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[WWcvs] pg: This is a rewrite of the Inequalities context that makes a number of improvements over the older version.
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From: dpvc v. a. <we...@ma...> - 2007-08-26 19:17:15
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Log Message:
-----------
This is a rewrite of the Inequalities context that makes a number of
improvements over the older version.
First, the error messages are much better when students enter
incorrect answers.
Second, inequalities and intervals are now separate classes and so you
can enter both types of notation and they will stringify and texify
correctly, so there is no need for the stringifyAsInequalities flag
any longer.
Finally, there is a new Inequality() constructor that can be used to
coerce Intervals, Sets, and Unions to become their corresponding
inequalities, and vice versa, Interval(), Set() and Union() can be
used to coerce an Inequality to be represented in its interval-style
notation.
This is not backaward compatible with the ealier version, but since
that is only a couple of weeks old, I don't think it should be an
issue, as very few problems will have been written for it in that
time.
Modified Files:
--------------
pg/macros:
contextInequalities.pl
Revision Data
-------------
Index: contextInequalities.pl
===================================================================
RCS file: /webwork/cvs/system/pg/macros/contextInequalities.pl,v
retrieving revision 1.6
retrieving revision 1.7
diff -Lmacros/contextInequalities.pl -Lmacros/contextInequalities.pl -u -r1.6 -r1.7
--- macros/contextInequalities.pl
+++ macros/contextInequalities.pl
@@ -15,24 +15,17 @@
# Usage: loadMacros("contextInequalities.pl");
#
# Context("Inequalities");
- # $S1 = Formula("1 < x <= 4");
- # $S2 = Formula("(1,4]"); # either form is OK
+ # $S1 = Compute("1 < x <= 4");
+ # $S2 = Inequality("(1,4]"); # force interval to be inequality
#
# Context("Inequalities-Only");
- # $S1 = Formula("1 < x <= 4");
- # $S2 = Formula("(1,4]"); # generates an error
+ # $S1 = Compute("1 < x <= 4");
+ # $S2 = Inequality("(1,4]"); # generates an error
#
- # $S3 = Formula("x < -2 or x > 2"); # forms a Union
- # $S4 = Formula("x = 1"); # forms a Set
+ # $S3 = Compute("x < -2 or x > 2"); # forms a Union
+ # $S4 = Compute("x = 1"); # forms a Set
#
- # You can set the "stringifyAsInequalities" flag to 1 to force
- # output from the intervals, sets, and unions created in this
- # context to be output as inequalities rather than their
- # usual Inerval, Set or Union forms.
- #
- # Context("Inequalities")->flags->set(stringifyAsInequalities=>1);
- #
- # You can also set the "noneWord" flag to specify the string to
+ # You can set the "noneWord" flag to specify the string to
# use when the inequalities specify the empty set. By default,
# it is "NONE", but you can change it to other strings. Be sure
# that you use a string that is defined in the Context, however,
@@ -44,6 +37,24 @@
#
# creates an empty set as a named constant and uses that name.
#
+ # Inequalities and interval notation both can coexist side by
+ # side, but you may wish to convert from one to the other.
+ # Use Inequality() to convert from an Interval, Set or Union
+ # to an Inequality, and use Interval(), Set(), or Union() to
+ # convert from an Inequality object to one in interval notation.
+ # For example:
+ #
+ # $I0 = Compute("(1,2]"); # the interval (1,2]
+ # $I1 = Inequality($I); # the inequality 1 < x <= 2
+ #
+ # $I0 = Compute("1 < x <= 2"); # the inequality 1 < x <= 2
+ # $I1 = Interval($I0); # the interval (1,2]
+ #
+ # Note that ineqaulities and inervals can be compared and combined
+ # regardless of the format, so $I0 == $I1 is true in either example
+ # above.
