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# Copyright (c) 1997-2015
# Ewgenij Gawrilow, Michael Joswig (Technische Universitaet Berlin, Germany)
# http://www.polymake.org
#
# This program 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 2, or (at your option) any
# later version: http://www.gnu.org/licenses/gpl.txt.
#
# 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 the
# GNU General Public License for more details.
#-------------------------------------------------------------------------------
# This file contains methods to parse a polynomial from a string. If the ring
# is very complicated, it might be easier to access the user_function directly,
# which is why it is left available.
property_type Polynomial {
method construct(Ring, String) {
toPolynomial($_[2], $_[1], $_[1]->variables);
}
}
property_type Term {
method construct(Ring, String) {
parseTerm($_[2], $_[1]->variables);
}
}
# @category Data Conversion
# Read a [[Polynomial]] from a String.
# @param String s
# @param ARRAY vars
user_function toPolynomial {
my ($s, $ring, @vars) = @_;
# Remove white spaces.
$s =~ s/\s//g;
my $stilda = $s;
foreach my $var (@vars) {
my $varstring = "$var";
my $replacement = "m".("a" x (length($varstring)-1));
$varstring = quotemeta($varstring);
$stilda =~ s/$varstring/$replacement/g;
}
# Check for correct format of stilda:
$stilda =~ m/^[0123456789\/\*\^\-\+a\(\)m]*$/ or die "Input error: $stilda.";
return parseSumRecursively($s, $stilda, $ring, @vars);
}
sub parseSumRecursively {
my ($s,$stilda,$ring,@vars) = @_;
my ($op) = $stilda =~ m/^([\+\-]?)/x;
$s = substr($s,length($op),length($s));
$stilda = substr($stilda,length($op),length($stilda));
my @term = ();
my @termtilda = ();
my $hasbrackets = 0;
# Match the first summand. While matching unwrap the product structure.
while (($stilda !~ m/^[+-]/) && (length($stilda) > 0)) {
if ($stilda =~ m/^\(/) {
# If we have beginning brackets:
my ($factor) = $stilda =~ m/(\( (?: [^\(\)]* | (?0) )* \)) /x;
my ($hat, $pow) = $' =~ m/^(\^?)(\d*)/;
my $totallength = length($factor)+length($hat)+length($pow);
$hasbrackets = 1;
push @termtilda, $factor.$hat.$pow;
push @term, substr($s,0,$totallength);
$stilda = substr($stilda,$totallength,length($stilda));
$s = substr($s,$totallength,length($s));
} elsif (my ($factor) = $stilda =~ m/^([^\+\-\(\)]*)/x) {
# If we start with a factor in front:
push @termtilda, $factor;
push @term, substr($s,0,length($factor));
$stilda = substr($stilda,length($factor),length($stilda));
$s = substr($s,length($factor),length($s));
}
}
my $result = new Polynomial(1, $ring);
if ($hasbrackets) {
foreach my $factor (@termtilda) {
my $f = shift @term;
if (my ($inner, $pow) = $factor =~ m/^\((.*)\)\^?(\d*)$/) {
if ($pow) {
while ($pow>0) {
$result = $result * parseSumRecursively(substr($f,1,length($inner)),$inner,$ring,@vars);
$pow--;
}
} else {
$result = $result * parseSumRecursively(substr($f,1,length($inner)),$inner,$ring,@vars);
}
} else {
$factor =~ s/^\*?//;
$factor =~ s/\*?$//;
$f =~ s/^\*?//;
$f =~ s/\*?$//;
if (length($f)>0) {
# If there was more than a star.
$result = $result * parseTerm($f,$factor,@vars);
}
}
}
} else {
# We must have a monomial!
$result = new Polynomial(0, $ring) + parseTerm(pop @term, pop @termtilda, @vars);
}
if ($op eq "-") {
$result = -$result;
}
if (length($stilda) > 0) {
$result = parseSumRecursively($s,$stilda, $ring, @vars) + $result;
}
return $result;
}
sub parseTerm {
my ($s, $stilda, @vars) = @_;
# Sanity check:
# print "Parsing Monomial.\nS: ",$s,"\nST: ",$stilda,"\n";
($s !~ m/^\*(.*)/) or die "Incorrect monomial form.";
($s !~ m/(.*)\*$/) or die "Incorrect monomial form.";
if ($stilda !~ m/m/) {
if (index($stilda,"/")>-1) {
my ($a,$b) = $stilda =~ m/^(\d*)\/(\d*)/;
return new Rational($a,$b);
} else {
return $stilda;
}
}
my %varMap = ();
my $i = 0;
foreach my $v (@vars){
my $varstring = $v."";
$varMap{$varstring} = $i;
$i++;
}
my $nvars = @vars;
my $exp = new Vector<Int>($nvars);
my $totalcoef = 1;
while (length($s)>0) {
my ($coef,$star1,$varlength,$hat,$pow,$star2) = $stilda =~ m/^(\d*\/?\d*)(\*?)(ma*)(\^?)(\d*)(\*?)/;
my $varstring = substr($s, length($coef.$star1), length($varlength));
if ($pow) {
$exp->[$varMap{$varstring}] += $pow;
} else {
$exp->[$varMap{$varstring}] ++;
}
my $totallength = length($coef.$star1.$varlength.$hat.$pow.$star2);
$s = substr($s, $totallength, length($s));
$stilda = substr($stilda,$totallength,length($stilda));
if ($coef) {
if (index($coef,"/")>-1) {
my ($a,$b) = $coef =~ m/^(\d*)\/(\d*)/;
$totalcoef *= new Rational($a,$b);
} else {
$totalcoef *= $coef;
}
}
}
my $result = 1;
my $i = 0;
foreach my $var (@vars) {
my $pow = $exp->[$i];
while ($pow>0) {
$result = $result * $var;
$pow--;
}
$i++;
}
# print "Result: ",$result," ",$exp," ",%varMap,"\n";
if ($totalcoef != 1) {
return $totalcoef*$result;
} else {
return $result;
}
}
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