X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fmatrix.cpp;h=0bedb6bb1a1e506fc0017ea3243d66c64ed3797a;hp=1f2e0ea8c655f80968c9096ea392f7ec0de00e71;hb=274c1632d78ec31575c4b3b328d75ad95a7855aa;hpb=c5ca06e3a25226684028dec4bd8cba0833998be6

diff --git a/ginac/matrix.cpp b/ginac/matrix.cpp
index 1f2e0ea8..0bedb6bb 100644
--- a/ginac/matrix.cpp
+++ b/ginac/matrix.cpp
@@ -20,6 +20,7 @@
  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
  */
 
+#include <iostream>
 #include <algorithm>
 #include <map>
 #include <stdexcept>
@@ -35,7 +36,6 @@
 #include "print.h"
 #include "archive.h"
 #include "utils.h"
-#include "debugmsg.h"
 
 namespace GiNaC {
 
@@ -48,8 +48,7 @@ GINAC_IMPLEMENT_REGISTERED_CLASS(matrix, basic)
 /** Default ctor.  Initializes to 1 x 1-dimensional zero-matrix. */
 matrix::matrix() : inherited(TINFO_matrix), row(1), col(1)
 {
-	debugmsg("matrix default ctor",LOGLEVEL_CONSTRUCT);
-	m.push_back(_ex0());
+	m.push_back(_ex0);
 }
 
 void matrix::copy(const matrix & other)
@@ -75,18 +74,14 @@ DEFAULT_DESTROY(matrix)
 matrix::matrix(unsigned r, unsigned c)
   : inherited(TINFO_matrix), row(r), col(c)
 {
-	debugmsg("matrix ctor from unsigned,unsigned",LOGLEVEL_CONSTRUCT);
-	m.resize(r*c, _ex0());
+	m.resize(r*c, _ex0);
 }
 
 // protected
 
 /** Ctor from representation, for internal use only. */
 matrix::matrix(unsigned r, unsigned c, const exvector & m2)
-  : inherited(TINFO_matrix), row(r), col(c), m(m2)
-{
-	debugmsg("matrix ctor from unsigned,unsigned,exvector",LOGLEVEL_CONSTRUCT);
-}
+  : inherited(TINFO_matrix), row(r), col(c), m(m2) {}
 
 /** Construct matrix from (flat) list of elements. If the list has fewer
  *  elements than the matrix, the remaining matrix elements are set to zero.
@@ -95,8 +90,7 @@ matrix::matrix(unsigned r, unsigned c, const exvector & m2)
 matrix::matrix(unsigned r, unsigned c, const lst & l)
   : inherited(TINFO_matrix), row(r), col(c)
 {
-	debugmsg("matrix ctor from unsigned,unsigned,lst",LOGLEVEL_CONSTRUCT);
-	m.resize(r*c, _ex0());
+	m.resize(r*c, _ex0);
 
 	for (unsigned i=0; i<l.nops(); i++) {
 		unsigned x = i % c;
@@ -113,7 +107,6 @@ matrix::matrix(unsigned r, unsigned c, const lst & l)
 
 matrix::matrix(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
 {
-	debugmsg("matrix ctor from archive_node", LOGLEVEL_CONSTRUCT);
 	if (!(n.find_unsigned("row", row)) || !(n.find_unsigned("col", col)))
 		throw (std::runtime_error("unknown matrix dimensions in archive"));
 	m.reserve(row * col);
@@ -141,21 +134,22 @@ void matrix::archive(archive_node &n) const
 DEFAULT_UNARCHIVE(matrix)
 
 //////////
-// functions overriding virtual functions from bases classes
+// functions overriding virtual functions from base classes
 //////////
 
 // public
 
 void matrix::print(const print_context & c, unsigned level) const
 {
-	debugmsg("matrix print", LOGLEVEL_PRINT);
-
-	if (is_of_type(c, print_tree)) {
+	if (is_a<print_tree>(c)) {
 
 		inherited::print(c, level);
 
 	} else {
 
+		if (is_a<print_python_repr>(c))
+			c.s << class_name() << '(';
+
 		c.s << "[";
 		for (unsigned y=0; y<row-1; ++y) {
 			c.s << "[";
@@ -174,6 +168,9 @@ void matrix::print(const print_context & c, unsigned level) const
 		m[row*col-1].print(c);
 		c.s << "]]";
 
