X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fmul.cpp;h=351a72cbcfaa20210b9b8097b91bca5f2a5541b6;hp=db68b275ffbbc788a476bad5b9b9f814b30229ff;hb=d4df6322c4790ea932280602fdb584486f6101b6;hpb=87d731b215909cc8ab8ecdb8c05fcd717bf63fd2

diff --git a/ginac/mul.cpp b/ginac/mul.cpp
index db68b275..351a72cb 100644
--- a/ginac/mul.cpp
+++ b/ginac/mul.cpp
@@ -3,7 +3,7 @@
  *  Implementation of GiNaC's products of expressions. */
 
 /*
- *  GiNaC Copyright (C) 1999-2003 Johannes Gutenberg University Mainz, Germany
+ *  GiNaC Copyright (C) 1999-2006 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
@@ -17,7 +17,7 @@
  *
  *  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>
@@ -30,6 +30,7 @@
 #include "power.h"
 #include "operators.h"
 #include "matrix.h"
+#include "indexed.h"
 #include "lst.h"
 #include "archive.h"
 #include "utils.h"
@@ -40,7 +41,7 @@ GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(mul, expairseq,
   print_func<print_context>(&mul::do_print).
   print_func<print_latex>(&mul::do_print_latex).
   print_func<print_csrc>(&mul::do_print_csrc).
-  print_func<print_tree>(&inherited::do_print_tree).
+  print_func<print_tree>(&mul::do_print_tree).
   print_func<print_python_repr>(&mul::do_print_python_repr))
 
 
@@ -50,7 +51,7 @@ GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(mul, expairseq,
 
 mul::mul()
 {
-	tinfo_key = TINFO_mul;
+	tinfo_key = &mul::tinfo_static;
 }
 
 //////////
@@ -61,7 +62,7 @@ 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());
@@ -69,7 +70,7 @@ 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());
@@ -77,32 +78,32 @@ 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;
-	GINAC_ASSERT(vp!=0);
+	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);
@@ -128,8 +129,8 @@ void mul::print_overall_coeff(const print_context & c, const char *mul_sym) cons
 	const numeric &coeff = ex_to<numeric>(overall_coeff);
 	if (coeff.csgn() == -1)
 		c.s << '-';
-	if (!coeff.is_equal(_num1) &&
-		!coeff.is_equal(_num_1)) {
+	if (!coeff.is_equal(*_num1_p) &&
+		!coeff.is_equal(*_num_1_p)) {
 		if (coeff.is_rational()) {
 			if (coeff.is_negative())
 				(-coeff).print(c);
@@ -217,8 +218,12 @@ 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 "/"
@@ -421,7 +426,7 @@ ex mul::eval(int level) const
 		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)) {
+	           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);
@@ -460,6 +465,41 @@ 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
@@ -558,61 +598,100 @@ 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);
 				}
 			}
 		}
@@ -628,15 +707,7 @@ 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
@@ -672,7 +743,7 @@ int mul::compare_same_type(const basic & other) const
 unsigned mul::return_type() const
 {
 	if (seq.empty()) {
-		// mul without factors: should not happen, but commutes
+		// mul without factors: should not happen, but commutates
 		return return_types::commutative;
 	}
 	
@@ -692,8 +763,8 @@ 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;
@@ -702,10 +773,10 @@ 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();
@@ -715,17 +786,17 @@ 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
@@ -766,7 +837,7 @@ expair mul::combine_pair_with_coeff_to_pair(const expair & p,
 	
 ex mul::recombine_pair_to_ex(const expair & p) const
 {
-	if (ex_to<numeric>(p.coeff).is_equal(_num1)) 
+	if (ex_to<numeric>(p.coeff).is_equal(*_num1_p)) 
 		return p.rest;
 	else
 		return (new power(p.rest,p.coeff))->setflag(status_flags::dynallocated);
@@ -821,7 +892,21 @@ bool mul::can_make_flat(const expair & p) const
 	// this assertion will probably fail somewhere
 	// it would require a more careful make_flat, obeying the power laws
 	// probably should return true only if p.coeff is integer
-	return ex_to<numeric>(p.coeff).is_equal(_num1);
+	return ex_to<numeric>(p.coeff).is_equal(*_num1_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
@@ -833,18 +918,14 @@ ex mul::expand(unsigned options) const
 	// Now, look for all the factors that are sums and multiply each one out
 	// with the next one that is found while collecting the factors which are
 	// not sums
-	int number_of_adds = 0;
 	ex last_expanded = _ex1;
 
 	epvector non_adds;
 	non_adds.reserve(expanded_seq.size());
-	bool non_adds_has_sums = false; // Look for sums or powers of sums in the non_adds (we need this later)
 
-	epvector::const_iterator cit = expanded_seq.begin(), last = expanded_seq.end();
-	while (cit != last) {
+	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))) {
-			++number_of_adds;
 			if (is_exactly_a<add>(last_expanded)) {
 
 				// Expand a product of two sums, aggressive version.
@@ -862,6 +943,7 @@ ex mul::expand(unsigned options) const
 				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))
@@ -870,6 +952,7 @@ ex mul::expand(unsigned options) const
 						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))
@@ -878,69 +961,93 @@ ex mul::expand(unsigned options) const
 						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;
+
+				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);
+
 				// Multiply explicitly all non-numeric terms of add1 and add2:
-				for (epvector::const_iterator i1=add1begin; i1!=add1end; ++i1) {
+				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();
-					for (epvector::const_iterator i2=add2begin; i2!=add2end; ++i2) {
+					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);
+					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 = ex((new mul(i1->rest, i2->rest))->setflag(status_flags::dynallocated)).expand();
-						if (is_exactly_a<numeric>(rest))
+						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
+						} else {
 							distrseq.push_back(expair(rest, ex_to<numeric>(i1->coeff).mul_dyn(ex_to<numeric>(i2->coeff))));
+						}
 					}
 					tmp_accu += (new add(distrseq, oc))->setflag(status_flags::dynallocated);
 				}
 				last_expanded = tmp_accu;
 
 			} else {
-				non_adds.push_back(split_ex_to_pair(last_expanded));
+				if (!last_expanded.is_equal(_ex1))
+					non_adds.push_back(split_ex_to_pair(last_expanded));
 				last_expanded = cit->rest;
 			}
+
 		} else {
-			if (is_exactly_a<add>(cit->rest))
-				non_adds_has_sums = true;
 			non_adds.push_back(*cit);
 		}
-		++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)) {
-		const add & finaladd = ex_to<add>(last_expanded);
-
-		size_t n = finaladd.nops();
+		size_t n = last_expanded.nops();
 		exvector distrseq;
 		distrseq.reserve(n);
+		exvector 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;
-			expair new_factor = split_ex_to_pair(finaladd.op(i).expand());
-			factors.push_back(new_factor);
-
-			const mul & term = static_cast<const mul &>((new mul(factors, overall_coeff))->setflag(status_flags::dynallocated));
-
-			// The new term may have sums in it if e.g. a sqrt() of a sum in
-			// the non_adds meets a sqrt() of a sum in the factor from
-			// last_expanded. In this case we should re-expand the term.
-			if (non_adds_has_sums || is_exactly_a<add>(new_factor.rest))
-				distrseq.push_back(ex(term).expand());
-			else
-				distrseq.push_back(term.setflag(options == 0 ? status_flags::expanded : 0));
+			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));
-	return (new mul(non_adds, overall_coeff))->
-	        setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
+	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;
+	}
 }