* Implementation of GiNaC's non-commutative products of expressions. */
/*
- * GiNaC Copyright (C) 1999-2000 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
#include "ex.h"
#include "add.h"
#include "mul.h"
+#include "matrix.h"
#include "archive.h"
-#include "debugmsg.h"
#include "utils.h"
-#ifndef NO_GINAC_NAMESPACE
namespace GiNaC {
-#endif // ndef NO_GINAC_NAMESPACE
-GINAC_IMPLEMENT_REGISTERED_CLASS(ncmul, exprseq)
+GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(ncmul, exprseq,
+ print_func<print_context>(&ncmul::do_print).
+ print_func<print_tree>(&basic::do_print_tree).
+ print_func<print_csrc>(&ncmul::do_print_csrc).
+ print_func<print_python_repr>(&ncmul::do_print_csrc))
+
//////////
-// default constructor, destructor, copy constructor assignment operator and helpers
+// default constructor
//////////
-// public
-
ncmul::ncmul()
{
- debugmsg("ncmul default constructor",LOGLEVEL_CONSTRUCT);
- tinfo_key = TINFO_ncmul;
-}
-
-ncmul::~ncmul()
-{
- debugmsg("ncmul destructor",LOGLEVEL_DESTRUCT);
- destroy(0);
-}
-
-ncmul::ncmul(const ncmul & other)
-{
- debugmsg("ncmul copy constructor",LOGLEVEL_CONSTRUCT);
- copy(other);
-}
-
-const ncmul & ncmul::operator=(const ncmul & other)
-{
- debugmsg("ncmul operator=",LOGLEVEL_ASSIGNMENT);
- if (this != &other) {
- destroy(1);
- copy(other);
- }
- return *this;
-}
-
-// protected
-
-void ncmul::copy(const ncmul & other)
-{
- inherited::copy(other);
-}
-
-void ncmul::destroy(bool call_parent)
-{
- if (call_parent) inherited::destroy(call_parent);
+ tinfo_key = TINFO_ncmul;
}
//////////
// public
-ncmul::ncmul(const ex & lh, const ex & rh) :
- inherited(lh,rh)
+ncmul::ncmul(const ex & lh, const ex & rh) : inherited(lh,rh)
{
- debugmsg("ncmul constructor from ex,ex",LOGLEVEL_CONSTRUCT);
- tinfo_key = TINFO_ncmul;
+ tinfo_key = TINFO_ncmul;
}
-ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3) :
- inherited(f1,f2,f3)
+ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3) : inherited(f1,f2,f3)
{
- debugmsg("ncmul constructor from 3 ex",LOGLEVEL_CONSTRUCT);
- tinfo_key = TINFO_ncmul;
+ tinfo_key = TINFO_ncmul;
}
ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
- const ex & f4) : inherited(f1,f2,f3,f4)
+ const ex & f4) : inherited(f1,f2,f3,f4)
{
- debugmsg("ncmul constructor from 4 ex",LOGLEVEL_CONSTRUCT);
- tinfo_key = TINFO_ncmul;
+ tinfo_key = TINFO_ncmul;
}
ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
- const ex & f4, const ex & f5) : inherited(f1,f2,f3,f4,f5)
+ const ex & f4, const ex & f5) : inherited(f1,f2,f3,f4,f5)
{
- debugmsg("ncmul constructor from 5 ex",LOGLEVEL_CONSTRUCT);
- tinfo_key = TINFO_ncmul;
+ tinfo_key = TINFO_ncmul;
}
ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
- const ex & f4, const ex & f5, const ex & f6) :
- inherited(f1,f2,f3,f4,f5,f6)
+ const ex & f4, const ex & f5, const ex & f6) : inherited(f1,f2,f3,f4,f5,f6)
{
- debugmsg("ncmul constructor from 6 ex",LOGLEVEL_CONSTRUCT);
- tinfo_key = TINFO_ncmul;
+ tinfo_key = TINFO_ncmul;
}
ncmul::ncmul(const exvector & v, bool discardable) : inherited(v,discardable)
{
- debugmsg("ncmul constructor from exvector,bool",LOGLEVEL_CONSTRUCT);
- tinfo_key = TINFO_ncmul;
+ tinfo_key = TINFO_ncmul;
}
-ncmul::ncmul(exvector * vp) : inherited(vp)
+ncmul::ncmul(std::auto_ptr<exvector> vp) : inherited(vp)
{
- debugmsg("ncmul constructor from exvector *",LOGLEVEL_CONSTRUCT);
