X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fmul.cpp;h=3d33c78a129eeaeaaf9074bc291e76624e403da8;hp=f5c202252ba4f8f9a351107075680673ba0f6995;hb=a7693a0f710b49494f95ce5a4a0953752e69c7f9;hpb=2bb16a36176246de7cd5c1ab2044c43f5a35115b

diff --git a/ginac/mul.cpp b/ginac/mul.cpp
index f5c20225..3d33c78a 100644
--- a/ginac/mul.cpp
+++ b/ginac/mul.cpp
@@ -3,7 +3,7 @@
  *  Implementation of GiNaC's products of expressions. */
 
 /*
- *  GiNaC Copyright (C) 1999-2005 Johannes Gutenberg University Mainz, Germany
+ *  GiNaC Copyright (C) 1999-2008 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
@@ -34,6 +34,8 @@
 #include "lst.h"
 #include "archive.h"
 #include "utils.h"
+#include "symbol.h"
+#include "compiler.h"
 
 namespace GiNaC {
 
@@ -51,7 +53,7 @@ GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(mul, expairseq,
 
 mul::mul()
 {
-	tinfo_key = TINFO_mul;
+	tinfo_key = &mul::tinfo_static;
 }
 
 //////////
@@ -62,7 +64,7 @@ mul::mul()
 
 mul::mul(const ex & lh, const ex & rh)
 {
-	tinfo_key = TINFO_mul;
+	tinfo_key = &mul::tinfo_static;
 	overall_coeff = _ex1;
 	construct_from_2_ex(lh,rh);
 	GINAC_ASSERT(is_canonical());
@@ -70,7 +72,7 @@ mul::mul(const ex & lh, const ex & rh)
 
 mul::mul(const exvector & v)
 {
-	tinfo_key = TINFO_mul;
+	tinfo_key = &mul::tinfo_static;
 	overall_coeff = _ex1;
 	construct_from_exvector(v);
 	GINAC_ASSERT(is_canonical());
@@ -78,32 +80,32 @@ mul::mul(const exvector & v)
 
 mul::mul(const epvector & v)
 {
-	tinfo_key = TINFO_mul;
+	tinfo_key = &mul::tinfo_static;
 	overall_coeff = _ex1;
 	construct_from_epvector(v);
 	GINAC_ASSERT(is_canonical());
 }
 
-mul::mul(const epvector & v, const ex & oc)
+mul::mul(const epvector & v, const ex & oc, bool do_index_renaming)
 {
-	tinfo_key = TINFO_mul;
+	tinfo_key = &mul::tinfo_static;
 	overall_coeff = oc;
-	construct_from_epvector(v);
+	construct_from_epvector(v, do_index_renaming);
 	GINAC_ASSERT(is_canonical());
 }
 
-mul::mul(std::auto_ptr<epvector> vp, const ex & oc)
+mul::mul(std::auto_ptr<epvector> vp, const ex & oc, bool do_index_renaming)
 {
-	tinfo_key = TINFO_mul;
+	tinfo_key = &mul::tinfo_static;
 	GINAC_ASSERT(vp.get()!=0);
 	overall_coeff = oc;
-	construct_from_epvector(*vp);
+	construct_from_epvector(*vp, do_index_renaming);
 	GINAC_ASSERT(is_canonical());
 }
 
 mul::mul(const ex & lh, const ex & mh, const ex & rh)
 {
-	tinfo_key = TINFO_mul;
+	tinfo_key = &mul::tinfo_static;
 	exvector factors;
 	factors.reserve(3);
 	factors.push_back(lh);
@@ -218,8 +220,12 @@ void mul::do_print_csrc(const print_csrc & c, unsigned level) const
 		c.s << "(";
 
 	if (!overall_coeff.is_equal(_ex1)) {
-		overall_coeff.print(c, precedence());
-		c.s << "*";
+		if (overall_coeff.is_equal(_ex_1))
+			c.s << "-";
+		else {
+			overall_coeff.print(c, precedence());
+			c.s << "*";
+		}
 	}
 