+ #
+ ######################################################################
=cut
@@ -61,16 +72,16 @@
'>' => {precedence => .5, associativity => 'left', type => 'bin', string => ' > ',
class => 'Inequalities::BOP::inequality', eval => 'evalGreaterThan', combine => 1},
- '<=' => {precedence => .5, associativity => 'left', type => 'bin', string => ' <= ',
+ '<=' => {precedence => .5, associativity => 'left', type => 'bin', string => ' <= ', TeX => '\le ',
class => 'Inequalities::BOP::inequality', eval => 'evalLessThanOrEqualTo', combine => 1},
- '>=' => {precedence => .5, associativity => 'left', type => 'bin', string => ' >= ',
+ '>=' => {precedence => .5, associativity => 'left', type => 'bin', string => ' >= ', TeX => '\ge ',
class => 'Inequalities::BOP::inequality', eval => 'evalGreaterThanOrEqualTo', combine => 1},
'=' => {precedence => .5, associativity => 'left', type => 'bin', string => ' = ',
class => 'Inequalities::BOP::inequality', eval => 'evalEqualTo'},
- '!=' => {precedence => .5, associativity => 'left', type => 'bin', string => ' != ',
+ '!=' => {precedence => .5, associativity => 'left', type => 'bin', string => ' != ', TeX => '\ne ',
class => 'Inequalities::BOP::inequality', eval => 'evalNotEqualTo'},
'and' => {precedence => .45, associateivity => 'left', type => 'bin', string => " and ",
@@ -79,33 +90,42 @@
'or' => {precedence => .4, associateivity => 'left', type => 'bin', string => " or ",
TeX => '\hbox{ or }', class => 'Inequalities::BOP::or'},
);
- $context->flags->set(stringifyAsInequalities => 0, noneWord => 'NONE');
- $context->{cmpDefaults}{Inequalities} = {reduceSets=>1};
- $context->{cmpDefaults}{Interval} = {reduceSets=>1};
- $context->{cmpDefaults}{Union} = {reduceSets=>1};
- $context->{cmpDefaults}{Set} = {reduceSets=>1};
+ $context->operators->set(
+ '+' => {class => "Inequalities::BOP::add"},
+ '-' => {class => "Inequalities::BOP::subtract"},
+ );
+ $context->parens->set("(" => {type => "List", formIntervla => ']'}); # trap these later
+ $context->parens->set("[" => {type => "List", formIntervla => ')'}); # trap these later
$context->strings->remove("NONE");
$context->constants->add(NONE=>Value::Set->new());
+ $context->flags->set(noneWord => 'NONE');
$context->{parser}{Variable} = "Inequalities::Variable";
- $context->{value}{Interval} = "Inequalities::Interval";
- $context->{value}{Union} = "Inequalities::Union";
- $context->{value}{Set} = "Inequalities::Set";
+ $context->{value}{'Interval()'} = "Inequalities::MakeInterval";
+ $context->{value}{Inequality} = "Inequalities::Inequality";
+ $context->{value}{InequalityInterval} = "Inequalities::Interval";
+ $context->{value}{InequalityUnion} = "Inequalities::Union";
+ $context->{value}{InequalitySet} = "Inequalities::Set";
+ $context->{value}{List} = "Inequalities::List";
+ $context->{precedence}{Inequality} = $context->{precedence}{special};
+ $context->lists->set(List => {class => 'Inequalities::List::List'});
#
- # Disable interval notation in Context("Inequalities-Only");
+ # Disable interval notation in "Inequalities-Only" context
#
$context = $main::context{"Inequalities-Only"} = $context->copy;
- $context->parens->remove('(','[','{');
- $context->parens->redefine('(',from=>"Numeric");
- $context->parens->redefine('[',from=>"Numeric");
- $context->parens->redefine('{',from=>"Numeric");
- $context->parens->set(
- '(' => {formInterval=>0},
- '[' => {formInterval=>0}
+ $context->lists->set(
+ Interval => {class => 'Inequalities::List::notAllowed'},
+ Set => {class => 'Inequalities::List::notAllowed'},
+ Union => {class => 'Inequalities::List::notAllowed'},
);
- $context->lists->set(List => {class => 'Inequalities::List::List'});
- $context->operators->remove('U');
+ $context->operators->set('U' => {class => 'Inequalities::BOP::union'});
$context->constants->remove('R');
+
+ #
+ # Define the Inequality() constructor
+ #
+ main::PG_restricted_eval('sub Inequality {Value->Package("Inequality")->new(@_)}');
+
return;
