* Implementation of GiNaC's products of expressions. */
/*
- * GiNaC Copyright (C) 1999 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2007 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
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
- * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
*/
+#include <iostream>
#include <vector>
#include <stdexcept>
+#include <limits>
#include "mul.h"
#include "add.h"
#include "power.h"
-#include "debugmsg.h"
+#include "operators.h"
+#include "matrix.h"
+#include "indexed.h"
+#include "lst.h"
+#include "archive.h"
+#include "utils.h"
+#include "compiler.h"
-#ifndef NO_GINAC_NAMESPACE
namespace GiNaC {
-#endif // ndef NO_GINAC_NAMESPACE
+
+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>(&mul::do_print_tree).
+ print_func<print_python_repr>(&mul::do_print_python_repr))
+
//////////
-// default constructor, destructor, copy constructor assignment operator and helpers
+// default constructor
//////////
-// public
-
mul::mul()
{
- debugmsg("mul default constructor",LOGLEVEL_CONSTRUCT);
- tinfo_key = TINFO_mul;
+ tinfo_key = &mul::tinfo_static;
}
-mul::~mul()
+//////////
+// other constructors
+//////////
+
+// public
+
+mul::mul(const ex & lh, const ex & rh)
{
- debugmsg("mul destructor",LOGLEVEL_DESTRUCT);
- destroy(0);
+ tinfo_key = &mul::tinfo_static;
+ overall_coeff = _ex1;
+ construct_from_2_ex(lh,rh);
+ GINAC_ASSERT(is_canonical());
}
-mul::mul(mul const & other)
+mul::mul(const exvector & v)
{
- debugmsg("mul copy constructor",LOGLEVEL_CONSTRUCT);
- copy(other);
+ tinfo_key = &mul::tinfo_static;
+ overall_coeff = _ex1;
+ construct_from_exvector(v);
+ GINAC_ASSERT(is_canonical());
}
-mul const & mul::operator=(mul const & other)
+mul::mul(const epvector & v)
{
- debugmsg("mul operator=",LOGLEVEL_ASSIGNMENT);
- if (this != &other) {
- destroy(1);
- copy(other);
- }
- return *this;
+ tinfo_key = &mul::tinfo_static;
+ overall_coeff = _ex1;
+ construct_from_epvector(v);
+ GINAC_ASSERT(is_canonical());
}
-// protected
+mul::mul(const epvector & v, const ex & oc, bool do_index_renaming)
+{
+ tinfo_key = &mul::tinfo_static;
+ overall_coeff = oc;
+ construct_from_epvector(v, do_index_renaming);
+ GINAC_ASSERT(is_canonical());
+}
-void mul::copy(mul const & other)
+mul::mul(std::auto_ptr<epvector> vp, const ex & oc, bool do_index_renaming)
{
- expairseq::copy(other);
+ tinfo_key = &mul::tinfo_static;
+ GINAC_ASSERT(vp.get()!=0);
+ overall_coeff = oc;
+ construct_from_epvector(*vp, do_index_renaming);
+ GINAC_ASSERT(is_canonical());
}
-void mul::destroy(bool call_parent)
+mul::mul(const ex & lh, const ex & mh, const ex & rh)
{
- if (call_parent) expairseq::destroy(call_parent);
+ tinfo_key = &mul::tinfo_static;
+ exvector factors;
+ factors.reserve(3);
+ factors.push_back(lh);
+ factors.push_back(mh);
+ factors.push_back(rh);
+ overall_coeff = _ex1;
+ construct_from_exvector(factors);
+ GINAC_ASSERT(is_canonical());
}
//////////
-// other constructors
+// archiving
//////////
-// public
+DEFAULT_ARCHIVING(mul)
+
+//////////
+// functions overriding virtual functions from base classes
+//////////
-mul::mul(ex const & lh, ex const & rh)
+void mul::print_overall_coeff(const print_context & c, const char *mul_sym) const
{
- debugmsg("mul constructor from ex,ex",LOGLEVEL_CONSTRUCT);
- tinfo_key = TINFO_mul;
- overall_coeff=exONE();
- construct_from_2_ex(lh,rh);
- GINAC_ASSERT(is_canonical());
+ const numeric &coeff = ex_to<numeric>(overall_coeff);
+ if (coeff.csgn() == -1)
+ c.s << '-';
+ if (!coeff.is_equal(*_num1_p) &&
+ !coeff.is_equal(*_num_1_p)) {
+ if (coeff.is_rational()) {
+ if (coeff.is_negative())
+ (-coeff).print(c);
+ else
+ coeff.print(c);
+ } else {
+ if (coeff.csgn() == -1)
+ (-coeff).print(c, precedence());
+ else
+ coeff.print(c, precedence());
+ }
+ c.s << mul_sym;
+ }
}
-mul::mul(exvector const & v)
+void mul::do_print(const print_context & c, unsigned level) const
{
- debugmsg("mul constructor from exvector",LOGLEVEL_CONSTRUCT);
- tinfo_key = TINFO_mul;
- overall_coeff=exONE();
- construct_from_exvector(v);
- GINAC_ASSERT(is_canonical());
+ 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() <= level)
+ c.s << ')';
}
-/*
-mul::mul(epvector const & v, bool do_not_canonicalize)