 	// Print arguments, separated by "*" or "/"
@@ -311,7 +317,11 @@ int mul::degree(const ex & s) const
 	epvector::const_iterator i = seq.begin(), end = seq.end();
 	while (i != end) {
 		if (ex_to<numeric>(i->coeff).is_integer())
-			deg_sum += i->rest.degree(s) * ex_to<numeric>(i->coeff).to_int();
+			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;
@@ -324,7 +334,11 @@ int mul::ldegree(const ex & s) const
 	epvector::const_iterator i = seq.begin(), end = seq.end();
 	while (i != end) {
 		if (ex_to<numeric>(i->coeff).is_integer())
-			deg_sum += i->rest.ldegree(s) * ex_to<numeric>(i->coeff).to_int();
+			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;
@@ -410,7 +424,7 @@ ex mul::eval(int level) const
 		return *this;
 	}
 	
-	int seq_size = seq.size();
+	size_t seq_size = seq.size();
 	if (overall_coeff.is_zero()) {
 		// *(...,x;0) -> 0
 		return _ex0;
@@ -434,9 +448,81 @@ ex mul::eval(int level) const
 		}
 		return (new add(distrseq,
 		                ex_to<numeric>(addref.overall_coeff).
-		                mul_dyn(ex_to<numeric>(overall_coeff))))
-		      ->setflag(status_flags::dynallocated | status_flags::evaluated);
+		                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(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();
 }
 
@@ -461,6 +547,41 @@ ex mul::evalf(int level) const
 	return mul(s, overall_coeff.evalf(level));
 }
 
+void mul::find_real_imag(ex & rp, ex & ip) const
+{
+	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();
+}
+
+ex mul::real_part() const
+{
+	ex rp, ip;
+	find_real_imag(rp, ip);
+	return rp;
+}
+
+ex mul::imag_part() const
+{
+	ex rp, ip;
+	find_real_imag(rp, ip);
+	return ip;
+}
+
 ex mul::evalm() const
 {
 	// numeric*matrix
@@ -559,61 +680,100 @@ bool tryfactsubs(const ex & origfactor, const ex & patternfactor, int & nummatch
 	return true;
 }
 
+/** 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)
+{
+	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::has(const ex & pattern, unsigned options) const
+{
+	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);
-			bool succeed = true;
 			lst repls;
-
-			for (size_t j=0; j<it->first.nops(); j++) {
-				bool found=false;
-				for (size_t k=0; k<nops(); k++) {
-					if (currsubsed[k] || subsed[k])
-						continue;
-					if (tryfactsubs(op(k), it->first.op(j), nummatches, repls)) {
-						currsubsed[k] = true;
-						found = true;
-						break;
-					}
-				}
-				if (!found) {
-					succeed = false;
-					break;
-				}
-			}
-			if (!succeed)
+			
+			if(!algebraic_match_mul_with_mul(*this, it->first, repls, 0, nummatches, subsed, currsubsed))
 				continue;
 
-			bool foundfirstsubsedfactor = false;
-			for (size_t j=0; j<subsed.size(); j++) {
-				if (currsubsed[j]) {
-					if (foundfirstsubsedfactor)
-						subsresult[j] = op(j);
-					else {
-						foundfirstsubsedfactor = true;
-						subsresult[j] = op(j) * power(it->second.subs(ex(repls), subs_options::no_pattern) / it->first.subs(ex(repls), subs_options::no_pattern), nummatches);
-					}
+			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 {
 
-			int nummatches = std::numeric_limits<int>::max();
-			lst repls;
-
 			for (size_t j=0; j<this->nops(); j++) {
-				if (!subsed[j] && tryfactsubs(op(j), it->first, nummatches, repls)) {
+				int nummatches = std::numeric_limits<int>::max();
+				lst repls;
+				if (!subsed[j] && tryfactsubs(op(j), it->first, nummatches, repls)){
 					subsed[j] = true;
-					subsresult[j] = op(j) * power(it->second.subs(ex(repls), subs_options::no_pattern) / it->first.subs(ex(repls), subs_options::no_pattern), nummatches);
+					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);
 				}
 			}
 		}
@@ -629,15 +789,7 @@ ex mul::algebraic_subs_mul(const exmap & m, unsigned options) const
 	if (!subsfound)
 		return subs_one_level(m, options | subs_options::algebraic);
 
-	exvector ev; ev.reserve(nops());
-	for (size_t i=0; i<nops(); i++) {
-		if (subsed[i])
-			ev.push_back(subsresult[i]);
-		else
-			ev.push_back(op(i));
-	}
-
-	return (new mul(ev))->setflag(status_flags::dynallocated);
+	return ((*this)/divide_by)*multiply_by;
 }
 