}
@@ -121,7 +141,7 @@
#
# Check that the inequality is formed between a variable and a number,
-# or between a number and another compatable inequality. Otherwise,
+# or between a number and another compatible inequality. Otherwise,
# give an error.
#
# varPos and numPos tell which of lop or rop is the variable and which
@@ -129,7 +149,7 @@
#
sub _check {
my $self = shift;
- $self->{type} = Value::Type("Interval",2);
+ $self->{type} = $Value::Type{interval};
$self->{isInequality} = 1;
($self->{varPos},$self->{numPos}) =
($self->{lop}->class eq 'Variable' || $self->{lop}{isInequality} ? ('lop','rop') : ('rop','lop'));
@@ -162,7 +182,7 @@
sub _eval {
my $self = shift; my ($a,$b) = @_;
my $eval = $self->{def}{eval};
- my $I = $self->$eval(@_);
+ my $I = $self->Package("Inequality")->new($self->context,$self->$eval(@_),$self->{varName});
return $I->intersect($a) if Value::isValue($a) && $a->type eq 'Interval';
return $I->intersect($b) if Value::isValue($b) && $b->type eq 'Interval';
return $I;
@@ -252,10 +272,11 @@
sub _check {
my $self = shift;
- $self->Error("The operands of '%s' must be Intervals, Sets or Unions")
- unless $self->{lop}->isSetOfReals && $self->{rop}->isSetOfReals;
+ $self->Error("The operands of '%s' must be inequalities",$self->{bop})
+ unless $self->{lop}{isInequality} && $self->{rop}{isInequality};
$self->{type} = Value::Type("Interval",2);
$self->{varName} = $self->{lop}{varName} || $self->{rop}{varName};
+ $self->{isInequality} = 1;
}
sub _eval {$_[1]->intersect($_[2])}
@@ -269,10 +290,11 @@
sub _check {
my $self = shift;
- $self->Error("The operands of '%s' must be Intervals, Sets or Unions")
- unless $self->{lop}->isSetOfReals && $self->{rop}->isSetOfReals;
+ $self->Error("The operands of '%s' must be inequalities",$self->{bop})
+ unless $self->{lop}{isInequality} && $self->{rop}{isInequality};
$self->{type} = Value::Type("Interval",2);
$self->{varName} = $self->{lop}{varName} || $self->{rop}{varName};
+ $self->{isInequality} = 1;
}
sub _eval {$_[1] + $_[2]}
@@ -333,45 +355,171 @@
##################################################
#
-# For the Inequalities-Only context, we make lists
-# that report errors, so that students MUST produce
-# their intervals via inequalities.
+# Give an error when U is used.
#
-package Inequalities::List::List;
-our @ISA = ("Parser::List::List");
+package Inequalities::BOP::union;
+our @ISA = ("Parser::BOP::union");
sub _check {
my $self = shift;
+ $self->Error("You can't take unions of inequalities")
+ if $self->{lop}{isInequality} || $self->{rop}{isInequality};
$self->SUPER::_check(@_);
- $self->Error("You are not allowed to use intervals or sets in this context") if $self->{open};
+ $self->Error("Unions are not allowed in this context");
}
##################################################
#
-# Override the string and TeX methods
-# so that we can strinfigy as inequalities
-# rather than intervals.
+# Don't allow sums and differences of inequalities
#
-package Inequalities::Interval;
-our @ISA = ("Value::Interval");
+package Inequalities::BOP::add;
+our @ISA = ("Parser::BOP::add");
-sub new {
- my $self = shift; $self = $self->SUPER::new(@_);
- $self->{isValue} = 1;
- return $self;
+sub _check {
+ my $self = shift;
+ $self->SUPER::_check(@_);
+ $self->Error("Can't add inequalities (do you mean to use 'or'?)")
