* Implementation of GiNaC's products of expressions. */
/*
- * GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2003 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
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*/
+#include <iostream>
#include <vector>
#include <stdexcept>
+#include <limits>
#include "mul.h"
#include "add.h"
#include "power.h"
+#include "operators.h"
+#include "matrix.h"
+#include "lst.h"
#include "archive.h"
-#include "debugmsg.h"
#include "utils.h"
namespace GiNaC {
-GINAC_IMPLEMENT_REGISTERED_CLASS(mul, expairseq)
+GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(mul, expairseq,
+ print_func<print_context>(&mul::do_print).
+ print_func<print_latex>(&mul::do_print_latex).
+ print_func<print_csrc>(&mul::do_print_csrc).
+ print_func<print_tree>(&inherited::do_print_tree).
+ print_func<print_python_repr>(&mul::do_print_python_repr))
+
//////////
-// default ctor, dctor, copy ctor assignment operator and helpers
+// default constructor
//////////
mul::mul()
{
- debugmsg("mul default ctor",LOGLEVEL_CONSTRUCT);
tinfo_key = TINFO_mul;
}
-DEFAULT_COPY(mul)
-DEFAULT_DESTROY(mul)
-
//////////
-// other ctors
+// other constructors
//////////
// public
mul::mul(const ex & lh, const ex & rh)
{
- debugmsg("mul ctor from ex,ex",LOGLEVEL_CONSTRUCT);
tinfo_key = TINFO_mul;
- overall_coeff = _ex1();
+ overall_coeff = _ex1;
construct_from_2_ex(lh,rh);
GINAC_ASSERT(is_canonical());
}
mul::mul(const exvector & v)
{
- debugmsg("mul ctor from exvector",LOGLEVEL_CONSTRUCT);
tinfo_key = TINFO_mul;
- overall_coeff = _ex1();
+ overall_coeff = _ex1;
construct_from_exvector(v);
GINAC_ASSERT(is_canonical());
}
mul::mul(const epvector & v)
{
- debugmsg("mul ctor from epvector",LOGLEVEL_CONSTRUCT);
tinfo_key = TINFO_mul;
- overall_coeff = _ex1();
+ overall_coeff = _ex1;
construct_from_epvector(v);
GINAC_ASSERT(is_canonical());
}
mul::mul(const epvector & v, const ex & oc)
{
- debugmsg("mul ctor from epvector,ex",LOGLEVEL_CONSTRUCT);
tinfo_key = TINFO_mul;
overall_coeff = oc;
construct_from_epvector(v);
GINAC_ASSERT(is_canonical());
}
-mul::mul(epvector * vp, const ex & oc)
+mul::mul(std::auto_ptr<epvector> vp, const ex & oc)
{
- debugmsg("mul ctor from epvector *,ex",LOGLEVEL_CONSTRUCT);
tinfo_key = TINFO_mul;
GINAC_ASSERT(vp!=0);
overall_coeff = oc;
construct_from_epvector(*vp);
- delete vp;
GINAC_ASSERT(is_canonical());
}
mul::mul(const ex & lh, const ex & mh, const ex & rh)
{
- debugmsg("mul ctor from ex,ex,ex",LOGLEVEL_CONSTRUCT);
tinfo_key = TINFO_mul;
exvector factors;
factors.reserve(3);
factors.push_back(lh);
factors.push_back(mh);
factors.push_back(rh);
- overall_coeff = _ex1();
+ overall_coeff = _ex1;
construct_from_exvector(factors);
GINAC_ASSERT(is_canonical());
}
DEFAULT_ARCHIVING(mul)
//////////
-// functions overriding virtual functions from bases classes
+// functions overriding virtual functions from base classes
//////////
-// public
-
-void mul::print(std::ostream & os, unsigned upper_precedence) const
+void mul::print_overall_coeff(const print_context & c, const char *mul_sym) const
{
- debugmsg("mul print",LOGLEVEL_PRINT);
- if (precedence<=upper_precedence) os << "(";
- bool first = true;
- // first print the overall numeric coefficient:
- numeric coeff = ex_to_numeric(overall_coeff);
- if (coeff.csgn()==-1) os << '-';
- if (!coeff.is_equal(_num1()) &&
- !coeff.is_equal(_num_1())) {
+ const numeric &coeff = ex_to<numeric>(overall_coeff);
+ if (coeff.csgn() == -1)
+ c.s << '-';
+ if (!coeff.is_equal(_num1) &&
+ !coeff.is_equal(_num_1)) {
if (coeff.is_rational()) {
if (coeff.is_negative())
- os << -coeff;
+ (-coeff).print(c);
else
- os << coeff;
+ coeff.print(c);
} else {
- if (coeff.csgn()==-1)
- (-coeff).print(os, precedence);
+ if (coeff.csgn() == -1)
+ (-coeff).print(c, precedence());
else
- coeff.print(os, precedence);
+ coeff.print(c, precedence());
}
- os << '*';
+ c.s << mul_sym;
}
- // then proceed with the remaining factors:
- for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
- if (!first) {
- os << '*';
- } else {
- first=false;
- }
- recombine_pair_to_ex(*cit).print(os,precedence);
+}
+
+void mul::do_print(const print_context & c, unsigned level) const
+{
+ if (precedence() <= level)
