* multivariate polynomials and rational functions.
* These functions include polynomial quotient and remainder, GCD and LCM
* computation, square-free factorization and rational function normalization.
+ */
- *
+/*
* GiNaC Copyright (C) 1999 Johannes Gutenberg University Mainz, Germany
*
* This program is free software; you can redistribute it and/or modify
*/
#include <stdexcept>
+#include <algorithm>
+#include <map>
-#include "ginac.h"
+#include "normal.h"
+#include "basic.h"
+#include "ex.h"
+#include "add.h"
+#include "constant.h"
+#include "expairseq.h"
+#include "fail.h"
+#include "indexed.h"
+#include "inifcns.h"
+#include "lst.h"
+#include "mul.h"
+#include "ncmul.h"
+#include "numeric.h"
+#include "power.h"
+#include "relational.h"
+#include "series.h"
+#include "symbol.h"
+
+#ifndef NO_GINAC_NAMESPACE
+namespace GiNaC {
+#endif // ndef NO_GINAC_NAMESPACE
// If comparing expressions (ex::compare()) is fast, you can set this to 1.
// Some routines like quo(), rem() and gcd() will then return a quick answer
* Statistical information about symbols in polynomials
*/
-#include <algorithm>
-
/** This structure holds information about the highest and lowest degrees
* in which a symbol appears in two multivariate polynomials "a" and "b".
* A vector of these structures with information about all symbols in
numeric ex::integer_content(void) const
{
- ASSERT(bp!=0);
+ GINAC_ASSERT(bp!=0);
return bp->integer_content();
}
epvector::const_iterator itend = seq.end();
numeric c = numZERO();
while (it != itend) {
- ASSERT(!is_ex_exactly_of_type(it->rest,numeric));
- ASSERT(is_ex_exactly_of_type(it->coeff,numeric));
+ GINAC_ASSERT(!is_ex_exactly_of_type(it->rest,numeric));
+ GINAC_ASSERT(is_ex_exactly_of_type(it->coeff,numeric));
c = gcd(ex_to_numeric(it->coeff), c);
it++;
}
- ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
+ GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
c = gcd(ex_to_numeric(overall_coeff),c);
return c;
}
numeric mul::integer_content(void) const
{
-#ifdef DOASSERT
+#ifdef DO_GINAC_ASSERT
epvector::const_iterator it = seq.begin();
epvector::const_iterator itend = seq.end();
while (it != itend) {
- ASSERT(!is_ex_exactly_of_type(recombine_pair_to_ex(*it),numeric));
+ GINAC_ASSERT(!is_ex_exactly_of_type(recombine_pair_to_ex(*it),numeric));
++it;
}
-#endif // def DOASSERT
- ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
+#endif // def DO_GINAC_ASSERT
+ GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
return abs(ex_to_numeric(overall_coeff));
}
* Remembering
*/
-#include <map>
-
typedef pair<ex, ex> ex2;
typedef pair<ex, bool> exbool;
numeric ex::max_coefficient(void) const
{
- ASSERT(bp!=0);
+ GINAC_ASSERT(bp!=0);
return bp->max_coefficient();
}
{
epvector::const_iterator it = seq.begin();
epvector::const_iterator itend = seq.end();
- ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
+ GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
numeric cur_max = abs(ex_to_numeric(overall_coeff));
while (it != itend) {
numeric a;
- ASSERT(!is_ex_exactly_of_type(it->rest,numeric));
+ GINAC_ASSERT(!is_ex_exactly_of_type(it->rest,numeric));
a = abs(ex_to_numeric(it->coeff));
if (a > cur_max)
cur_max = a;
numeric mul::max_coefficient(void) const
{
-#ifdef DOASSERT
+#ifdef DO_GINAC_ASSERT
epvector::const_iterator it = seq.begin();
epvector::const_iterator itend = seq.end();
while (it != itend) {
- ASSERT(!is_ex_exactly_of_type(recombine_pair_to_ex(*it),numeric));
+ GINAC_ASSERT(!is_ex_exactly_of_type(recombine_pair_to_ex(*it),numeric));
it++;
}
-#endif // def DOASSERT
- ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
+#endif // def DO_GINAC_ASSERT
+ GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
return abs(ex_to_numeric(overall_coeff));
}
ex ex::smod(const numeric &xi) const
{
- ASSERT(bp!=0);
+ GINAC_ASSERT(bp!=0);
return bp->smod(xi);
}
ex numeric::smod(const numeric &xi) const
{
+#ifndef NO_GINAC_NAMESPACE
+ return GiNaC::smod(*this, xi);
+#else // ndef NO_GINAC_NAMESPACE
return ::smod(*this, xi);
+#endif // ndef NO_GINAC_NAMESPACE
}
ex add::smod(const numeric &xi) const
epvector::const_iterator it = seq.begin();
epvector::const_iterator itend = seq.end();
while (it != itend) {
- ASSERT(!is_ex_exactly_of_type(it->rest,numeric));
+ GINAC_ASSERT(!is_ex_exactly_of_type(it->rest,numeric));
+#ifndef NO_GINAC_NAMESPACE
+ numeric coeff = GiNaC::smod(ex_to_numeric(it->coeff), xi);
+#else // ndef NO_GINAC_NAMESPACE
numeric coeff = ::smod(ex_to_numeric(it->coeff), xi);
