X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fncmul.cpp;h=f086e49235568573d19f5513dad93b930c8e79c6;hp=7d2364e2e6107650473707347fa48b524087786a;hb=8cffcdf13d817a47f217f1a1043317d95969e070;hpb=9eab44408b9213d8909b7a9e525f404ad06064dd

diff --git a/ginac/ncmul.cpp b/ginac/ncmul.cpp
index 7d2364e2..f086e492 100644
--- a/ginac/ncmul.cpp
+++ b/ginac/ncmul.cpp
@@ -3,7 +3,7 @@
  *  Implementation of GiNaC's non-commutative products of expressions. */
 
 /*
- *  GiNaC Copyright (C) 1999 Johannes Gutenberg University Mainz, Germany
+ *  GiNaC Copyright (C) 1999-2019 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
@@ -17,516 +17,544 @@
  *
  *  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 <algorithm>
-#include <iostream>
-#include <stdexcept>
-
 #include "ncmul.h"
 #include "ex.h"
 #include "add.h"
 #include "mul.h"
-#include "debugmsg.h"
+#include "clifford.h"
+#include "matrix.h"
+#include "archive.h"
+#include "indexed.h"
+#include "utils.h"
+
+#include <algorithm>
+#include <iostream>
+#include <stdexcept>
 
 namespace GiNaC {
 
+GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(ncmul, exprseq,
+  print_func<print_context>(&ncmul::do_print).
+  print_func<print_tree>(&ncmul::do_print_tree).
+  print_func<print_csrc>(&ncmul::do_print_csrc).
+  print_func<print_python_repr>(&ncmul::do_print_csrc))
+
+
+//////////
+// default constructor
+//////////
+
+ncmul::ncmul()
+{
+}
+
 //////////
-// default constructor, destructor, copy constructor assignment operator and helpers
+// other constructors
 //////////
 
 // public
 
-ncmul::ncmul()
+ncmul::ncmul(const ex & lh, const ex & rh) : inherited{lh,rh}
 {
-    debugmsg("ncmul default constructor",LOGLEVEL_CONSTRUCT);
-    tinfo_key = TINFO_ncmul;
 }
 
-ncmul::~ncmul()
+ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3) : inherited{f1,f2,f3}
 {
-    debugmsg("ncmul destructor",LOGLEVEL_DESTRUCT);
-    destroy(0);
 }
 
-ncmul::ncmul(ncmul const & other)
+ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
+             const ex & f4) : inherited{f1,f2,f3,f4}
 {
-    debugmsg("ncmul copy constructor",LOGLEVEL_CONSTRUCT);
-    copy(other);
 }
 
-ncmul const & ncmul::operator=(ncmul const & other)
+ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
+             const ex & f4, const ex & f5) : inherited{f1,f2,f3,f4,f5}
 {
-    debugmsg("ncmul operator=",LOGLEVEL_ASSIGNMENT);
-    if (this != &other) {
-        destroy(1);
-        copy(other);
-    }
-    return *this;
 }
 
-// protected
+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}
+{
+}
 
-void ncmul::copy(ncmul const & other)
+ncmul::ncmul(const exvector & v) : inherited(v)
 {
-    exprseq::copy(other);
 }
 
-void ncmul::destroy(bool call_parent)
+ncmul::ncmul(exvector && v) : inherited(std::move(v))
 {
-    if (call_parent) exprseq::destroy(call_parent);
 }
 
 //////////
-// other constructors
+// archiving
+//////////
+
+
+//////////
+// functions overriding virtual functions from base classes
 //////////
 
 // public
 
-ncmul::ncmul(ex const & lh, ex const & rh) :
-    exprseq(lh,rh)
+void ncmul::do_print(const print_context & c, unsigned level) const
 {
-    debugmsg("ncmul constructor from ex,ex",LOGLEVEL_CONSTRUCT);
-    tinfo_key = TINFO_ncmul;
+	printseq(c, '(', '*', ')', precedence(), level);
 }
 
-ncmul::ncmul(ex const & f1, ex const & f2, ex const & f3) :
-    exprseq(f1,f2,f3)
+void ncmul::do_print_csrc(const print_context & c, unsigned level) const
 {
-    debugmsg("ncmul constructor from 3 ex",LOGLEVEL_CONSTRUCT);
-    tinfo_key = TINFO_ncmul;
+	c.s << class_name();
+	printseq(c, '(', ',', ')', precedence(), precedence());
 }
 