+ c.s << '(';
+
+ print_overall_coeff(c, "*");
+
+ epvector::const_iterator it = seq.begin(), itend = seq.end();
+ bool first = true;
+ while (it != itend) {
+ if (!first)
+ c.s << '*';
+ else
+ first = false;
+ recombine_pair_to_ex(*it).print(c, precedence());
+ ++it;
}
- if (precedence<=upper_precedence) os << ")";
+
+ if (precedence() <= level)
+ c.s << ')';
}
-void mul::printraw(std::ostream & os) const
+void mul::do_print_latex(const print_latex & c, unsigned level) const
{
- debugmsg("mul printraw",LOGLEVEL_PRINT);
+ if (precedence() <= level)
+ c.s << "{(";
+
+ print_overall_coeff(c, " ");
+
+ // Separate factors into those with negative numeric exponent
+ // and all others
+ epvector::const_iterator it = seq.begin(), itend = seq.end();
+ exvector neg_powers, others;
+ while (it != itend) {
+ GINAC_ASSERT(is_exactly_a<numeric>(it->coeff));
+ if (ex_to<numeric>(it->coeff).is_negative())
+ neg_powers.push_back(recombine_pair_to_ex(expair(it->rest, -(it->coeff))));
+ else
+ others.push_back(recombine_pair_to_ex(*it));
+ ++it;
+ }
+
+ if (!neg_powers.empty()) {
+
+ // Factors with negative exponent are printed as a fraction
+ c.s << "\\frac{";
+ mul(others).eval().print(c);
+ c.s << "}{";
+ mul(neg_powers).eval().print(c);
+ c.s << "}";
+
+ } else {
- os << "*(";
- for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
- os << "(";
- (*it).rest.bp->printraw(os);
- os << ",";
- (*it).coeff.bp->printraw(os);
- os << "),";
+ // All other factors are printed in the ordinary way
+ exvector::const_iterator vit = others.begin(), vitend = others.end();
+ while (vit != vitend) {
+ c.s << ' ';
+ vit->print(c, precedence());
+ ++vit;
+ }
}
- os << ",hash=" << hashvalue << ",flags=" << flags;
- os << ")";
+
+ if (precedence() <= level)
+ c.s << ")}";
}
-void mul::printcsrc(std::ostream & os, unsigned type, unsigned upper_precedence) const
+void mul::do_print_csrc(const print_csrc & c, unsigned level) const
{
- debugmsg("mul print csrc", LOGLEVEL_PRINT);
- if (precedence <= upper_precedence)
- os << "(";
+ if (precedence() <= level)
+ c.s << "(";
- if (!overall_coeff.is_equal(_ex1())) {
- overall_coeff.bp->printcsrc(os,type,precedence);
- os << "*";
+ if (!overall_coeff.is_equal(_ex1)) {
+ overall_coeff.print(c, precedence());
+ c.s << "*";
}
-
+
// Print arguments, separated by "*" or "/"
- epvector::const_iterator it = seq.begin();
- epvector::const_iterator itend = seq.end();
+ epvector::const_iterator it = seq.begin(), itend = seq.end();
while (it != itend) {
// If the first argument is a negative integer power, it gets printed as "1.0/<expr>"
- if (it == seq.begin() && ex_to_numeric(it->coeff).is_integer() && it->coeff.compare(_num0()) < 0) {
- if (type == csrc_types::ctype_cl_N)
- os << "recip(";
- else
- os << "1.0/";
+ bool needclosingparenthesis = false;
+ if (it == seq.begin() && it->coeff.info(info_flags::negint)) {
+ if (is_a<print_csrc_cl_N>(c)) {
+ c.s << "recip(";
+ needclosingparenthesis = true;
+ } else
+ c.s << "1.0/";
}
// If the exponent is 1 or -1, it is left out
- if (it->coeff.compare(_ex1()) == 0 || it->coeff.compare(_num_1()) == 0)
- it->rest.bp->printcsrc(os, type, precedence);
+ if (it->coeff.is_equal(_ex1) || it->coeff.is_equal(_ex_1))
+ it->rest.print(c, precedence());
+ else if (it->coeff.info(info_flags::negint))
+ // Outer parens around ex needed for broken GCC parser:
+ (ex(power(it->rest, -ex_to<numeric>(it->coeff)))).print(c, level);
else
- // outer parens around ex needed for broken gcc-2.95 parser:
- (ex(power(it->rest, abs(ex_to_numeric(it->coeff))))).bp->printcsrc(os, type, upper_precedence);
+ // Outer parens around ex needed for broken GCC parser:
+ (ex(power(it->rest, ex_to<numeric>(it->coeff)))).print(c, level);
+
+ if (needclosingparenthesis)
+ c.s << ")";
// Separator is "/" for negative integer powers, "*" otherwise
++it;
if (it != itend) {
- if (ex_to_numeric(it->coeff).is_integer() && it->coeff.compare(_num0()) < 0)
- os << "/";
+ if (it->coeff.info(info_flags::negint))
+ c.s << "/";
else
- os << "*";
+ c.s << "*";
}
}
- if (precedence <= upper_precedence)
- os << ")";
+
+ if (precedence() <= level)
+ c.s << ")";
+}
+
+void mul::do_print_python_repr(const print_python_repr & c, unsigned level) const