+ if $self->{lop}{isInequality} || $self->{rop}{isInequality};
}
-sub make {
- my $self = shift; $self = $self->SUPER::make(@_);
- $self->{isValue} = 1;
- return $self;
+##################################################
+#
+# Don't allow sums and differences of inequalities
+#
+package Inequalities::BOP::subtract;
+our @ISA = ("Parser::BOP::subtract");
+
+sub _check {
+ my $self = shift;
+ $self->SUPER::_check(@_);
+ $self->Error("Can't subtract inequalities")
+ if $self->{lop}{isInequality} || $self->{rop}{isInequality};
+}
+
+##################################################
+#
+# For the Inequalities-Only context, report
+# an error for Intervals, Sets or Union notation.
+#
+package Inequalities::List::notAllowed;
+our @ISA = ("Parser::List::List");
+
+sub _check {(shift)->Error("You are not allowed to use intervals or sets in this context")}
+
+
+##################################################
+##################################################
+#
+# Subclasses of the Interval, Set, and Union classes
+# that stringify as inequalities
+#
+
+#
+# Some common routines to all three classes
+#
+package Inequalities::common;
+
+#
+# Turn the object back into its usual Value version
+#
+sub demote {
+ my $self = shift; my $context = $self->context;
+ my $other = shift; $other = $self unless defined $other;
+ return $other unless Value::classMatch($other,"Inequality");
+ $context->Package($other->type)->make($context,$other->makeData);
+}
+
+#
+# Needed to get Interval data in the right order for make(),
+# and demote all the items in a Union
+#
+sub makeData {(shift)->value}
+
+#
+# Recursively mark Intervals and Sets in a Union as Inequalities
+#
+sub updateParts {}
+
+#
+# Demote the operands to normal Value objects and
+# perform the action, then remake the result into
+# an Inequality again.
+#
+sub apply {
+ my $self = shift; my $context = $self->context;
+ my $method = shift; my $other = shift;
+ $context->Package("Inequality")->new($context,
+ $self->demote->$method($self->demote($other),@_),
+ $self->{varName});
+}
+
+sub add {(shift)->apply("add",@_)}
+sub sub {(shift)->apply("sub",@_)}
+sub reduce {(shift)->apply("reduce",@_)}
+sub intersect {(shift)->apply("intersect",@_)}
+
+#
+# The name to use for error messages in answer checkers
+#
+sub class {"Inequality"}
+sub cmp_class {"an Inequality"}
+sub showClass {"an Inequality"}
+sub typeRef {
+ my $self = shift;
+ return Value::Type($self->type, $self->length, $Value::Type{number});
+}
+
+#
+# Get the precedence based on the type rather than the class.
+#
+sub precedence {
+ my $self = shift; my $precedence = $self->context->{precedence};
+ return $precedence->{$self->type}-$precedence->{Interval}+$precedence->{$self->class};
+}
+
+#
+# Produce better error messages for inequalities
+#
+sub cmp_checkUnionReduce {
+ my $self = shift; my $student = shift; my $ans = shift; my $nth = shift || '';
+ if (Value::classMatch($student,"Inequality")) {
+ return unless $ans->{studentsMustReduceUnions} &&
+ $ans->{showUnionReduceWarnings} &&
+ !$ans->{isPreview} && !Value::isFormula($student);
+ my ($result,$error) = $student->isReduced;
+ return unless $error;
+ return {
+ "overlaps" => "Your$nth answer contains overlapping inequalities",
+ "overlaps in sets" => "Your$nth answer contains equalities that are already included elsewhere",
+ "uncombined intervals" => "Your$nth answer can be simplified by combining some inequalities",
+ # shouldn't get the following ones from inequalities
+ "uncombined sets" => "",
+ "repeated elements in set" => "",
+ "repeated elements" => "",
+ }->{$error};
+ } else {
+ return unless Value::can($student,"isReduced");
+ return Value::cmp_checkUnionReduce($self,$student,$ans,$nth,@_)