+void mul::do_print_latex(const print_latex & c, unsigned level) const
{
- debugmsg("mul constructor from epvector,bool",LOGLEVEL_CONSTRUCT);
- tinfo_key = TINFO_mul;
- if (do_not_canonicalize) {
- seq=v;
-#ifdef EXPAIRSEQ_USE_HASHTAB
- combine_same_terms(); // to build hashtab
-#endif // def EXPAIRSEQ_USE_HASHTAB
- } else {
- construct_from_epvector(v);
- }
- GINAC_ASSERT(is_canonical());
+ 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 {
+
+ // 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;
+ }
+ }
+
+ if (precedence() <= level)
+ c.s << ")}";
}
-*/
-mul::mul(epvector const & v)
+void mul::do_print_csrc(const print_csrc & c, unsigned level) const
{
- debugmsg("mul constructor from epvector",LOGLEVEL_CONSTRUCT);
- tinfo_key = TINFO_mul;
- overall_coeff=exONE();
- construct_from_epvector(v);
- GINAC_ASSERT(is_canonical());
+ if (precedence() <= level)
+ c.s << "(";
+
+ if (!overall_coeff.is_equal(_ex1)) {
+ if (overall_coeff.is_equal(_ex_1))
+ c.s << "-";
+ else {
+ overall_coeff.print(c, precedence());
+ c.s << "*";
+ }
+ }
+
+ // Print arguments, separated by "*" or "/"
+ 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>"
+ 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.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 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 (it->coeff.info(info_flags::negint))
+ c.s << "/";
+ else
+ c.s << "*";
+ }
+ }
+
+ if (precedence() <= level)
+ c.s << ")";
}
-mul::mul(epvector const & v, ex const & oc)
+void mul::do_print_python_repr(const print_python_repr & c, unsigned level) const
{
- debugmsg("mul constructor from epvector,ex",LOGLEVEL_CONSTRUCT);
- tinfo_key = TINFO_mul;
- overall_coeff=oc;
- construct_from_epvector(v);
- GINAC_ASSERT(is_canonical());
+ c.s << class_name() << '(';
+ op(0).print(c);
+ for (size_t i=1; i<nops(); ++i) {
+ c.s << ',';
+ op(i).print(c);
+ }
+ c.s << ')';
}
-mul::mul(epvector * vp, ex const & oc)
+bool mul::info(unsigned inf) const
{
- debugmsg("mul constructor 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());
+ switch (inf) {
+ case info_flags::polynomial:
+ case info_flags::integer_polynomial:
+ case info_flags::cinteger_polynomial:
+ case info_flags::rational_polynomial:
+ case info_flags::crational_polynomial:
+ case info_flags::rational_function: {
+ 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: {
+ 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;
+ }
+ }
+ return inherited::info(inf);
}
-mul::mul(ex const & lh, ex const & mh, ex const & rh)
+int mul::degree(const ex & s) const
{
- debugmsg("mul constructor 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=exONE();
- construct_from_exvector(factors);
- GINAC_ASSERT(is_canonical());
+ // Sum up degrees of factors
+ int deg_sum = 0;
+ epvector::const_iterator i = seq.begin(), end = seq.end();
+ while (i != end) {
+ if (ex_to<numeric>(i->coeff).is_integer())
+ deg_sum += recombine_pair_to_ex(*i).degree(s);
+ else {
+ if (i->rest.has(s))
+ throw std::runtime_error("mul::degree() undefined degree because of non-integer exponent");
+ }
+ ++i;
+ }
+ return deg_sum;
}
-//////////
-// functions overriding virtual functions from bases classes
-//////////
+int mul::ldegree(const ex & s) const
+{
+ // Sum up degrees of factors
+ int deg_sum = 0;
+ epvector::const_iterator i = seq.begin(), end = seq.end();
+ while (i != end) {
+ if (ex_to<numeric>(i->coeff).is_integer())
+ deg_sum += recombine_pair_to_ex(*i).ldegree(s);
+ else {
+ if (i->rest.has(s))
+ throw std::runtime_error("mul::ldegree() undefined degree because of non-integer exponent");
+ }
+ ++i;
+ }
+ return deg_sum;
+}
-// public
+ex mul::coeff(const ex & s, int n) const
+{
+ exvector coeffseq;
+ coeffseq.reserve(seq.size()+1);
+
+ 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 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 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);
+ }
+ ++i;
+ }
+ if (coeff_found) {
+ coeffseq.push_back(overall_coeff);
+ return (new mul(coeffseq))->setflag(status_flags::dynallocated);
+ }
+
+ return _ex0;
+}
-basic * mul::duplicate() const
+/** 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
{
- debugmsg("mul duplicate",LOGLEVEL_ASSIGNMENT);
- return new mul(*this);
