* computation, square-free factorization and rational function normalization. */
/*
- * GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
*
* 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
int deg_b = b.degree(*(it->sym));
it->deg_a = deg_a;
it->deg_b = deg_b;
- it->max_deg = max(deg_a, deg_b);
+ it->max_deg = std::max(deg_a,deg_b);
it->ldeg_a = a.ldegree(*(it->sym));
it->ldeg_b = b.ldegree(*(it->sym));
it++;
}
#endif
if (check_args && (!a.info(info_flags::rational_polynomial) ||
- !b.info(info_flags::rational_polynomial)))
+ !b.info(info_flags::rational_polynomial)))
throw(std::invalid_argument("divide: arguments must be polynomials over the rationals"));
// Find first symbol
numeric rgc = gc.inverse();
ex p = a * rgc;
ex q = b * rgc;
- int maxdeg = max(p.degree(x), q.degree(x));
-
+ int maxdeg = std::max(p.degree(x),q.degree(x));
+
// Find evaluation point
- numeric mp = p.max_coefficient(), mq = q.max_coefficient();
+ numeric mp = p.max_coefficient();
+ numeric mq = q.max_coefficient();
numeric xi;
if (mp > mq)
xi = mq * _num2() + _num2();
// Cancel trivial common factor
int ldeg_a = var->ldeg_a;
int ldeg_b = var->ldeg_b;
- int min_ldeg = min(ldeg_a, ldeg_b);
+ int min_ldeg = std::min(ldeg_a,ldeg_b);
if (min_ldeg > 0) {
ex common = power(x, min_ldeg);
//std::clog << "trivial common factor " << common << endl;
// as defined by get_first_symbol() is made positive)
const symbol *x;
if (get_first_symbol(den, x)) {
- GINAC_ASSERT(is_ex_exactly_of_type(den.unit(*x),numeric));
+ GINAC_ASSERT(is_ex_exactly_of_type(den.unit(*x),numeric));
if (ex_to_numeric(den.unit(*x)).is_negative()) {
num *= _ex_1();
den *= _ex_1();
ex add::normal(lst &sym_lst, lst &repl_lst, int level) const
{
if (level == 1)
- return (new lst(*this, _ex1()))->setflag(status_flags::dynallocated);
+ return (new lst(replace_with_symbol(*this, sym_lst, repl_lst), _ex1()))->setflag(status_flags::dynallocated);
else if (level == -max_recursion_level)
throw(std::runtime_error("max recursion level reached"));
- // Normalize and expand children, chop into summands
- exvector o;
- o.reserve(seq.size()+1);
+ // Normalize and expand children, chop into summands and split each
+ // one into numerator and denominator
+ exvector nums, dens;
+ nums.reserve(seq.size()+1);
+ dens.reserve(seq.size()+1);
epvector::const_iterator it = seq.begin(), itend = seq.end();
while (it != itend) {
if (is_ex_exactly_of_type(n.op(0), add)) {
epvector::const_iterator bit = ex_to_add(n.op(0)).seq.begin(), bitend = ex_to_add(n.op(0)).seq.end();
while (bit != bitend) {
- o.push_back((new lst(recombine_pair_to_ex(*bit), n.op(1)))->setflag(status_flags::dynallocated));
+ nums.push_back(recombine_pair_to_ex(*bit));
+ dens.push_back(n.op(1));
bit++;
}
// split it into numerator and denominator
GINAC_ASSERT(ex_to_numeric(ex_to_add(n.op(0)).overall_coeff).is_rational());
numeric overall = ex_to_numeric(ex_to_add(n.op(0)).overall_coeff);
- o.push_back((new lst(overall.numer(), overall.denom() * n.op(1)))->setflag(status_flags::dynallocated));
- } else
- o.push_back(n);
+ nums.push_back(overall.numer());
+ dens.push_back(overall.denom() * n.op(1));
+ } else {
+ nums.push_back(n.op(0));
+ dens.push_back(n.op(1));
+ }
it++;
}
- o.push_back(overall_coeff.bp->normal(sym_lst, repl_lst, level-1));
+ ex n = overall_coeff.bp->normal(sym_lst, repl_lst, level-1);
+ nums.push_back(n.op(0));
+ dens.push_back(n.op(1));
+ GINAC_ASSERT(nums.size() == dens.size());
- // o is now a vector of {numerator, denominator} lists
+ // Now, nums is a vector of all numerators and dens is a vector of
+ // all denominators
- // Determine common denominator
- ex den = _ex1();
- exvector::const_iterator ait = o.begin(), aitend = o.end();
+ // Add fractions sequentially
+ exvector::const_iterator num_it = nums.begin(), num_itend = nums.end();
+ exvector::const_iterator den_it = dens.begin(), den_itend = dens.end();
//std::clog << "add::normal uses the following summands:\n";
- while (ait != aitend) {
-//std::clog << " num = " << ait->op(0) << ", den = " << ait->op(1) << endl;
- den = lcm(ait->op(1), den, false);
- ait++;
+//std::clog << " num = " << *num_it << ", den = " << *den_it << endl;
+ ex num = *num_it++, den = *den_it++;
+ while (num_it != num_itend) {
+//std::clog << " num = " << *num_it << ", den = " << *den_it << endl;
+ ex co_den1, co_den2;
+ ex g = gcd(den, *den_it, &co_den1, &co_den2, false);
+ num = (num * co_den2) + (*num_it * co_den1);
+ den *= co_den2; // this is the lcm(den, *den_it)
+ num_it++; den_it++;
}
//std::clog << " common denominator = " << den << endl;
- // Add fractions
- if (den.is_equal(_ex1())) {
-
- // Common denominator is 1, simply add all fractions
- exvector num_seq;
- for (ait=o.begin(); ait!=aitend; ait++) {
- num_seq.push_back(ait->op(0) / ait->op(1));
- }
- return (new lst((new add(num_seq))->setflag(status_flags::dynallocated), den))->setflag(status_flags::dynallocated);
-
- } else {
-
- // Perform fractional addition
- exvector num_seq;
- for (ait=o.begin(); ait!=aitend; ait++) {
- ex q;
- if (!divide(den, ait->op(1), q, false)) {
- // should not happen
- throw(std::runtime_error("invalid expression in add::normal, division failed"));
- }
- num_seq.push_back((ait->op(0) * q).expand());
- }
- ex num = (new add(num_seq))->setflag(status_flags::dynallocated);
-
- // Cancel common factors from num/den
- return frac_cancel(num, den);
- }
+ // Cancel common factors from num/den
+ return frac_cancel(num, den);
}
ex mul::normal(lst &sym_lst, lst &repl_lst, int level) const
{
if (level == 1)
- return (new lst(*this, _ex1()))->setflag(status_flags::dynallocated);
+ return (new lst(replace_with_symbol(*this, sym_lst, repl_lst), _ex1()))->setflag(status_flags::dynallocated);
else if (level == -max_recursion_level)
throw(std::runtime_error("max recursion level reached"));
ex power::normal(lst &sym_lst, lst &repl_lst, int level) const
{
if (level == 1)
- return (new lst(*this, _ex1()))->setflag(status_flags::dynallocated);
+ return (new lst(replace_with_symbol(*this, sym_lst, repl_lst), _ex1()))->setflag(status_flags::dynallocated);
else if (level == -max_recursion_level)
throw(std::runtime_error("max recursion level reached"));
git://www.ginac.de / ginac.git / blobdiff