $s1 = [];
        foreach ($tests as $key => $test) {
            $s1[] = stack_ast_container::make_from_teacher_source('p'.$key.':dispdp('.$test[0].', '.$test[3] .')',
                '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $options->set_option('simplify', false);

        $at1 = new stack_cas_session2($s1, $options, 0);
        $this->assertTrue($at1->get_valid());
        $at1->instantiate();

        foreach ($tests as $key => $test) {
            $cs = $at1->get_by_key('p'.$key);
            if ($tests[$key][6] === '') {
                // No errors.
                $this->assertTrue($cs->get_valid());
                $this->assertEquals($test[5], $cs->get_display());
            } else {
                $this->assertFalse($cs->get_valid());
                $this->assertEquals($test[6], $cs->get_errors('implode'));
            }
        }
    }

    public function test_numerical_decimalplaces(): void {

        $tests = stack_numbers_test_data::get_raw_test_data_decimalplaces();
        $s1 = [];
        foreach ($tests as $key => $test) {
            $s1[] = stack_ast_container::make_from_teacher_source('p'.$key.':decimalplaces('.$test[0].', '.$test[1] .')',
                '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $options->set_option('simplify', false);

        $at1 = new stack_cas_session2($s1, $options, 0);
        $this->assertTrue($at1->get_valid());
        $at1->instantiate();

        foreach ($tests as $key => $test) {
            $cs = $at1->get_by_key('p'.$key);
            if ($tests[$key][3] === '') {
                // No errors.
                $this->assertTrue($cs->get_valid());
                $this->assertEquals($test[2], $cs->get_value());
            } else {
                $this->assertFalse($cs->get_valid());
                $this->assertEquals($test[3], $cs->get_errors('implode'));
            }
        }
    }

    public function test_dispdp(): void {

        // @codingStandardsIgnoreStart

        // Tests in the following form.
        // 0. Input string.
        // 1. Number of decimal places.
        // 2. Latex displayed form.
        // 3. Latex displayed form, contiental comma.
        // 4. Value form after rounding.
        // E.g. dispdp(3.14159,2) -> displaydp(3.14,2).

        // @codingStandardsIgnoreEnd

        $tests = [
            ['3.14159', '2', '3.14', '3{,}14', '3.14', 'displaydp(3.14,2)'],
            ['100', '1', '100.0', '100{,}0', '100.0', 'displaydp(100.0,1)', ''],
            ['100', '2', '100.00', '100{,}00', '100.00', 'displaydp(100.0,2)'],
            ['100', '3', '100.000', '100{,}000', '100.000', 'displaydp(100.0,3)'],
            ['100', '4', '100.0000', '100{,}0000', '100.0000', 'displaydp(100.0,4)'],
            ['100', '5', '100.00000', '100{,}00000', '100.00000', 'displaydp(100.0,5)'],
            ['0.99', '1', '1.0', '1{,}0', '1.0', 'displaydp(1.0,1)'],
        ];

        foreach ($tests as $key => $c) {
            $s1[] = stack_ast_container::make_from_teacher_source("p{$key}:dispdp({$c[0]},{$c[1]})",
                '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $options->set_option('simplify', false);
        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();
        foreach ($tests as $key => $c) {
            $cs = $at1->get_by_key('p'.$key);
            $this->assertEquals($c[2], $cs->get_display());
            $this->assertEquals($c[4], $cs->get_dispvalue());
            $this->assertEquals($c[5], $cs->get_value());
        }

        // Now check comma output as well.
        $s1 = [
            stack_ast_container::make_from_teacher_source('stackfltsep:","', '',
            new stack_cas_security(), []),
        ];
        foreach ($tests as $key => $c) {
            $s1[] = stack_ast_container::make_from_teacher_source("p{$key}:dispdp({$c[0]},{$c[1]})",
            '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $options->set_option('simplify', false);
        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();
        foreach ($tests as $key => $c) {
            $cs = $at1->get_by_key('p'.$key);
            $this->assertEquals($c[3], $cs->get_display());
            $this->assertEquals($c[4], $cs->get_dispvalue());
            $this->assertEquals($c[5], $cs->get_value());
        }
    }

    public function test_dispdp_systematic(): void {

        $cs = stack_ast_container::make_from_teacher_source("L:makelist(dispdp(10^-1+10^-k,k+1),k,12,20)",
                '', new stack_cas_security(), []);
        $s1[] = $cs;

        $options = new stack_options();
        $options->set_option('simplify', true);
        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();
        // The purpose of this test is to ilustrate how numerical precision runs out.
        // This is currently in the 16th decimal place, where we loose the 10^-k from the displayed output.
        $this->assertEquals('\left[ 0.1000000000010 , 0.10000000000010 , 0.100000000000010 , 0.1000000000000010 , '.
            '0.10000000000000010 , 0.100000000000000000 , 0.1000000000000000000 , 0.10000000000000000000 , '.
            '0.100000000000000000000 \right]', $s1[0]->get_display());
        // Even more worryingly, the "value" of the expression looses this at the 14th place.
        // This is because of the precision specified in the "string" routine of Maxima, which sends "values" from Maxima to PHP.
        $expected = '[displaydp(.100000000001,13),displaydp(0.1,14),displaydp(0.1,15),displaydp(0.1,16),displaydp(0.1,17),'.
            'displaydp(0.1,18),displaydp(0.1,19),displaydp(0.1,20),displaydp(0.1,21)]';
        $expectval = '[0.1000000000010,0.10000000000010,0.100000000000010,0.1000000000000010,0.10000000000000010,' .
            '0.100000000000000000,0.1000000000000000000,0.10000000000000000000,0.100000000000000000000]';
        if ($this->adapt_to_new_maxima('5.32.2')) {
            $expected = '[displaydp(0.100000000001,13),displaydp(0.1,14),displaydp(0.1,15),displaydp(0.1,16),'.
                'displaydp(0.1,17),displaydp(0.1,18),displaydp(0.1,19),displaydp(0.1,20),displaydp(0.1,21)]';
            $expectval = '[0.1000000000010,0.10000000000010,0.100000000000010,0.1000000000000010,0.10000000000000010,' .
                '0.100000000000000000,0.1000000000000000000,0.10000000000000000000,0.100000000000000000000]';
        }
        $this->assertEquals($expectval, $s1[0]->get_dispvalue());
        $this->assertEquals($expected, $s1[0]->get_value());
    }

    public function test_dispdp_systematic_longer(): void {

        $cs = stack_ast_container::make_from_teacher_source("fpprintprec:16", '', new stack_cas_security(), []);
        $s1[] = $cs;
        $cs = stack_ast_container::make_from_teacher_source("L:makelist(dispdp(10^-1+10^-k,k+1),k,12,20)", '',
            new stack_cas_security(), []);
        $s1[] = $cs;

        $options = new stack_options();
        $options->set_option('simplify', true);
        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();
        $this->assertEquals('\left[ 0.1000000000010 , 0.10000000000010 , 0.100000000000010 , 0.1000000000000010 , '.
            '0.10000000000000010 , 0.100000000000000000 , 0.1000000000000000000 , 0.10000000000000000000 , '.
            '0.100000000000000000000 \right]', $s1[1]->get_display());
        // Note the difference, having increased fpprintprec:16 which is the maximum value permitted in Maxima.
        $expected = '[displaydp(0.100000000001,13),displaydp(0.1000000000001,14),displaydp(0.10000000000001,15),'.
            'displaydp(0.100000000000001,16),displaydp(.1000000000000001,17),'.
            'displaydp(0.1,18),displaydp(0.1,19),displaydp(0.1,20),displaydp(0.1,21)]';
        $expectval = '[0.1000000000010,0.10000000000010,0.100000000000010,0.1000000000000010,0.10000000000000010,' .
            '0.100000000000000000,0.1000000000000000000,0.10000000000000000000,0.100000000000000000000]';
        if ($this->adapt_to_new_maxima('5.32.2')) {
            $expected = '[displaydp(0.100000000001,13),displaydp(0.1000000000001,14),displaydp(0.10000000000001,15),'.
                'displaydp(0.100000000000001,16),displaydp(0.1000000000000001,17),'.
                // We get more decimal places preserved here that the above test cases.
                'displaydp(0.1,18),displaydp(0.1,19),displaydp(0.1,20),displaydp(0.1,21)]';
            $expectval = '[0.1000000000010,0.10000000000010,0.100000000000010,0.1000000000000010,0.10000000000000010,' .
                '0.100000000000000000,0.1000000000000000000,0.10000000000000000000,0.100000000000000000000]';
        }
        $this->assertEquals($expectval, $s1[1]->get_dispvalue());
        $this->assertEquals($expected, $s1[1]->get_value());
    }

    public function test_dispsf(): void {

        // @codingStandardsIgnoreStart

        // Tests in the following form.
        // 0. Input string.
        // 1. Number of significant figures.
        // 2. Displayed form.
        // 3. Value form after rounding.
        // E.g. dispsf(3.14159,2) -> displaydp(3.1,1).