+{
+ c.s << class_name() << '(';
+ op(0).print(c);
+ for (size_t i=1; i<nops(); ++i) {
+ c.s << ',';
+ op(i).print(c);
+ }
+ c.s << ')';
}
bool mul::info(unsigned inf) const
case info_flags::rational_polynomial:
case info_flags::crational_polynomial:
case info_flags::rational_function: {
- for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
+ epvector::const_iterator i = seq.begin(), end = seq.end();
+ while (i != end) {
if (!(recombine_pair_to_ex(*i).info(inf)))
return false;
+ ++i;
}
return overall_coeff.info(inf);
}
case info_flags::algebraic: {
- for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
+ epvector::const_iterator i = seq.begin(), end = seq.end();
+ while (i != end) {
if ((recombine_pair_to_ex(*i).info(inf)))
return true;
+ ++i;
}
return false;
}
int mul::degree(const ex & s) const
{
+ // Sum up degrees of factors
int deg_sum = 0;
- for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
- if (ex_to_numeric(cit->coeff).is_integer())
- deg_sum+=cit->rest.degree(s) * ex_to_numeric(cit->coeff).to_int();
+ epvector::const_iterator i = seq.begin(), end = seq.end();
+ while (i != end) {
+ if (ex_to<numeric>(i->coeff).is_integer())
+ deg_sum += i->rest.degree(s) * ex_to<numeric>(i->coeff).to_int();
+ ++i;
}
return deg_sum;
}
int mul::ldegree(const ex & s) const
{
+ // Sum up degrees of factors
int deg_sum = 0;
- for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
- if (ex_to_numeric(cit->coeff).is_integer())
- deg_sum+=cit->rest.ldegree(s) * ex_to_numeric(cit->coeff).to_int();
+ epvector::const_iterator i = seq.begin(), end = seq.end();
+ while (i != end) {
+ if (ex_to<numeric>(i->coeff).is_integer())
+ deg_sum += i->rest.ldegree(s) * ex_to<numeric>(i->coeff).to_int();
+ ++i;
}
return deg_sum;
}
if (n==0) {
// product of individual coeffs
// if a non-zero power of s is found, the resulting product will be 0
- epvector::const_iterator it = seq.begin();
- while (it!=seq.end()) {
- coeffseq.push_back(recombine_pair_to_ex(*it).coeff(s,n));
- ++it;
+ epvector::const_iterator i = seq.begin(), end = seq.end();
+ while (i != end) {
+ coeffseq.push_back(recombine_pair_to_ex(*i).coeff(s,n));
+ ++i;
}
coeffseq.push_back(overall_coeff);
return (new mul(coeffseq))->setflag(status_flags::dynallocated);
}
- epvector::const_iterator it=seq.begin();
- bool coeff_found = 0;
- while (it!=seq.end()) {
- ex t = recombine_pair_to_ex(*it);
- ex c = t.coeff(s,n);
+ epvector::const_iterator i = seq.begin(), end = seq.end();
+ bool coeff_found = false;
+ while (i != end) {
+ ex t = recombine_pair_to_ex(*i);
+ ex c = t.coeff(s, n);
if (!c.is_zero()) {
coeffseq.push_back(c);
coeff_found = 1;
} else {
coeffseq.push_back(t);
}
- ++it;
+ ++i;
}
if (coeff_found) {
coeffseq.push_back(overall_coeff);
return (new mul(coeffseq))->setflag(status_flags::dynallocated);
}
- return _ex0();
+ return _ex0;
}
+/** Perform automatic term rewriting rules in this class. In the following
+ * x, x1, x2,... stand for a symbolic variables of type ex and c, c1, c2...
+ * stand for such expressions that contain a plain number.
+ * - *(...,x;0) -> 0
+ * - *(+(x1,x2,...);c) -> *(+(*(x1,c),*(x2,c),...))
+ * - *(x;1) -> x
+ * - *(;c) -> c
+ *
+ * @param level cut-off in recursive evaluation */
ex mul::eval(int level) const
{
- // simplifications *(...,x;0) -> 0
- // *(+(x,y,...);c) -> *(+(*(x,c),*(y,c),...)) (c numeric())
- // *(x;1) -> x
- // *(;c) -> c
-
- debugmsg("mul eval",LOGLEVEL_MEMBER_FUNCTION);
-
- epvector * evaled_seqp = evalchildren(level);
- if (evaled_seqp!=0) {
+ std::auto_ptr<epvector> evaled_seqp = evalchildren(level);
+ if (evaled_seqp.get()) {
// do more evaluation later
- return (new mul(evaled_seqp,overall_coeff))->
+ return (new mul(evaled_seqp, overall_coeff))->
setflag(status_flags::dynallocated);
}
#ifdef DO_GINAC_ASSERT
- for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
- GINAC_ASSERT((!is_ex_exactly_of_type((*cit).rest,mul)) ||
- (!(ex_to_numeric((*cit).coeff).is_integer())));
- GINAC_ASSERT(!(cit->is_canonical_numeric()));
- if (is_ex_exactly_of_type(recombine_pair_to_ex(*cit),numeric))
- printtree(std::cerr,0);
- GINAC_ASSERT(!is_ex_exactly_of_type(recombine_pair_to_ex(*cit),numeric));
+ epvector::const_iterator i = seq.begin(), end = seq.end();