+		if (is_a<print_python_repr>(c))
+			c.s << ')';
+
 	}
 }
 
@@ -198,21 +195,9 @@ ex & matrix::let_op(int i)
 	return m[i];
 }
 
-/** expands the elements of a matrix entry by entry. */
-ex matrix::expand(unsigned options) const
-{
-	exvector tmp(row*col);
-	for (unsigned i=0; i<row*col; ++i)
-		tmp[i] = m[i].expand(options);
-	
-	return matrix(row, col, tmp);
-}
-
 /** Evaluate matrix entry by entry. */
 ex matrix::eval(int level) const
 {
-	debugmsg("matrix eval",LOGLEVEL_MEMBER_FUNCTION);
-	
 	// check if we have to do anything at all
 	if ((level==1)&&(flags & status_flags::evaluated))
 		return *this;
@@ -232,30 +217,6 @@ ex matrix::eval(int level) const
 											   status_flags::evaluated );
 }
 
-/** Evaluate matrix numerically entry by entry. */
-ex matrix::evalf(int level) const
-{
-	debugmsg("matrix evalf",LOGLEVEL_MEMBER_FUNCTION);
-		
-	// check if we have to do anything at all
-	if (level==1)
-		return *this;
-	
-	// emergency break
-	if (level == -max_recursion_level) {
-		throw (std::runtime_error("matrix::evalf(): recursion limit exceeded"));
-	}
-	
-	// evalf() entry by entry
-	exvector m2(row*col);
-	--level;
-	for (unsigned r=0; r<row; ++r)
-		for (unsigned c=0; c<col; ++c)
-			m2[r*col+c] = m[r*col+c].evalf(level);
-	
-	return matrix(row, col, m2);
-}
-
 ex matrix::subs(const lst & ls, const lst & lr, bool no_pattern) const
 {
 	exvector m2(row * col);
@@ -263,15 +224,15 @@ ex matrix::subs(const lst & ls, const lst & lr, bool no_pattern) const
 		for (unsigned c=0; c<col; ++c)
 			m2[r*col+c] = m[r*col+c].subs(ls, lr, no_pattern);
 
-	return ex(matrix(row, col, m2)).bp->basic::subs(ls, lr, no_pattern);
+	return matrix(row, col, m2).basic::subs(ls, lr, no_pattern);
 }
 
 // protected
 
 int matrix::compare_same_type(const basic & other) const
 {
-	GINAC_ASSERT(is_exactly_of_type(other, matrix));
-	const matrix & o = static_cast<matrix &>(const_cast<basic &>(other));
+	GINAC_ASSERT(is_exactly_a<matrix>(other));
+	const matrix &o = static_cast<const matrix &>(other);
 	
 	// compare number of rows
 	if (row != o.rows())
@@ -293,11 +254,21 @@ int matrix::compare_same_type(const basic & other) const
 	return 0;
 }
 
+bool matrix::match_same_type(const basic & other) const
+{
+	GINAC_ASSERT(is_exactly_a<matrix>(other));
+	const matrix & o = static_cast<const matrix &>(other);
+	
+	// The number of rows and columns must be the same. This is necessary to
+	// prevent a 2x3 matrix from matching a 3x2 one.
+	return row == o.rows() && col == o.cols();
+}
+
 /** Automatic symbolic evaluation of an indexed matrix. */
 ex matrix::eval_indexed(const basic & i) const
 {
-	GINAC_ASSERT(is_of_type(i, indexed));
-	GINAC_ASSERT(is_ex_of_type(i.op(0), matrix));
+	GINAC_ASSERT(is_a<indexed>(i));
+	GINAC_ASSERT(is_a<matrix>(i.op(0)));
 
 	bool all_indices_unsigned = static_cast<const indexed &>(i).all_index_values_are(info_flags::nonnegint);
 
@@ -308,7 +279,7 @@ ex matrix::eval_indexed(const basic & i) const
 		if (row != 1 && col != 1)
 			throw (std::runtime_error("matrix::eval_indexed(): vector must have exactly 1 index"));
 
-		const idx & i1 = ex_to_idx(i.op(1));
+		const idx & i1 = ex_to<idx>(i.op(1));
 
 		if (col == 1) {
 
@@ -318,7 +289,7 @@ ex matrix::eval_indexed(const basic & i) const
 
 			// Index numeric -> return vector element
 			if (all_indices_unsigned) {
-				unsigned n1 = ex_to_numeric(i1.get_value()).to_int();
+				unsigned n1 = ex_to<numeric>(i1.get_value()).to_int();
 				if (n1 >= row)
 					throw (std::runtime_error("matrix::eval_indexed(): value of index exceeds number of vector elements"));
 				return (*this)(n1, 0);
@@ -332,7 +303,7 @@ ex matrix::eval_indexed(const basic & i) const
 