        // @codingStandardsIgnoreEnd

        $tests = [
            ['3.14159', '2', '3.1', 'displaydp(3.1,1)'],
            ['100', '1', '100', '100'],
            ['100', '2', '100', '100'],
            ['100', '3', '100', '100'],
            ['100', '4', '100.0', 'displaydp(100,1)'],
            ['100', '5', '100.00', 'displaydp(100,2)'],
            ['100.00000000000001', '3', '100', '100'],
            ['99', '1', '100', '100'],
            ['0.99', '1', '1', '1'],
            ['-0.99', '1', '-1', '-1'],
            ['0.0000049', '1', '0.000005', 'displaydp(5.0e-6,6)'],
            ['0', '1', '0', '0'],
            ['0.0', '1', '0', '0'],
            ['0', '2', '0.0', 'displaydp(0,1)'],
            ['0', '3', '0.00', 'displaydp(0,2)'],
        ];

        foreach ($tests as $key => $c) {
            $s = "p{$key}:dispsf({$c[0]},{$c[1]})";
            $s1[] = stack_ast_container::make_from_teacher_source($s, '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $options->set_option('simplify', false);
        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();

        foreach ($tests as $key => $c) {
            $cs = $at1->get_by_key('p'.$key);
            $this->assertEquals($c[2], $cs->get_display());
            $this->assertEquals($c[3], strtolower($cs->get_value()));
        }
    }

    public function test_significantfigures_errors(): void {

        $tests = [
            ['significantfigures(%pi/3,3)', '1.05', ''],
            [
                'significantfigures(%pi/blah,3)', 'p1',
                'sigfigsfun(x,n,d) requires a real number, or a list of real numbers, ' .
                'as a first argument.  Received:  %pi/blah',
            ],
            [
                'significantfigures(%pi/3,n)', 'p2',
                'sigfigsfun(x,n,d) requires an integer as a second argument. Received:  n',
            ],
        ];

        foreach ($tests as $key => $c) {
            $s1[] = stack_ast_container::make_from_teacher_source("p".$key.':'.$c[0],
                    '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();

        foreach ($tests as $key => $c) {
            $this->assertEquals($c[1], $s1[$key]->get_value());
            $this->assertEquals($c[2], $s1[$key]->get_errors());
        }
    }

    public function test_significantfigures_list(): void {

        $tests = [
            [
                'significantfigures([0.2,0.4,0.5,0.6,0.7,0.8,1]*1.9,3)',
                '[0.38,0.76,0.95,1.14,1.33,1.52,1.9]',
            ],
        ];

        foreach ($tests as $key => $c) {
            $s1[] = stack_ast_container::make_from_teacher_source("p".$key.':'.$c[0],
                    '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();

        foreach ($tests as $key => $c) {
            $this->assertEquals($c[1], $s1[$key]->get_value());
        }
    }

    public function test_sf(): void {

        // @codingStandardsIgnoreStart

        // Tests in the following form.
        // 0. Input string.
        // 1. Number of significant figures.
        // 2. Latex displayed form.
        // 3. Latex displayed form, contiental comma.
        // E.g. significantfigures(3.14159,2) -> 3.1.

        // @codingStandardsIgnoreEnd

        $tests = [
            ['lg(19)', '4', '1.279', '1{,}279'],
            ['pi', '4', '3.142', '3{,}142'],
            ['sqrt(27)', '8', '5.1961524', '5{,}1961524'],
            ['-5.985', '3', '-5.99', '-5{,}99'],
        ];

        foreach ($tests as $key => $c) {
            $s = "p{$key}:significantfigures({$c[0]},{$c[1]})";
            $s1[] = stack_ast_container::make_from_teacher_source($s, '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $options->set_option('simplify', false);
        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();

        foreach ($tests as $key => $c) {
            $this->assertEquals($c[2], $s1[$key]->get_display());
        }

        // Now check comma output as well.
        $s1 = [
            stack_ast_container::make_from_teacher_source('stackfltsep:","', '',
            new stack_cas_security(), []),
        ];
        foreach ($tests as $key => $c) {
            $s = "p{$key}:significantfigures({$c[0]},{$c[1]})";
            $s1[] = stack_ast_container::make_from_teacher_source($s, '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $options->set_option('simplify', false);
        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();

        foreach ($tests as $key => $c) {
            $this->assertEquals($c[3], $s1[$key + 1]->get_display());
        }
    }

    public function test_scientific_notation(): void {

        // @codingStandardsIgnoreStart

        // Tests in the following form.
        // 0. Input string.
        // 1. Number of significant figures.
        // 2. Latex displayed form.
        // 3. Latex displayed form, contiental comma.
        // E.g. scientific_notation(314.159,2) -> 3.1\times 10^2.
        // 4. Dispvalue form, that is how it should be typed in.
        // 5. Value.
        // 6. Optional: what happens to the display with simp:true.
        // 7. Optional: what happens to the dispvalue form with simp:true.
        // 8. Optional: what happens to the value form with simp:true.

        // @codingStandardsIgnoreEnd

        $tests = [
            ['2.998e8', '2', '3.00 \times 10^{8}', '3{,}00 \times 10^{8}', '3.00E8', 'displaysci(3,2,8)'],
            ['-2.998e8', '2', '-3.00 \times 10^{8}', '-3{,}00 \times 10^{8}', '-3.00E8', 'displaysci(-3,2,8)'],
            ['6.626e-34', '2', '6.63 \times 10^{-34}', '6{,}63 \times 10^{-34}', '6.63E-34', 'displaysci(6.63,2,-34)'],
            [
                '-6.626e-34', '2', '-6.63 \times 10^{-34}', '-6{,}63 \times 10^{-34}', '-6.63E-34',
                'displaysci(-6.63,2,-34)',
            ],
            ['6.022e23', '2', '6.02 \times 10^{23}', '6{,}02 \times 10^{23}', '6.02E23', 'displaysci(6.02,2,23)'],
            ['5.985e30', '2', '5.99 \times 10^{30}', '5{,}99 \times 10^{30}', '5.99E30', 'displaysci(5.99,2,30)'],
            ['-5.985e30', '2', '-5.99 \times 10^{30}', '-5{,}99 \times 10^{30}', '-5.99E30', 'displaysci(-5.99,2,30)'],
            ['1.6726e-27', '2', '1.67 \times 10^{-27}', '1{,}67 \times 10^{-27}', '1.67E-27', 'displaysci(1.67,2,-27)'],
            ['1e5', '2', '1.00 \times 10^{5}', '1{,}00 \times 10^{5}', '1.00E5', 'displaysci(1,2,5)'],
            ['1.9e5', '2', '1.90 \times 10^{5}', '1{,}90 \times 10^{5}', '1.90E5', 'displaysci(1.9,2,5)'],
            ['1.0e9', '2', '1.00 \times 10^{9}', '1{,}00 \times 10^{9}', '1.00E9', 'displaysci(1,2,9)'],
            ['100000', '2', '1.00 \times 10^{5}', '1{,}00 \times 10^{5}', '1.00E5', 'displaysci(1,2,5)'],
            ['110000', '2', '1.10 \times 10^{5}', '1{,}10 \times 10^{5}', '1.10E5', 'displaysci(1.1,2,5)'],
            ['54e3', '2', '5.40 \times 10^{4}', '5{,}40 \times 10^{4}', '5.40E4', 'displaysci(5.4,2,4)'],

            [
                '0.00000000000067452', '2', '6.75 \times 10^{-13}', '6{,}75 \times 10^{-13}', '6.75E-13',
                'displaysci(6.75,2,-13)',
            ],
            [
                '-0.00000000000067452', '2', '-6.75 \times 10^{-13}', '-6{,}75 \times 10^{-13}', '-6.75E-13',
                'displaysci(-6.75,2,-13)',
            ],
            [
                '-0.0000000000006', '2', '-6.00 \times 10^{-13}', '-6{,}00 \times 10^{-13}', '-6.00E-13',
                'displaysci(-6,2,-13)',
            ],
            [
                '0.0000000000000000000005555', '2', '5.56 \times 10^{-22}', '5{,}56 \times 10^{-22}', '5.56E-22',
                'displaysci(5.56,2,-22)',
            ],
            [
                '0.00000000000000000000055', '2', '5.50 \times 10^{-22}', '5{,}50 \times 10^{-22}', '5.50E-22',
                'displaysci(5.5,2,-22)',
            ],
            [
                '-0.0000000000000000000005555', '2', '-5.56 \times 10^{-22}', '-5{,}56 \times 10^{-22}', '-5.56E-22',
                'displaysci(-5.56,2,-22)',
            ],
            [
                '67260000000000000000000000', '2', '6.73 \times 10^{25}', '6{,}73 \times 10^{25}', '6.73E25',
                'displaysci(6.73,2,25)',
            ],
            [
                '67000000000000000000000000', '2', '6.70 \times 10^{25}', '6{,}70 \times 10^{25}', '6.70E25',
                'displaysci(6.7,2,25)',
            ],
            [
                '-67260000000000000000000000', '2', '-6.73 \times 10^{25}', '-6{,}73 \times 10^{25}', '-6.73E25',
                'displaysci(-6.73,2,25)',
            ],
            [
                '-67000000000000000000000000', '2', '-6.70 \times 10^{25}', '-6{,}70 \times 10^{25}', '-6.70E25',
                'displaysci(-6.7,2,25)',
            ],

            ['0.001', '2', '1.00 \times 10^{-3}', '1{,}00 \times 10^{-3}', '1.00E-3', 'displaysci(1,2,-3)'],
            ['-0.001', '2', '-1.00 \times 10^{-3}', '-1{,}00 \times 10^{-3}', '-1.00E-3', 'displaysci(-1,2,-3)'],
            ['10', '2', '1.00 \times 10^{1}', '1{,}00 \times 10^{1}', '1.00E1', 'displaysci(1,2,1)'],
            ['2', '0', '2 \times 10^{0}', '2 \times 10^{0}', '2E0', 'displaysci(2,0,0)'],
            ['300', '0', '3 \times 10^{2}', '3 \times 10^{2}', '3E2', 'displaysci(3,0,2)'],
            ['4321.768', '3', '4.322 \times 10^{3}', '4{,}322 \times 10^{3}', '4.322E3', 'displaysci(4.322,3,3)'],
            ['-53000', '2', '-5.30 \times 10^{4}', '-5{,}30 \times 10^{4}', '-5.30E4', 'displaysci(-5.3,2,4)'],
            ['6720000000', '3', '6.720 \times 10^{9}', '6{,}720 \times 10^{9}', '6.720E9', 'displaysci(6.72,3,9)'],
            [
                '6.0221409e23', '4', '6.0221 \times 10^{23}', '6{,}0221 \times 10^{23}', '6.0221E23',
                'displaysci(6.0221,4,23)',
            ],
            [
                '1.6022e-19', '4', '1.6022 \times 10^{-19}', '1{,}6022 \times 10^{-19}', '1.6022E-19',
                'displaysci(1.6022,4,-19)',
            ],
            ['1.55E8', '2', '1.55 \times 10^{8}', '1{,}55 \times 10^{8}', '1.55E8', 'displaysci(1.55,2,8)'],