 // protected
@@ -693,8 +845,8 @@ unsigned mul::return_type() const
 		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()) {
-				// diffent types -> mul is ncc
-				return return_types::noncommutative_composite;
+					// different types -> mul is ncc
+					return return_types::noncommutative_composite;
 			}
 		}
 		++i;
@@ -703,10 +855,10 @@ unsigned mul::return_type() const
 	return all_commutative ? return_types::commutative : return_types::noncommutative;
 }
    
-unsigned mul::return_type_tinfo() const
+tinfo_t mul::return_type_tinfo() const
 {
 	if (seq.empty())
-		return tinfo_key;  // mul without factors: should not happen
+		return this;  // mul without factors: should not happen
 	
 	// return type_info of first noncommutative element
 	epvector::const_iterator i = seq.begin(), end = seq.end();
@@ -716,17 +868,17 @@ unsigned mul::return_type_tinfo() const
 		++i;
 	}
 	// no noncommutative element found, should not happen
-	return tinfo_key;
+	return this;
 }
 
-ex mul::thisexpairseq(const epvector & v, const ex & 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(std::auto_ptr<epvector> vp, const ex & 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(const ex & e) const
@@ -841,6 +993,24 @@ bool mul::can_be_further_expanded(const ex & e)
 
 ex mul::expand(unsigned options) const
 {
+	{
+	// trivial case: expanding the monomial (~ 30% of all calls)
+		epvector::const_iterator i = seq.begin(), seq_end = seq.end();
+		while ((i != seq.end()) &&  is_a<symbol>(i->rest) && i->coeff.info(info_flags::integer))
+			++i;
+		if (i == seq_end) {
+			setflag(status_flags::expanded);
+			return *this;
+		}
+	}
+
+	// do not rename indices if the object has no indices at all
+	if ((!(options & expand_options::expand_rename_idx)) && 
+			this->info(info_flags::has_indices))
+		options |= expand_options::expand_rename_idx;
+
+	const bool skip_idx_rename = !(options & expand_options::expand_rename_idx);
+
 	// First, expand the children
 	std::auto_ptr<epvector> expanded_seqp = expandchildren(options);
 	const epvector & expanded_seq = (expanded_seqp.get() ? *expanded_seqp : seq);
@@ -896,28 +1066,34 @@ ex mul::expand(unsigned options) const
 				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;
 
-				for (epvector::const_iterator i=add1begin; i!=add1end; ++i) {
-					add_indices = get_all_dummy_indices(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(i->rest);
-					add2_dummy_indices.insert(add2_dummy_indices.end(), add_indices.begin(), add_indices.end());
-				}
+				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());
-				lst dummy_subs = rename_dummy_indices_uniquely(add1_dummy_indices, add2_dummy_indices);
+					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;
-					distrseq.clear();
-					ex i2_new = (dummy_subs.op(0).nops()>0? 
-								 i2->rest.subs((lst)dummy_subs.op(0), (lst)dummy_subs.op(1), subs_options::no_pattern) : i2->rest);
+					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:
@@ -925,13 +1101,12 @@ ex mul::expand(unsigned options) const
 						if (is_exactly_a<numeric>(rest)) {
 							oc += ex_to<numeric>(rest).mul(ex_to<numeric>(i1->coeff).mul(ex_to<numeric>(i2->coeff)));
 						} else {
-							distrseq.push_back(expair(rest, ex_to<numeric>(i1->coeff).mul_dyn(ex_to<numeric>(i2->coeff))));
+							distrseq2.push_back(expair(rest, ex_to<numeric>(i1->coeff).mul_dyn(ex_to<numeric>(i2->coeff))));
 						}
 					}
-					tmp_accu += (new add(distrseq, oc))->setflag(status_flags::dynallocated);
-				}
+					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));
@@ -949,12 +1124,18 @@ ex mul::expand(unsigned options) const
 		size_t n = last_expanded.nops();
 		exvector distrseq;
 		distrseq.reserve(n);
-		exvector va = get_all_dummy_indices(mul(non_adds));
-		sort(va.begin(), va.end(), ex_is_less());
+		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;
-			factors.push_back(split_ex_to_pair(rename_dummy_indices_uniquely(va, last_expanded.op(i))));
+			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());