 			// Index numeric -> return vector element
 			if (all_indices_unsigned) {
-				unsigned n1 = ex_to_numeric(i1.get_value()).to_int();
+				unsigned n1 = ex_to<numeric>(i1.get_value()).to_int();
 				if (n1 >= col)
 					throw (std::runtime_error("matrix::eval_indexed(): value of index exceeds number of vector elements"));
 				return (*this)(0, n1);
@@ -342,8 +313,8 @@ ex matrix::eval_indexed(const basic & i) const
 	} else if (i.nops() == 3) {
 
 		// Two indices
-		const idx & i1 = ex_to_idx(i.op(1));
-		const idx & i2 = ex_to_idx(i.op(2));
+		const idx & i1 = ex_to<idx>(i.op(1));
+		const idx & i2 = ex_to<idx>(i.op(2));
 
 		if (!i1.get_dim().is_equal(row))
 			throw (std::runtime_error("matrix::eval_indexed(): dimension of first index must match number of rows"));
@@ -356,7 +327,7 @@ ex matrix::eval_indexed(const basic & i) const
 
 		// Both indices numeric -> return matrix element
 		if (all_indices_unsigned) {
-			unsigned n1 = ex_to_numeric(i1.get_value()).to_int(), n2 = ex_to_numeric(i2.get_value()).to_int();
+			unsigned n1 = ex_to<numeric>(i1.get_value()).to_int(), n2 = ex_to<numeric>(i2.get_value()).to_int();
 			if (n1 >= row)
 				throw (std::runtime_error("matrix::eval_indexed(): value of first index exceeds number of rows"));
 			if (n2 >= col)
@@ -373,17 +344,17 @@ ex matrix::eval_indexed(const basic & i) const
 /** Sum of two indexed matrices. */
 ex matrix::add_indexed(const ex & self, const ex & other) const
 {
-	GINAC_ASSERT(is_ex_of_type(self, indexed));
-	GINAC_ASSERT(is_ex_of_type(self.op(0), matrix));
-	GINAC_ASSERT(is_ex_of_type(other, indexed));
+	GINAC_ASSERT(is_a<indexed>(self));
+	GINAC_ASSERT(is_a<matrix>(self.op(0)));
+	GINAC_ASSERT(is_a<indexed>(other));
 	GINAC_ASSERT(self.nops() == 2 || self.nops() == 3);
 
 	// Only add two matrices
 	if (is_ex_of_type(other.op(0), matrix)) {
 		GINAC_ASSERT(other.nops() == 2 || other.nops() == 3);
 
-		const matrix &self_matrix = ex_to_matrix(self.op(0));
-		const matrix &other_matrix = ex_to_matrix(other.op(0));
+		const matrix &self_matrix = ex_to<matrix>(self.op(0));
+		const matrix &other_matrix = ex_to<matrix>(other.op(0));
 
 		if (self.nops() == 2 && other.nops() == 2) { // vector + vector
 
@@ -409,11 +380,11 @@ ex matrix::add_indexed(const ex & self, const ex & other) const
 /** Product of an indexed matrix with a number. */
 ex matrix::scalar_mul_indexed(const ex & self, const numeric & other) const
 {
-	GINAC_ASSERT(is_ex_of_type(self, indexed));
-	GINAC_ASSERT(is_ex_of_type(self.op(0), matrix));
+	GINAC_ASSERT(is_a<indexed>(self));
+	GINAC_ASSERT(is_a<matrix>(self.op(0)));
 	GINAC_ASSERT(self.nops() == 2 || self.nops() == 3);
 
-	const matrix &self_matrix = ex_to_matrix(self.op(0));
+	const matrix &self_matrix = ex_to<matrix>(self.op(0));
 
 	if (self.nops() == 2)
 		return indexed(self_matrix.mul(other), self.op(1));
@@ -424,10 +395,10 @@ ex matrix::scalar_mul_indexed(const ex & self, const numeric & other) const
 /** Contraction of an indexed matrix with something else. */
 bool matrix::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
 {
-	GINAC_ASSERT(is_ex_of_type(*self, indexed));
-	GINAC_ASSERT(is_ex_of_type(*other, indexed));
+	GINAC_ASSERT(is_a<indexed>(*self));
+	GINAC_ASSERT(is_a<indexed>(*other));
 	GINAC_ASSERT(self->nops() == 2 || self->nops() == 3);
-	GINAC_ASSERT(is_ex_of_type(self->op(0), matrix));
+	GINAC_ASSERT(is_a<matrix>(self->op(0)));
 
