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[WWcvs] pg: Inequalities that are evaluated and turned into intervals now properly retain the order of operands (x > 10 remains x > 10
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From: dpvc v. a. <we...@ma...> - 2008-12-30 08:27:09
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Log Message:
-----------
Inequalities that are evaluated and turned into intervals now properly
retain the order of operands (x > 10 remains x > 10 rather than
becoming 10 < x).
Unions of the form "x < a or x > a" will be displayed as "x != a" instead,
and "a < x < b or b < x < c" will be shown as "a < x < c and x != b"
instead. This behavior is controlled by the showNotEquals context
flag. Setting it to zero prevents conversion of unions to their
not-equal forms.
Modified Files:
--------------
pg/macros:
contextInequalities.pl
Revision Data
-------------
Index: contextInequalities.pl
===================================================================
RCS file: /webwork/cvs/system/pg/macros/contextInequalities.pl,v
retrieving revision 1.18
retrieving revision 1.19
diff -Lmacros/contextInequalities.pl -Lmacros/contextInequalities.pl -u -r1.18 -r1.19
--- macros/contextInequalities.pl
+++ macros/contextInequalities.pl
@@ -114,11 +114,11 @@
'+' => {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->parens->set("(" => {type => "List", formInterval => ']'}); # trap these later
+ $context->parens->set("[" => {type => "List", formInterval => ')'}); # trap these later
$context->strings->remove("NONE");
$context->constants->add(NONE=>Value::Set->new());
- $context->flags->set(noneWord => 'NONE');
+ $context->flags->set(noneWord => 'NONE', showNotEquals => 1);
$context->{parser}{Variable} = "Inequalities::Variable";
$context->{value}{'Interval()'} = "Inequalities::MakeInterval";
$context->{value}{Inequality} = "Inequalities::Inequality";
@@ -218,8 +218,8 @@
sub evalGreaterThan {
my ($self,$a,$b) = @_; my $context = $self->context;
my $I = Value::Infinity->new;
- return $self->Package("Interval")->new($context,'(',$b,$I,')') if $self->{varPos} eq 'lop';
- return $self->Package("Interval")->new($context,'(',-$I,$a,')');
+ return $self->Package("Interval")->new($context,'(',$b,$I,')')->with(reversed=>1) if $self->{varPos} eq 'lop';
+ return $self->Package("Interval")->new($context,'(',-$I,$a,')')->with(reversed=>1);
}
sub evalLessThanOrEqualTo {
@@ -232,8 +232,8 @@
sub evalGreaterThanOrEqualTo {
my ($self,$a,$b) = @_; my $context = $self->context;
my $I = Value::Infinity->new;
- return $self->Package("Interval")->new($context,'[',$b,$I,')') if $self->{varPos} eq 'lop';
- return $self->Package("Interval")->new($context,'(',-$I,$a,']');
+ return $self->Package("Interval")->new($context,'[',$b,$I,')')->with(reversed=>1) if $self->{varPos} eq 'lop';
+ return $self->Package("Interval")->new($context,'(',-$I,$a,']')->with(reversed=>1);
}
sub evalEqualTo {
@@ -249,7 +249,7 @@
return $self->Package("Union")->new($context,
$self->Package("Interval")->new($context,'(',-$I,$x,')'),
$self->Package("Interval")->new($context,'(',$x,$I,')')
- );
+ )->with(notEqual=>1);
}
#
@@ -534,19 +534,28 @@
sub type {"Interval"}
+sub updateParts {
+ my $self = shift;
+ $self->{leftInfinite} = 1 if $self->{data}[0]->{isInfinite};
+ $self->{rightInfinite} = 1 if $self->{data}[1]->{isInfinite};
+}
+
sub string {
my $self = shift;
my ($a,$b,$open,$close) = $self->value;
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 ')' ? ' < ' : ' <= ');
- my $inequality = "";
- $inequality .= $a->string.$left unless $self->{leftInfinite};
- $inequality .= $x;
- $inequality .= $right.$b->string unless $self->{rightInfinite};
- $inequality = "-infinity < $x < infinity" if $inequality eq $x;
- return $inequality;
+ if ($self->{leftInfinite}) {
+ return "-infinity < $x < infinity" if $self->{rightInfinite};
+ return $b->string . ($close eq ')' ? ' > ' : ' >= ') . $x if $self->{reversed};
+ return $x . ($close eq ')' ? ' < ' : ' <= ') . $b->string;
+ } elsif ($self->{rightInfinite}) {
+ return $x . ($open eq '(' ? ' > ' : ' >= ') . $a->string if $self->{reversed};
+ return $a->string . ($open eq '(' ? ' < ' : ' <= ') . $x;
+ } else {
+ return $a->string . ($open eq '(' ? ' < ' : ' <= ') .