+ std::auto_ptr<epvector> evaled_seqp = evalchildren(level);
+ if (evaled_seqp.get()) {
+ // do more evaluation later
+ return (new mul(evaled_seqp, overall_coeff))->
+ setflag(status_flags::dynallocated);
+ }
+
+#ifdef DO_GINAC_ASSERT
+ 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(*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));
+ return *this;
+ }
+
+ size_t seq_size = seq.size();
+ if (overall_coeff.is_zero()) {
+ // *(...,x;0) -> 0
+ return _ex0;
+ } else if (seq_size==0) {
+ // *(;c) -> c
+ return overall_coeff;
+ } 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_exactly_a<add>((*seq.begin()).rest) &&
+ ex_to<numeric>((*seq.begin()).coeff).is_equal(*_num1_p)) {
+ // *(+(x,y,...);c) -> +(*(x,c),*(y,c),...) (c numeric(), no powers of +())
+ 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)))
+ )->setflag(status_flags::dynallocated | status_flags::evaluated);
+ } else if ((seq_size >= 2) && (! (flags & status_flags::expanded))) {
+ // Strip the content and the unit part from each term. Thus
+ // things like (-x+a)*(3*x-3*a) automagically turn into - 3*(x-a)2
+
+ epvector::const_iterator last = seq.end();
+ epvector::const_iterator i = seq.begin();
+ epvector::const_iterator j = seq.begin();
+ std::auto_ptr<epvector> s(new epvector);
+ numeric oc = *_num1_p;
+ bool something_changed = false;
+ while (i!=last) {
+ if (likely(! (is_a<add>(i->rest) && i->coeff.is_equal(_ex1)))) {
+ // power::eval has such a rule, no need to handle powers here
+ ++i;
+ continue;
+ }
+
+ // XXX: What is the best way to check if the polynomial is a primitive?
+ numeric c = i->rest.integer_content();
+ const numeric& lead_coeff =
+ ex_to<numeric>(ex_to<add>(i->rest).seq.begin()->coeff).div_dyn(c);
+ const bool canonicalizable = lead_coeff.is_integer();
+
+ // XXX: The main variable is chosen in a random way, so this code
+ // does NOT transform the term into the canonical form (thus, in some
+ // very unlucky event it can even loop forever). Hopefully the main
+ // variable will be the same for all terms in *this
+ const bool unit_normal = lead_coeff.is_pos_integer();
+ if (likely((c == *_num1_p) && ((! canonicalizable) || unit_normal))) {
+ ++i;
+ continue;
+ }
+
+ if (! something_changed) {
+ s->reserve(seq_size);
+ something_changed = true;
+ }
+
+ while ((j!=i) && (j!=last)) {
+ s->push_back(*j);
+ ++j;
+ }
+
+ if (! unit_normal)
+ c = c.mul(*_num_1_p);
+
+ oc = oc.mul(c);
+
+ // divide add by the number in place to save at least 2 .eval() calls
+ const add& addref = ex_to<add>(i->rest);
+ add* primitive = new add(addref);
+ primitive->setflag(status_flags::dynallocated);
+ primitive->clearflag(status_flags::hash_calculated);
+ primitive->overall_coeff = ex_to<numeric>(primitive->overall_coeff).div_dyn(c);
+ for (epvector::iterator ai = primitive->seq.begin();
+ ai != primitive->seq.end(); ++ai)
+ ai->coeff = ex_to<numeric>(ai->coeff).div_dyn(c);
+
+ s->push_back(expair(*primitive, _ex1));
+
+ ++i;
+ ++j;
+ }
+ if (something_changed) {
+ while (j!=last) {
+ s->push_back(*j);
+ ++j;
+ }
+ return (new mul(s, ex_to<numeric>(overall_coeff).mul_dyn(oc))
+ )->setflag(status_flags::dynallocated);
+ }
+ }
+
+ return this->hold();
}
-bool mul::info(unsigned inf) const
+ex mul::evalf(int level) const
{
- // TODO: optimize
- if (inf==info_flags::polynomial || inf==info_flags::integer_polynomial || inf==info_flags::rational_polynomial || inf==info_flags::rational_function) {
- for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
- if (!(recombine_pair_to_ex(*it).info(inf)))
- return false;
- }
- return true;
- } else {
- return expairseq::info(inf);
- }
-}
-
-typedef vector<int> intvector;
-
-int mul::degree(symbol const & s) const
-{
- int deg_sum=0;
- for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
- deg_sum+=(*cit).rest.degree(s) * ex_to_numeric((*cit).coeff).to_int();
- }
- return deg_sum;
-}
-
-int mul::ldegree(symbol const & s) const
-{
- int deg_sum=0;
- for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
- deg_sum+=(*cit).rest.ldegree(s) * ex_to_numeric((*cit).coeff).to_int();
- }
- return deg_sum;
-}
-
-ex mul::coeff(symbol const & s, int const n) const
-{
- exvector coeffseq;
- coeffseq.reserve(seq.size()+1);
-
