* Implementation of GiNaC's products of expressions. */
/*
- * GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
#include "debugmsg.h"
#include "utils.h"
-#ifndef NO_NAMESPACE_GINAC
namespace GiNaC {
-#endif // ndef NO_NAMESPACE_GINAC
GINAC_IMPLEMENT_REGISTERED_CLASS(mul, expairseq)
//////////
-// default constructor, destructor, copy constructor assignment operator and helpers
+// default ctor, dctor, copy ctor assignment operator and helpers
//////////
-// public
-
mul::mul()
{
- debugmsg("mul default constructor",LOGLEVEL_CONSTRUCT);
- tinfo_key = TINFO_mul;
-}
-
-mul::~mul()
-{
- debugmsg("mul destructor",LOGLEVEL_DESTRUCT);
- destroy(0);
-}
-
-mul::mul(const mul & other)
-{
- debugmsg("mul copy constructor",LOGLEVEL_CONSTRUCT);
- copy(other);
-}
-
-const mul & mul::operator=(const mul & other)
-{
- debugmsg("mul operator=",LOGLEVEL_ASSIGNMENT);
- if (this != &other) {
- destroy(1);
- copy(other);
- }
- return *this;
+ debugmsg("mul default ctor",LOGLEVEL_CONSTRUCT);
+ tinfo_key = TINFO_mul;
}
-// protected
-
-void mul::copy(const mul & other)
-{
- inherited::copy(other);
-}
-
-void mul::destroy(bool call_parent)
-{
- if (call_parent) inherited::destroy(call_parent);
-}
+DEFAULT_COPY(mul)
+DEFAULT_DESTROY(mul)
//////////
-// other constructors
+// other ctors
//////////
// public
mul::mul(const ex & lh, const ex & rh)
{
- debugmsg("mul constructor from ex,ex",LOGLEVEL_CONSTRUCT);
- tinfo_key = TINFO_mul;
- overall_coeff=_ex1();
- construct_from_2_ex(lh,rh);
- GINAC_ASSERT(is_canonical());
+ debugmsg("mul ctor from ex,ex",LOGLEVEL_CONSTRUCT);
+ tinfo_key = TINFO_mul;
+ overall_coeff = _ex1();
+ construct_from_2_ex(lh,rh);
+ GINAC_ASSERT(is_canonical());
}
mul::mul(const exvector & v)
{
- debugmsg("mul constructor from exvector",LOGLEVEL_CONSTRUCT);
- tinfo_key = TINFO_mul;
- overall_coeff=_ex1();
- construct_from_exvector(v);
- GINAC_ASSERT(is_canonical());
+ debugmsg("mul ctor from exvector",LOGLEVEL_CONSTRUCT);
+ tinfo_key = TINFO_mul;
+ overall_coeff = _ex1();
+ construct_from_exvector(v);
+ GINAC_ASSERT(is_canonical());
}
-/*
-mul::mul(const epvector & v, bool do_not_canonicalize)
-{
- 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());
-}
-*/
-
mul::mul(const epvector & v)
{
- debugmsg("mul constructor from epvector",LOGLEVEL_CONSTRUCT);
- tinfo_key = TINFO_mul;
- overall_coeff=_ex1();
- construct_from_epvector(v);
- GINAC_ASSERT(is_canonical());
+ debugmsg("mul ctor from epvector",LOGLEVEL_CONSTRUCT);
+ tinfo_key = TINFO_mul;
+ overall_coeff = _ex1();
+ construct_from_epvector(v);
+ GINAC_ASSERT(is_canonical());
}
mul::mul(const epvector & v, const ex & oc)
{
- debugmsg("mul constructor from epvector,ex",LOGLEVEL_CONSTRUCT);
- tinfo_key = TINFO_mul;
- overall_coeff=oc;
- construct_from_epvector(v);
- GINAC_ASSERT(is_canonical());
+ 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)
{
- 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());
+ 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 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=_ex1();
- construct_from_exvector(factors);
- GINAC_ASSERT(is_canonical());
+ 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();
+ construct_from_exvector(factors);
+ GINAC_ASSERT(is_canonical());
}
//////////
// archiving
//////////
-/** Construct object from archive_node. */
-mul::mul(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
-{
- debugmsg("mul constructor from archive_node", LOGLEVEL_CONSTRUCT);
-}
-
-/** Unarchive the object. */
-ex mul::unarchive(const archive_node &n, const lst &sym_lst)
-{