+ while (i != end) {
+ GINAC_ASSERT((!is_exactly_a<mul>(i->rest)) ||
+ (!(ex_to<numeric>(i->coeff).is_integer())));
+ GINAC_ASSERT(!(i->is_canonical_numeric()));
+ if (is_exactly_a<numeric>(recombine_pair_to_ex(*i)))
+ print(print_tree(std::cerr));
+ GINAC_ASSERT(!is_exactly_a<numeric>(recombine_pair_to_ex(*i)));
/* for paranoia */
- expair p = split_ex_to_pair(recombine_pair_to_ex(*cit));
- GINAC_ASSERT(p.rest.is_equal((*cit).rest));
- GINAC_ASSERT(p.coeff.is_equal((*cit).coeff));
+ expair p = split_ex_to_pair(recombine_pair_to_ex(*i));
+ GINAC_ASSERT(p.rest.is_equal(i->rest));
+ GINAC_ASSERT(p.coeff.is_equal(i->coeff));
/* end paranoia */
+ ++i;
}
#endif // def DO_GINAC_ASSERT
if (flags & status_flags::evaluated) {
GINAC_ASSERT(seq.size()>0);
- GINAC_ASSERT(seq.size()>1 || !overall_coeff.is_equal(_ex1()));
+ GINAC_ASSERT(seq.size()>1 || !overall_coeff.is_equal(_ex1));
return *this;
}
int seq_size = seq.size();
- if (overall_coeff.is_equal(_ex0())) {
+ if (overall_coeff.is_zero()) {
// *(...,x;0) -> 0
- return _ex0();
+ return _ex0;
} else if (seq_size==0) {
// *(;c) -> c
return overall_coeff;
- } else if (seq_size==1 && overall_coeff.is_equal(_ex1())) {
+ } else if (seq_size==1 && overall_coeff.is_equal(_ex1)) {
// *(x;1) -> x
return recombine_pair_to_ex(*(seq.begin()));
} else if ((seq_size==1) &&
- is_ex_exactly_of_type((*seq.begin()).rest,add) &&
- ex_to_numeric((*seq.begin()).coeff).is_equal(_num1())) {
+ is_exactly_a<add>((*seq.begin()).rest) &&
+ ex_to<numeric>((*seq.begin()).coeff).is_equal(_num1)) {
// *(+(x,y,...);c) -> +(*(x,c),*(y,c),...) (c numeric(), no powers of +())
- const add & addref = ex_to_add((*seq.begin()).rest);
- epvector distrseq;
- distrseq.reserve(addref.seq.size());
- for (epvector::const_iterator cit=addref.seq.begin(); cit!=addref.seq.end(); ++cit) {
- distrseq.push_back(addref.combine_pair_with_coeff_to_pair(*cit, overall_coeff));
+ const add & addref = ex_to<add>((*seq.begin()).rest);
+ std::auto_ptr<epvector> distrseq(new epvector);
+ distrseq->reserve(addref.seq.size());
+ epvector::const_iterator i = addref.seq.begin(), end = addref.seq.end();
+ while (i != end) {
+ distrseq->push_back(addref.combine_pair_with_coeff_to_pair(*i, overall_coeff));
+ ++i;
}
return (new add(distrseq,
- ex_to_numeric(addref.overall_coeff).
- mul_dyn(ex_to_numeric(overall_coeff))))
+ ex_to<numeric>(addref.overall_coeff).
+ mul_dyn(ex_to<numeric>(overall_coeff))))
->setflag(status_flags::dynallocated | status_flags::evaluated);
}
return this->hold();
if (level==-max_recursion_level)
throw(std::runtime_error("max recursion level reached"));
- epvector s;
- s.reserve(seq.size());
-
+ std::auto_ptr<epvector> s(new epvector);
+ s->reserve(seq.size());
+
--level;
- for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
- s.push_back(combine_ex_with_coeff_to_pair((*it).rest.evalf(level),
- (*it).coeff));
+ epvector::const_iterator i = seq.begin(), end = seq.end();
+ while (i != end) {
+ s->push_back(combine_ex_with_coeff_to_pair(i->rest.evalf(level),
+ i->coeff));
+ ++i;
}
- return mul(s,overall_coeff.evalf(level));
+ return mul(s, overall_coeff.evalf(level));
}
-ex mul::simplify_ncmul(const exvector & v) const
+ex mul::evalm() const
{
- throw(std::logic_error("mul::simplify_ncmul() should never have been called!"));
+ // numeric*matrix
+ if (seq.size() == 1 && seq[0].coeff.is_equal(_ex1)
+ && is_a<matrix>(seq[0].rest))
+ return ex_to<matrix>(seq[0].rest).mul(ex_to<numeric>(overall_coeff));
+
+ // Evaluate children first, look whether there are any matrices at all
+ // (there can be either no matrices or one matrix; if there were more
+ // than one matrix, it would be a non-commutative product)
+ std::auto_ptr<epvector> s(new epvector);
+ s->reserve(seq.size());
+
+ bool have_matrix = false;
+ epvector::iterator the_matrix;
+
+ epvector::const_iterator i = seq.begin(), end = seq.end();
+ while (i != end) {
+ const ex &m = recombine_pair_to_ex(*i).evalm();
+ s->push_back(split_ex_to_pair(m));
+ if (is_a<matrix>(m)) {
+ have_matrix = true;
+ the_matrix = s->end() - 1;
+ }
+ ++i;
+ }
+
+ if (have_matrix) {
+
+ // The product contained a matrix. We will multiply all other factors
+ // into that matrix.