- 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;
- }
- 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);
- if (!c.is_zero()) {
- coeffseq.push_back(c);
- coeff_found=1;
- } else {
- coeffseq.push_back(t);
- }
- ++it;
- }
- if (coeff_found) {
- coeffseq.push_back(overall_coeff);
- return (new mul(coeffseq))->setflag(status_flags::dynallocated);
- }
-
- return exZERO();
+ if (level==1)
+ return mul(seq,overall_coeff);
+
+ if (level==-max_recursion_level)
+ throw(std::runtime_error("max recursion level reached"));
+
+ std::auto_ptr<epvector> s(new epvector);
+ s->reserve(seq.size());
+
+ --level;
+ 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));
}
-ex mul::eval(int level) const
+void mul::find_real_imag(ex & rp, ex & ip) const
{
- // simplifications *(...,x;0) -> 0
- // *(+(x,y,...);c) -> *(+(*(x,c),*(y,c),...)) (c numeric())
- // *(x;1) -> x
- // *(;c) -> c
+ rp = overall_coeff.real_part();
+ ip = overall_coeff.imag_part();
+ for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
+ ex factor = recombine_pair_to_ex(*i);
+ ex new_rp = factor.real_part();
+ ex new_ip = factor.imag_part();
+ if(new_ip.is_zero()) {
+ rp *= new_rp;
+ ip *= new_rp;
+ } else {
+ ex temp = rp*new_rp - ip*new_ip;
+ ip = ip*new_rp + rp*new_ip;
+ rp = temp;
+ }
+ }
+ rp = rp.expand();
+ ip = ip.expand();
+}
- debugmsg("mul eval",LOGLEVEL_MEMBER_FUNCTION);
+ex mul::real_part() const
+{
+ ex rp, ip;
+ find_real_imag(rp, ip);
+ return rp;
+}
- epvector * evaled_seqp=evalchildren(level);
- if (evaled_seqp!=0) {
- // do more evaluation later
- return (new mul(evaled_seqp,overall_coeff))->
- setflag(status_flags::dynallocated);
- }
+ex mul::imag_part() const
+{
+ ex rp, ip;
+ find_real_imag(rp, ip);
+ return ip;
+}
-#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_numeric_with_coeff_1()));
- if (is_ex_exactly_of_type(recombine_pair_to_ex(*cit),numeric)) {
- printtree(cerr,0);
- }
- GINAC_ASSERT(!is_ex_exactly_of_type(recombine_pair_to_ex(*cit),numeric));
- /* 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));
- /* end paranoia */
- }
-#endif // def DO_GINAC_ASSERT
+ex mul::evalm() const
+{
+ // 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);
+}
- if (flags & status_flags::evaluated) {
- GINAC_ASSERT(seq.size()>0);
- GINAC_ASSERT((seq.size()>1)||!overall_coeff.is_equal(exONE()));
- return *this;
- }
-
- int seq_size=seq.size();
- if (overall_coeff.is_equal(exZERO())) {
- // *(...,x;0) -> 0
- return exZERO();
- } else if (seq_size==0) {
- // *(;c) -> c
- return overall_coeff;
- } else if ((seq_size==1)&&overall_coeff.is_equal(exONE())) {
- // *(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(numONE())) {
- // *(+(x,y,...);c) -> +(*(x,c),*(y,c),...) (c numeric(), no powers of +())
- add const & 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));
- }
- return (new add(distrseq,
- ex_to_numeric(addref.overall_coeff).
- mul_dyn(ex_to_numeric(overall_coeff))))
- ->setflag(status_flags::dynallocated |
- status_flags::evaluated );
- }
- return this->hold();
-}
-
-exvector mul::get_indices(void) const
-{
- // return union of indices of factors
- exvector iv;
- for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
- exvector subiv=(*cit).rest.get_indices();
- iv.reserve(iv.size()+subiv.size());
- for (exvector::const_iterator cit2=subiv.begin(); cit2!=subiv.end(); ++cit2) {
- iv.push_back(*cit2);
- }
- }
- return iv;
-}
-
-ex mul::simplify_ncmul(exvector const & v) const
-{
- throw(std::logic_error("mul::simplify_ncmul() should never have been called!"));
+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);
}
-// protected
+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;
+}
-int mul::compare_same_type(basic const & other) const
+/** Checks wheter e matches to the pattern pat and the (possibly to be updated)
+ * list of replacements repls. This matching is in the sense of algebraic
+ * substitutions. Matching starts with pat.op(factor) of the pattern because
+ * the factors before this one have already been matched. The (possibly
+ * updated) number of matches is in nummatches. subsed[i] is true for factors
+ * that already have been replaced by previous substitutions and matched[i]
+ * is true for factors that have been matched by the current match.
