Add a parserLogb.pl macro for logarithms with base b.

htdocs/js/MathQuill/mqeditor.js

@@ -309,6 +309,9 @@
 			{ id: 'sqrt', latex: '\\sqrt', tooltip: 'square root (sqrt)', icon: '\\sqrt{\\text{ }}' },
 			{ id: 'nthroot', latex: '\\root', tooltip: 'nth root (root)', icon: '\\sqrt[\\text{ }]{\\text{ }}' },
 			{ id: 'exponent', latex: '^', tooltip: 'exponent (^)', icon: '\\text{ }^\\text{ }' },
+			...(cfgOptions.logsChangeBase
+				? []
+				: [{ id: 'subscript', latex: '_', tooltip: 'subscript (_)', icon: '\\text{  }_\\text{  }' }]),
 			{ id: 'infty', latex: '\\infty', tooltip: 'infinity (inf)', icon: '\\infty' },
 			{ id: 'pi', latex: '\\pi', tooltip: 'pi (pi)', icon: '\\pi' },
 			{ id: 'vert', latex: '\\vert', tooltip: 'such that (vert)', icon: '|' },

lib/Parser/Context/Default.pm

@@ -443,6 +443,7 @@ $flags = {
 	parseAlternatives          => 0,              # 1 = allow parsing of alternative tokens in the context
 	convertFullWidthCharacters => 0,              # 1 = convert Unicode full width characters to ASCII positions
 	useMathQuill               => 0,
+	mathQuillOpts              => {},
 };
 
 ############################################################################

macros/PG.pl

@@ -979,9 +979,11 @@ sub ENDDOCUMENT {
 				my $mq_part_opts = $ansHash->{mathQuillOpts} // $mq_opts;
 				next if $mq_part_opts =~ /^\s*disabled\s*$/i;
 
-				my $context = $ansHash->{correct_value}->context if $ansHash->{correct_value};
-				$mq_part_opts->{rootsAreExponents} = 0
-					if $context && $context->functions->get('root') && !defined $mq_part_opts->{rootsAreExponents};
+				if ($ansHash->{correct_value}) {
+					for (keys %{ $ansHash->{correct_value}->context->flag('mathQuillOpts') }) {
+						$mq_part_opts->{$_} = 0 unless defined $mq_part_opts->{$_};
+					}
+				}
 
 				my $name = "MaThQuIlL_$response";
 				RECORD_EXTRA_ANSWERS($name);