            ['-0.01', '1', '-1.0 \times 10^{-2}', '-1{,}0 \times 10^{-2}', '-1.0E-2', 'displaysci(-1,1,-2)'],
            [
                '-0.00000001', '3', '-1.000 \times 10^{-8}', '-1{,}000 \times 10^{-8}', '-1.000E-8',
                'displaysci(-1,3,-8)',
            ],
            ['-0.00000001', '1', '-1.0 \times 10^{-8}', '-1{,}0 \times 10^{-8}', '-1.0E-8', 'displaysci(-1,1,-8)'],
            ['-0.00000001', '0', '-1 \times 10^{-8}', '-1 \times 10^{-8}', '-1E-8', 'displaysci(-1,0,-8)'],
            ['-1000', '2', '-1.00 \times 10^{3}', '-1{,}00 \times 10^{3}', '-1.00E3', 'displaysci(-1,2,3)'],
            ['31415.927', '3', '3.142 \times 10^{4}', '3{,}142 \times 10^{4}', '3.142E4', 'displaysci(3.142,3,4)'],
            ['-31415.927', '3', '-3.142 \times 10^{4}', '-3{,}142 \times 10^{4}', '-3.142E4', 'displaysci(-3.142,3,4)'],
            ['155.5', '2', '1.56 \times 10^{2}', '1{,}56 \times 10^{2}', '1.56E2', 'displaysci(1.56,2,2)'],
            ['15.55', '2', '1.56 \times 10^{1}', '1{,}56 \times 10^{1}', '1.56E1', 'displaysci(1.56,2,1)'],
            ['777.7', '2', '7.78 \times 10^{2}', '7{,}78 \times 10^{2}', '7.78E2', 'displaysci(7.78,2,2)'],
            ['775.5', '2', '7.76 \times 10^{2}', '7{,}76 \times 10^{2}', '7.76E2', 'displaysci(7.76,2,2)'],
            ['775.55', '2', '7.76 \times 10^{2}', '7{,}76 \times 10^{2}', '7.76E2', 'displaysci(7.76,2,2)'],
            ['0.5555', '2', '5.56 \times 10^{-1}', '5{,}56 \times 10^{-1}', '5.56E-1', 'displaysci(5.56,2,-1)'],
            ['0.05555', '2', '5.56 \times 10^{-2}', '5{,}56 \times 10^{-2}', '5.56E-2', 'displaysci(5.56,2,-2)'],

            [
                'cos(23*pi/180)', '3', '9.205 \times 10^{-1}', '9{,}205 \times 10^{-1}', '9.205E-1',
                'displaysci(9.205,3,-1)',
            ],
            ['9000', '1', '9.0 \times 10^{3}', '9{,}0 \times 10^{3}', '9.0E3', 'displaysci(9,1,3)'],
            ['8000', '0', '8 \times 10^{3}', '8 \times 10^{3}', '8E3', 'displaysci(8,0,3)'],
            // Edge case.  Want these ones to be 1*10^3, not 10.0*10^2.
            ['1000', '2', '1.00 \times 10^{3}', '1{,}00 \times 10^{3}', '1.00E3', 'displaysci(1,2,3)'],
            // If we don't supply a number of decimal places, then we return a value form.
            // This is entered as scientific_notation(x).
            // This is displayed normally (without a \times) and always returns a *float*.
            // Notice this has different behaviour with simp:true.
            [
                '7000', '', '7.0\cdot 10^3', '7{,}0\cdot 10^3', '7.0*10^3', '7.0*10^3',
                '7000.0', '7000.0', '7000.0', '7000{,}0',
            ],
            [
                '1000', '', '1.0\cdot 10^3', '1{,}0\cdot 10^3', '1.0*10^3', '1.0*10^3',
                '1000.0', '1000.0', '1000.0', '1000{,}0',
            ],
            [
                '-1000', '', '-1.0\cdot 10^3', '-1{,}0\cdot 10^3', '-(1.0*10^3)', '(-1.0)*10^3',
                '-1000.0', '-1000.0', '-1000.0', '-1000{,}0',
            ],
            [
                '1e50', '', '1.0\cdot 10^{50}', '1{,}0\cdot 10^{50}', '1.0*10^50', '1.0*10^50',
                '1.0E+50', '1.0E+50', '1.0E+50', null,
            ],
            // @codingStandardsIgnoreStart

            // In some versions of Maxima this comes out as -\frac{1.0}{10^8} with simp:true.
            // Adding in compile(scientific_notation)$ after the function definition cures this,
            // but breaks some versions of Maxima.
            // Maxima 5.38.1 gives -1.0*10^-8, which is what we actually want.
            // Pass: 36.1, 31.3, 38.1, 39.0, 41.0.
            // Fail: 37.0, 37.1, 37.2, 37.3.

            // @codingStandardsIgnoreEnd
            [
                '-0.00000001', '', '-1.0\cdot 10^ {- 8 }', '-1{,}0\cdot 10^ {- 8 }', '-(1.0*10^-8)', '(-1.0)*10^-8',
                '-1.0E-8', '-1.0E-8', '-1.0E-8', null,
            ],
            [
                '-0.000000001', '', '-1.0\cdot 10^ {- 9 }', '-1{,}0\cdot 10^ {- 9 }', '-(1.0*10^-9)', '(-1.0)*10^-9',
                '-1.0E-9', '-1.0E-9', '-1.0E-9', null,
            ],
            [
                '-0.000000000001', '', '-1.0\cdot 10^ {- 12 }', '-1{,}0\cdot 10^ {- 12 }', '-(1.0*10^-12)', '(-1.0)*10^-12',
                '-1.0E-12', '-1.0E-12', '-1.0E-12', null,
            ],
        ];

        $s1 = [];
        foreach ($tests as $key => $c) {
            $s = "p{$key}:scientific_notation({$c[0]},{$c[1]})";
            if ($c[1] == '') {
                $s = "p{$key}:scientific_notation({$c[0]})";
            }
            $s1[] = stack_ast_container::make_from_teacher_source($s, '', new stack_cas_security(), []);
        }

        foreach ($tests as $key => $c) {
            if (!$s1[$key]->get_valid()) {
                // Help output which test fails.
                $this->assertTrue($c[0]);
            }
        }

        $options = new stack_options();
        $options->set_option('simplify', false);
        $at1 = new stack_cas_session2($s1, $options, 0);
        $this->assertTrue($at1->get_valid());
        $at1->instantiate();

        $this->assertEquals($at1->get_errors(), '');
        // All these tests should work with simp:false.
        foreach ($tests as $key => $c) {
            if ($s1[$key]->is_correctly_evaluated()) {
                // Turn 1.0E-5 to lower case 1.0e-5.
                $this->assertEquals($c[2], $this->prepare_actual_maths_floats($s1[$key]->get_display()));
                $this->assertEquals($c[4], $this->prepare_actual_maths_floats($s1[$key]->get_dispvalue()));
                $this->assertEquals($c[5], $this->prepare_actual_maths_floats($s1[$key]->get_value()));
            } else {
                // Help output which test fails.
                $this->assertEquals(null, $c[0]);
            }
        }

        // Does simp:true make any difference?
        // For some tests it does.

        $s2 = [];
        foreach ($tests as $key => $c) {
            $s = "p{$key}:scientific_notation({$c[0]},{$c[1]})";
            if ($c[1] == '') {
                $s = "p{$key}:scientific_notation({$c[0]})";
            }
            $s2[] = stack_ast_container::make_from_teacher_source($s, '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $options->set_option('simplify', true);
        $at2 = new stack_cas_session2($s2, $options, 0);
        $at2->instantiate();

        $this->assertEquals('', $at2->get_errors());
        foreach ($tests as $key => $c) {
            $simpdisp = $c[2];
            if (array_key_exists(6, $c)) {
                $simpdisp = $c[6];
            }
            $dispval = $c[4];
            if (array_key_exists(7, $c)) {
                $dispval = $c[7];
            }
            $val = $c[5];
            if (array_key_exists(8, $c)) {
                $val = $c[8];
            }
            $this->assertEquals($simpdisp, $this->prepare_actual_maths_floats($s2[$key]->get_display()));
            $this->assertEquals($dispval, $this->prepare_actual_maths_floats($s2[$key]->get_dispvalue()));
            $this->assertEquals($val, $this->prepare_actual_maths_floats($s2[$key]->get_value()));
        }

        // Now check comma output as well.
        $s2 = [
            stack_ast_container::make_from_teacher_source('stackfltsep:","', '',
            new stack_cas_security(), []),
        ];
        foreach ($tests as $key => $c) {
            $s = "p{$key}:scientific_notation({$c[0]},{$c[1]})";
            if ($c[1] == '') {
                $s = "p{$key}:scientific_notation({$c[0]})";
            }
            $s2[] = stack_ast_container::make_from_teacher_source($s, '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $options->set_option('simplify', true);
        $at2 = new stack_cas_session2($s2, $options, 0);
        $at2->instantiate();

        $this->assertEquals('', $at2->get_errors());
        foreach ($tests as $key => $c) {
            $simpdisp = $c[3];
            if (array_key_exists(6, $c)) {
                $simpdisp = $c[9];
            }
            $dispval = $c[4];
            if (array_key_exists(7, $c)) {
                $dispval = $c[7];
            }
            $val = $c[5];
            if (array_key_exists(8, $c)) {
                $val = $c[8];
            }
            // TO-DO: update prepare_actual_maths_floats for comma separated values.
            if ($simpdisp !== null) {
                $this->assertEquals($simpdisp, $this->prepare_actual_maths_floats($s2[$key + 1]->get_display()));
            }
            $this->assertEquals($dispval, $this->prepare_actual_maths_floats($s2[$key + 1]->get_dispvalue()));
            $this->assertEquals($val, $this->prepare_actual_maths_floats($s2[$key + 1]->get_value()));
        }
    }

    public function test_pm_simp_false(): void {

        $cs = [
            'c0:a#pm#b',
            'c1:x = (-b #pm# sqrt(b^2-4*a*c))/(2*a)',
            'c2:b#pm#a^2',
            'c3:(b#pm#a)^2',
            'c4:#pm#a',
            'c5:#pm#a^2',
            'c6:#pm#sqrt(1-x)',
            'c7:(a#pm#b)^2',
            'c8:x = #pm#b',
            'c9:sin(x#pm#a)^2',
        ];

        foreach ($cs as $s) {
            $s1[] = stack_ast_container::make_from_student_source($s, '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $options->set_option('simplify', false);

        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();