- return (new mul(n, sym_lst))->setflag(status_flags::dynallocated);
-}
-
-/** Archive the object. */
-void mul::archive(archive_node &n) const
-{
- inherited::archive(n);
-}
+DEFAULT_ARCHIVING(mul)
//////////
// functions overriding virtual functions from bases classes
// public
-basic * mul::duplicate() const
-{
- debugmsg("mul duplicate",LOGLEVEL_ASSIGNMENT);
- return new mul(*this);
-}
-
-void mul::print(ostream & os, unsigned upper_precedence) 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())) {
- if (coeff.is_rational()) {
- if (coeff.is_negative())
- os << -coeff;
- else
- os << coeff;
- } else {
- if (coeff.csgn()==-1)
- (-coeff).print(os, precedence);
- else
- coeff.print(os, precedence);
- }
- os << '*';
- }
- // 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);
- }
- if (precedence<=upper_precedence) os << ")";
-}
-
-void mul::printraw(ostream & os) const
-{
- debugmsg("mul printraw",LOGLEVEL_PRINT);
-
- 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 << "),";
- }
- os << ",hash=" << hashvalue << ",flags=" << flags;
- os << ")";
-}
-
-void mul::printcsrc(ostream & os, unsigned type, unsigned upper_precedence) const
-{
- debugmsg("mul print csrc", LOGLEVEL_PRINT);
- if (precedence <= upper_precedence)
- os << "(";
-
- if (!overall_coeff.is_equal(_ex1())) {
- overall_coeff.bp->printcsrc(os,type,precedence);
- os << "*";
- }
-
- // Print arguments, separated by "*" or "/"
- epvector::const_iterator it = seq.begin();
- epvector::const_iterator 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/";
- }
-
- // 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);
- 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);
-
- // 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 << "/";
- else
- os << "*";
- }
- }
- if (precedence <= upper_precedence)
- os << ")";
+void mul::print(const print_context & c, unsigned level) const
+{
+ debugmsg("mul print", LOGLEVEL_PRINT);
+
+ if (is_of_type(c, print_tree)) {
+
+ inherited::print(c, level);
+
+ } else if (is_of_type(c, print_csrc)) {
+
+ if (precedence <= level)
+ c.s << "(";
+
+ if (!overall_coeff.is_equal(_ex1())) {
+ overall_coeff.bp->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>"
+ if (it == seq.begin() && ex_to_numeric(it->coeff).is_integer() && it->coeff.compare(_num0()) < 0) {
+ if (is_of_type(c, print_csrc_cl_N))
+ c.s << "recip(";
+ 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.print(c, precedence);
+ else {
+ // Outer parens around ex needed for broken gcc-2.95 parser:
+ (ex(power(it->rest, abs(ex_to_numeric(it->coeff))))).print(c, level);
+ }
+
+ // Separator is "/" for negative integer powers, "*" otherwise
+ ++it;
+ if (it != itend) {
+ if (ex_to_numeric(it->coeff).is_integer() && it->coeff.compare(_num0()) < 0)
+ c.s << "/";
+ else
+ c.s << "*";
+ }
+ }
+
+ if (precedence <= level)
+ c.s << ")";
+
+ } else {
+
+ if (precedence <= level)
+ c.s << "(";
+
+ bool first = true;
+
+ // First print the overall numeric coefficient
+ 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())
+ (-coeff).print(c);
+ else
+ coeff.print(c);
+ } else {
+ if (coeff.csgn() == -1)
+ (-coeff).print(c, precedence);
+ else
+ coeff.print(c, precedence);
+ }
+ c.s << '*';
+ }
+
+ // Then proceed with the remaining factors
+ epvector::const_iterator it = seq.begin(), itend = seq.end();
+ while (it != itend) {
+ if (!first) {
+ c.s << '*';
+ } else {
+ first = false;
+ }
+ recombine_pair_to_ex(*it).print(c, precedence);
+ it++;
+ }
+
+ if (precedence <= level)
+ c.s << ")";
+ }
}
bool mul::info(unsigned inf) const