-ncmul::ncmul(ex const & f1, ex const & f2, ex const & f3,
-      ex const & f4) : exprseq(f1,f2,f3,f4)
+bool ncmul::info(unsigned inf) const
 {
-    debugmsg("ncmul constructor from 4 ex",LOGLEVEL_CONSTRUCT);
-    tinfo_key = TINFO_ncmul;
+	return inherited::info(inf);
 }
 
-ncmul::ncmul(ex const & f1, ex const & f2, ex const & f3,
-      ex const & f4, ex const & f5) : exprseq(f1,f2,f3,f4,f5)
-{
-    debugmsg("ncmul constructor from 5 ex",LOGLEVEL_CONSTRUCT);
-    tinfo_key = TINFO_ncmul;
-}
+typedef std::vector<std::size_t> uintvector;
 
-ncmul::ncmul(ex const & f1, ex const & f2, ex const & f3,
-      ex const & f4, ex const & f5, ex const & f6) :
-    exprseq(f1,f2,f3,f4,f5,f6)
+ex ncmul::expand(unsigned options) const
 {
-    debugmsg("ncmul constructor from 6 ex",LOGLEVEL_CONSTRUCT);
-    tinfo_key = TINFO_ncmul;
+	// First, expand the children
+	exvector v = expandchildren(options);
+	const exvector &expanded_seq = v.empty() ? this->seq : v;
+	
+	// Now, look for all the factors that are sums and remember their
+	// position and number of terms.
+	uintvector positions_of_adds(expanded_seq.size());
+	uintvector 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;
+	for (auto & it : expanded_seq) {
+		if (is_exactly_a<add>(it)) {
+			positions_of_adds[number_of_adds] = current_position;
+			size_t num_ops = it.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) {
+		if (!v.empty())
+			return dynallocate<ncmul>(std::move(v)).setflag(options == 0 ? status_flags::expanded : 0);
+		else
+			return *this;
+	}
+
+	// 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);
+
+	uintvector k(number_of_adds);
+
+	/* Rename indices in the static members of the product */
+	exvector expanded_seq_mod;
+	size_t j = 0;
+	exvector va;
+
+	for (size_t i=0; i<expanded_seq.size(); i++) {
+		if (i == positions_of_adds[j]) {
+			expanded_seq_mod.push_back(_ex1);
+			j++;
+		} else {
+			expanded_seq_mod.push_back(rename_dummy_indices_uniquely(va, expanded_seq[i], true));
+		}
+	}
+
+	while (true) {
+		exvector term = expanded_seq_mod;
+		for (size_t i=0; i<number_of_adds; i++) {
+			term[positions_of_adds[i]] = rename_dummy_indices_uniquely(va, expanded_seq[positions_of_adds[i]].op(k[i]), true);
+		}
+
+		distrseq.push_back(dynallocate<ncmul>(std::move(term)).setflag(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 dynallocate<add>(distrseq).setflag(options == 0 ? status_flags::expanded : 0);
+}
+
+int ncmul::degree(const ex & s) const
+{
+	if (is_equal(ex_to<basic>(s)))
+		return 1;
+
+	// Sum up degrees of factors
+	int deg_sum = 0;
+	for (auto & i : seq)
+		deg_sum += i.degree(s);
+	return deg_sum;
+}
+
+int ncmul::ldegree(const ex & s) const
+{
+	if (is_equal(ex_to<basic>(s)))
+		return 1;
+
+	// Sum up degrees of factors
+	int deg_sum = 0;
+	for (auto & i : seq)
+		deg_sum += i.degree(s);
+	return deg_sum;
+}
+
+ex ncmul::coeff(const ex & s, int n) const
+{
+	if (is_equal(ex_to<basic>(s)))
+		return n==1 ? _ex1 : _ex0;
+
+	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
+		for (auto & it : seq)
+			coeffseq.push_back(it.coeff(s,n));
+		return dynallocate<ncmul>(std::move(coeffseq));
+	}
+		 
+	bool coeff_found = false;
+	for (auto & i : seq) {
+		ex c = i.coeff(s,n);
+		if (c.is_zero()) {
+			coeffseq.push_back(i);
+		} else {
+			coeffseq.push_back(c);
+			coeff_found = true;
+		}
+	}
+
+	if (coeff_found)
+		return dynallocate<ncmul>(std::move(coeffseq));
+	
+	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_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,...)
+ */
+ex ncmul::eval() const
+{
+	// 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 (flags & status_flags::evaluated) {
+		return *this;
+	}
+
+	// ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) ->
+	//     ncmul(...,x1,x2,...,x3,x4,...)  (associativity)
+	size_t factors = 0;
+	for (auto & it : seq)
+		factors += count_factors(it);
+	
+	exvector assocseq;
+	assocseq.reserve(factors);
+	make_flat_inserter mf(seq, true);
+	for (auto & it : seq) {
+		ex factor = mf.handle_factor(it, 1);
+		append_factors(assocseq, factor);
+	}
+	
+	// ncmul(x) -> x
+	if (assocseq.size()==1) return *(seq.begin());
+
+	// ncmul() -> 1
+	if (assocseq.empty()) return _ex1;
+
+	// determine return types
+	unsignedvector rettypes(assocseq.size());
+	size_t i = 0;
+	size_t count_commutative=0;
+	size_t count_noncommutative=0;
+	size_t count_noncommutative_composite=0;
+	for (auto & it : assocseq) {
+		rettypes[i] = it.return_type();
+		switch (rettypes[i]) {
+		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);
+		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(dynallocate<ncmul>(std::move(noncommutativeseq)));
+		return dynallocate<mul>(std::move(commutativeseq));
+	}
+		
+	// 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;
+		std::vector<return_type_t> rttinfos;
+		evv.reserve(assoc_num);
+		rttinfos.reserve(assoc_num);
+
+		for (auto & it : assocseq) {
+			return_type_t ti = it.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(it);
+					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(it);
+			}
+		}
+
+		size_t evv_num = evv.size();
+#ifdef DO_GINAC_ASSERT
+		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_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(dynallocate<ncmul>(evv[i]));
+		
+		return dynallocate<mul>(splitseq);
+	}
+	
+	return dynallocate<ncmul>(assocseq).setflag(status_flags::evaluated);
+}
+
+ex ncmul::evalm() const
+{
+	// Evaluate children first
+	exvector s;
+	s.reserve(seq.size());
+	for (auto & it : seq)
+		s.push_back(it.evalm());
+
+	// If there are only matrices, simply multiply them
+	auto 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 dynallocate<ncmul>(std::move(s));
+}
+
+ex ncmul::thiscontainer(const exvector & v) const
+{
+	return dynallocate<ncmul>(v);
+}
+
+ex ncmul::thiscontainer(exvector && v) const
+{
+	return dynallocate<ncmul>(std::move(v));
+}
+
+ex ncmul::conjugate() const
+{
+	if (return_type() != return_types::noncommutative) {
+		return exprseq::conjugate();
+	}
+
+	if (!is_clifford_tinfo(return_type_tinfo())) {
+		return exprseq::conjugate();
+	}
+
+	exvector ev;
+	ev.reserve(nops());
+	for (auto i=end(); i!=begin();) {
+		--i;
+		ev.push_back(i->conjugate());
+	}
+	return dynallocate<ncmul>(std::move(ev));
+}
+
+ex ncmul::real_part() const
+{
+	return basic::real_part();
+}
+
+ex ncmul::imag_part() const
+{
+	return basic::imag_part();
 }
 