        $this->assertEquals('a#pm#b', $s1[0]->get_value());
        $this->assertEquals('{a \pm b}', $s1[0]->get_display());
        $this->assertEquals('x = (-b#pm#sqrt(b^2-4*a*c))/(2*a)', $s1[1]->get_value());
        $this->assertEquals('x=\frac{{-b \pm \sqrt{b^2-4\cdot a\cdot c}}}{2\cdot a}', $s1[1]->get_display());
        $this->assertEquals('b#pm#a^2', $s1[2]->get_value());
        $this->assertEquals('{b \pm a^2}', $s1[2]->get_display());
        $this->assertEquals('(b#pm#a)^2', $s1[3]->get_value());
        $this->assertEquals('{\left({b \pm a}\right)}^2', $s1[3]->get_display());
        $this->assertEquals('"#pm#"(a)', $s1[4]->get_value());
        $this->assertEquals('\pm a', $s1[4]->get_display());
        $this->assertEquals('"#pm#"(a^2)', $s1[5]->get_value());
        $this->assertEquals('\pm a^2', $s1[5]->get_display());
        $this->assertEquals('"#pm#"(sqrt(1-x))', $s1[6]->get_value());
        $this->assertEquals('\pm \sqrt{1-x}', $s1[6]->get_display());
        $this->assertEquals('(a#pm#b)^2', $s1[7]->get_value());
        $this->assertEquals('{\left({a \pm b}\right)}^2', $s1[7]->get_display());
        $this->assertEquals('x = "#pm#"(b)', $s1[8]->get_value());
        $this->assertEquals('x= \pm b', $s1[8]->get_display());
        $this->assertEquals('sin(x#pm#a)^2', $s1[9]->get_value());
        $this->assertEquals('\sin ^2\left({x \pm a}\right)', $s1[9]->get_display());
    }

    public function test_pm_simp_true(): void {

        $cs = [
            'c1:a#pm#b',
            'c2:x=(-b #pm# sqrt(b^2-4*a*c))/(2*a)',
            'c3:b#pm#a^2',
            'c4:(b#pm#a)^2',
            'c5:#pm#a',
            'c6:#pm#a^2',
            'c7:#pm#sqrt(1-x)',
            'c8:(a#pm#b)^2',
            'c9:x=#pm#b',
            'c10:sin(x#pm#a)^2',
        ];

        foreach ($cs as $s) {
            $s1[] = stack_ast_container::make_from_student_source($s, '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $options->set_option('simplify', true);

        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();

        $this->assertEquals('a#pm#b', $s1[0]->get_value());
        $this->assertEquals('{a \pm b}', $s1[0]->get_display());
        $this->assertEquals('x = (-b#pm#sqrt(b^2-4*a*c))/(2*a)', $s1[1]->get_value());
        $this->assertEquals('x=\frac{{-b \pm \sqrt{b^2-4\cdot a\cdot c}}}{2\cdot a}', $s1[1]->get_display());
        $this->assertEquals('b#pm#a^2', $s1[2]->get_value());
        $this->assertEquals('{b \pm a^2}', $s1[2]->get_display());
        $this->assertEquals('(b#pm#a)^2', $s1[3]->get_value());
        $this->assertEquals('{\left({b \pm a}\right)}^2', $s1[3]->get_display());
        $this->assertEquals('"#pm#"(a)', $s1[4]->get_value());
        $this->assertEquals('\pm a', $s1[4]->get_display());
        $this->assertEquals('"#pm#"(a^2)', $s1[5]->get_value());
        $this->assertEquals('\pm a^2', $s1[5]->get_display());
        $this->assertEquals('"#pm#"(sqrt(1-x))', $s1[6]->get_value());
        $this->assertEquals('\pm \sqrt{1-x}', $s1[6]->get_display());
        $this->assertEquals('(a#pm#b)^2', $s1[7]->get_value());
        $this->assertEquals('{\left({a \pm b}\right)}^2', $s1[7]->get_display());
        $this->assertEquals('x = "#pm#"(b)', $s1[8]->get_value());
        $this->assertEquals('x= \pm b', $s1[8]->get_display());
        $this->assertEquals('sin(x#pm#a)^2', $s1[9]->get_value());
        $this->assertEquals('\sin ^2\left({x \pm a}\right)', $s1[9]->get_display());
    }

    public function test_logic_nouns(): void {

        // Nouns forms of logic operators are added by student validation.
        $s1 = [];
        $s1[] = stack_ast_container::make_from_teacher_source('p0:x=1 or x=2', '', new stack_cas_security(), []);
        $s1[] = stack_ast_container::make_from_student_source('p1:x=1 or x=2', '', new stack_cas_security(), []);
        $s1[] = stack_ast_container::make_from_teacher_source('p2:noun_logic_remove(p1)',
                '', new stack_cas_security(), []);
        $s1[] = stack_ast_container::make_from_teacher_source('p3:ev(p2)', '', new stack_cas_security(), []);

        $options = new stack_options();
        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();

        // Teachers must use nouns if the mean it, otherwise things get evaluated.
        $this->assertEquals('false', $s1[0]->get_value());
        // Students always have nouns.
        $this->assertEquals('x = 1 nounor x = 2', $s1[1]->get_value());
        // No extra evaluation at this point, but nouns have been removed.
        $this->assertEquals('x = 1 or x = 2', $s1[2]->get_value());
        // However, display forces an evaluation, and hence the result.
        $this->assertEquals('\mathbf{False}', $s1[2]->get_display());
        $this->assertEquals('false', $s1[3]->get_value());
    }

    public function test_natural_domain(): void {

        // Cases should be in the form array('input', 'value', 'display').
        $cases = [];
        $cases[] = ['x', 'all', '\mathbb{R}'];
        $cases[] = ['1/(x^2+1)', 'all', '\mathbb{R}'];
        $cases[] = ['1/x', 'realset(x,%union(oo(0,inf),oo(-inf,0)))', '{x \not\in {\left \{0 \right \}}}'];
        $cases[] = [
            '1+1/x^2+1/(x-1)', 'realset(x,%union(oo(0,1),oo(1,inf),oo(-inf,0)))',
            '{x \not\in {\left \{0 , 1 \right \}}}',
        ];
        $cases[] = [
            '1+1/x^2+1/(x-1)+3/(x-2)', 'realset(x,%union(oo(0,1),oo(1,2),oo(2,inf),oo(-inf,0)))',
            '{x \not\in {\left \{0 , 1 , 2 \right \}}}',
        ];
        $cases[] = ['log(x)', 'realset(x,oo(0,inf))', '{x \in {\left( 0,\, \infty \right)}}'];
        $cases[] = ['1/sqrt(x-1)+1/sqrt(3-x)', 'realset(x,oo(1,3))', '{x \in {\left( 1,\, 3\right)}}'];

        foreach ($cases as $i => $case) {
            $s = 'd'.$i.':natural_domain('.$case[0].')';
            $s1[] = stack_ast_container::make_from_teacher_source($s, '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();

        foreach ($cases as $i => $case) {
            $this->assertEquals($case[1], $s1[$i]->get_value());
            $this->assertEquals($case[2], $s1[$i]->get_display());
            $i++;
        }
    }

    public function test_union_tex(): void {

        // Cases should be in the form array('input value', 'display').
        $cases[] = ['%union(a,b,c)', 'a \cup b \cup c'];
        $cases[] = [
            '%union(oo(1,2),oo(3,4),oo(4,5))',
            '\left( 1,\, 2\right) \cup \left( 3,\, 4\right) \cup \left( 4,\, 5\right)',
        ];
        $cases[] = ['%union(a,b+1,d)', 'a \cup \left(b+1\right) \cup d'];
        $cases[] = ['%union({5,6})', '\left \{5 , 6 \right \}'];

        $cases[] = ['%intersection(a,b,c)', 'a \cap b \cap c'];
        $cases[] = [
            '%intersection(oo(1,2),oo(3,4),oo(4,5))',
            '\left( 1,\, 2\right) \cap \left( 3,\, 4\right) \cap \left( 4,\, 5\right)',
        ];
        $cases[] = ['%intersection(a,b+1,d)', 'a \cap \left(b+1\right) \cap d'];
        $cases[] = ['%intersection({5,6})', '\left \{5 , 6 \right \}'];

        // Add brackets.  Even when not strictly needed.
        $cases[] = [
            '%union({1,2},A,B,%intersection(C,D,E))',
            '\left \{1 , 2 \right \} \cup A \cup B \cup \left(C \cap D \cap E\right)',
        ];
        $cases[] = [
            '%intersection({1,2},A,B,%union(C,D,E))',
            '\left \{1 , 2 \right \} \cap A \cap B \cap \left(C \cup D \cup E\right)',
        ];

        foreach ($cases as $i => $case) {
            $s = 'd'.$i.':'.$case[0];
            $s1[] = stack_ast_container::make_from_teacher_source($s, '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();

        foreach ($cases as $i => $case) {
            $this->assertEquals($case[0], $s1[$i]->get_value());
            $this->assertEquals($case[1], $s1[$i]->get_display());
            $i++;
        }
    }

    public function test_stack_disp_comma_separate(): void {

        // Cases should be in the form array('input', 'value', 'display').
        $cases = [];
        // Note in this case we do output Maxima's "%pi", not just pi.
        $cases[] = ['[a,b,sin(pi/7)]', '"a, b, sin(%pi/7)"', '\\text{a, b, sin(\\%pi/7)}'];

        foreach ($cases as $i => $case) {
            $s = 'd'.$i.':stack_disp_comma_separate('.$case[0].')';
            $s1[] = stack_ast_container::make_from_teacher_source($s, '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();

        foreach ($cases as $i => $case) {
            $this->assertEquals($case[1], $s1[$i]->get_value());
            $this->assertEquals($case[2], $s1[$i]->get_display());
            $i++;
        }
    }

    public function test_stack_disp_innards_ntuple(): void {

        // Cases should be in the form array('input', 'value', 'display').
        $cases = [];
        $cases[] = ['ntuple(a,b,c,dotdotdot)', 'ntuple(a,b,c,dotdotdot)', '\\left(a, b, c, \\ldots\\right)'];
        $cases[] = ['sequenceify([a,b,c])', 'sequence(a,b,c)', 'a, b, c'];

        foreach ($cases as $i => $case) {
            $s = 'd'.$i.':'.$case[0];
            $s1[] = stack_ast_container::make_from_teacher_source($s, '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();

        foreach ($cases as $i => $case) {
            $this->assertEquals($case[1], $s1[$i]->get_value());
            $this->assertEquals($case[2], $s1[$i]->get_display());
            $i++;
        }
    }

    public function test_stack_stackintfmt(): void {

        // Cases should be in the form array('input', 'value', 'display').
        $cases = [];