- tinfo_key = TINFO_ncmul;
+ tinfo_key = TINFO_ncmul;
}
//////////
// archiving
//////////
-/** Construct object from archive_node. */
-ncmul::ncmul(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
-{
- debugmsg("ncmul constructor from archive_node", LOGLEVEL_CONSTRUCT);
-}
-
-/** Unarchive the object. */
-ex ncmul::unarchive(const archive_node &n, const lst &sym_lst)
-{
- return (new ncmul(n, sym_lst))->setflag(status_flags::dynallocated);
-}
-
-/** Archive the object. */
-void ncmul::archive(archive_node &n) const
-{
- inherited::archive(n);
-}
-
-
+DEFAULT_ARCHIVING(ncmul)
+
//////////
-// functions overriding virtual functions from bases classes
+// functions overriding virtual functions from base classes
//////////
// public
-basic * ncmul::duplicate() const
-{
- debugmsg("ncmul duplicate",LOGLEVEL_ASSIGNMENT);
- return new ncmul(*this);
-}
-
-void ncmul::print(ostream & os, unsigned upper_precedence) const
+void ncmul::do_print(const print_context & c, unsigned level) const
{
- debugmsg("ncmul print",LOGLEVEL_PRINT);
- printseq(os,'(','%',')',precedence,upper_precedence);
+ printseq(c, '(', '*', ')', precedence(), level);
}
-void ncmul::printraw(ostream & os) const
+void ncmul::do_print_csrc(const print_context & c, unsigned level) const
{
- debugmsg("ncmul printraw",LOGLEVEL_PRINT);
-
- os << "%(";
- for (exvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
- (*it).bp->printraw(os);
- os << ",";
- }
- os << ",hash=" << hashvalue << ",flags=" << flags;
- os << ")";
-}
-
-void ncmul::printcsrc(ostream & os, unsigned upper_precedence) const
-{
- debugmsg("ncmul print csrc",LOGLEVEL_PRINT);
- exvector::const_iterator it;
- exvector::const_iterator itend = seq.end()-1;
- os << "ncmul(";
- for (it=seq.begin(); it!=itend; ++it) {
- (*it).bp->printcsrc(os,precedence);
- os << ",";
- }
- (*it).bp->printcsrc(os,precedence);
- os << ")";
+ c.s << class_name();
+ printseq(c, '(', ',', ')', precedence(), precedence());
}
bool ncmul::info(unsigned inf) const
{
- throw(std::logic_error("which flags have to be implemented in ncmul::info()?"));
+ return inherited::info(inf);
}
-typedef vector<int> intvector;
+typedef std::vector<int> intvector;
ex ncmul::expand(unsigned options) const
{
- exvector sub_expanded_seq;
- intvector positions_of_adds;
- intvector number_of_add_operands;
-
- exvector expanded_seq=expandchildren(options);
-
- 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;
- exvector::const_iterator last=expanded_seq.end();
- for (exvector::const_iterator cit=expanded_seq.begin(); cit!=last; ++cit) {
- if (is_ex_exactly_of_type((*cit),add)) {
- positions_of_adds[number_of_adds]=current_position;
- const add & expanded_addref=ex_to_add(*cit);
- number_of_add_operands[number_of_adds]=expanded_addref.seq.size();
- number_of_expanded_terms *= expanded_addref.seq.size();
- number_of_adds++;
- }
- current_position++;
- }
-
- if (number_of_adds==0) {
- return (new ncmul(expanded_seq,1))->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) {
- exvector term;
- term=expanded_seq;
- for (l=0; l<number_of_adds; l++) {
- GINAC_ASSERT(is_ex_exactly_of_type(expanded_seq[positions_of_adds[l]],add));
- const add & addref=ex_to_add(expanded_seq[positions_of_adds[l]]);
- term[positions_of_adds[l]]=addref.recombine_pair_to_ex(addref.seq[k[l]]);
- }