+ matrix m = ex_to<matrix>(the_matrix->rest);
+ s->erase(the_matrix);
+ ex scalar = (new mul(s, overall_coeff))->setflag(status_flags::dynallocated);
+ return m.mul_scalar(scalar);
+
+ } else
+ return (new mul(s, overall_coeff))->setflag(status_flags::dynallocated);
+}
+
+ex mul::eval_ncmul(const exvector & v) const
+{
+ if (seq.empty())
+ return inherited::eval_ncmul(v);
+
+ // Find first noncommutative element and call its eval_ncmul()
+ epvector::const_iterator i = seq.begin(), end = seq.end();
+ while (i != end) {
+ if (i->rest.return_type() == return_types::noncommutative)
+ return i->rest.eval_ncmul(v);
+ ++i;
+ }
+ return inherited::eval_ncmul(v);
+}
+
+bool tryfactsubs(const ex & origfactor, const ex & patternfactor, int & nummatches, lst & repls)
+{
+ ex origbase;
+ int origexponent;
+ int origexpsign;
+
+ if (is_exactly_a<power>(origfactor) && origfactor.op(1).info(info_flags::integer)) {
+ origbase = origfactor.op(0);
+ int expon = ex_to<numeric>(origfactor.op(1)).to_int();
+ origexponent = expon > 0 ? expon : -expon;
+ origexpsign = expon > 0 ? 1 : -1;
+ } else {
+ origbase = origfactor;
+ origexponent = 1;
+ origexpsign = 1;
+ }
+
+ ex patternbase;
+ int patternexponent;
+ int patternexpsign;
+
+ if (is_exactly_a<power>(patternfactor) && patternfactor.op(1).info(info_flags::integer)) {
+ patternbase = patternfactor.op(0);
+ int expon = ex_to<numeric>(patternfactor.op(1)).to_int();
+ patternexponent = expon > 0 ? expon : -expon;
+ patternexpsign = expon > 0 ? 1 : -1;
+ } else {
+ patternbase = patternfactor;
+ patternexponent = 1;
+ patternexpsign = 1;
+ }
+
+ lst saverepls = repls;
+ if (origexponent < patternexponent || origexpsign != patternexpsign || !origbase.match(patternbase,saverepls))
+ return false;
+ repls = saverepls;
+
+ int newnummatches = origexponent / patternexponent;
+ if (newnummatches < nummatches)
+ nummatches = newnummatches;
+ return true;
+}
+
+ex mul::algebraic_subs_mul(const exmap & m, unsigned options) const
+{
+ std::vector<bool> subsed(seq.size(), false);
+ exvector subsresult(seq.size());
+
+ for (exmap::const_iterator it = m.begin(); it != m.end(); ++it) {
+
+ if (is_exactly_a<mul>(it->first)) {
+
+ int nummatches = std::numeric_limits<int>::max();
+ std::vector<bool> currsubsed(seq.size(), false);
+ bool succeed = true;
+ lst repls;
+
+ for (size_t j=0; j<it->first.nops(); j++) {
+ bool found=false;
+ for (size_t k=0; k<nops(); k++) {
+ if (currsubsed[k] || subsed[k])
+ continue;
+ if (tryfactsubs(op(k), it->first.op(j), nummatches, repls)) {
+ currsubsed[k] = true;
+ found = true;
+ break;
+ }
+ }
+ if (!found) {
+ succeed = false;
+ break;
+ }
+ }
+ if (!succeed)
+ continue;
+
+ bool foundfirstsubsedfactor = false;
+ for (size_t j=0; j<subsed.size(); j++) {
+ if (currsubsed[j]) {
+ if (foundfirstsubsedfactor)
+ subsresult[j] = op(j);
+ else {
+ foundfirstsubsedfactor = true;
+ subsresult[j] = op(j) * power(it->second.subs(ex(repls), subs_options::no_pattern) / it->first.subs(ex(repls), subs_options::no_pattern), nummatches);
+ }
+ subsed[j] = true;
+ }
+ }
+
+ } else {
+
+ int nummatches = std::numeric_limits<int>::max();
+ lst repls;
+
+ for (size_t j=0; j<this->nops(); j++) {
+ if (!subsed[j] && tryfactsubs(op(j), it->first, nummatches, repls)) {
+ subsed[j] = true;
+ subsresult[j] = op(j) * power(it->second.subs(ex(repls), subs_options::no_pattern) / it->first.subs(ex(repls), subs_options::no_pattern), nummatches);
+ }
+ }
+ }
+ }
+
+ bool subsfound = false;
+ for (size_t i=0; i<subsed.size(); i++) {
+ if (subsed[i]) {
+ subsfound = true;
+ break;
+ }
+ }
+ if (!subsfound)
+ return subs_one_level(m, options | subs_options::algebraic);
+
+ exvector ev; ev.reserve(nops());
+ for (size_t i=0; i<nops(); i++) {
+ if (subsed[i])
+ ev.push_back(subsresult[i]);
+ else
+ ev.push_back(op(i));
+ }
+
+ return (new mul(ev))->setflag(status_flags::dynallocated);
}
// protected
* @see ex::diff */
ex mul::derivative(const symbol & s) const
{
+ size_t num = seq.size();
exvector addseq;
- addseq.reserve(seq.size());
+ addseq.reserve(num);
// D(a*b*c) = D(a)*b*c + a*D(b)*c + a*b*D(c)
- for (unsigned i=0; i!=seq.size(); ++i) {
- epvector mulseq = seq;
- mulseq[i] = split_ex_to_pair(power(seq[i].rest,seq[i].coeff - _ex1()) *
- seq[i].rest.diff(s));
- addseq.push_back((new mul(mulseq,overall_coeff*seq[i].coeff))->setflag(status_flags::dynallocated));
+ epvector mulseq = seq;
+ epvector::const_iterator i = seq.begin(), end = seq.end();
+ epvector::iterator i2 = mulseq.begin();