        $cases[] = ['73', '73', '73'];
        $cases[] = ['(stackintfmt:"~2r",n0)', '73', '1001001'];
        $cases[] = ['(stackintfmt:"~7r",n0)', '73', '133'];
        $cases[] = ['(stackintfmt:"~r",n0)', '73', '\text{seventy-three}'];
        $cases[] = ['(stackintfmt:"~:r",n0)', '73', '\text{seventy-third}'];
        $cases[] = ['(stackintfmt:"~@R",n0)', '73', 'LXXIII'];
        $cases[] = ['(stackintfmt:"~:d",123456789)', '123456789', '123,456,789'];
        $cases[] = ['(stackintfmt:"~,,\',,:d",123456789)', '123456789', '123,456,789'];
        $cases[] = ['(stackintfmt:"~,,\' ,:d",123456789)', '123456789', '123\\ 456\\ 789'];

        foreach ($cases as $i => $case) {
            $s = 'n' . $i . ':' . $case[0];
            $s1[] = stack_ast_container::make_from_teacher_source($s, '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $s = new stack_cas_session2($s1, $options, 0);
        $s->instantiate();

        foreach ($cases as $i => $case) {
            $this->assertEquals($case[1], $s1[$i]->get_value());
            $this->assertEquals($case[2], $s1[$i]->get_display());
            $i++;
        }
    }

    public function test_stack_stack_equiv_find_step(): void {

        $r1 = [
            'ta:[lg(25,5),stackeq(lg(5^2,5)),stackeq(2*lg(5,5)),stackeq(2*1),stackeq(2)]',
            'sa1:[lg(25,5),stackeq(lg(5^2,5)),stackeq(2)]',
            'sa0:[lg(25,5),stackeq(2)]',
        ];
        foreach ($r1 as $s) {
            $s1[] = stack_ast_container::make_from_teacher_source($s, '', new stack_cas_security(), []);
        }

        $t1 = [];
        $t1[] = ['stack_equiv_find_step(stackeq(2*lg(5,5)), ta)', '[3]'];
        $t1[] = ['stack_equiv_find_step(2*lg(5,5), ta)', '[3]'];
        $t1[] = ['stack_equiv_find_step(stackeq(lg(5,5)), ta)', '[]'];
        $t1[] = ['stack_equiv_find_step(stackeq(lg(5^2,5)), sa1)', '[2]'];
        $t1[] = ['stack_equiv_find_step(lg(5^2,5), sa1)', '[2]'];
        $t1[] = ['stack_equiv_find_step(stackeq(lg(5^2,5)), sa0)', '[]'];
        $t1[] = ['stack_equiv_find_step(lg(5^2,5), sa0)', '[]'];

        foreach ($t1 as $i => $case) {
            $s = 'n' . $i . ':' . $case[0];
            $s1[] = stack_ast_container::make_from_teacher_source($s, '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $options->set_option('simplify', false);
        $s = new stack_cas_session2($s1, $options, 0);
        $s->instantiate();

        $i = 3;
        foreach ($t1 as $t) {
            $this->assertEquals($t[1], $s1[$i]->get_value());
            $i++;
        }
    }

    public function test_dispvalue(): void {

        // These are tests of test-case generation.

        $tests = [
            ['x=dispdp(0.5,3)', 'x=0.500', 'x = 0.500', 'x = displaydp(0.5,3)'],
            [
                'x=1 nounor x=3.75E3', 'x=1\,{\text{ or }}\, x=3750.0',
                'x = 1 or x = 3750.0', 'x = 1 nounor x = 3750.0',
            ],
            [
                '[x^2-1,stackeq((x-1)*(x+1))]', '\left[ x^2-1 , =\left(x-1\right)\cdot \left(x+1\right) \right]',
                '[x^2-1,=(x-1)*(x+1)]', '[x^2-1,stackeq((x-1)*(x+1))]',
            ],
            [
                'nounint(sin(pi*x),x)', '\int {\sin \left( \pi\cdot x \right)}{\;\mathrm{d}x}',
                'int(sin(%pi*x),x)', '\'int(sin(%pi*x),x)',
            ],
            // Teachers may now use 'int(...) in STACK 4.3.
            // We should probably just get rid of "nounint" in the near future.
            [
                '\'int(cos(x),x)', '\int {\cos \left( x \right)}{\;\mathrm{d}x}',
                'int(cos(x),x)', '\'int(cos(x),x)',
            ],
        ];

        foreach ($tests as $key => $c) {
            $s1[] = stack_ast_container::make_from_teacher_source("p{$key}:{$c[0]}",
                '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $options->set_option('simplify', false);
        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();
        foreach ($tests as $key => $c) {
            $cs = $at1->get_by_key('p'.$key);
            $this->assertEquals($c[1], $cs->get_display());
            $this->assertEquals($c[2], $cs->get_dispvalue());
            $this->assertEquals($c[3], $cs->get_value());
        }
    }

    public function test_stack_strip_percent(): void {

        $tests = [
            'assume(x>0)',
            'eq1:x^2*\'diff(y,x)+3*y*x=sin(x)/x',
            'sol1:ode2(eq1,y,x)',
            'sol2:stack_strip_percent(y=(%c-cos(x))/x^3,k)',
            'sol3:stack_strip_percent(y=(%c-cos(x))/x^3,[k])',
        ];

        foreach ($tests as $key => $c) {
            $s1[] = stack_ast_container::make_from_teacher_source($c,
                    '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();

        $this->assertEquals('y = (%c-cos(x))/x^3', $s1[2]->get_value());
        $this->assertEquals('y = (k[1]-cos(x))/x^3', $s1[3]->get_value());
        $this->assertEquals('y = (k-cos(x))/x^3', $s1[4]->get_value());
    }

    public function test_stack_quantile_gamma(): void {

        // This command has lisp throw an error.
        $tests = ['p:quantile_gamma(0.5,26896/81,81/164)'];

        foreach ($tests as $key => $c) {
            $s1[] = stack_ast_container::make_from_teacher_source($c,
                    '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();

        $actual = $s1[0]->get_dispvalue();
        if (strpos($actual, 'quantile_gamma(') !== false) {
            // Seems that the distrib package is not available. Skip this test.
            $this->markTestSkipped('Skipping because it seems the distrib package is not installed.');
        }
        $this->assertEquals('163.835395267', $actual);
    }

    public function test_stack_parse_inequalities(): void {

        // This command has lisp throw an error.
        $tests = ['f(x) := if x < 0 then (if x < 1 then 1 else 2) else 3;', 'v1:f(-5);', 'v2:f(4);'];

        foreach ($tests as $key => $c) {
            $s1[] = stack_ast_container::make_from_teacher_source($c,
                    '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();

        $this->assertEquals('1', $s1[1]->get_dispvalue());
        $this->assertEquals('3', $s1[2]->get_dispvalue());
        $this->assertEquals('f(x):=if x < 0 then (if x < 1 then 1 else 2) else 3', $s1[0]->get_value());
    }

    public function test_stack_rat(): void {

        $tests = [
            's1 : 8.5*sin(rat(2*pi*((0.37/1.86440677966E-4)-(5.8/0.22))))', 's2:1',
            'm:MAXIMA_VERSION_NUM',
        ];

        foreach ($tests as $key => $c) {
            $s1[] = stack_ast_container::make_from_teacher_source($c,
                    '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $options->set_option('simplify', false);
        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();

        $maximaversion = $s1[2]->get_value();
        if ($maximaversion == '34.1') {
            $this->assertEquals('8.5*sin(66940295262037*%pi/17092461650)', $s1[0]->get_dispvalue());
        } else {
            $this->assertEquals('8.5*sin((66940295262037*%pi)/17092461650)', $s1[0]->get_dispvalue());
        }
    }

    public function test_stack_pmpoly(): void {

        $tests = [
            's1:-(4*x^7)+3*x^5-2*x^3+x',
            'p1:-a/b', 'p2:(-a)/b', 'p3:-(a/b)',
            'pm1:a#pm#b',
        ];

        foreach ($tests as $key => $c) {
            $s1[] = stack_ast_container::make_from_teacher_source($c,
                    '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $options->set_option('simplify', false);
        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();

        $this->assertEquals('-(4*x^7)+3*x^5+(-2)*x^3+x', $s1[0]->get_value());
        $this->assertEquals('-(4*x^7)+3*x^5-2*x^3+x', $s1[0]->get_dispvalue());
        $this->assertEquals('-4\cdot x^7+3\cdot x^5-2\cdot x^3+x', $s1[0]->get_display());

        $this->assertEquals('(-a)/b', $s1[1]->get_value());
        $this->assertEquals('(-a)/b', $s1[1]->get_dispvalue());
        $this->assertEquals('\frac{-a}{b}', $s1[1]->get_display());

        $this->assertEquals('(-a)/b', $s1[2]->get_value());
        $this->assertEquals('(-a)/b', $s1[2]->get_dispvalue());
        $this->assertEquals('\frac{-a}{b}', $s1[2]->get_display());

        $this->assertEquals('-(a/b)', $s1[3]->get_value());
        $this->assertEquals('-(a/b)', $s1[3]->get_dispvalue());
        $this->assertEquals('-\frac{a}{b}', $s1[3]->get_display());

        $this->assertEquals('a#pm#b', $s1[4]->get_value());
        $this->assertEquals('a+-b', $s1[4]->get_dispvalue());
        $this->assertEquals('{a \pm b}', $s1[4]->get_display());
    }

    public function test_stack_pm_maximaoutput(): void {

        $tests = ['a*b+c*d+-A*B'];

        foreach ($tests as $key => $c) {
            $s1[] = stack_ast_container::make_from_teacher_source($c,
                    '', new stack_cas_security(), []);
        }