- distrseq.push_back((new ncmul(term,1))->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;
- }
-
- return (new add(distrseq))->setflag(status_flags::dynallocated |
- status_flags::expanded);
-}
-
-int ncmul::degree(const symbol & s) const
-{
- int deg_sum=0;
- for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
- deg_sum+=(*cit).degree(s);
- }
- return deg_sum;
-}
-
-int ncmul::ldegree(const symbol & s) const
-{
- int deg_sum=0;
- for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
- deg_sum+=(*cit).ldegree(s);
- }
- return deg_sum;
-}
-
-ex ncmul::coeff(const symbol & s, int n) const
-{
- exvector coeffseq;
- coeffseq.reserve(seq.size());
-
- if (n==0) {
- // product of individual coeffs
- // if a non-zero power of s is found, the resulting product will be 0
- exvector::const_iterator it=seq.begin();
- while (it!=seq.end()) {
- coeffseq.push_back((*it).coeff(s,n));
- ++it;
- }
- return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
- }
-
- exvector::const_iterator it=seq.begin();
- bool coeff_found=0;
- while (it!=seq.end()) {
- ex c=(*it).coeff(s,n);
- if (!c.is_zero()) {
- coeffseq.push_back(c);
- coeff_found=1;
- } else {
- coeffseq.push_back(*it);
- }
- ++it;
- }
-
- if (coeff_found) return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
-
- return _ex0();
-}
-
-unsigned ncmul::count_factors(const ex & e) const
-{
- if ((is_ex_exactly_of_type(e,mul)&&(e.return_type()!=return_types::commutative))||
- (is_ex_exactly_of_type(e,ncmul))) {
- unsigned factors=0;
- for (unsigned i=0; i<e.nops(); i++)
- factors += count_factors(e.op(i));
-
- return factors;
- }
- return 1;
-}
-
+ // First, expand the children
+ exvector expanded_seq = expandchildren(options);
+
+ // Now, look for all the factors that are sums and remember their
+ // position and number of terms.
+ intvector positions_of_adds(expanded_seq.size());
+ intvector number_of_add_operands(expanded_seq.size());
+
+ size_t number_of_adds = 0;
+ size_t number_of_expanded_terms = 1;
+
+ size_t current_position = 0;
+ exvector::const_iterator last = expanded_seq.end();
+ for (exvector::const_iterator cit=expanded_seq.begin(); cit!=last; ++cit) {
+ if (is_exactly_a<add>(*cit)) {
+ positions_of_adds[number_of_adds] = current_position;
+ size_t num_ops = cit->nops();
+ number_of_add_operands[number_of_adds] = num_ops;
+ number_of_expanded_terms *= num_ops;
+ number_of_adds++;
+ }
+ ++current_position;
+ }
+
+ // If there are no sums, we are done
+ if (number_of_adds == 0)
+ return (new ncmul(expanded_seq, true))->
+ setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
+
+ // Now, form all possible products of the terms of the sums with the
+ // remaining factors, and add them together
+ exvector distrseq;
+ distrseq.reserve(number_of_expanded_terms);
+
+ intvector k(number_of_adds);
+
+ while (true) {
+ exvector term = expanded_seq;
+ for (size_t i=0; i<number_of_adds; i++)
+ term[positions_of_adds[i]] = expanded_seq[positions_of_adds[i]].op(k[i]);
+ distrseq.push_back((new ncmul(term, true))->
+ setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)));
+
+ // increment k[]
+ int l = number_of_adds-1;
+ while ((l>=0) && ((++k[l]) >= number_of_add_operands[l])) {
+ k[l] = 0;
+ l--;
+ }
+ if (l<0)
+ break;
+ }
+
+ return (new add(distrseq))->
+ setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
+}
+
