*/
/*
- * GiNaC Copyright (C) 1999 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2000 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
#include "numeric.h"
#include "power.h"
#include "relational.h"
-#include "series.h"
+#include "pseries.h"
#include "symbol.h"
#include "utils.h"
-#ifndef NO_GINAC_NAMESPACE
+#ifndef NO_NAMESPACE_GINAC
namespace GiNaC {
-#endif // ndef NO_GINAC_NAMESPACE
+#endif // ndef NO_NAMESPACE_GINAC
// 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
x = static_cast<symbol *>(e.bp);
return true;
} else if (is_ex_exactly_of_type(e, add) || is_ex_exactly_of_type(e, mul)) {
- for (int i=0; i<e.nops(); i++)
+ for (unsigned i=0; i<e.nops(); i++)
if (get_first_symbol(e.op(i), x))
return true;
} else if (is_ex_exactly_of_type(e, power)) {
if (is_ex_exactly_of_type(e, symbol)) {
add_symbol(static_cast<symbol *>(e.bp), v);
} else if (is_ex_exactly_of_type(e, add) || is_ex_exactly_of_type(e, mul)) {
- for (int i=0; i<e.nops(); i++)
+ for (unsigned i=0; i<e.nops(); i++)
collect_symbols(e.op(i), v);
} else if (is_ex_exactly_of_type(e, power)) {
collect_symbols(e.op(0), v);
{
if (e.info(info_flags::rational))
return lcm(ex_to_numeric(e).denom(), l);
- else if (is_ex_exactly_of_type(e, add) || is_ex_exactly_of_type(e, mul)) {
+ else if (is_ex_exactly_of_type(e, add)) {
numeric c = _num1();
- for (int i=0; i<e.nops(); i++) {
+ for (unsigned i=0; i<e.nops(); i++)
c = lcmcoeff(e.op(i), c);
- }
+ return lcm(c, l);
+ } else if (is_ex_exactly_of_type(e, mul)) {
+ numeric c = _num1();
+ for (unsigned i=0; i<e.nops(); i++)
+ c *= lcmcoeff(e.op(i), _num1());
return lcm(c, l);
} else if (is_ex_exactly_of_type(e, power))
- return lcmcoeff(e.op(0), l);
+ return pow(lcmcoeff(e.op(0), l), ex_to_numeric(e.op(1)));
return l;
}
/** Compute LCM of denominators of coefficients of a polynomial.
* Given a polynomial with rational coefficients, this function computes
* the LCM of the denominators of all coefficients. This can be used
- * To bring a polynomial from Q[X] to Z[X].
+ * to bring a polynomial from Q[X] to Z[X].
*
- * @param e multivariate polynomial
+ * @param e multivariate polynomial (need not be expanded)
* @return LCM of denominators of coefficients */
static numeric lcm_of_coefficients_denominators(const ex &e)
{
- return lcmcoeff(e.expand(), _num1());
+ return lcmcoeff(e, _num1());
+}
+
+/** Bring polynomial from Q[X] to Z[X] by multiplying in the previously
+ * determined LCM of the coefficient's denominators.
+ *
+ * @param e multivariate polynomial (need not be expanded)
+ * @param lcm LCM to multiply in */
+
+static ex multiply_lcm(const ex &e, const numeric &lcm)
+{
+ if (is_ex_exactly_of_type(e, mul)) {
+ ex c = _ex1();
+ numeric lcm_accum = _num1();
+ for (unsigned i=0; i<e.nops(); i++) {
+ numeric op_lcm = lcmcoeff(e.op(i), _num1());
+ c *= multiply_lcm(e.op(i), op_lcm);
+ lcm_accum *= op_lcm;
+ }
+ c *= lcm / lcm_accum;
+ return c;
+ } else if (is_ex_exactly_of_type(e, add)) {
+ ex c = _ex0();
+ for (unsigned i=0; i<e.nops(); i++)
+ c += multiply_lcm(e.op(i), lcm);
+ return c;
+ } else if (is_ex_exactly_of_type(e, power)) {
+ return pow(multiply_lcm(e.op(0), lcm.power(ex_to_numeric(e.op(1)).inverse())), e.op(1));
+ } else
+ return e * lcm;
}
ex numeric::smod(const numeric &xi) const
{
-#ifndef NO_GINAC_NAMESPACE
+#ifndef NO_NAMESPACE_GINAC
return GiNaC::smod(*this, xi);
-#else // ndef NO_GINAC_NAMESPACE
+#else // ndef NO_NAMESPACE_GINAC
return ::smod(*this, xi);
-#endif // ndef NO_GINAC_NAMESPACE
+#endif // ndef NO_NAMESPACE_GINAC
}
ex add::smod(const numeric &xi) const
epvector::const_iterator itend = seq.end();
while (it != itend) {
GINAC_ASSERT(!is_ex_exactly_of_type(it->rest,numeric));
-#ifndef NO_GINAC_NAMESPACE
+#ifndef NO_NAMESPACE_GINAC
numeric coeff = GiNaC::smod(ex_to_numeric(it->coeff), xi);
-#else // ndef NO_GINAC_NAMESPACE
+#else // ndef NO_NAMESPACE_GINAC
numeric coeff = ::smod(ex_to_numeric(it->coeff), xi);
-#endif // ndef NO_GINAC_NAMESPACE
+#endif // ndef NO_NAMESPACE_GINAC
if (!coeff.is_zero())
newseq.push_back(expair(it->rest, coeff));
it++;
}
GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
-#ifndef NO_GINAC_NAMESPACE
+#ifndef NO_NAMESPACE_GINAC
numeric coeff = GiNaC::smod(ex_to_numeric(overall_coeff), xi);