+ $x . ($close eq ')' ? ' < ' : ' <= ') . $b->string;
+ }
}
sub TeX {
@@ -556,14 +565,17 @@
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 '(' ? ' < ' : ' \le ');
- my $right = ($close eq ')' ? ' < ' : ' \le ');
- my $inequality = "";
- $inequality .= $a->string.$left unless $self->{leftInfinite};
- $inequality .= $x;
- $inequality .= $right.$b->string unless $self->{rightInfinite};
- $inequality = "-\\infty < $x < \\infty " if $inequality eq $x;
- return $inequality;
+ if ($self->{leftInfinite}) {
+ return "-\\infty < $x < \\infty" if $self->{rightInfinite};
+ return $b->TeX . ($close eq ')' ? ' > ' : ' \ge ') . $x if $self->{reversed};
+ return $x . ($close eq ')' ? ' < ' : ' \le ') . $b->TeX;
+ } elsif ($self->{rightInfinite}) {
+ return $x . ($open eq '(' ? ' > ' : ' \ge ') . $a->TeX if $self->{reversed};
+ return $a->TeX . ($open eq '(' ? ' < ' : ' \le ') . $x;
+ } else {
+ return $a->TeX . ($open eq '(' ? ' < ' : ' \le ') .
+ $x . ($close eq ')' ? ' < ' : ' \le ') . $b->TeX;
+ }
}
##################################################
@@ -607,28 +619,88 @@
sub string {
my $self = shift;
my $equation = shift; shift; shift; my $prec = shift;
- my $op = ($equation->{context} || $self->context)->{operators}{'or'};
- my @intervals = ();
+ my $context = ($equation->{context} || $self->context);
+ my $X = $self->{varName} || ($context->variables->names)[0];
+ $X = $context->{variables}{$X}{string} if defined $context->{variables}{$X}{string};
+ my $op = $context->{operators}{'or'};
+ my $showNE = $self->getFlag("showNotEquals",1);
+ my @intervals = (); my @points = (); my $interval;
foreach my $x (@{$self->data}) {
$x->{format} = $self->{format} if defined $self->{format};
- push(@intervals,$x->string($equation))
+ if ($x->type eq 'Interval' && $showNE) {
+ if (defined($interval)) {
+ if ($interval->{data}[1] == $x->{data}[0]) {
+ push(@points,$X . ' != ' . $x->{data}[0]->string);
+ $interval = $interval->with(isCopy=>1, data=>[$interval->value]) unless $interval->{isCopy};
+ $interval->{data}[1] = $x->{data}[1];
+ $interval->{rightInfinite} = 1 if $x->{rightInfinite};
+ next;
+ }
+ push(@intervals,$self->stringAnd($interval,$equation,@points));
+ }
+ $interval = $x; @points = (); next;
+ }
+ if (defined($interval)) {
+ push(@intervals,$self->stringAnd($interval,$equation,@points));
+ $interval = undef; @points = ();
+ }
+ push(@intervals,$x->string($equation));
}
+ push(@intervals,$self->stringAnd($interval,$equation,@points)) if defined($interval);
my $string = join($op->{string} || ' or ',@intervals);
$string = '('.$string.')' if defined($prec) && $prec > ($op->{precedence} || 1.5);
return $string;
}
+sub stringAnd {
+ my $self = shift; my $interval = shift; my $equation = shift;
+ unshift(@_,$interval->string($equation)) unless $interval->{leftInfinite} && $interval->{rightInfinite};
+ return join(" and ", @_);
+}
+
sub TeX {
my $self = shift;
my $equation = shift; shift; shift; my $prec = shift;
+ my $context = $equation->{context} || $self->context;
+ 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 $op = ($equation->{context} || $self->context)->{operators}{'or'};
- my @intervals = ();
- foreach my $x (@{$self->data}) {push(@intervals,$x->TeX($equation))}
+ my $showNE = $self->getFlag("showNotEquals",1);
+ my @intervals = (); my $interval; my @points = ();
+ foreach my $x (@{$self->data}) {
+ $x->{format} = $self->{format} if defined $self->{format};
+ if ($x->type eq 'Interval' && $showNE) {
+ if (defined($interval)) {
+ if ($interval->{data}[1] == $x->{data}[0]) {
+ push(@points,$X . ' \ne ' . $x->{data}[0]->TeX);
+ $interval = $interval->with(isCopy=>1, data=>[$interval->value]) unless $interval->{isCopy};
+ $interval->{data}[1] = $x->{data}[1];
+ $interval->{rightInfinite} = 1 if $x->{rightInfinite};
+ next;
+ }
+ push(@intervals,$self->TeXAnd($interval,$equation,@points));
+ }
+ $interval = $x; @points = (); next;
+ }
+ if (defined($interval)) {
+ push(@intervals,$self->TeXAnd($interval,$equation,@points));
+ $interval = undef; @points = ();
+ }
+ push(@intervals,$x->TeX($equation));
+ }
+ push(@intervals,$self->TeXAnd($interval,$equation,@points)) if defined($interval);
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 TeXAnd {
+ my $self = shift; my $interval = shift; my $equation = shift;
+ unshift(@_,$interval->TeX($equation)) unless $interval->{leftInfinite} && $interval->{rightInfinite};
+ return join('\hbox{ and }', @_);
+}
+
##################################################
package Inequalities::Set;
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