+ while (i != end) {
+ expair ep = split_ex_to_pair(power(i->rest, i->coeff - _ex1) *
+ i->rest.diff(s));
+ ep.swap(*i2);
+ addseq.push_back((new mul(mulseq, overall_coeff * i->coeff))->setflag(status_flags::dynallocated));
+ ep.swap(*i2);
+ ++i; ++i2;
}
return (new add(addseq))->setflag(status_flags::dynallocated);
}
return inherited::compare_same_type(other);
}
-bool mul::is_equal_same_type(const basic & other) const
-{
- return inherited::is_equal_same_type(other);
-}
-
-unsigned mul::return_type(void) const
+unsigned mul::return_type() const
{
- if (seq.size()==0) {
+ if (seq.empty()) {
// mul without factors: should not happen, but commutes
return return_types::commutative;
}
- bool all_commutative = 1;
- unsigned rt;
- epvector::const_iterator cit_noncommutative_element; // point to first found nc element
+ bool all_commutative = true;
+ epvector::const_iterator noncommutative_element; // point to first found nc element
- for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
- rt=(*cit).rest.return_type();
- if (rt==return_types::noncommutative_composite) return rt; // one ncc -> mul also ncc
- if ((rt==return_types::noncommutative)&&(all_commutative)) {
+ epvector::const_iterator i = seq.begin(), end = seq.end();
+ while (i != end) {
+ unsigned rt = i->rest.return_type();
+ if (rt == return_types::noncommutative_composite)
+ return rt; // one ncc -> mul also ncc
+ if ((rt == return_types::noncommutative) && (all_commutative)) {
// first nc element found, remember position
- cit_noncommutative_element = cit;
- all_commutative = 0;
+ noncommutative_element = i;
+ all_commutative = false;
}
- if ((rt==return_types::noncommutative)&&(!all_commutative)) {
+ if ((rt == return_types::noncommutative) && (!all_commutative)) {
// another nc element found, compare type_infos
- if ((*cit_noncommutative_element).rest.return_type_tinfo()!=(*cit).rest.return_type_tinfo()) {
+ if (noncommutative_element->rest.return_type_tinfo() != i->rest.return_type_tinfo()) {
// diffent types -> mul is ncc
return return_types::noncommutative_composite;
}
}
+ ++i;
}
// all factors checked
return all_commutative ? return_types::commutative : return_types::noncommutative;
}
-unsigned mul::return_type_tinfo(void) const
+unsigned mul::return_type_tinfo() const
{
- if (seq.size()==0)
+ if (seq.empty())
return tinfo_key; // mul without factors: should not happen
// return type_info of first noncommutative element
- for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
- if ((*cit).rest.return_type()==return_types::noncommutative)
- return (*cit).rest.return_type_tinfo();
+ epvector::const_iterator i = seq.begin(), end = seq.end();
+ while (i != end) {
+ if (i->rest.return_type() == return_types::noncommutative)
+ return i->rest.return_type_tinfo();
+ ++i;
}
// no noncommutative element found, should not happen
return tinfo_key;
ex mul::thisexpairseq(const epvector & v, const ex & oc) const
{
- return (new mul(v,oc))->setflag(status_flags::dynallocated);
+ return (new mul(v, oc))->setflag(status_flags::dynallocated);
}
-ex mul::thisexpairseq(epvector * vp, const ex & oc) const
+ex mul::thisexpairseq(std::auto_ptr<epvector> vp, const ex & oc) const
{
- return (new mul(vp,oc))->setflag(status_flags::dynallocated);
+ return (new mul(vp, oc))->setflag(status_flags::dynallocated);
}
expair mul::split_ex_to_pair(const ex & e) const
{
- if (is_ex_exactly_of_type(e,power)) {
- const power & powerref = ex_to_power(e);
- if (is_ex_exactly_of_type(powerref.exponent,numeric))
+ if (is_exactly_a<power>(e)) {
+ const power & powerref = ex_to<power>(e);
+ if (is_exactly_a<numeric>(powerref.exponent))
return expair(powerref.basis,powerref.exponent);
}
- return expair(e,_ex1());
+ return expair(e,_ex1);
}
expair mul::combine_ex_with_coeff_to_pair(const ex & e,
{
// to avoid duplication of power simplification rules,
// we create a temporary power object
- // otherwise it would be hard to correctly simplify
+ // otherwise it would be hard to correctly evaluate
// expression like (4^(1/3))^(3/2)
- if (are_ex_trivially_equal(c,_ex1()))
+ if (c.is_equal(_ex1))
return split_ex_to_pair(e);
-
+
return split_ex_to_pair(power(e,c));
}
{
// to avoid duplication of power simplification rules,
// we create a temporary power object
- // otherwise it would be hard to correctly simplify
+ // otherwise it would be hard to correctly evaluate
// expression like (4^(1/3))^(3/2)
- if (are_ex_trivially_equal(c,_ex1()))
+ if (c.is_equal(_ex1))