 	// Only contract with other matrices
 	if (!is_ex_of_type(other->op(0), matrix))
@@ -435,14 +406,12 @@ bool matrix::contract_with(exvector::iterator self, exvector::iterator other, ex
 
 	GINAC_ASSERT(other->nops() == 2 || other->nops() == 3);
 
-	const matrix &self_matrix = ex_to_matrix(self->op(0));
-	const matrix &other_matrix = ex_to_matrix(other->op(0));
+	const matrix &self_matrix = ex_to<matrix>(self->op(0));
+	const matrix &other_matrix = ex_to<matrix>(other->op(0));
 
 	if (self->nops() == 2) {
-		unsigned self_dim = (self_matrix.col == 1) ? self_matrix.row : self_matrix.col;
 
 		if (other->nops() == 2) { // vector * vector (scalar product)
-			unsigned other_dim = (other_matrix.col == 1) ? other_matrix.row : other_matrix.col;
 
 			if (self_matrix.col == 1) {
 				if (other_matrix.col == 1) {
@@ -461,7 +430,7 @@ bool matrix::contract_with(exvector::iterator self, exvector::iterator other, ex
 					*self = self_matrix.mul(other_matrix.transpose())(0, 0);
 				}
 			}
-			*other = _ex1();
+			*other = _ex1;
 			return true;
 
 		} else { // vector * matrix
@@ -472,7 +441,7 @@ bool matrix::contract_with(exvector::iterator self, exvector::iterator other, ex
 					*self = indexed(self_matrix.mul(other_matrix), other->op(2));
 				else
 					*self = indexed(self_matrix.transpose().mul(other_matrix), other->op(2));
-				*other = _ex1();
+				*other = _ex1;
 				return true;
 			}
 
@@ -482,7 +451,7 @@ bool matrix::contract_with(exvector::iterator self, exvector::iterator other, ex
 					*self = indexed(other_matrix.mul(self_matrix), other->op(1));
 				else
 					*self = indexed(other_matrix.mul(self_matrix.transpose()), other->op(1));
-				*other = _ex1();
+				*other = _ex1;
 				return true;
 			}
 		}
@@ -492,28 +461,28 @@ bool matrix::contract_with(exvector::iterator self, exvector::iterator other, ex
 		// A_ij * B_jk = (A*B)_ik
 		if (is_dummy_pair(self->op(2), other->op(1))) {
 			*self = indexed(self_matrix.mul(other_matrix), self->op(1), other->op(2));
-			*other = _ex1();
+			*other = _ex1;
 			return true;
 		}
 
 		// A_ij * B_kj = (A*Btrans)_ik
 		if (is_dummy_pair(self->op(2), other->op(2))) {
 			*self = indexed(self_matrix.mul(other_matrix.transpose()), self->op(1), other->op(1));
-			*other = _ex1();
+			*other = _ex1;
 			return true;
 		}
 
 		// A_ji * B_jk = (Atrans*B)_ik
 		if (is_dummy_pair(self->op(1), other->op(1))) {
 			*self = indexed(self_matrix.transpose().mul(other_matrix), self->op(2), other->op(2));
-			*other = _ex1();
+			*other = _ex1;
 			return true;
 		}
 
 		// A_ji * B_kj = (B*A)_ki
 		if (is_dummy_pair(self->op(1), other->op(2))) {
 			*self = indexed(other_matrix.mul(self_matrix), other->op(1), self->op(2));
-			*other = _ex1();
+			*other = _ex1;
 			return true;
 		}
 	}
@@ -537,10 +506,10 @@ matrix matrix::add(const matrix & other) const
 		throw std::logic_error("matrix::add(): incompatible matrices");
 	
 	exvector sum(this->m);
-	exvector::iterator i;
-	exvector::const_iterator ci;
-	for (i=sum.begin(), ci=other.m.begin(); i!=sum.end(); ++i, ++ci)
-		(*i) += (*ci);
+	exvector::iterator i = sum.begin(), end = sum.end();
+	exvector::const_iterator ci = other.m.begin();
+	while (i != end)
+		*i++ += *ci++;
 	