+ */
+bool algebraic_match_mul_with_mul(const mul &e, const ex &pat, lst &repls,
+ int factor, int &nummatches, const std::vector<bool> &subsed,
+ std::vector<bool> &matched)
{
- return expairseq::compare_same_type(other);
+ if (factor == pat.nops())
+ return true;
+
+ for (size_t i=0; i<e.nops(); ++i) {
+ if(subsed[i] || matched[i])
+ continue;
+ lst newrepls = repls;
+ int newnummatches = nummatches;
+ if (tryfactsubs(e.op(i), pat.op(factor), newnummatches, newrepls)) {
+ matched[i] = true;
+ if (algebraic_match_mul_with_mul(e, pat, newrepls, factor+1,
+ newnummatches, subsed, matched)) {
+ repls = newrepls;
+ nummatches = newnummatches;
+ return true;
+ }
+ else
+ matched[i] = false;
+ }
+ }
+
+ return false;
}
-bool mul::is_equal_same_type(basic const & other) const
+bool mul::has(const ex & pattern, unsigned options) const
{
- return expairseq::is_equal_same_type(other);
+ if(!(options&has_options::algebraic))
+ return basic::has(pattern,options);
+ if(is_a<mul>(pattern)) {
+ lst repls;
+ int nummatches = std::numeric_limits<int>::max();
+ std::vector<bool> subsed(seq.size(), false);
+ std::vector<bool> matched(seq.size(), false);
+ if(algebraic_match_mul_with_mul(*this, pattern, repls, 0, nummatches,
+ subsed, matched))
+ return true;
+ }
+ return basic::has(pattern, options);
+}
+
+ex mul::algebraic_subs_mul(const exmap & m, unsigned options) const
+{
+ std::vector<bool> subsed(seq.size(), false);
+ exvector subsresult(seq.size());
+ ex divide_by = 1;
+ ex multiply_by = 1;
+
+ for (exmap::const_iterator it = m.begin(); it != m.end(); ++it) {
+
+ if (is_exactly_a<mul>(it->first)) {
+retry1:
+ int nummatches = std::numeric_limits<int>::max();
+ std::vector<bool> currsubsed(seq.size(), false);
+ lst repls;
+
+ if(!algebraic_match_mul_with_mul(*this, it->first, repls, 0, nummatches, subsed, currsubsed))
+ continue;
+
+ for (size_t j=0; j<subsed.size(); j++)
+ if (currsubsed[j])
+ subsed[j] = true;
+ ex subsed_pattern
+ = it->first.subs(ex(repls), subs_options::no_pattern);
+ divide_by *= power(subsed_pattern, nummatches);
+ ex subsed_result
+ = it->second.subs(ex(repls), subs_options::no_pattern);
+ multiply_by *= power(subsed_result, nummatches);
+ goto retry1;
+
+ } else {
+
+ for (size_t j=0; j<this->nops(); j++) {
+ int nummatches = std::numeric_limits<int>::max();
+ lst repls;
+ if (!subsed[j] && tryfactsubs(op(j), it->first, nummatches, repls)){
+ subsed[j] = true;
+ ex subsed_pattern
+ = it->first.subs(ex(repls), subs_options::no_pattern);
+ divide_by *= power(subsed_pattern, nummatches);
+ ex subsed_result
+ = it->second.subs(ex(repls), subs_options::no_pattern);
+ multiply_by *= power(subsed_result, 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);
+
+ return ((*this)/divide_by)*multiply_by;
}
-unsigned mul::return_type(void) const
+// protected
+
+/** Implementation of ex::diff() for a product. It applies the product rule.
+ * @see ex::diff */
+ex mul::derivative(const symbol & s) const
{
- if (seq.size()==0) {
- // mul without factors: should not happen, but commutes
- return return_types::commutative;
- }
+ size_t num = seq.size();
+ exvector addseq;
+ addseq.reserve(num);
+
+ // D(a*b*c) = D(a)*b*c + a*D(b)*c + a*b*D(c)
+ 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);
+}
- bool all_commutative=1;
- unsigned rt;
- epvector::const_iterator cit_noncommutative_element; // point to first found nc element
+int mul::compare_same_type(const basic & other) const
+{
+ return inherited::compare_same_type(other);
+}
- 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)) {
- // first nc element found, remember position
- cit_noncommutative_element=cit;
- all_commutative=0;
- }
- 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()) {
- // diffent types -> mul is ncc
- return return_types::noncommutative_composite;
- }
- }
- }
- // all factors checked
- return all_commutative ? return_types::commutative : return_types::noncommutative;
+unsigned mul::return_type() const
+{
+ if (seq.empty()) {
+ // mul without factors: should not happen, but commutates
+ return return_types::commutative;
+ }
+
+ bool all_commutative = true;
+ epvector::const_iterator noncommutative_element; // point to first found nc element
+
+ 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
+ noncommutative_element = i;
+ all_commutative = false;
+ }
+ if ((rt == return_types::noncommutative) && (!all_commutative)) {
+ // another nc element found, compare type_infos