+int ncmul::degree(const ex & s) const
+{
+ // Sum up degrees of factors
+ int deg_sum = 0;
+ exvector::const_iterator i = seq.begin(), end = seq.end();
+ while (i != end) {
+ deg_sum += i->degree(s);
+ ++i;
+ }
+ return deg_sum;
+}
+
+int ncmul::ldegree(const ex & s) const
+{
+ // Sum up degrees of factors
+ int deg_sum = 0;
+ exvector::const_iterator i = seq.begin(), end = seq.end();
+ while (i != end) {
+ deg_sum += i->degree(s);
+ ++i;
+ }
+ return deg_sum;
+}
+
+ex ncmul::coeff(const ex & s, int n) const
+{
+ exvector coeffseq;
+ coeffseq.reserve(seq.size());
+
+ if (n == 0) {
+ // product of individual coeffs
+ // if a non-zero power of s is found, the resulting product will be 0
+ exvector::const_iterator it=seq.begin();
+ while (it!=seq.end()) {
+ coeffseq.push_back((*it).coeff(s,n));
+ ++it;
+ }
+ return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
+ }
+
+ exvector::const_iterator i = seq.begin(), end = seq.end();
+ bool coeff_found = false;
+ while (i != end) {
+ ex c = i->coeff(s,n);
+ if (c.is_zero()) {
+ coeffseq.push_back(*i);
+ } else {
+ coeffseq.push_back(c);
+ coeff_found = true;
+ }
+ ++i;
+ }
+
+ if (coeff_found) return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
+
+ return _ex0;
+}
+
+size_t ncmul::count_factors(const ex & e) const
+{
+ if ((is_exactly_a<mul>(e)&&(e.return_type()!=return_types::commutative))||
+ (is_exactly_a<ncmul>(e))) {
+ size_t factors=0;
+ for (size_t i=0; i<e.nops(); i++)
+ factors += count_factors(e.op(i));
+
+ return factors;
+ }
+ return 1;
+}
+
void ncmul::append_factors(exvector & v, const ex & e) const
{
- if ((is_ex_exactly_of_type(e,mul)&&(e.return_type()!=return_types::commutative))||
- (is_ex_exactly_of_type(e,ncmul))) {
- for (unsigned i=0; i<e.nops(); i++)
- append_factors(v,e.op(i));
-
- return;
- }
- v.push_back(e);
-}
-
-typedef vector<unsigned> unsignedvector;
-typedef vector<exvector> exvectorvector;
-
+ if ((is_exactly_a<mul>(e)&&(e.return_type()!=return_types::commutative))||
+ (is_exactly_a<ncmul>(e))) {
+ for (size_t i=0; i<e.nops(); i++)
+ append_factors(v, e.op(i));
+ } else
+ v.push_back(e);
+}
+
+typedef std::vector<unsigned> unsignedvector;
+typedef std::vector<exvector> exvectorvector;
+
+/** 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.
+ * - ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) -> ncmul(...,x1,x2,...,x3,x4,...) (associativity)
+ * - ncmul(x) -> x
+ * - ncmul() -> 1
+ * - ncmul(...,c1,...,c2,...) -> *(c1,c2,ncmul(...)) (pull out commutative elements)
+ * - ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2)) (collect elements of same type)
+ * - ncmul(x1,x2,x3,...) -> x::eval_ncmul(x1,x2,x3,...)
+ *
+ * @param level cut-off in recursive evaluation */
ex ncmul::eval(int level) const
{
- // simplifications: ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) ->
- // ncmul(...,x1,x2,...,x3,x4,...) (associativity)
- // ncmul(x) -> x
- // ncmul() -> 1
- // ncmul(...,c1,...,c2,...) ->
- // *(c1,c2,ncmul(...)) (pull out commutative elements)
- // ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))
- // (collect elements of same type)
- // ncmul(x1,x2,x3,...) -> x::eval_ncmul(x1,x2,x3,...)
- // the following rule would be nice, but produces a recursion,
- // which must be trapped by introducing a flag that the sub-ncmuls()
- // are already evaluated (maybe later...)