return p;
-
+
return split_ex_to_pair(power(recombine_pair_to_ex(p),c));
}
ex mul::recombine_pair_to_ex(const expair & p) const
{
- if (ex_to_numeric(p.coeff).is_equal(_num1()))
+ if (ex_to<numeric>(p.coeff).is_equal(_num1))
return p.rest;
else
- return power(p.rest,p.coeff);
+ return (new power(p.rest,p.coeff))->setflag(status_flags::dynallocated);
}
bool mul::expair_needs_further_processing(epp it)
{
- if (is_ex_exactly_of_type((*it).rest,mul) &&
- ex_to_numeric((*it).coeff).is_integer()) {
+ if (is_exactly_a<mul>(it->rest) &&
+ ex_to<numeric>(it->coeff).is_integer()) {
// combined pair is product with integer power -> expand it
*it = split_ex_to_pair(recombine_pair_to_ex(*it));
return true;
}
- if (is_ex_exactly_of_type((*it).rest,numeric)) {
- expair ep=split_ex_to_pair(recombine_pair_to_ex(*it));
+ if (is_exactly_a<numeric>(it->rest)) {
+ expair ep = split_ex_to_pair(recombine_pair_to_ex(*it));
if (!ep.is_equal(*it)) {
// combined pair is a numeric power which can be simplified
*it = ep;
return true;
}
- if (ex_to_numeric((*it).coeff).is_equal(_num1())) {
+ if (it->coeff.is_equal(_ex1)) {
// combined pair has coeff 1 and must be moved to the end
return true;
}
return false;
}
-ex mul::default_overall_coeff(void) const
+ex mul::default_overall_coeff() const
{
- return _ex1();
+ return _ex1;
}
void mul::combine_overall_coeff(const ex & c)
{
- GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
- GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
- overall_coeff = ex_to_numeric(overall_coeff).mul_dyn(ex_to_numeric(c));
+ GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
+ GINAC_ASSERT(is_exactly_a<numeric>(c));
+ overall_coeff = ex_to<numeric>(overall_coeff).mul_dyn(ex_to<numeric>(c));
}
void mul::combine_overall_coeff(const ex & c1, const ex & c2)
{
- GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
- GINAC_ASSERT(is_ex_exactly_of_type(c1,numeric));
- GINAC_ASSERT(is_ex_exactly_of_type(c2,numeric));
- overall_coeff = ex_to_numeric(overall_coeff).mul_dyn(ex_to_numeric(c1).power(ex_to_numeric(c2)));
+ GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
+ GINAC_ASSERT(is_exactly_a<numeric>(c1));
+ GINAC_ASSERT(is_exactly_a<numeric>(c2));
+ overall_coeff = ex_to<numeric>(overall_coeff).mul_dyn(ex_to<numeric>(c1).power(ex_to<numeric>(c2)));
}
bool mul::can_make_flat(const expair & p) const
{
- GINAC_ASSERT(is_ex_exactly_of_type(p.coeff,numeric));
+ GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
// this assertion will probably fail somewhere
// it would require a more careful make_flat, obeying the power laws
// probably should return true only if p.coeff is integer
- return ex_to_numeric(p.coeff).is_equal(_num1());
+ return ex_to<numeric>(p.coeff).is_equal(_num1);
}
ex mul::expand(unsigned options) const
{
- if (flags & status_flags::expanded)
- return *this;
-
- exvector sub_expanded_seq;
-
- epvector * expanded_seqp = expandchildren(options);
-
- const epvector & expanded_seq = expanded_seqp==0 ? seq : *expanded_seqp;
-
+ // First, expand the children
+ std::auto_ptr<epvector> expanded_seqp = expandchildren(options);
+ const epvector & expanded_seq = (expanded_seqp.get() ? *expanded_seqp : seq);
+
+ // Now, look for all the factors that are sums and multiply each one out
+ // with the next one that is found while collecting the factors which are
+ // not sums
int number_of_adds = 0;
+ ex last_expanded = _ex1;
epvector non_adds;
non_adds.reserve(expanded_seq.size());
- epvector::const_iterator cit = expanded_seq.begin();
- epvector::const_iterator last = expanded_seq.end();
- ex last_expanded = _ex1();
- while (cit!=last) {
- if (is_ex_exactly_of_type((*cit).rest,add) &&
- ((*cit).coeff.is_equal(_ex1()))) {
+ epvector::const_iterator cit = expanded_seq.begin(), last = expanded_seq.end();
+ while (cit != last) {
+ if (is_exactly_a<add>(cit->rest) &&
+ (cit->coeff.is_equal(_ex1))) {
++number_of_adds;
- if (is_ex_exactly_of_type(last_expanded,add)) {
- // expand adds
- const add & add1 = ex_to_add(last_expanded);
- const add & add2 = ex_to_add((*cit).rest);
- int n1 = add1.nops();
- int n2 = add2.nops();
- exvector distrseq;
- distrseq.reserve(n1*n2);
- for (int i1=0; i1<n1; ++i1) {
- for (int i2=0; i2<n2; ++i2) {
- distrseq.push_back(add1.op(i1)*add2.op(i2));
+ if (is_exactly_a<add>(last_expanded)) {
+
+ // Expand a product of two sums, aggressive version.
+ // Caring for the overall coefficients in separate loops can
+ // sometimes give a performance gain of up to 15%!