{
- // TODO: optimize
- if (inf==info_flags::polynomial ||
- inf==info_flags::integer_polynomial ||
- inf==info_flags::cinteger_polynomial ||
- inf==info_flags::rational_polynomial ||
- inf==info_flags::crational_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 overall_coeff.info(inf);
- } else {
- return inherited::info(inf);
- }
-}
-
-typedef vector<int> intvector;
-
-int mul::degree(const symbol & 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(const symbol & 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(const symbol & 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 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 _ex0();
+ 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: {
+ for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
+ if (!(recombine_pair_to_ex(*i).info(inf)))
+ return false;
+ }
+ return overall_coeff.info(inf);
+ }
+ case info_flags::algebraic: {
+ for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
+ if ((recombine_pair_to_ex(*i).info(inf)))
+ return true;
+ }
+ return false;
+ }
+ }
+ return inherited::info(inf);
+}
+
+int mul::degree(const ex & s) const
+{
+ 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();
+ }
+ return deg_sum;
+}
+
+int mul::ldegree(const ex & s) const
+{
+ 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();
+ }
+ return deg_sum;
+}
+
+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 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 _ex0();
}
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) {
- // do more evaluation later
- return (new mul(evaled_seqp,overall_coeff))->
- setflag(status_flags::dynallocated);
- }
-
+ // 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) {
+ // do more evaluation later
+ 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_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 */
- }
+ 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))
+ print(print_tree(std::cerr));
+ 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
-
- if (flags & status_flags::evaluated) {
- GINAC_ASSERT(seq.size()>0);
- GINAC_ASSERT((seq.size()>1)||!overall_coeff.is_equal(_ex1()));
- return *this;
- }
-
- int seq_size=seq.size();
- if (overall_coeff.is_equal(_ex0())) {
- // *(...,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_ex_exactly_of_type((*seq.begin()).rest,add) &&
- 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));
- }
- 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;
+
+ if (flags & status_flags::evaluated) {
+ GINAC_ASSERT(seq.size()>0);
+ GINAC_ASSERT(seq.size()>1 || !overall_coeff.is_equal(_ex1()));
+ return *this;
+ }
+
+ int seq_size = seq.size();
+ if (overall_coeff.is_equal(_ex0())) {
+ // *(...,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_ex_exactly_of_type((*seq.begin()).rest,add) &&
+ 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));
+ }
+ 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();
+}
+
+ex mul::evalf(int level) const
+{
+ if (level==1)
+ return mul(seq,overall_coeff);
+
+ if (level==-max_recursion_level)
+ throw(std::runtime_error("max recursion level reached"));
+
+ epvector s;
+ 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));
+ }
+ return mul(s,overall_coeff.evalf(level));
}
ex mul::simplify_ncmul(const exvector & v) const
{
- throw(std::logic_error("mul::simplify_ncmul() should never have been called!"));
+ throw(std::logic_error("mul::simplify_ncmul() should never have been called!"));
}
// protected
+/** Implementation of ex::diff() for a product. It applies the product rule.