        $expected = '([Root] ([Op: +] ([Op: *] ([Id] a), ([Id] b)), ' .
                '([Op: +-] ([Op: *] ([Id] c), ([Id] d)), ([Op: *] ([Id] A), ([Id] B)))))';
        $this->assertEquals($expected, $s1[0]->get_ast_test());

        $options = new stack_options();
        $options->set_option('simplify', false);
        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();

        $this->assertEquals('(a*b+c*d)#pm#A*B', $s1[0]->get_value());
        $this->assertEquals('(a*b+c*d)+-A*B', $s1[0]->get_dispvalue());
        $this->assertEquals('{a\cdot b+c\cdot d \pm A\cdot B}',
                $s1[0]->get_display());

        // The evaluated form contains the +- operator.
        $expected = '([Op: #pm#] ([Group] ([Op: +] ([Op: *] ([Id] a), ([Id] b)), ' .
                '([Op: *] ([Id] c), ([Id] d)))), ([Op: *] ([Id] A), ([Id] B)))';
        $this->assertEquals($expected, $s1[0]->get_ast_test());
    }

    public function test_stack_pm_taylor(): void {

        $tests = ['ta:ev(taylor(10*cos(2*x),x,%pi/4,2),simp)'];

        foreach ($tests as $key => $c) {
            $s1[] = stack_ast_container::make_from_teacher_source($c,
                    '', new stack_cas_security(), []);
        }

        $expected = '([Root] ([Op: :] ([Id] ta), ([FunctionCall: ([Id] block)] ([List] ([Id] %_sev_e), ' .
            '([Id] %_sev_s)),([Op: :] ([Id] %_sev_s), ([Id] simp)),([Op: :] ([Id] simp), ([Bool] true)),([Op: :] ' .
            '([Id] %_sev_e), ([FunctionCall: ([Id] taylor)] ([Op: *] ([Int] 10), ([FunctionCall: ([Id] cos)] ([Op: *] ' .
            '([Int] 2), ([Id] x)))),([Id] x),([Op: /] ([Id] %pi), ([Int] 4)),([Int] 2))),([Op: :] ' .
            '([Id] simp), ([Id] %_sev_s)),([FunctionCall: ([Id] ev)] ([FunctionCall: ([Id] %_E)] ' .
            '([Id] %_sev_e)),([Id] simp)))))';
        $this->assertEquals($expected, $s1[0]->get_ast_test());

        $options = new stack_options();
        $options->set_option('simplify', false);
        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();

        $this->assertEquals('(20*%pi-80*x)/4', $s1[0]->get_value());
        $this->assertEquals('(20*%pi-80*x)/4', $s1[0]->get_dispvalue());
        $this->assertEquals('\frac{20\cdot \pi-80\cdot x}{4}',
                $s1[0]->get_display());

        $expected = '([Op: /] ([Group] ([Op: *] ([Int] 20), ([Op: *] ([Op: -] ([Id] %pi), ([Int] 80)), ([Id] x)))), ' .
            '([Int] 4))';
        $this->assertEquals($expected, $s1[0]->get_ast_test());
    }

    public function test_stack_scientific_notationp(): void {

        $truetests = [
            '3*10^2',
            '3.1*10^2',
            '3*10^-2',
            '3.3*10^2',
            '3.0*10^2',
            '-3*10^2',
            '-3.1*10^2',
            '-3*10^-2',
                // Special edge case.
            '3.3*10',
        ];

        $s1 = [];
        foreach ($truetests as $key => $c) {
            $s1[] = stack_ast_container::make_from_teacher_source('scientific_notationp(' . $c . ')',
                    '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $options->set_option('simplify', false);
        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();

        foreach ($s1 as $key => $test) {
            $this->assertEquals('true', $test->get_value());
        }

        $truetests = [
            '3',
            '-3',
            '3.1',
            '3E-5',
            '310^-2',
            'a',
            '312/1000',
            '3.3*x',
            '3.3*sin(x)',
            '3/9*10^2',
            '3.3*10^2.78',
            '3.3*10^x',
            '3.3*a^2',
            '3.3*7^2',
        ];

        $s1 = [];
        foreach ($truetests as $key => $c) {
            $s1[] = stack_ast_container::make_from_teacher_source('scientific_notationp(' . $c . ')',
                    '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $options->set_option('simplify', false);
        $at1 = new stack_cas_session2($s1, $options, 0);
        $at1->instantiate();

        foreach ($s1 as $key => $test) {
            $this->assertEquals('false', $test->get_value());
        }
    }

    public function test_stack_regex_match_exactp(): void {

        $t1 = [];
        $t1[] = ['regex_match_exactp("(aaa)*(b|d)c", "aaaaaabc")', 'true'];
        $t1[] = ['regex_match_exactp("(aaa)*(b|d)c", "dc")', 'true'];
        $t1[] = ['regex_match_exactp("(aaa)*(b|d)c", "aaaaaaabc")', 'false'];
        $t1[] = ['regex_match_exactp("(aaa)*(b|d)c", "aaaaaaabc")', 'false'];

        foreach ($t1 as $i => $case) {
            $s = 'n' . $i . ':' . $case[0];
            $s1[] = stack_ast_container::make_from_teacher_source($s, '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $s = new stack_cas_session2($s1, $options, 0);
        $s->instantiate();

        foreach ($t1 as $i => $t) {
            $this->assertEquals($t[1], $s1[$i]->get_value());
        }
    }

    public function test_stack_at_units_sigfigs(): void {

        $t1 = [];
        $t1[] = ['simp:false', 'false'];
        $t1[] = [
            'node_result:ATUnitsSigFigs(1*kg,1000*g,[1,3],"1 kg")',
            '[true,true,"ATUnits_compatible_units kg. ",""]',
        ];

        foreach ($t1 as $i => $case) {
            $s1[] = stack_ast_container::make_from_teacher_source($case[0], '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $s = new stack_cas_session2($s1, $options, 0);
        $s->instantiate();

        foreach ($t1 as $i => $t) {
            $this->assertEquals($t[1], $s1[$i]->get_value());
        }
    }

    public function test_stack_rational_numberp(): void {

        $s1 = [];
        $t1 = [];
        $t1[] = ['simp:false', 'false'];
        $t1[] = ['l0:safe_op(2/3)', '"/"'];
        $t1[] = ['l1:[1,-2,2/3,-4/3, 4/16, 9/3]', '[1,-2,2/3,(-4)/3,4/16,9/3]'];
        $t1[] = ['l2:map(rational_numberp, l1);', '[false,false,true,true,true,true]'];
        $t1[] = ['l3:get_safe_ops(a+b/c)', '{"+","/"}'];

        foreach ($t1 as $i => $case) {
            $s1[] = stack_ast_container::make_from_teacher_source($case[0], '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $s = new stack_cas_session2($s1, $options, 0);
        $s->instantiate();

        foreach ($t1 as $i => $t) {
            $this->assertEquals($t[1], $s1[$i]->get_value());
        }

        $s1 = [];
        $t1 = [];
        $t1[] = ['simp:true', 'true'];
        $t1[] = ['l0:safe_op(2/3)', '"/"'];
        $t1[] = ['l1:[1,-2,2/3,-4/3, 4/16, 9/3]', '[1,-2,2/3,-(4/3),1/4,3]'];
        $t1[] = ['l2:map(rational_numberp, l1);', '[false,false,true,true,true,false]'];
        $t1[] = ['l3:get_safe_ops(a+b/c)', '{"+","/"}'];

        foreach ($t1 as $i => $case) {
            $s1[] = stack_ast_container::make_from_teacher_source($case[0], '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $s = new stack_cas_session2($s1, $options, 0);
        $s->instantiate();

        foreach ($t1 as $i => $t) {
            $this->assertEquals($t[1], $s1[$i]->get_value());
        }
    }

    public function test_stack_numerical_not_alg_equiv_edge(): void {

        $s1 = [];
        $t1 = [];
        $t1[] = ['numerical_not_alg_equiv(p2/p1,p2/p1)', 'false'];
        $t1[] = ['numerical_not_alg_equiv(2,p1)', 'true'];
        $t1[] = ['numerical_not_alg_equiv(p2,2)', 'true'];
        $t1[] = ['numerical_not_alg_equiv(x,p1)', 'true'];
        $t1[] = ['numerical_not_alg_equiv(p2,x)', 'true'];

        foreach ($t1 as $i => $case) {
            $s1[] = stack_ast_container::make_from_teacher_source($case[0], '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $s = new stack_cas_session2($s1, $options, 0);
        $s->instantiate();

        foreach ($t1 as $i => $t) {
            $this->assertEquals($t[1], $s1[$i]->get_value());
        }
    }

    public function test_stack_blockexternal(): void {

        $s1 = [];
        $t1 = [];
        // Block external commands, such as ordergreat, are pulled out the front.
        // So they apply to the whole session.
        $t1[] = ['f:x*y*z+a', 'y*z*x+a'];
        $t1[] = ['ordergreat(x,z,y)', '__s1'];
        $t1[] = ['g:x*y*z+1', 'y*z*x+1'];
        $t1[] = ['h:exdowncase(X*Y*Z)', 'y*z*x'];
        $t1[] = ['k:ev(exdowncase(X*Y*Z),simp)', 'y*z*x'];
        $t1[] = ['ATAlgEquiv(exdowncase(x),x)', '[true,true,"",""]'];

        foreach ($t1 as $i => $case) {
            $s1[] = stack_ast_container::make_from_teacher_source($case[0], '', new stack_cas_security(), []);
        }

        $options = new stack_options();
        $s = new stack_cas_session2($s1, $options, 0);
        $s->instantiate();

        $a = [];
        foreach ($s->get_contextvariables() as $i => $v) {
            $a[$i] = $v->get_evaluationform();
        }
        // Note that ordergreat is no longer a context variable.  It's in the preamble.
        $this->assertEquals([], $a);

        foreach ($t1 as $i => $t) {
            $this->assertEquals($t[1], $s1[$i]->get_value());
        }
    }

    public function test_silent_tellsimp(): void {

        $qv = "matchdeclare(pmpatex1,true);\nmatchdeclare(pmpatex2,true);" .
            "tellsimpafter((pmpatex1 #pm# pmpatex2)!,(pmpatex1^2) #pm# pmpatex2);\n" .
            "p1:(b #pm# c)!;";
        $qv = new stack_cas_keyval($qv, null, 123);