+ if (noncommutative_element->rest.return_type_tinfo() != i->rest.return_type_tinfo()) {
+ // different 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
+tinfo_t mul::return_type_tinfo() const
{
- if (seq.size()==0) {
- // mul without factors: should not happen
- return tinfo_key;
- }
- // 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();
- }
- }
- // no noncommutative element found, should not happen
- return tinfo_key;
+ if (seq.empty())
+ return this; // mul without factors: should not happen
+
+ // return type_info of first noncommutative element
+ 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 this;
}
-ex mul::thisexpairseq(epvector const & v, ex const & oc) const
+ex mul::thisexpairseq(const epvector & v, const ex & oc, bool do_index_renaming) const
{
- return (new mul(v,oc))->setflag(status_flags::dynallocated);
+ return (new mul(v, oc, do_index_renaming))->setflag(status_flags::dynallocated);
}
-ex mul::thisexpairseq(epvector * vp, ex const & oc) const
+ex mul::thisexpairseq(std::auto_ptr<epvector> vp, const ex & oc, bool do_index_renaming) const
{
- return (new mul(vp,oc))->setflag(status_flags::dynallocated);
+ return (new mul(vp, oc, do_index_renaming))->setflag(status_flags::dynallocated);
}
-expair mul::split_ex_to_pair(ex const & e) const
+expair mul::split_ex_to_pair(const ex & e) const
{
- if (is_ex_exactly_of_type(e,power)) {
- power const & powerref=ex_to_power(e);
- if (is_ex_exactly_of_type(powerref.exponent,numeric)) {
- return expair(powerref.basis,powerref.exponent);
- }
- }
- return expair(e,exONE());
+ 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);
}
-
-expair mul::combine_ex_with_coeff_to_pair(ex const & e,
- ex const & c) const
+
+expair mul::combine_ex_with_coeff_to_pair(const ex & e,
+ const ex & c) const
{
- // to avoid duplication of power simplification rules,
- // we create a temporary power object
- // otherwise it would be hard to correctly simplify
- // expression like (4^(1/3))^(3/2)
- if (are_ex_trivially_equal(c,exONE())) {
- 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 evaluate
+ // expression like (4^(1/3))^(3/2)
+ if (c.is_equal(_ex1))
+ return split_ex_to_pair(e);
+
+ return split_ex_to_pair(power(e,c));
}
-
-expair mul::combine_pair_with_coeff_to_pair(expair const & p,
- ex const & c) const
+
+expair mul::combine_pair_with_coeff_to_pair(const expair & p,
+ const ex & c) const
{
- // to avoid duplication of power simplification rules,
- // we create a temporary power object
- // otherwise it would be hard to correctly simplify
- // expression like (4^(1/3))^(3/2)
- if (are_ex_trivially_equal(c,exONE())) {
- return p;
- }
- return split_ex_to_pair(power(recombine_pair_to_ex(p),c));
+ // to avoid duplication of power simplification rules,
+ // we create a temporary power object
+ // otherwise it would be hard to correctly evaluate
+ // expression like (4^(1/3))^(3/2)
+ 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(expair const & p) const
+
+ex mul::recombine_pair_to_ex(const expair & p) const
{
- // if (p.coeff.compare(exONE())==0) {
- // if (are_ex_trivially_equal(p.coeff,exONE())) {
- if (ex_to_numeric(p.coeff).is_equal(numONE())) {
- return p.rest;
- } else {
- return power(p.rest,p.coeff);
- }
+ if (ex_to<numeric>(p.coeff).is_equal(*_num1_p))
+ return p.rest;
+ else
+ 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()) {
- // 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 (!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(numONE())) {
- // combined pair has coeff 1 and must be moved to the end
- return true;
- }
- }
- return false;
+ 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_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 (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 exONE();
+ return _ex1;
}
-void mul::combine_overall_coeff(ex const & c)
+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(ex const & c1, ex const & c2)
+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(expair const & p) const
+bool mul::can_make_flat(const expair & p) const
{
- GINAC_ASSERT(is_ex_exactly_of_type(p.coeff,numeric));
- // 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(numONE());
+ 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_p);
+}
+
+bool mul::can_be_further_expanded(const ex & e)
+{
+ if (is_exactly_a<mul>(e)) {
+ for (epvector::const_iterator cit = ex_to<mul>(e).seq.begin(); cit != ex_to<mul>(e).seq.end(); ++cit) {
+ if (is_exactly_a<add>(cit->rest) && cit->coeff.info(info_flags::posint))