+ }
+}
+
+
+##################################################
+
+package Inequalities::Interval;
+our @ISA = ("Inequalities::common", "Value::Interval");
+
+sub type {"Interval"}
+
+sub makeData {
+ my ($a,$b,$open,$close) = (shift)->value;
+ return ($open,$a,$b,$close);
}
sub string {
my $self = shift;
- return $self->SUPER::string(@_) unless $self->getFlag('stringifyAsInequalities');
my ($a,$b,$open,$close) = $self->value;
- my $x = ($self->context->variables->names)[0];
+ my $x = $self->{varName} || ($self->context->variables->names)[0];
$x = $context->{variables}{$x}{string} if defined $context->{variables}{$x}{string};
my $left = ($open eq '(' ? ' < ' : ' <= ');
my $right = ($close eq ')' ? ' < ' : ' <= ');
@@ -385,10 +533,9 @@
sub TeX {
my $self = shift;
- return $self->SUPER::TeX(@_) unless $self->getFlag('stringifyAsInequalities');
my ($a,$b,$open,$close) = $self->value;
my $context = $self->context;
- my $x = ($context->variables->names)[0];
+ my $x = $self->{varName} || ($context->variables->names)[0];
$x = $context->{variables}{$x}{TeX} if defined $context->{variables}{$x}{TeX};
$x =~ s/^([^_]+)_?(\d+)$/$1_{$2}/;
my $left = ($open eq '(' ? ' < ' : ' <= ');
@@ -401,32 +548,46 @@
return $inequality;
}
-sub cmp_class {"an Inequality"}
-
##################################################
-#
-# Override the string and TeX methods
-# so that we can strinfigy as inequalities
-# rather than unions.
-#
+
package Inequalities::Union;
-our @ISA = ("Value::Union");
+our @ISA = ("Inequalities::common", "Value::Union");
-sub new {
- my $self = shift; $self = $self->SUPER::new(@_);
- $self->{isValue} = 1;
- return $self;
+sub type {"Union"}
+
+#
+# Mark all the parts of the union as inequalities
+#
+sub updateParts {
+ my $self = shift;
+ foreach my $I (@{$self->{data}}) {
+ $I->{varName} = $self->{varName};
+ $I->{reduceSets} = $I->{"is".$I->type} = 1;
+ bless $I, $self->Package("Inequality".$I->type);
+ $I->updateParts;
+ }
}
+#
+# Update the intervals and sets when a new union is made
+#
sub make {
- my $self = shift; $self = $self->SUPER::make(@_);
- $self->{isValue} = 1;
+ my $self = (shift)->SUPER::make(@_);
+ $self->updateParts;
return $self;
}
+#
+# Demote all the items in the union
+#
+sub makeData {
+ my $self = shift; my @U = ();
+ foreach my $I (@{$self->{data}}) {push(@U,$I->demote)}
+ return @U;
+}
+
sub string {
my $self = shift;
- return $self->SUPER::string(@_) unless $self->getFlag('stringifyAsInequality');
my $equation = shift; shift; shift; my $prec = shift;
my $op = ($equation->{context} || $self->context)->{operators}{'or'};
my @intervals = ();
@@ -435,49 +596,31 @@
push(@intervals,$x->string($equation))
}
my $string = join($op->{string} || ' or ',@intervals);
- $string = '('.$string.')' if $prec > ($op->{precedence} || 1.5);
+ $string = '('.$string.')' if defined($prec) && $prec > ($op->{precedence} || 1.5);
return $string;
}
sub TeX {
my $self = shift;
- return $self->SUPER::TeX(@_) unless $self->getFlag('stringifyAsInequality');
my $equation = shift; shift; shift; my $prec = shift;
my $op = ($equation->{context} || $self->context)->{operators}{'or'};
my @intervals = ();
foreach my $x (@{$self->data}) {push(@intervals,$x->TeX($equation))}
- my $TeX = join($op->{TeX} || $op->{string} || ' or ',@intervals);
- $TeX = '\left('.$TeX.'\right)' if $prec > ($op->{precedence} || 1.5);
+ my $TeX = join($op->{TeX} || $op->{string} || '\hbox{ or }',@intervals);
+ $TeX = '\left('.$TeX.'\right)' if defined($prec) && $prec > ($op->{precedence} || 1.5);
return $TeX;
}
-sub cmp_class {"an Inequality"}
-
##################################################
-#
-# Override the string and TeX methods
-# so that we can strinfigy as inequalities
-# rather than sets.