        $at1 = $qv->get_session();
        $at1->instantiate();
        $cs = $at1->get_by_key('p1');
        $this->assertEquals("b^2#pm#c", $cs->get_value());
    }

    public function test_eval_in_block(): void {

        $qv = "f:ev(2*x,x=2);\n" .
            "ev(g:3*x,x=3);\n" .
            "h:5*x,x=5;\n".
            "k:36;";
        $qv = new stack_cas_keyval($qv, null, 123);
        $this->assertTrue($qv->get_valid());

        $session = $qv->get_session();
        $s1 = stack_ast_container::make_from_teacher_source('[f,g,h,k]', '', new stack_cas_security(), []);
        $session->add_statement($s1);
        $this->assertTrue($session->get_valid());

        $session->instantiate();
        $this->assertTrue($session->is_instantiated());

        $this->assertEquals('[4,9,25,36]', $s1->get_value());
    }

    public function test_confirm_induced_timeout(): void {

        $qv = "p:1;\n" .
              "for i:1 thru 2^100 do p:p+(-1)^i;\n";
        $qv = new stack_cas_keyval($qv, null, 123);
        $this->assertTrue($qv->get_valid());

        $session = $qv->get_session();
        $s1 = stack_ast_container::make_from_teacher_source('p', '', new stack_cas_security(), []);
        $session->add_statement($s1);
        $this->assertTrue($session->get_valid());

        $session->instantiate();
        $this->assertFalse($session->is_instantiated());
        $this->assertEquals('CAS failed to return any data due to timeout.', $s1->get_errors());
    }

    public function test_complex_number_display(): void {

        // These test cases get wrapped in the general display_complex(ex) function to test the default conversion.
        $cases = [];
        $cases[] = ['3+2*%i', '3+2\,\mathrm{i}'];
        $cases[] = ['-3+2*%i', '-3+2\,\mathrm{i}'];
        $cases[] = ['-3-2*%i', '-3-2\,\mathrm{i}'];
        $cases[] = ['3-2*%i', '3-2\,\mathrm{i}'];
        $cases[] = ['1+%i', '1+\mathrm{i}'];
        $cases[] = ['1-%i', '1-\mathrm{i}'];
        $cases[] = ['3/2+%i', '\frac{3}{2}+\mathrm{i}'];
        $cases[] = ['(3+2*%i)/2', '\frac{3}{2}+\mathrm{i}'];
        $cases[] = ['%i', '\mathrm{i}'];
        $cases[] = ['-%i', '-\mathrm{i}'];
        $cases[] = ['a+b*%i', 'a+\mathrm{i}\,b'];
        $cases[] = ['-a+b*%i', '-a+\mathrm{i}\,b'];
        $cases[] = ['a-b*%i', 'a-\mathrm{i}\,b'];
        $cases[] = ['%i * 3/5', '\frac{3}{5}\,\mathrm{i}'];
        // Note this is not displayed as \frac{\mathrm{i}}{5} by design.
        $cases[] = ['%i/5', '\frac{1}{5}\,\mathrm{i}'];
        $cases[] = ['%i/sqrt(2)', '\frac{1}{\sqrt{2}}\,\mathrm{i}'];
        // Note this function simplifies its arguments.
        $cases[] = ['2*%i/sqrt(2)', '\sqrt{2}\,\mathrm{i}'];
        $cases[] = ['%i * p/q', '\mathrm{i}\,\frac{p}{q}'];
        $cases[] = ['%i * sqrt(2)', '\sqrt{2}\,\mathrm{i}'];
        $cases[] = ['%i * sqrt(2)/5', '\frac{\sqrt{2}}{5}\,\mathrm{i}'];
        $cases[] = ['%i * %pi', '\pi\,\mathrm{i}'];
        $cases[] = ['%i * 2*%pi', '2\cdot \pi\,\mathrm{i}'];
        $cases[] = ['%i * 2*%pi/3', '\frac{2\cdot \pi}{3}\,\mathrm{i}'];
        $cases[] = ['-1/8+(sqrt(3)-36)/8*%i', '-\frac{1}{8}+\frac{\sqrt{3}-36}{8}\,\mathrm{i}'];
        $cases[] = ['-(((4*sqrt(3)-9)*%i+4)/2)', '-2-\frac{4\cdot \sqrt{3}-9}{2}\,\mathrm{i}'];
        $cases[] = ['((4*sqrt(3)-9)*%i+4)/2', '2+\frac{4\cdot \sqrt{3}-9}{2}\,\mathrm{i}'];

        $s1 = [];
        foreach ($cases as $k => $case) {
            $s1[] = stack_ast_container::make_from_teacher_source('display_complex(' . $case[0] . ')',
                '', new stack_cas_security(), []);
        }
        $options = new stack_options();
        $options->set_option('simplify', false);
        $session = new stack_cas_session2($s1, $options, 0);
        $this->assertTrue($session->get_valid());

        $session->instantiate();
        $this->assertTrue($session->is_instantiated());

        foreach ($cases as $k => $case) {
            $this->assertEquals($case[1], $s1[$k]->get_display());
        }

        $cases = [];
        $cases[] = ['disp_complex(3,2)', '3+2\,\mathrm{i}'];
        $cases[] = ['disp_complex(2/4,1)', '\frac{2}{4}+1\,\mathrm{i}'];
        $cases[] = ['disp_complex(0,2)', '0+2\,\mathrm{i}'];
        $cases[] = ['disp_complex(0,1)', '0+1\,\mathrm{i}'];
        // This is not displayed as i/2 by design.
        $cases[] = ['disp_complex(null,1/2)', '\frac{1}{2}\,\mathrm{i}'];
        $cases[] = ['disp_complex(null,2)', '2\,\mathrm{i}'];
        $cases[] = ['disp_complex(null,-2)', '-2\,\mathrm{i}'];
        $cases[] = ['disp_complex(1,null)', '1+\mathrm{i}'];
        $cases[] = ['disp_complex(1,-null)', '1-\mathrm{i}'];
        $cases[] = ['disp_complex(null,-null)', '-\mathrm{i}'];
        $cases[] = ['disp_complex(a,b)', 'a+\mathrm{i}\,b'];
        // This simplifies the second argumet in order to pull out the unary minus.
        // This is a feature, not a bug!
        $cases[] = ['disp_complex(a,(-b^2)/b)', 'a-\mathrm{i}\,b'];
        $cases[] = ['disp_complex(a,b^2/b)', 'a+\mathrm{i}\,\frac{b^2}{b}'];

        $s1 = [];
        foreach ($cases as $k => $case) {
            $s1[] = stack_ast_container::make_from_teacher_source($case[0], '', new stack_cas_security(), []);
        }
        $options = new stack_options();
        $options->set_option('simplify', false);
        $session = new stack_cas_session2($s1, $options, 0);
        $this->assertTrue($session->get_valid());

        $session->instantiate();
        $this->assertTrue($session->is_instantiated());

        foreach ($cases as $k => $case) {
            $this->assertEquals($case[1], $s1[$k]->get_display());
        }
    }

    public function test_complex_number_display_options(): void {

        // These test cases get wrapped in the general display_complex(ex) function to test the default conversion.
        $cases = [];
        $cases[] = ['3+2*%i', '3+2\,\mathrm{j}'];
        $cases[] = ['-3+2*%i', '-3+2\,\mathrm{j}'];
        $cases[] = ['-3-2*%i', '-3-2\,\mathrm{j}'];
        $cases[] = ['3-2*%i', '3-2\,\mathrm{j}'];
        $cases[] = ['1+%i', '1+\mathrm{j}'];
        $cases[] = ['1-%i', '1-\mathrm{j}'];

        $cases[] = ['-3+2*%j', '-3+2\,\mathrm{j}'];

        $s1 = [];
        foreach ($cases as $k => $case) {
            $s1[] = stack_ast_container::make_from_teacher_source('display_complex(' . $case[0] . ')',
                '', new stack_cas_security(), []);
        }
        $options = new stack_options();
        $options->set_option('simplify', false);
        $options->set_option('complexno', 'j');
        $session = new stack_cas_session2($s1, $options, 0);
        $this->assertTrue($session->get_valid());

        $session->instantiate();
        $this->assertTrue($session->is_instantiated());

        foreach ($cases as $k => $case) {
            $this->assertEquals($case[1], $s1[$k]->get_display());
        }
    }

    public function test_parens_delect_display(): void {

        $cases = [];
        $cases[] = ['disp_parens(a+b)+c', '\left( a+b \right)+c'];
        $cases[] = ['int(disp_parens(x-2),x)', '\int {\left( x-2 \right)}{\;\mathrm{d}x}'];
        $cases[] = [
            'disp_parens(display_complex(1+%i))*x^2+disp_parens(display_complex(1-%i))',
            '\left( 1+\mathrm{i} \right)\cdot x^2+\left( 1-\mathrm{i} \right)',
        ];
        $cases[] = ['disp_select(a+b)+c', '\color{red}{\underline{a+b}}+c'];
        $cases[] = ['disp_select(a+b)^3', '{\color{red}{\underline{a+b}}}^3'];
        $cases[] = ['remove_disp(disp_select(a+b)+c)', 'a+b+c'];

        $s1 = [];
        foreach ($cases as $k => $case) {
            $s1[] = stack_ast_container::make_from_teacher_source($case[0], '', new stack_cas_security(), []);
        }
        $options = new stack_options();
        $options->set_option('simplify', false);
        $session = new stack_cas_session2($s1, $options, 0);
        $this->assertTrue($session->get_valid());

        $session->instantiate();
        $this->assertTrue($session->is_instantiated());

        foreach ($cases as $k => $case) {
            $this->assertEquals($case[1], $s1[$k]->get_display());
        }
    }

    public function test_parens_select(): void {

        $cases = [];
        $cases[] = ['select(integerp, 3)', '\color{red}{\underline{3}}'];
        $cases[] = ['select(integerp, 0.5)', '0.5'];
        $cases[] = [
            'select(integerp, 1+x+0.5*x^2)',
            '\color{red}{\underline{1}}+x+0.5\cdot x^{\color{red}{\underline{2}}}',
        ];
        $cases[] = [
            'select(zeroMulp, (1-1)*x^2+0*x+1)',
            '\left(1-1\right)\cdot x^2+\color{red}{\underline{0\cdot x}}+1',
        ];