+ return true;
+ }
+ } else if (is_exactly_a<power>(e)) {
+ if (is_exactly_a<add>(e.op(0)) && e.op(1).info(info_flags::posint))
+ return true;
+ }
+ return false;
}
ex mul::expand(unsigned options) const
{
- exvector sub_expanded_seq;
- intvector positions_of_adds;
- intvector number_of_add_operands;
-
- epvector * expanded_seqp=expandchildren(options);
-
- epvector const & expanded_seq = expanded_seqp==0 ? seq : *expanded_seqp;
-
- positions_of_adds.resize(expanded_seq.size());
- number_of_add_operands.resize(expanded_seq.size());
-
- int number_of_adds=0;
- int number_of_expanded_terms=1;
-
- unsigned current_position=0;
- epvector::const_iterator last=expanded_seq.end();
- for (epvector::const_iterator cit=expanded_seq.begin(); cit!=last; ++cit) {
- if (is_ex_exactly_of_type((*cit).rest,add)&&
- (ex_to_numeric((*cit).coeff).is_equal(numONE()))) {
- positions_of_adds[number_of_adds]=current_position;
- add const & expanded_addref=ex_to_add((*cit).rest);
- int addref_nops=expanded_addref.nops();
- number_of_add_operands[number_of_adds]=addref_nops;
- number_of_expanded_terms *= addref_nops;
- number_of_adds++;
- }
- current_position++;
- }
-
- if (number_of_adds==0) {
- if (expanded_seqp==0) {
- return this->setflag(status_flags::expanded);
- }
- return (new mul(expanded_seqp,overall_coeff))->
- setflag(status_flags::dynallocated ||
- status_flags::expanded);
- }
-
- exvector distrseq;
- distrseq.reserve(number_of_expanded_terms);
-
- intvector k;
- k.resize(number_of_adds);
-
- int l;
- for (l=0; l<number_of_adds; l++) {
- k[l]=0;
- }
-
- while (1) {
- epvector term;
- term=expanded_seq;
- for (l=0; l<number_of_adds; l++) {
- add const & addref=ex_to_add(expanded_seq[positions_of_adds[l]].rest);
- GINAC_ASSERT(term[positions_of_adds[l]].coeff.compare(exONE())==0);
- term[positions_of_adds[l]]=split_ex_to_pair(addref.op(k[l]));
- }
- /*
- cout << "mul::expand() term begin" << endl;
- for (epvector::const_iterator cit=term.begin(); cit!=term.end(); ++cit) {
- cout << "rest" << endl;
- (*cit).rest.printtree(cout);
- cout << "coeff" << endl;
- (*cit).coeff.printtree(cout);
- }
- cout << "mul::expand() term end" << endl;
- */
- distrseq.push_back((new mul(term,overall_coeff))->
- setflag(status_flags::dynallocated |
- status_flags::expanded));
-
- // increment k[]
- l=number_of_adds-1;
- while ((l>=0)&&((++k[l])>=number_of_add_operands[l])) {
- k[l]=0;
- l--;
- }
- if (l<0) break;
- }
-
- if (expanded_seqp!=0) {
- delete expanded_seqp;
- }
- /*
- cout << "mul::expand() distrseq begin" << endl;
- for (exvector::const_iterator cit=distrseq.begin(); cit!=distrseq.end(); ++cit) {
- (*cit).printtree(cout);
- }
- cout << "mul::expand() distrseq end" << endl;
- */
-
- return (new add(distrseq))->setflag(status_flags::dynallocated |
- status_flags::expanded);
+ const bool skip_idx_rename = ! info(info_flags::has_indices);
+ // 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
+ ex last_expanded = _ex1;
+
+ epvector non_adds;
+ non_adds.reserve(expanded_seq.size());
+
+ for (epvector::const_iterator cit = expanded_seq.begin(); cit != expanded_seq.end(); ++cit) {
+ if (is_exactly_a<add>(cit->rest) &&
+ (cit->coeff.is_equal(_ex1))) {
+ 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);
+
+ exvector add1_dummy_indices, add2_dummy_indices, add_indices;
+ lst dummy_subs;
+
+ if (!skip_idx_rename) {
+ for (epvector::const_iterator i=add1begin; i!=add1end; ++i) {
+ add_indices = get_all_dummy_indices_safely(i->rest);
+ add1_dummy_indices.insert(add1_dummy_indices.end(), add_indices.begin(), add_indices.end());
+ }
+ for (epvector::const_iterator i=add2begin; i!=add2end; ++i) {
+ add_indices = get_all_dummy_indices_safely(i->rest);
+ add2_dummy_indices.insert(add2_dummy_indices.end(), add_indices.begin(), add_indices.end());
+ }
+
+ sort(add1_dummy_indices.begin(), add1_dummy_indices.end(), ex_is_less());
+ sort(add2_dummy_indices.begin(), add2_dummy_indices.end(), ex_is_less());
+ dummy_subs = rename_dummy_indices_uniquely(add1_dummy_indices, add2_dummy_indices);
+ }
+
+ // Multiply explicitly all non-numeric terms of add1 and add2:
+ for (epvector::const_iterator i2=add2begin; i2!=add2end; ++i2) {
+ // We really have to combine terms here in order to compactify
+ // the result. Otherwise it would become waayy tooo bigg.
+ numeric oc(*_num0_p);
+ epvector distrseq2;
+ distrseq2.reserve(add1.seq.size());
+ const ex i2_new = (skip_idx_rename || (dummy_subs.op(0).nops() == 0) ?