-ncmul::ncmul(exvector const & v, bool discardable) : exprseq(v,discardable)
-{
-    debugmsg("ncmul constructor from exvector,bool",LOGLEVEL_CONSTRUCT);
-    tinfo_key = TINFO_ncmul;
-}
+// protected
 
-ncmul::ncmul(exvector * vp) : exprseq(vp)
+/** Implementation of ex::diff() for a non-commutative product. It applies
+ *  the product rule.
+ *  @see ex::diff */
+ex ncmul::derivative(const symbol & s) const
 {
-    debugmsg("ncmul constructor from exvector *",LOGLEVEL_CONSTRUCT);
-    tinfo_key = TINFO_ncmul;
+	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(dynallocate<ncmul>(ncmulseq));
+		e.swap(ncmulseq[i]);
+	}
+	return dynallocate<add>(addseq);
 }
-    
-//////////
-// functions overriding virtual functions from bases classes
-//////////
 
-// public
-
-basic * ncmul::duplicate() const
+int ncmul::compare_same_type(const basic & other) const
 {
-    debugmsg("ncmul duplicate",LOGLEVEL_ASSIGNMENT);
-    return new ncmul(*this);
+	return inherited::compare_same_type(other);
 }
 
-bool ncmul::info(unsigned inf) const
+unsigned ncmul::return_type() const
 {
-    throw(std::logic_error("which flags have to be implemented in ncmul::info()?"));
-}
+	if (seq.empty())
+		return return_types::commutative;
 
-typedef vector<int> intvector;
+	bool all_commutative = true;
+	exvector::const_iterator noncommutative_element; // point to first found nc element
 