+
+ const int sizedifference = ex_to<add>(last_expanded).seq.size()-ex_to<add>(cit->rest).seq.size();
+ // add2 is for the inner loop and should be the bigger of the two sums
+ // in the presence of asymptotically good sorting:
+ const add& add1 = (sizedifference<0 ? ex_to<add>(last_expanded) : ex_to<add>(cit->rest));
+ const add& add2 = (sizedifference<0 ? ex_to<add>(cit->rest) : ex_to<add>(last_expanded));
+ const epvector::const_iterator add1begin = add1.seq.begin();
+ const epvector::const_iterator add1end = add1.seq.end();
+ const epvector::const_iterator add2begin = add2.seq.begin();
+ const epvector::const_iterator add2end = add2.seq.end();
+ epvector distrseq;
+ distrseq.reserve(add1.seq.size()+add2.seq.size());
+ // Multiply add2 with the overall coefficient of add1 and append it to distrseq:
+ if (!add1.overall_coeff.is_zero()) {
+ if (add1.overall_coeff.is_equal(_ex1))
+ distrseq.insert(distrseq.end(),add2begin,add2end);
+ else
+ for (epvector::const_iterator i=add2begin; i!=add2end; ++i)
+ distrseq.push_back(expair(i->rest, ex_to<numeric>(i->coeff).mul_dyn(ex_to<numeric>(add1.overall_coeff))));
+ }
+ // Multiply add1 with the overall coefficient of add2 and append it to distrseq:
+ if (!add2.overall_coeff.is_zero()) {
+ if (add2.overall_coeff.is_equal(_ex1))
+ distrseq.insert(distrseq.end(),add1begin,add1end);
+ else
+ for (epvector::const_iterator i=add1begin; i!=add1end; ++i)
+ distrseq.push_back(expair(i->rest, ex_to<numeric>(i->coeff).mul_dyn(ex_to<numeric>(add2.overall_coeff))));
+ }
+ // Compute the new overall coefficient and put it together:
+ ex tmp_accu = (new add(distrseq, add1.overall_coeff*add2.overall_coeff))->setflag(status_flags::dynallocated);
+ // Multiply explicitly all non-numeric terms of add1 and add2:
+ for (epvector::const_iterator i1=add1begin; i1!=add1end; ++i1) {
+ // We really have to combine terms here in order to compactify
+ // the result. Otherwise it would become waayy tooo bigg.
+ numeric oc;
+ distrseq.clear();
+ for (epvector::const_iterator i2=add2begin; i2!=add2end; ++i2) {
+ // Don't push_back expairs which might have a rest that evaluates to a numeric,
+ // since that would violate an invariant of expairseq:
+ const ex rest = (new mul(i1->rest, i2->rest))->setflag(status_flags::dynallocated);
+ if (is_exactly_a<numeric>(rest))
+ oc += ex_to<numeric>(rest).mul(ex_to<numeric>(i1->coeff).mul(ex_to<numeric>(i2->coeff)));
+ else
+ distrseq.push_back(expair(rest, ex_to<numeric>(i1->coeff).mul_dyn(ex_to<numeric>(i2->coeff))));
}
+ tmp_accu += (new add(distrseq, oc))->setflag(status_flags::dynallocated);
}
- last_expanded = (new add(distrseq))->setflag(status_flags::dynallocated | status_flags::expanded);
+ last_expanded = tmp_accu;
+
} else {
non_adds.push_back(split_ex_to_pair(last_expanded));
- last_expanded = (*cit).rest;
+ last_expanded = cit->rest;
}
} else {
non_adds.push_back(*cit);
}
++cit;
}
- if (expanded_seqp)
- delete expanded_seqp;
-
- if (is_ex_exactly_of_type(last_expanded,add)) {
- add const & finaladd = ex_to_add(last_expanded);
+
+ // Now the only remaining thing to do is to multiply the factors which
+ // were not sums into the "last_expanded" sum
+ if (is_exactly_a<add>(last_expanded)) {
+ const add & finaladd = ex_to<add>(last_expanded);
exvector distrseq;
- int n = finaladd.nops();
+ size_t n = finaladd.nops();
distrseq.reserve(n);
- for (int i=0; i<n; ++i) {
+ for (size_t i=0; i<n; ++i) {
epvector factors = non_adds;
factors.push_back(split_ex_to_pair(finaladd.op(i)));
- distrseq.push_back((new mul(factors,overall_coeff))->setflag(status_flags::dynallocated | status_flags::expanded));
+ distrseq.push_back((new mul(factors, overall_coeff))->
+ setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)));
}
return ((new add(distrseq))->
- setflag(status_flags::dynallocated | status_flags::expanded));
+ setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)));
}
non_adds.push_back(split_ex_to_pair(last_expanded));
- return (new mul(non_adds,overall_coeff))->
- setflag(status_flags::dynallocated | status_flags::expanded);
+ return (new mul(non_adds, overall_coeff))->
+ setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
}
* @see mul::expand()
* @return pointer to epvector containing expanded representation or zero
* pointer, if sequence is unchanged. */
-epvector * mul::expandchildren(unsigned options) const
+std::auto_ptr<epvector> mul::expandchildren(unsigned options) const
{
- epvector::const_iterator last = seq.end();
+ const epvector::const_iterator last = seq.end();
epvector::const_iterator cit = seq.begin();
while (cit!=last) {
const ex & factor = recombine_pair_to_ex(*cit);
if (!are_ex_trivially_equal(factor,expanded_factor)) {
// something changed, copy seq, eval and return it
- epvector *s = new epvector;
+ std::auto_ptr<epvector> s(new epvector);
s->reserve(seq.size());
// copy parts of seq which are known not to have changed
s->push_back(*cit2);
++cit2;
}
+
// copy first changed element
s->push_back(split_ex_to_pair(expanded_factor));
++cit2;
+
// copy rest
while (cit2!=last) {
s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit2).expand(options)));
++cit;
}
- return 0; // nothing has changed
+ return std::auto_ptr<epvector>(0); // nothing has changed
}
-//////////
-// static member variables
-//////////
-
-// protected
-
-unsigned mul::precedence = 50;
-
} // namespace GiNaC
git://www.ginac.de / ginac.git / blobdiff