macros/parsers/parserLogb.pl

@@ -0,0 +1,213 @@
+################################################################################
+# WeBWorK Online Homework Delivery System
+# Copyright © 2000-2020 The WeBWorK Project, http://openwebwork.sf.net/
+#
+# This program is free software; you can redistribute it and/or modify it under
+# the terms of either: (a) the GNU General Public License as published by the
+# Free Software Foundation; either version 2, or (at your option) any later
+# version, or (b) the "Artistic License" which comes with this package.
+#
+# This program 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 either the GNU General Public License or the
+# Artistic License for more details.
+################################################################################
+
+=head1 NAME
+
+parserLogb.pl - defines a C<logb(b, x)> function for the logarithm with base b
+evaluated at x.
+
+=head1 DESCRIPTION
+
+This file defines the code necessary to add to any context a C<logb(b, x)>
+function that evaluates the logarithm with base b at x.  For example,
+C<Compute("logb(3, 5)")> would return the equivalent of
+C<Compute("log(5)/log(3)"> although it will be displayed as a logarithm with
+base b.
+
+To accomplish this, put the line
+
+    loadMacros("parserLogb.pl");
+
+at the beginning of your problem file, then set the Context to the one you wish
+to use in the problem.  Then use the command:
+
+    Parser::Logb->Enable;
+
+(You can also pass the Enable command a pointer to a context if you wish to
+alter a context other than the current one.)
+
+Once that is done, you (and students) can enter logarithms with base b by using
+the C<logb()> function.  You can use C<logb()> both within C<Formula()> and
+C<Compute()> calls, and in Perl expressions, such as
+
+	$ans = Compute("logb(3, 5)";
+    $n   = logb(3, 5);
+
+to obtain the logarithm with base b.  Note that by default C<logb()> will
+produce an error message for logarithms evaluated at zero or negative numbers or
+if the base is zero or negative.
+
+However, if you enable C<logb()> in a context that allows complex numbers, you
+may want to allow logarithms of negative numbers or with negative bases.  To do
+this, use
+
+    Parser::Logb->EnableComplex;
+
+(again, you can pass a context to be altered, if you wish).  This will force
+logarithms of negative values or with negative bases to be promoted to complex
+numbers.  So
+
+    Parser::Logb->EnableComplex;
+    $z = logb(3, -9);
+    $y = logb(-3, 9);
+
+would produce the equivalent of C<$z = Compute("log(-9)/log(3)");> and
+C<$y = Compute("log(9)/log(-3)");> except that they will be displayed as
+logarithms with base 3 or -3 respectively.
+
+Note that if MathQuill is enabled, then students will be able to enter the
+logarithm with base C<b> evaluated at C<x> by typing C<log_b(x)>. To facilitate
+students entering such answers, a subscript button is present in the MathQuill
+toolbar for answers with the C<logb> function enabled.
+
+=cut
+
+BEGIN { strict->import }
+
+loadMacros('MathObjects.pl');
+
+sub _parserLogb_init { }
+
+sub logb { Parser::Function->call('logb', @_); }
+
+package Parser::Logb;
+
+sub Enable {
+	my ($self, $context, $complex) = @_;
+	$context = main::Context() unless Value::isContext($context);
+	$context->functions->add(logb => { class => 'Parser::Logb::Function::numeric2' });
+	$context->functions->set(logb => { negativeIsComplex => 1 }) if $complex;
+	$context->flag('mathQuillOpts')->{logsChangeBase} = 0;
+	return;
+}
+
+sub EnableComplex {
+	my ($self, $context) = @_;
+	$self->Enable($context, 1);
+	return;
+}
+
+package Parser::Logb::Function::numeric2;
+our @ISA = qw(Parser::Function);
+
+# Check for numeric arguments
+sub _check {
+	my $self    = shift;
+	my $context = $self->context;
+	return if ($self->checkArgCount(2));
+	$self->{type} = $Value::Type{number};
+	return if $context->flag('allowBadFunctionInputs');
+	my ($b, $x) = @{ $self->{params} };
+	$self->Error('Function "%s" must have numeric inputs', $self->{name})
+		unless $b->isNumber && $x->isNumber;
+	$self->{type} = $Value::Type{complex} if $x->isComplex || $b->isComplex;
+	return;
+}
+
+# Check that the inputs are OK and call the named routine
+sub _call {
+	my ($self, $name, @inputs) = @_;
+	$self->Error('Function "%s" has too many inputs', $name) if scalar(@inputs) > 2;
+	$self->Error('Function "%s" has too few inputs',  $name) if scalar(@inputs) < 2;
+	return $self->$name($self->checkArguments($name, @inputs));
+}
+
+# Call the appropriate routine
+sub _eval {
+	my ($self, @inputs) = @_;
+	my $name = $self->{name};
+	return $self->$name($self->checkArguments($name, @inputs));
+}
+
+# Check that the parameters are OK
+sub checkArguments {
+	my ($self, $name, @inputs) = @_;
+	my $context = $self->context;
+	my ($b, $x) = (map { Value::makeValue($_, $context) } @inputs);
+	$self->Error('Function "%s" must have numeric inputs', $name)
+		unless $b->isNumber && $x->isNumber;
+	return ($b, $x);
+}
+
+# Compute log base b using log(x)/log(b)
+# If b < 0 or x < 0, either promote to a complex or throw an error.
+sub logb {
+	my ($self, $b, $x) = @_;
+	$self->Error('Invalid base %s logarithm of %s', $b)
+		if $x->value == 0 || $b->value == 0;
+	if (($x->isReal && $x->value < 0) || ($b->isReal && $b->value < 0)) {
+		my $context = $x->context;
+		$self->Error('Invalid base %s logarithm of %s', $b, $x)
+			unless $context->functions->get('logb')->{negativeIsComplex};
+		$x = $self->Package('Complex')->promote($context, $x);
+		$b = $self->Package('Complex')->promote($context, $b);
+	}
+	return log($x) / log($b);
+}
+
+# Implement differentiation: (logb(b, u))' -> u'/(u * ln(b)) - b'/(b * ln(u)) * logb(b, u)
+sub D {
+	my ($self, $x) = @_;
+	my $equation = $self->{equation};
+	my $BOP      = $self->Item('BOP');
+	my $NUM      = $self->Item('Number');
+	my ($b, $u) = @{ $self->{params} };
+	my $D = $BOP->new(
+		$equation,
+		'/',
+		$u->D($x),
+		$BOP->new(
+			$equation, '*', $u->copy($equation),
+			$self->Item('Function')->new($equation, 'ln', [ $b->copy($equation) ], $b->{isConstant})
+		)
+	);
+	$D = $BOP->new(
+		$equation,
+		'-', $D,
+		$BOP->new(
+			$equation,
+			'*',
+			$BOP->new(
+				$equation,
+				'/',
+				$b->D($x),
+				$BOP->new(
+					$equation, '*', $b->copy($equation),
+					$self->Item('Function')->new($equation, 'ln', [ $b->copy($equation) ], $b->{isConstant})
+				)
+			),
+			$self->copy($equation)
+		)
+	) if $b->getVariables->{$x};
+	return $D->reduce;
+}
+
+# Output TeX using \log_{b}(x)
+sub TeX {
+	my ($self, $precedence, $showparens, $position, $outerRight, $power) = @_;
+	$showparens = '' unless defined $showparens;
+	my $fn            = $self->{equation}{context}{operators}{'fn'};
+	my $fn_precedence = $fn->{parenPrecedence} || $fn->{precedence};
+	my ($b, $x) = @{ $self->{params} };
+	my $TeX = '\log_{' . $b->TeX . '}\left(' . $x->TeX . '\right)';
+	$TeX = '\left(' . $TeX . '\right)'
+		if $showparens eq 'all'
+		|| $showparens eq 'extra'
+		|| (defined($precedence) && $precedence > $fn_precedence)
+		|| (defined($precedence) && $precedence == $fn_precedence && $showparens eq 'same');
+	return $TeX;
+}
+
+1;

macros/parsers/parserRoot.pl

@@ -82,6 +82,7 @@ sub Enable {
 	$context = main::Context() unless Value::isContext($context);
 	$context->functions->add(root => { class => 'parser::Root::Function::numeric2' },);
 	$context->functions->set(root => { negativeIsComplex => 1 }) if $complex;
+	$context->flag('mathQuillOpts')->{rootsAreExponents} = 0;
 }
 
 sub EnableComplex {