+ * @see ex::diff */
+ex mul::derivative(const symbol & s) const
+{
+ exvector addseq;
+ addseq.reserve(seq.size());
+
+ // 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));
+ }
+ return (new add(addseq))->setflag(status_flags::dynallocated);
+}
+
int mul::compare_same_type(const basic & other) const
{
- return inherited::compare_same_type(other);
+ return inherited::compare_same_type(other);
}
bool mul::is_equal_same_type(const basic & other) const
{
- return inherited::is_equal_same_type(other);
+ return inherited::is_equal_same_type(other);
}
unsigned mul::return_type(void) const
{
- if (seq.size()==0) {
- // 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
-
- 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;
+ if (seq.size()==0) {
+ // 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
+
+ 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_tinfo(void) 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.size()==0)
+ 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();
+ }
+ // 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
{
- 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)) {
- return expair(powerref.basis,powerref.exponent);
- }
- }
- return expair(e,_ex1());
+ if (is_ex_exactly_of_type(e,power)) {
+ const power & powerref = ex_to_power(e);
+ if (is_ex_exactly_of_type(powerref.exponent,numeric))
+ return expair(powerref.basis,powerref.exponent);
+ }
+ return expair(e,_ex1());
}
-
+
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,_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
+ // expression like (4^(1/3))^(3/2)
+ if (are_ex_trivially_equal(c,_ex1()))
+ return split_ex_to_pair(e);
+
+ return split_ex_to_pair(power(e,c));
}
-
+
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,_ex1())) {
- 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 simplify
+ // expression like (4^(1/3))^(3/2)
+ if (are_ex_trivially_equal(c,_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 (p.coeff.compare(_ex1())==0) {
- // if (are_ex_trivially_equal(p.coeff,_ex1())) {
- if (ex_to_numeric(p.coeff).is_equal(_num1())) {
- return p.rest;
- } else {
- return power(p.rest,p.coeff);
- }
+ if (ex_to_numeric(p.coeff).is_equal(_num1()))
+ return p.rest;
+ else
+ return power(p.rest,p.coeff);
}
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(_num1())) {
- // combined pair has coeff 1 and must be moved to the end
- return true;
- }
- }
- return false;
+ 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(_num1())) {
+ // combined pair has coeff 1 and must be moved to the end
+ return true;
+ }
+ }
+ return false;
}
ex mul::default_overall_coeff(void) 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_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));
}
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_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)));
}
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(_num1());
+ 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(_num1());
}
ex mul::expand(unsigned options) const
{
- exvector sub_expanded_seq;
- intvector positions_of_adds;
- intvector number_of_add_operands;
-
- epvector * expanded_seqp=expandchildren(options);
-
- const epvector & 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(_num1()))) {
- positions_of_adds[number_of_adds]=current_position;
- const add & expanded_addref=ex_to_add((*cit).rest);
- unsigned 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++) {
- const add & addref=ex_to_add(expanded_seq[positions_of_adds[l]].rest);
- GINAC_ASSERT(term[positions_of_adds[l]].coeff.compare(_ex1())==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);
-}
-
+ 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;
+
+ int number_of_adds = 0;
+ 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()))) {
+ ++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));
+ }
+ }
+ last_expanded = (new add(distrseq))->setflag(status_flags::dynallocated | status_flags::expanded);
+ } else {
+ non_adds.push_back(split_ex_to_pair(last_expanded));
+ 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);
+ exvector distrseq;
+ int n = finaladd.nops();
+ distrseq.reserve(n);
+ for (int 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));
+ }
+ return ((new add(distrseq))->
+ setflag(status_flags::dynallocated | status_flags::expanded));
+ }
+ non_adds.push_back(split_ex_to_pair(last_expanded));
+ return (new mul(non_adds,overall_coeff))->
+ setflag(status_flags::dynallocated | status_flags::expanded);
+}
+
+
//////////
// new virtual functions which can be overridden by derived classes
//////////
// non-virtual functions in this class
//////////
+
+/** 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. */
epvector * mul::expandchildren(unsigned options) 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
- 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
+ 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
+ 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;
-const type_info & typeid_mul=typeid(some_mul);
+unsigned mul::precedence = 50;
-#ifndef NO_NAMESPACE_GINAC
} // namespace GiNaC
-#endif // ndef NO_NAMESPACE_GINAC
git://www.ginac.de / ginac.git / blobdiff