- // ncmul(x1,x2,...,X,y1,y2,...) ->
- // ncmul(ncmul(x1,x2,...),X,ncmul(y1,y2,...)
- // (X noncommutative_composite)
-
- if ((level==1)&&(flags & status_flags::evaluated)) {
- return *this;
- }
-
- exvector evaledseq=evalchildren(level);
-
- // ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) ->
- // ncmul(...,x1,x2,...,x3,x4,...) (associativity)
- unsigned factors=0;
- for (exvector::const_iterator cit=evaledseq.begin(); cit!=evaledseq.end(); ++cit) {
- factors += count_factors(*cit);
- }
-
- exvector assocseq;
- assocseq.reserve(factors);
- for (exvector::const_iterator cit=evaledseq.begin(); cit!=evaledseq.end(); ++cit) {
- append_factors(assocseq,*cit);
- }
-
- // ncmul(x) -> x
- if (assocseq.size()==1) return *(seq.begin());
-
- // ncmul() -> 1
- if (assocseq.size()==0) return _ex1();
-
- // determine return types
- unsignedvector rettypes;
- rettypes.reserve(assocseq.size());
- unsigned i=0;
- unsigned count_commutative=0;
- unsigned count_noncommutative=0;
- unsigned count_noncommutative_composite=0;
- for (exvector::const_iterator cit=assocseq.begin(); cit!=assocseq.end(); ++cit) {
- switch (rettypes[i]=(*cit).return_type()) {
- case return_types::commutative:
- count_commutative++;
- break;
- case return_types::noncommutative:
- count_noncommutative++;
- break;
- case return_types::noncommutative_composite:
- count_noncommutative_composite++;
- break;
- default:
- throw(std::logic_error("ncmul::eval(): invalid return type"));
- }
- ++i;
- }
- GINAC_ASSERT(count_commutative+count_noncommutative+count_noncommutative_composite==assocseq.size());
-
- // ncmul(...,c1,...,c2,...) ->
- // *(c1,c2,ncmul(...)) (pull out commutative elements)
- if (count_commutative!=0) {
- exvector commutativeseq;
- commutativeseq.reserve(count_commutative+1);
- exvector noncommutativeseq;
- noncommutativeseq.reserve(assocseq.size()-count_commutative);
- for (i=0; i<assocseq.size(); ++i) {
- if (rettypes[i]==return_types::commutative) {
- commutativeseq.push_back(assocseq[i]);
- } else {
- noncommutativeseq.push_back(assocseq[i]);
- }
- }
- commutativeseq.push_back((new ncmul(noncommutativeseq,1))->
- setflag(status_flags::dynallocated));
- return (new mul(commutativeseq))->setflag(status_flags::dynallocated);
- }
-
- // ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))
- // (collect elements of same type)
-
- if (count_noncommutative_composite==0) {
- // there are neither commutative nor noncommutative_composite
- // elements in assocseq
- GINAC_ASSERT(count_commutative==0);
-
- exvectorvector evv;
- unsignedvector rttinfos;
- evv.reserve(assocseq.size());
- rttinfos.reserve(assocseq.size());
-
- for (exvector::const_iterator cit=assocseq.begin(); cit!=assocseq.end(); ++cit) {
- unsigned ti=(*cit).return_type_tinfo();
- // search type in vector of known types
- for (i=0; i<rttinfos.size(); ++i) {
- if (ti==rttinfos[i]) {
- evv[i].push_back(*cit);
- break;
- }
- }
- if (i>=rttinfos.size()) {
- // new type
- rttinfos.push_back(ti);
- evv.push_back(exvector());
- (*(evv.end()-1)).reserve(assocseq.size());
- (*(evv.end()-1)).push_back(*cit);
- }
- }
-
+ // The following additional rule would be nice, but produces a recursion,
+ // which must be trapped by introducing a flag that the sub-ncmuls()
+ // are already evaluated (maybe later...)
+ // ncmul(x1,x2,...,X,y1,y2,...) ->
+ // ncmul(ncmul(x1,x2,...),X,ncmul(y1,y2,...)