+#endif // ndef NO_GINAC_NAMESPACE
if (!coeff.is_zero())
newseq.push_back(expair(it->rest, coeff));
it++;
}
- ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
+ GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
+#ifndef NO_GINAC_NAMESPACE
+ numeric coeff = GiNaC::smod(ex_to_numeric(overall_coeff), xi);
+#else // ndef NO_GINAC_NAMESPACE
numeric coeff = ::smod(ex_to_numeric(overall_coeff), xi);
+#endif // ndef NO_GINAC_NAMESPACE
return (new add(newseq,coeff))->setflag(status_flags::dynallocated);
}
ex mul::smod(const numeric &xi) const
{
-#ifdef DOASSERT
+#ifdef DO_GINAC_ASSERT
epvector::const_iterator it = seq.begin();
epvector::const_iterator itend = seq.end();
while (it != itend) {
- ASSERT(!is_ex_exactly_of_type(recombine_pair_to_ex(*it),numeric));
+ GINAC_ASSERT(!is_ex_exactly_of_type(recombine_pair_to_ex(*it),numeric));
it++;
}
-#endif // def DOASSERT
+#endif // def DO_GINAC_ASSERT
mul * mulcopyp=new mul(*this);
- ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
- mulcopyp->overall_coeff=::smod(ex_to_numeric(overall_coeff),xi);
+ GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
+#ifndef NO_GINAC_NAMESPACE
+ mulcopyp->overall_coeff = GiNaC::smod(ex_to_numeric(overall_coeff),xi);
+#else // ndef NO_GINAC_NAMESPACE
+ mulcopyp->overall_coeff = ::smod(ex_to_numeric(overall_coeff),xi);
+#endif // ndef NO_GINAC_NAMESPACE
mulcopyp->clearflag(status_flags::evaluated);
mulcopyp->clearflag(status_flags::hash_calculated);
return mulcopyp->setflag(status_flags::dynallocated);
}
-/** Exception thrown by heur_gcd() to signal failure */
+/** Exception thrown by heur_gcd() to signal failure. */
class gcdheu_failed {};
/** Compute GCD of multivariate polynomials using the heuristic GCD algorithm.
ex gcd(const ex &a, const ex &b, ex *ca, ex *cb, bool check_args)
{
// Some trivial cases
- if (a.is_zero()) {
+ ex aex = a.expand(), bex = b.expand();
+ if (aex.is_zero()) {
if (ca)
*ca = exZERO();
if (cb)
*cb = exONE();
return b;
}
- if (b.is_zero()) {
+ if (bex.is_zero()) {
if (ca)
*ca = exONE();
if (cb)
*cb = exZERO();
return a;
}
- if (a.is_equal(exONE()) || b.is_equal(exONE())) {
+ if (aex.is_equal(exONE()) || bex.is_equal(exONE())) {
if (ca)
*ca = a;
if (cb)
return a;
}
#endif
- if (is_ex_exactly_of_type(a, numeric) && is_ex_exactly_of_type(b, numeric)) {
- numeric g = gcd(ex_to_numeric(a), ex_to_numeric(b));
+ if (is_ex_exactly_of_type(aex, numeric) && is_ex_exactly_of_type(bex, numeric)) {
+ numeric g = gcd(ex_to_numeric(aex), ex_to_numeric(bex));
if (ca)
- *ca = ex_to_numeric(a) / g;
+ *ca = ex_to_numeric(aex) / g;
if (cb)
- *cb = ex_to_numeric(b) / g;
+ *cb = ex_to_numeric(bex) / g;
return g;
}
if (check_args && !a.info(info_flags::rational_polynomial) || !b.info(info_flags::rational_polynomial)) {
- cerr << "a=" << a << endl;
- cerr << "b=" << b << endl;
throw(std::invalid_argument("gcd: arguments must be polynomials over the rationals"));
}
if (min_ldeg > 0) {
ex common = power(*x, min_ldeg);
//clog << "trivial common factor " << common << endl;
- return gcd((a / common).expand(), (b / common).expand(), ca, cb, false) * common;
+ return gcd((aex / common).expand(), (bex / common).expand(), ca, cb, false) * common;
}
// Try to eliminate variables
if (var->deg_a == 0) {
//clog << "eliminating variable " << *x << " from b" << endl;
- ex c = b.content(*x);
- ex g = gcd(a, c, ca, cb, false);
+ ex c = bex.content(*x);
+ ex g = gcd(aex, c, ca, cb, false);
if (cb)
- *cb *= b.unit(*x) * b.primpart(*x, c);
+ *cb *= bex.unit(*x) * bex.primpart(*x, c);
return g;
} else if (var->deg_b == 0) {
//clog << "eliminating variable " << *x << " from a" << endl;
- ex c = a.content(*x);
- ex g = gcd(c, b, ca, cb, false);
+ ex c = aex.content(*x);
+ ex g = gcd(c, bex, ca, cb, false);
if (ca)
- *ca *= a.unit(*x) * a.primpart(*x, c);
+ *ca *= aex.unit(*x) * aex.primpart(*x, c);
return g;
}
// Try heuristic algorithm first, fall back to PRS if that failed
ex g;
try {
- g = heur_gcd(a.expand(), b.expand(), ca, cb, var);
+ g = heur_gcd(aex, bex, ca, cb, var);
} catch (gcdheu_failed) {
g = *new ex(fail());
}
if (is_ex_exactly_of_type(g, fail)) {
//clog << "heuristics failed\n";
- g = sr_gcd(a, b, x);
+ g = sr_gcd(aex, bex, x);
if (ca)
- divide(a, g, *ca, false);
+ divide(aex, g, *ca, false);
if (cb)
- divide(b, g, *cb, false);
+ divide(bex, g, *cb, false);
}
return g;
}
else
return e;
}
+
+#ifndef NO_GINAC_NAMESPACE
+} // namespace GiNaC
+#endif // ndef NO_GINAC_NAMESPACE
git://www.ginac.de / ginac.git / blobdiff