+ i2->rest :
+ i2->rest.subs(ex_to<lst>(dummy_subs.op(0)),
+ ex_to<lst>(dummy_subs.op(1)), subs_options::no_pattern));
+ for (epvector::const_iterator i1=add1begin; i1!=add1end; ++i1) {
+ // 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_new))->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 {
+ distrseq2.push_back(expair(rest, ex_to<numeric>(i1->coeff).mul_dyn(ex_to<numeric>(i2->coeff))));
+ }
+ }
+ tmp_accu += (new add(distrseq2, oc))->setflag(status_flags::dynallocated);
+ }
+ last_expanded = tmp_accu;
+ } else {
+ if (!last_expanded.is_equal(_ex1))
+ non_adds.push_back(split_ex_to_pair(last_expanded));
+ last_expanded = cit->rest;
+ }
+
+ } else {
+ non_adds.push_back(*cit);
+ }
+ }
+
+ // 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)) {
+ size_t n = last_expanded.nops();
+ exvector distrseq;
+ distrseq.reserve(n);
+ exvector va;
+ if (! skip_idx_rename) {
+ va = get_all_dummy_indices_safely(mul(non_adds));
+ sort(va.begin(), va.end(), ex_is_less());
+ }
+
+ for (size_t i=0; i<n; ++i) {
+ epvector factors = non_adds;
+ if (skip_idx_rename)
+ factors.push_back(split_ex_to_pair(last_expanded.op(i)));
+ else
+ factors.push_back(split_ex_to_pair(rename_dummy_indices_uniquely(va, last_expanded.op(i))));
+ ex term = (new mul(factors, overall_coeff))->setflag(status_flags::dynallocated);
+ if (can_be_further_expanded(term)) {
+ distrseq.push_back(term.expand());
+ } else {
+ if (options == 0)
+ ex_to<basic>(term).setflag(status_flags::expanded);
+ distrseq.push_back(term);
+ }
+ }
+
+ return ((new add(distrseq))->
+ setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)));
+ }
+
+ non_adds.push_back(split_ex_to_pair(last_expanded));
+ ex result = (new mul(non_adds, overall_coeff))->setflag(status_flags::dynallocated);
+ if (can_be_further_expanded(result)) {
+ return result.expand();
+ } else {
+ if (options == 0)
+ ex_to<basic>(result).setflag(status_flags::expanded);
+ return result;
+ }
}
+
//////////
// new virtual functions which can be overridden by derived classes
//////////
// non-virtual functions in this class
//////////
-epvector * mul::expandchildren(unsigned options) const
-{
- epvector::const_iterator last=seq.end();
- epvector::const_iterator cit=seq.begin();
- while (cit!=last) {
- ex const & factor=recombine_pair_to_ex(*cit);
- ex const & expanded_factor=factor.expand(options);
- if (!are_ex_trivially_equal(factor,expanded_factor)) {
-
- // something changed, copy seq, eval and return it
- epvector *s=new epvector;
- s->reserve(seq.size());
-
- // copy parts of seq which are known not to have changed
- epvector::const_iterator cit2=seq.begin();
- while (cit2!=cit) {
- 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)));
- ++cit2;
- }
- return s;
- }
- ++cit;
- }
-
- return 0; // nothing has changed
-}
-
-//////////
-// static member variables
-//////////
-
-// protected
-unsigned mul::precedence=50;
-
-
-//////////
-// global constants
-//////////
-
-const mul some_mul;
-type_info const & typeid_mul=typeid(some_mul);
+/** Member-wise expand the expairs representing this sequence. This must be
+ * overridden from expairseq::expandchildren() and done iteratively in order
+ * to allow for early cancallations and thus safe memory.
+ *
+ * @see mul::expand()
+ * @return pointer to epvector containing expanded representation or zero
+ * pointer, if sequence is unchanged. */
+std::auto_ptr<epvector> mul::expandchildren(unsigned options) const
+{
+ const epvector::const_iterator last = seq.end();
+ epvector::const_iterator cit = seq.begin();
+ while (cit!=last) {
+ const ex & factor = recombine_pair_to_ex(*cit);
+ const ex & expanded_factor = factor.expand(options);
+ if (!are_ex_trivially_equal(factor,expanded_factor)) {
+
+ // something changed, copy seq, eval and return it
+ std::auto_ptr<epvector> s(new epvector);
+ s->reserve(seq.size());
+
+ // copy parts of seq which are known not to have changed
+ epvector::const_iterator cit2 = seq.begin();
+ while (cit2!=cit) {
+ 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)));
+ ++cit2;
+ }
+ return s;
+ }
+ ++cit;
+ }
+
+ return std::auto_ptr<epvector>(0); // nothing has changed
+}
-#ifndef NO_GINAC_NAMESPACE
} // namespace GiNaC
-#endif // ndef NO_GINAC_NAMESPACE
git://www.ginac.de / ginac.git / blobdiff