+ // (X noncommutative_composite)
+
+ if ((level==1) && (flags & status_flags::evaluated)) {
+ return *this;
+ }
+
+ exvector evaledseq=evalchildren(level);
+
+ // ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) ->
+ // ncmul(...,x1,x2,...,x3,x4,...) (associativity)
+ size_t factors = 0;
+ exvector::const_iterator cit = evaledseq.begin(), citend = evaledseq.end();
+ while (cit != citend)
+ factors += count_factors(*cit++);
+
+ exvector assocseq;
+ assocseq.reserve(factors);
+ cit = evaledseq.begin();
+ while (cit != citend)
+ append_factors(assocseq, *cit++);
+
+ // ncmul(x) -> x
+ if (assocseq.size()==1) return *(seq.begin());
+
+ // ncmul() -> 1
+ if (assocseq.empty()) return _ex1;
+
+ // determine return types
+ unsignedvector rettypes;
+ rettypes.reserve(assocseq.size());
+ size_t i = 0;
+ size_t count_commutative=0;
+ size_t count_noncommutative=0;
+ size_t count_noncommutative_composite=0;
+ cit = assocseq.begin(); citend = assocseq.end();
+ while (cit != citend) {
+ switch (rettypes[i] = cit->return_type()) {
+ case return_types::commutative:
+ count_commutative++;
+ break;
+ case return_types::noncommutative:
+ count_noncommutative++;
+ break;
+ case return_types::noncommutative_composite:
+ count_noncommutative_composite++;
+ break;
+ default:
+ throw(std::logic_error("ncmul::eval(): invalid return type"));
+ }
+ ++i; ++cit;
+ }
+ GINAC_ASSERT(count_commutative+count_noncommutative+count_noncommutative_composite==assocseq.size());
+
+ // ncmul(...,c1,...,c2,...) ->
+ // *(c1,c2,ncmul(...)) (pull out commutative elements)
+ if (count_commutative!=0) {
+ exvector commutativeseq;
+ commutativeseq.reserve(count_commutative+1);
+ exvector noncommutativeseq;
+ noncommutativeseq.reserve(assocseq.size()-count_commutative);
+ size_t num = assocseq.size();
+ for (size_t i=0; i<num; ++i) {
+ if (rettypes[i]==return_types::commutative)
+ commutativeseq.push_back(assocseq[i]);
+ else
+ noncommutativeseq.push_back(assocseq[i]);
+ }
+ commutativeseq.push_back((new ncmul(noncommutativeseq,1))->setflag(status_flags::dynallocated));
+ return (new mul(commutativeseq))->setflag(status_flags::dynallocated);
+ }
+
+ // ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))
+ // (collect elements of same type)
+
+ if (count_noncommutative_composite==0) {
+ // there are neither commutative nor noncommutative_composite
+ // elements in assocseq
+ GINAC_ASSERT(count_commutative==0);
+
+ size_t assoc_num = assocseq.size();
+ exvectorvector evv;
+ unsignedvector rttinfos;
+ evv.reserve(assoc_num);
+ rttinfos.reserve(assoc_num);
+
+ cit = assocseq.begin(), citend = assocseq.end();
+ while (cit != citend) {
+ unsigned ti = cit->return_type_tinfo();
+ size_t rtt_num = rttinfos.size();
+ // search type in vector of known types
+ for (i=0; i<rtt_num; ++i) {
+ if (ti == rttinfos[i]) {
+ evv[i].push_back(*cit);
+ break;
+ }
+ }
+ if (i >= rtt_num) {
+ // new type
+ rttinfos.push_back(ti);
+ evv.push_back(exvector());
+ (evv.end()-1)->reserve(assoc_num);
+ (evv.end()-1)->push_back(*cit);
+ }
+ ++cit;
+ }
+