-#
+
package Inequalities::Set;
-our @ISA = ("Value::Set");
+our @ISA = ("Inequalities::common", "Value::Set");
-sub new {
- my $self = shift; $self = $self->SUPER::new(@_);
- $self->{isValue} = 1;
- return $self;
-}
-
-sub make {
- my $self = shift; $self = $self->SUPER::make(@_);
- $self->{isValue} = 1;
- return $self;
-}
+sub type {"Set"}
sub string {
my $self = shift; my $equation = shift;
- return $self->SUPER::string($equation,@_) unless $self->getFlag('stringifyAsInequality');
- my $x = ($self->context->variables->names)[0];
+ my $x = $self->{varName} || ($self->context->variables->names)[0];
$x = $context->{variables}{$x}{string} if defined $context->{variables}{$x}{string};
my @coords = ();
foreach my $a (@{$self->data}) {
@@ -494,8 +637,7 @@
sub TeX {
my $self = shift; my $equation = shift;
- return $self->SUPER::TeX($equation,@_) unless $self->getFlag('stringifyAsInequality');
- my $x = ($self->context->variables->names)[0];
+ my $x = $self->{varName} || ($self->context->variables->names)[0];
$x = $context->{variables}{$x}{TeX} if defined $context->{variables}{$x}{TeX};
$x =~ s/^([^_]+)_?(\d+)$/$1_{$2}/;
my @coords = ();
@@ -508,10 +650,82 @@
}
}
return '\hbox{'.$self->getFlag('noneWord').'}' unless scalar(@coords);
- return join(" or ",@coords);
+ return join('\hbox{ or }',@coords);
}
-sub cmp_class {"an Equality"}
+##################################################
+#
+# A class for making inequalities by hand
+#
+package Inequalities::Inequality;
+our @ISA = ('Value');
+
+sub new {
+ my $self = shift; my $class = ref($self) || $self;
+ my $context = (Value::isContext($_[0]) ? shift : $self->context);
+ my $S = shift; my $x = shift;
+ $S = Value::makeValue($S,context=>$context);
+ if (Value::classMatch($S,"Inequality")) {
+ if (defined($x)) {$S->{varName} = $x; $S->updateParts}
+ return $S;
+ }
+ $x = ($self->context->variables->names)[0] unless $x;
+ $S = bless $S->inContext($context), $self->Package("Inequality".$S->type);
+ $S->{varName} = $x; $S->{reduceSets} = $S->{"is".$S->Type} = 1;
+ $S->updateParts;
+ return $S;
+}
+
+##################################################
+#
+# Allow Interval() to coerce types to Value::Interval
+#
+package Inequalities::MakeInterval;
+our @ISA = ("Value::Interval");
+
+sub new {
+ my $self = shift;
+ $self = $self->SUPER::new(@_);
+ $self = $self->demote if $self->classMatch("Inequality");
+ return $self;
+}
+
+##################################################
+#
+# Mark this as a list of inequalities (if it is)
+#
+package Inequalities::List;
+our @ISA = ("Value::List");
+
+sub new {
+ my $self = (shift)->SUPER::new(@_);
+ return $self unless $self->{type} =~ m/^(unknown|Interval|Set|Union)$/;
+ foreach my $x (@{$self->{data}}) {return $self unless Value::classMatch($x,'Inequality')}
+ $self->{type} = 'Inequality';
+ return $self;
+}
+
+package Inequalities::List::List;
+our @ISA = ("Parser::List::List");
+
+sub _check {
+ my $self = shift; $self->SUPER::_check(@_);
+ if ($self->canBeInUnion) {
+ #
+ # Convert lists that look like intervals into intervals
+ # and then check if they are OK.
+ #
+ bless $self, $self->context->{lists}{Interval}{class};
+ $self->{type} = $Value::Type{interval};
+ $self->{parens} = $self->context->{parens}{interval};
+ $self->_check;
+ } else {
+ my $entryType = $self->typeRef->{entryType};
+ return unless $entryType->{name} =~ m/^(unknown|Interval|Set|Union)$/;
+ foreach my $x (@{$self->{coords}}) {return unless $x->{isInequality}};
+ $entryType->{name} = "Inequality";
+ }
+}
##################################################
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