-#else // ndef NO_GINAC_NAMESPACE
+#else // ndef NO_NAMESPACE_GINAC
numeric coeff = ::smod(ex_to_numeric(overall_coeff), xi);
-#endif // ndef NO_GINAC_NAMESPACE
+#endif // ndef NO_NAMESPACE_GINAC
return (new add(newseq,coeff))->setflag(status_flags::dynallocated);
}
#endif // def DO_GINAC_ASSERT
mul * mulcopyp=new mul(*this);
GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
-#ifndef NO_GINAC_NAMESPACE
+#ifndef NO_NAMESPACE_GINAC
mulcopyp->overall_coeff = GiNaC::smod(ex_to_numeric(overall_coeff),xi);
-#else // ndef NO_GINAC_NAMESPACE
+#else // ndef NO_NAMESPACE_GINAC
mulcopyp->overall_coeff = ::smod(ex_to_numeric(overall_coeff),xi);
-#endif // ndef NO_GINAC_NAMESPACE
+#endif // ndef NO_NAMESPACE_GINAC
mulcopyp->clearflag(status_flags::evaluated);
mulcopyp->clearflag(status_flags::hash_calculated);
return mulcopyp->setflag(status_flags::dynallocated);
ex gcd(const ex &a, const ex &b, ex *ca, ex *cb, bool check_args)
{
+ // Partially factored cases (to avoid expanding large expressions)
+ if (is_ex_exactly_of_type(a, mul)) {
+ if (is_ex_exactly_of_type(b, mul) && b.nops() > a.nops())
+ goto factored_b;
+factored_a:
+ ex g = _ex1();
+ ex acc_ca = _ex1();
+ ex part_b = b;
+ for (unsigned i=0; i<a.nops(); i++) {
+ ex part_ca, part_cb;
+ g *= gcd(a.op(i), part_b, &part_ca, &part_cb, check_args);
+ acc_ca *= part_ca;
+ part_b = part_cb;
+ }
+ if (ca)
+ *ca = acc_ca;
+ if (cb)
+ *cb = part_b;
+ return g;
+ } else if (is_ex_exactly_of_type(b, mul)) {
+ if (is_ex_exactly_of_type(a, mul) && a.nops() > b.nops())
+ goto factored_a;
+factored_b:
+ ex g = _ex1();
+ ex acc_cb = _ex1();
+ ex part_a = a;
+ for (unsigned i=0; i<b.nops(); i++) {
+ ex part_ca, part_cb;
+ g *= gcd(part_a, b.op(i), &part_ca, &part_cb, check_args);
+ acc_cb *= part_cb;
+ part_a = part_ca;
+ }
+ if (ca)
+ *ca = part_a;
+ if (cb)
+ *cb = acc_cb;
+ return g;
+ }
+
// Some trivial cases
ex aex = a.expand(), bex = b.expand();
if (aex.is_zero()) {
g = *new ex(fail());
}
if (is_ex_exactly_of_type(g, fail)) {
-// clog << "heuristics failed" << endl;
+//clog << "heuristics failed" << endl;
g = sr_gcd(aex, bex, x);
if (ca)
divide(aex, g, *ca, false);
static ex replace_with_symbol(const ex &e, lst &sym_lst, lst &repl_lst)
{
// Expression already in repl_lst? Then return the assigned symbol
- for (int i=0; i<repl_lst.nops(); i++)
+ for (unsigned i=0; i<repl_lst.nops(); i++)
if (repl_lst.op(i).is_equal(e))
return sym_lst.op(i);
}
-/*
- * Helper function for fraction cancellation (returns cancelled fraction n/d)
- */
+/** Fraction cancellation.
+ * @param n numerator
+ * @param d denominator
+ * @return cancelled fraction n/d */
static ex frac_cancel(const ex &n, const ex &d)
{
ex num = n;
ex den = d;
- ex pre_factor = _ex1();
+ numeric pre_factor = _num1();
// Handle special cases where numerator or denominator is 0
if (num.is_zero())
// More special cases
if (is_ex_exactly_of_type(den, numeric))
return num / den;
- if (num.is_zero())
- return _ex0();
// Bring numerator and denominator to Z[X] by multiplying with
// LCM of all coefficients' denominators
- ex num_lcm = lcm_of_coefficients_denominators(num);
- ex den_lcm = lcm_of_coefficients_denominators(den);
- num *= num_lcm;
- den *= den_lcm;
+ numeric num_lcm = lcm_of_coefficients_denominators(num);
+ numeric den_lcm = lcm_of_coefficients_denominators(den);
+ num = multiply_lcm(num, num_lcm);
+ den = multiply_lcm(den, den_lcm);
pre_factor = den_lcm / num_lcm;
// Cancel GCD from numerator and denominator
}
-/** Implementation of ex::normal() for series. It normalizes each coefficient and
+/** Implementation of ex::normal() for pseries. It normalizes each coefficient and
* replaces the series by a temporary symbol.
* @see ex::normal */
-ex series::normal(lst &sym_lst, lst &repl_lst, int level) const
+ex pseries::normal(lst &sym_lst, lst &repl_lst, int level) const
{
epvector new_seq;
new_seq.reserve(seq.size());
it++;
}
- ex n = series(var, point, new_seq);
+ ex n = pseries(var, point, new_seq);
return replace_with_symbol(n, sym_lst, repl_lst);
}
return e;
}
-#ifndef NO_GINAC_NAMESPACE
+#ifndef NO_NAMESPACE_GINAC
} // namespace GiNaC
-#endif // ndef NO_GINAC_NAMESPACE
+#endif // ndef NO_NAMESPACE_GINAC
git://www.ginac.de / ginac.git / blobdiff