+ size_t evv_num = evv.size();
#ifdef DO_GINAC_ASSERT
- GINAC_ASSERT(evv.size()==rttinfos.size());
- GINAC_ASSERT(evv.size()>0);
- unsigned s=0;
- for (i=0; i<evv.size(); ++i) {
- s += evv[i].size();
- }
- GINAC_ASSERT(s==assocseq.size());
+ GINAC_ASSERT(evv_num == rttinfos.size());
+ GINAC_ASSERT(evv_num > 0);
+ size_t s=0;
+ for (i=0; i<evv_num; ++i)
+ s += evv[i].size();
+ GINAC_ASSERT(s == assoc_num);
#endif // def DO_GINAC_ASSERT
-
- // if all elements are of same type, simplify the string
- if (evv.size()==1) {
- return evv[0][0].simplify_ncmul(evv[0]);
- }
-
- exvector splitseq;
- splitseq.reserve(evv.size());
- for (i=0; i<evv.size(); ++i) {
- splitseq.push_back((new ncmul(evv[i]))->
- setflag(status_flags::dynallocated));
- }
-
- return (new mul(splitseq))->setflag(status_flags::dynallocated);
- }
-
- return (new ncmul(assocseq))->setflag(status_flags::dynallocated |
- status_flags::evaluated);
-}
-
-exvector ncmul::get_indices(void) const
-{
- // return union of indices of factors
- exvector iv;
- for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
- exvector subiv=(*cit).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 ncmul::subs(const lst & ls, const lst & lr) const
-{
- return ncmul(subschildren(ls, lr));
-}
-
-ex ncmul::thisexprseq(const exvector & v) const
-{
- return (new ncmul(v))->setflag(status_flags::dynallocated);
-}
-
-ex ncmul::thisexprseq(exvector * vp) const
-{
- return (new ncmul(vp))->setflag(status_flags::dynallocated);
+
+ // if all elements are of same type, simplify the string
+ if (evv_num == 1)
+ return evv[0][0].eval_ncmul(evv[0]);
+
+ exvector splitseq;
+ splitseq.reserve(evv_num);
+ for (i=0; i<evv_num; ++i)
+ splitseq.push_back((new ncmul(evv[i]))->setflag(status_flags::dynallocated));
+
+ return (new mul(splitseq))->setflag(status_flags::dynallocated);
+ }
+
+ return (new ncmul(assocseq))->setflag(status_flags::dynallocated |
+ status_flags::evaluated);
+}
+
+ex ncmul::evalm() const
+{
+ // Evaluate children first
+ std::auto_ptr<exvector> s(new exvector);
+ s->reserve(seq.size());
+ exvector::const_iterator it = seq.begin(), itend = seq.end();
+ while (it != itend) {
+ s->push_back(it->evalm());
+ it++;
+ }
+
+ // If there are only matrices, simply multiply them
+ it = s->begin(); itend = s->end();
+ if (is_a<matrix>(*it)) {
+ matrix prod(ex_to<matrix>(*it));
+ it++;
+ while (it != itend) {
+ if (!is_a<matrix>(*it))
+ goto no_matrix;
+ prod = prod.mul(ex_to<matrix>(*it));
+ it++;
+ }
+ return prod;
+ }
+
+no_matrix:
+ return (new ncmul(s))->setflag(status_flags::dynallocated);
+}
+
+ex ncmul::thiscontainer(const exvector & v) const
+{
+ return (new ncmul(v))->setflag(status_flags::dynallocated);
+}
+
+ex ncmul::thiscontainer(std::auto_ptr<exvector> vp) const
+{
+ return (new ncmul(vp))->setflag(status_flags::dynallocated);
}
// protected
-int ncmul::compare_same_type(const basic & other) const
-{
- return inherited::compare_same_type(other);
+/** Implementation of ex::diff() for a non-commutative product. It applies
+ * the product rule.