-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;
-            add const & 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++) {
-            ASSERT(is_ex_exactly_of_type(expanded_seq[positions_of_adds[l]],add));
-            add const & 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(symbol const & 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(symbol const & 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(symbol const & s, int const 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 exZERO();
-}
-
-unsigned ncmul::count_factors(ex const & 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 (int i=0; i<e.nops(); i++) {
-            factors += count_factors(e.op(i));
-        }
-        return factors;
-    }
-    return 1;
-}
-        
-void ncmul::append_factors(exvector & v, ex const & e) const
-{
-    if ((is_ex_exactly_of_type(e,mul)&&(e.return_type()!=return_types::commutative))||
-        (is_ex_exactly_of_type(e,ncmul))) {
-        for (int 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;
-
-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 exONE();
-
-    // 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;
-    }
-    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
-        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);
-            }
-        }
-
-#ifdef DOASSERT
-        ASSERT(evv.size()==rttinfos.size());
-        ASSERT(evv.size()>0);
-        unsigned s=0;
-        for (i=0; i<evv.size(); ++i) {
-            s += evv[i].size();
-        }
-        ASSERT(s==assocseq.size());
-#endif // def DOASSERT
-        
-        // 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(lst const & ls, lst const & lr) const
-{
-    return ncmul(subschildren(ls, lr));
-}
-
-ex ncmul::thisexprseq(exvector const & v) const
-{
-    return (new ncmul(v))->setflag(status_flags::dynallocated);
-}
-
-ex ncmul::thisexprseq(exvector * vp) const
-{
-    return (new ncmul(vp))->setflag(status_flags::dynallocated);
+	auto 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())
+					return return_types::noncommutative_composite;
+		}
+		++i;
+	}
+	// all factors checked
+	GINAC_ASSERT(!all_commutative); // not all factors should commutate, because this is a ncmul();
+	return all_commutative ? return_types::commutative : return_types::noncommutative;
 }
 
-// protected
+return_type_t ncmul::return_type_tinfo() const
+{
+	if (seq.empty())
+		return make_return_type_t<ncmul>();
 
-int ncmul::compare_same_type(basic const & other) const
-{
-    return exprseq::compare_same_type(other);
-}
-
-unsigned ncmul::return_type(void) 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
-    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
-{
-    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;
+	// return type_info of first noncommutative element
+	for (auto & i : seq)
+		if (i.return_type() == return_types::noncommutative)
+			return i.return_type_tinfo();
+
+	// no noncommutative element found, should not happen
+	return make_return_type_t<ncmul>();
 }
 
 //////////
@@ -541,54 +569,58 @@ unsigned ncmul::return_type_tinfo(void) const
 
 exvector ncmul::expandchildren(unsigned options) const
 {
-    exvector s;
-    s.reserve(seq.size());
+	auto cit = this->seq.begin(), end = this->seq.end();
+	while (cit != end) {
+		const ex & expanded_ex = cit->expand(options);
+		if (!are_ex_trivially_equal(*cit, expanded_ex)) {
 
-    for (exvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
-        s.push_back((*it).expand(options));
-    }
-    return s;
-}
+			// copy first part of seq which hasn't changed
+			exvector s(this->seq.begin(), cit);
+			s.reserve(this->seq.size());
 
-exvector const & ncmul::get_factors(void) const
-{
-    return seq;
-}
-
-//////////
-// static member variables
-//////////
+			// insert changed element
+			s.push_back(expanded_ex);
+			++cit;
 
-// protected
+			// copy rest
+			while (cit != end) {
+				s.push_back(cit->expand(options));
+				++cit;
+			}
 
-unsigned ncmul::precedence=50;
+			return s;
+		}
 
+		++cit;
+	}
 
-//////////
-// global constants
-//////////
+	return exvector(); // nothing has changed
+}
 
-const ncmul some_ncmul;
-type_info const & typeid_ncmul=typeid(some_ncmul);
+const exvector & ncmul::get_factors() const
+{
+	return seq;
+}
 
 //////////
 // friend functions
 //////////
 
-ex nonsimplified_ncmul(exvector const & v)
+ex reeval_ncmul(const exvector & v)
 {
-    return (new ncmul(v))->setflag(status_flags::dynallocated);
+	return dynallocate<ncmul>(v);
 }
 
-ex simplified_ncmul(exvector const & v)
+ex hold_ncmul(const exvector & v)
 {
-    if (v.size()==0) {
-        return exONE();
-    } 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 dynallocate<ncmul>(v).setflag(status_flags::evaluated);
 }
 
+GINAC_BIND_UNARCHIVER(ncmul);
+
 } // namespace GiNaC