        $s1 = [];
        foreach ($cases as $k => $case) {
            $s1[] = stack_ast_container::make_from_teacher_source($case[0], '', new stack_cas_security(), []);
        }
        $options = new stack_options();
        $options->set_option('simplify', false);
        $session = new stack_cas_session2($s1, $options, 0);
        $this->assertTrue($session->get_valid());

        $session->instantiate();
        $this->assertTrue($session->is_instantiated());

        foreach ($cases as $k => $case) {
            $this->assertEquals($case[1], $s1[$k]->get_display());
        }
    }

    public function test_fboundp(): void {

        $cases = [];
        $cases[] = ['fboundp(sinner)', 'false'];
        $cases[] = ['fboundp(sin)', 'true'];
        $cases[] = ['fboundp("+")', 'true'];
        $cases[] = ['fboundp(expand)', 'true'];
        // A STACK defined function.
        $cases[] = ['fboundp(intervalp)', 'true'];

        $s1 = [];
        foreach ($cases as $k => $case) {
            $s1[] = stack_ast_container::make_from_teacher_source($case[0], '', new stack_cas_security(), []);
        }
        $options = new stack_options();
        $options->set_option('simplify', false);
        $session = new stack_cas_session2($s1, $options, 0);
        $this->assertTrue($session->get_valid());

        $session->instantiate();
        $this->assertTrue($session->is_instantiated());

        foreach ($cases as $k => $case) {
            $this->assertEquals($case[1], $s1[$k]->get_value());
        }
    }

    public function test_diag(): void {

        $cases = [];
        $cases[] = [
            'j1:jordan(matrix([1,2,3,4],[5,6,7,8],[2,3,4,5],[6,7,8,9]))',
            '[[10-2*sqrt(31),1],[2*sqrt(31)+10,1],[0,1,1]]',
        ];
        $cases[] = [
            'j2:dispJordan(j1)',
            'matrix([10-2*sqrt(31),0,0,0],[0,2*sqrt(31)+10,0,0],[0,0,0,0],[0,0,0,0])',
        ];

        $s1 = [];
        foreach ($cases as $k => $case) {
            $s1[] = stack_ast_container::make_from_teacher_source($case[0], '', new stack_cas_security(), []);
        }
        $options = new stack_options();
        $options->set_option('simplify', true);
        $session = new stack_cas_session2($s1, $options, 0);
        $this->assertTrue($session->get_valid());

        $session->instantiate();
        $this->assertTrue($session->is_instantiated());
        foreach ($cases as $k => $case) {
            $this->assertEquals($case[1], $s1[$k]->get_value());
        }
    }

    public function test_cartesian_product(): void {

        $cases = [];
        $cases[] = [
            'cartesian_product({1, 2}, {3, 4})',
            '{[1,3],[1,4],[2,3],[2,4]}',
        ];

        $s1 = [];
        foreach ($cases as $k => $case) {
            $s1[] = stack_ast_container::make_from_teacher_source($case[0], '', new stack_cas_security(), []);
        }
        $options = new stack_options();
        $options->set_option('simplify', true);
        $session = new stack_cas_session2($s1, $options, 0);
        $this->assertTrue($session->get_valid());

        $session->instantiate();
        $this->assertTrue($session->is_instantiated());
        foreach ($cases as $k => $case) {
            $this->assertEquals($case[1], $s1[$k]->get_value());
        }
    }

    public function test_keyword_end(): void {

        $cases = [
            'v1: (-x^2+1)/(x^2+1)^2', 'v2: 1/(x^2+1)-(2*x^2)/(x^2+1)^2', 'end:3',
            't1:ATAlgEquiv(v1, v2)', 'v3:end^2',
        ];

        $s1 = [];
        foreach ($cases as $case) {
            $s1[] = stack_ast_container::make_from_teacher_source($case, '', new stack_cas_security(), []);
        }
        $options = new stack_options();
        $options->set_option('simplify', true);
        $session = new stack_cas_session2($s1, $options, 0);
        $this->assertTrue($session->get_valid());

        $session->instantiate();
        $this->assertTrue($session->is_instantiated());
        $v3 = $session->get_by_key('v3');
        $this->assertEquals('9', $v3->get_value());
        $t1 = $session->get_by_key('t1');
        $this->assertEquals('[true,true,"",""]', $t1->get_value());

    }

    public function test_use_at(): void {

        // This testcase arose as issue #762.
        $cases = [
            'k1:4',
            'k2:5',
            'k3:2',
            'f1:x2^2-k1*u',
            'f2:k2*x1-k3*x2+u',
            'f3:x_1',
            'u0: 1',
            'f10:at(f1,[u=u0])',
            'f20:at(f2,[u=u0])',
            'eq1:f10=0',
            'eq2:f20=0',
            'sol:solve([eq1,eq2],[x1,x2])',
            's1:sol[1]',
            's2:sol[2]',
            'x11:rhs(s1[1])',
            'x12:rhs(s1[2])',
            'x21:rhs(s2[1])',
            'x22:rhs(s2[2])',
            'P1:matrix([x11],[x12])',
            'P2: matrix([x21],[x22])',
            'var:[x1, x2]',
            'inp:[u]',
            'sys:[f1, f2]',
            'A:jacobian(sys,var)',
            'B:jacobian(sys, inp)',
            'A1:at(A,[x1=x11,x2=x12, u=u0])',
            'B1:at(B,[x1=x11,x2=x12, u=u0])',
            'A2:at(A,[x1=x21, x2=x22, u=u0])',
            'B2:at(B,[x1=x21, x2=x22, u=u0])',
        ];

        $s1 = [];
        foreach ($cases as $case) {
            $s1[] = stack_ast_container::make_from_teacher_source($case, '', new stack_cas_security(), []);
        }
        $options = new stack_options();
        $options->set_option('simplify', true);
        $session = new stack_cas_session2($s1, $options, 0);
        $this->assertTrue($session->get_valid());

        $session->instantiate();
        $this->assertTrue($session->is_instantiated());
        $v3 = $session->get_by_key('A2');
        $this->assertEquals('matrix([0,4],[5,-2])', $v3->get_value());
        $t1 = $session->get_by_key('B2');
        $this->assertEquals('matrix([-4],[1])', $t1->get_value());
    }

    public function test_s_test(): void {

        $cases = ['t1:s_assert(a,b)'];

        $s1 = [];
        foreach ($cases as $case) {
            $s1[] = stack_ast_container::make_from_teacher_source($case, '', new stack_cas_security(), []);
        }
        $options = new stack_options();
        $options->set_option('simplify', false);
        $session = new stack_cas_session2($s1, $options, 0);
        $this->assertTrue($session->get_valid());

        $session->instantiate();
        $this->assertTrue($session->is_instantiated());
        $this->assertEquals('s_assert: STACK expected \' b \' but was given \' a \'.', $session->get_errors());
    }

    public function test_let(): void {

        // Note, the rule deliberarly does not correspond to normal mathematics!
        $cases = [
            'matchdeclare([a, a1, a2], true)',
            'p:(let(sin(a)^2, 1-cos(a)^3), letsimp(sin(x)^4))',
        ];
        $s1 = [];
        foreach ($cases as $case) {
            $s1[] = stack_ast_container::make_from_teacher_source($case, '', new stack_cas_security(), []);
        }
        $options = new stack_options();
        $options->set_option('simplify', true);
        $session = new stack_cas_session2($s1, $options, 0);
        $this->assertTrue($session->get_valid());
        $session->instantiate();
        $this->assertTrue($session->is_instantiated());
        $p = $session->get_by_key('p');
        $this->assertEquals('cos(x)^6-2*cos(x)^3+1', $p->get_value());
    }

    public function test_let_matrix(): void {

        $cases = ['orderless(I);',
            'matchdeclare([a],true)',
            '(let(I*a, a), let(I^2, I), true)',
            'p:letsimp(expand((A+I)^3))',
        ];
        $s1 = [];
        foreach ($cases as $case) {
            $s1[] = stack_ast_container::make_from_teacher_source($case, '', new stack_cas_security(), []);
        }
        $options = new stack_options();
        $options->set_option('simplify', true);
        $session = new stack_cas_session2($s1, $options, 0);
        $this->assertTrue($session->get_valid());
        $session->instantiate();
        $this->assertTrue($session->is_instantiated());
        $p = $session->get_by_key('p');
        $this->assertEquals('A^3+3*A^2+3*A+I', $p->get_value());

        $cases = ['orderless(I)',
            'matchdeclare ([A], true)',
            '(let(A*I,A), true)',
            'p:letsimp(expand((X-I)^3))',
        ];
        $s1 = [];
        foreach ($cases as $case) {
            $s1[] = stack_ast_container::make_from_teacher_source($case, '', new stack_cas_security(), []);
        }
        $options = new stack_options();
        $options->set_option('simplify', true);
        $session = new stack_cas_session2($s1, $options, 0);
        $this->assertTrue($session->get_valid());
        $session->instantiate();
        $this->assertTrue($session->is_instantiated());
        $p = $session->get_by_key('p');
        $this->assertEquals('X^3-3*X^2+3*X-1', $p->get_value());
    }

    public function test_stackmaximaversion(): void {

        // This test ensures that we are not running against different
        // version number of the STACK-Maxima scripts. For example,
        // old image in a server setup or a cache layer somewhere.

        $scriptversion = file_get_contents(__DIR__ . '/../stack/maxima/stackmaxima.mac');
        $scriptversion = explode('stackmaximaversion:', $scriptversion);
        $scriptversion = $scriptversion[count($scriptversion) - 1];
        $scriptversion = explode('$', $scriptversion)[0];

        $cs = stack_ast_container::make_from_teacher_source('stackmaximaversion', 'version-check');

        $session = new stack_cas_session2([$cs]);

        $session->get_valid();
        $session->instantiate();

        $this->assertEquals($scriptversion, $cs->get_value(),
            'To fix this: Check STACK-Maxima script versions, purge caches and/or regenerate images.');
    }
}