+ * @see ex::diff */
+ex ncmul::derivative(const symbol & s) const
+{
+ 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)
+ exvector ncmulseq = seq;
+ for (size_t i=0; i<num; ++i) {
+ ex e = seq[i].diff(s);
+ e.swap(ncmulseq[i]);
+ addseq.push_back((new ncmul(ncmulseq))->setflag(status_flags::dynallocated));
+ e.swap(ncmulseq[i]);
+ }
+ return (new add(addseq))->setflag(status_flags::dynallocated);
}
-unsigned ncmul::return_type(void) const
+int ncmul::compare_same_type(const basic & other) const
{
- if (seq.size()==0) {
- // ncmul without factors: should not happen, but commutes
- return return_types::commutative;
- }
-
- bool all_commutative=1;
- unsigned rt;
- exvector::const_iterator cit_noncommutative_element; // point to first found nc element
-
- for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
- rt=(*cit).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).return_type_tinfo()!=(*cit).return_type_tinfo()) {
- // diffent types -> mul is ncc
- return return_types::noncommutative_composite;
- }
- }
- }
- // all factors checked
- GINAC_ASSERT(!all_commutative); // not all factors should commute, because this is a ncmul();
- return all_commutative ? return_types::commutative : return_types::noncommutative;
+ return inherited::compare_same_type(other);
+}
+
+unsigned ncmul::return_type() const
+{
+ if (seq.empty())
+ return return_types::commutative;
+
+ bool all_commutative = true;
+ exvector::const_iterator noncommutative_element; // point to first found nc element
+
+ exvector::const_iterator i = seq.begin(), end = seq.end();
+ while (i != end) {
+ unsigned rt = i->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->return_type_tinfo() != i->return_type_tinfo()) {
+ // diffent types -> mul is ncc
+ return return_types::noncommutative_composite;
+ }
+ }
+ ++i;
+ }
+ // all factors checked
+ GINAC_ASSERT(!all_commutative); // not all factors should commute, because this is a ncmul();
+ return all_commutative ? return_types::commutative : return_types::noncommutative;
}
-unsigned ncmul::return_type_tinfo(void) const
+unsigned ncmul::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 (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
- if ((*cit).return_type()==return_types::noncommutative) {
- return (*cit).return_type_tinfo();
- }
- }
- // no noncommutative element found, should not happen
- return tinfo_key;
+ if (seq.empty())
+ return tinfo_key;
+
+ // return type_info of first noncommutative element
+ exvector::const_iterator i = seq.begin(), end = seq.end();
+ while (i != end) {
+ if (i->return_type() == return_types::noncommutative)
+ return i->return_type_tinfo();
+ ++i;
+ }
+
+ // no noncommutative element found, should not happen
+ return tinfo_key;
}
//////////
exvector ncmul::expandchildren(unsigned options) const
{
- exvector s;
- s.reserve(seq.size());
-
- for (exvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
- s.push_back((*it).expand(options));
- }
- return s;
+ exvector s;
+ s.reserve(seq.size());
+ exvector::const_iterator it = seq.begin(), itend = seq.end();
+ while (it != itend) {
+ s.push_back(it->expand(options));
+ it++;
+ }
+ return s;
}
-const exvector & ncmul::get_factors(void) const
+const exvector & ncmul::get_factors() const
{
- return seq;
+ return seq;
}
-//////////
-// static member variables
-//////////
-
-// protected
-
-unsigned ncmul::precedence=50;
-
-
-//////////
-// global constants
-//////////
-
-const ncmul some_ncmul;
-const type_info & typeid_ncmul=typeid(some_ncmul);
-
//////////
// friend functions
//////////
-ex nonsimplified_ncmul(const exvector & v)
+ex reeval_ncmul(const exvector & v)
{
- return (new ncmul(v))->setflag(status_flags::dynallocated);
+ return (new ncmul(v))->setflag(status_flags::dynallocated);
}
-ex simplified_ncmul(const exvector & v)
+ex hold_ncmul(const exvector & v)
{
- if (v.size()==0) {
- return _ex1();
- } else if (v.size()==1) {
- return v[0];
- }
- return (new ncmul(v))->setflag(status_flags::dynallocated |
- status_flags::evaluated);
+ if (v.empty())
+ return _ex1;
+ else if (v.size() == 1)
+ return v[0];
+ else
+ return (new ncmul(v))->setflag(status_flags::dynallocated |
+ status_flags::evaluated);
}
-#ifndef NO_GINAC_NAMESPACE
} // namespace GiNaC
-#endif // ndef NO_GINAC_NAMESPACE
git://www.ginac.de / ginac.git / blobdiff