 	return matrix(row,col,sum);
 }
@@ -555,10 +524,10 @@ matrix matrix::sub(const matrix & other) const
 		throw std::logic_error("matrix::sub(): incompatible matrices");
 	
 	exvector dif(this->m);
-	exvector::iterator i;
-	exvector::const_iterator ci;
-	for (i=dif.begin(), ci=other.m.begin(); i!=dif.end(); ++i, ++ci)
-		(*i) -= (*ci);
+	exvector::iterator i = dif.begin(), end = dif.end();
+	exvector::const_iterator ci = other.m.begin();
+	while (i != end)
+		*i++ -= *ci++;
 	
 	return matrix(row,col,dif);
 }
@@ -625,32 +594,31 @@ matrix matrix::pow(const ex & expn) const
 		// Integer cases are computed by successive multiplication, using the
 		// obvious shortcut of storing temporaries, like A^4 == (A*A)*(A*A).
 		if (expn.info(info_flags::integer)) {
-			numeric k;
-			matrix prod(row,col);
+			numeric b = ex_to<numeric>(expn);
+			matrix A(row,col);
 			if (expn.info(info_flags::negative)) {
-				k = -ex_to_numeric(expn);
-				prod = this->inverse();
+				b *= -1;
+				A = this->inverse();
 			} else {
-				k = ex_to_numeric(expn);
-				prod = *this;
+				A = *this;
 			}
-			matrix result(row,col);
+			matrix C(row,col);
 			for (unsigned r=0; r<row; ++r)
-				result(r,r) = _ex1();
-			numeric b(1);
-			// this loop computes the representation of k in base 2 and
-			// multiplies the factors whenever needed:
-			while (b.compare(k)<=0) {
-				b *= numeric(2);
-				numeric r(mod(k,b));
-				if (!r.is_zero()) {
-					k -= r;
-					result = result.mul(prod);
+				C(r,r) = _ex1;
+			// This loop computes the representation of b in base 2 from right
+			// to left and multiplies the factors whenever needed.  Note
+			// that this is not entirely optimal but close to optimal and
+			// "better" algorithms are much harder to implement.  (See Knuth,
+			// TAoCP2, section "Evaluation of Powers" for a good discussion.)
+			while (b!=1) {
+				if (b.is_odd()) {
+					C = C.mul(A);
+					b -= 1;
 				}
-				if (b.compare(k)<=0)
-					prod = prod.mul(prod);
+				b *= _num1_2;  // b /= 2, still integer.
+				A = A.mul(A);
 			}
-			return result;
+			return A.mul(C);
 		}
 	}
 	throw (std::runtime_error("matrix::pow(): don't know how to handle exponent"));
@@ -723,9 +691,10 @@ ex matrix::determinant(unsigned algo) const
 	bool numeric_flag = true;
 	bool normal_flag = false;
 	unsigned sparse_count = 0;  // counts non-zero elements
-	for (exvector::const_iterator r=m.begin(); r!=m.end(); ++r) {
+	exvector::const_iterator r = m.begin(), rend = m.end();
+	while (r != rend) {
 		lst srl;  // symbol replacement list
-		ex rtest = (*r).to_rational(srl);
+		ex rtest = r->to_rational(srl);
 		if (!rtest.is_zero())
 			++sparse_count;
 		if (!rtest.info(info_flags::numeric))
@@ -733,6 +702,7 @@ ex matrix::determinant(unsigned algo) const
 		if (!rtest.info(info_flags::crational_polynomial) &&
 			 rtest.info(info_flags::rational_function))
 			normal_flag = true;
+		++r;
 	}
 	
 	// Here is the heuristics in case this routine has to decide:
@@ -785,7 +755,7 @@ ex matrix::determinant(unsigned algo) const
 			int sign;
 			sign = tmp.division_free_elimination(true);
 			if (sign==0)
-				return _ex0();
+				return _ex0;
 			ex det = tmp.m[row*col-1];
 			// factor out accumulated bogus slag
 			for (unsigned d=0; d<row-2; ++d)
@@ -797,10 +767,13 @@ ex matrix::determinant(unsigned algo) const
 		default: {
 			// This is the minor expansion scheme.  We always develop such
 			// that the smallest minors (i.e, the trivial 1x1 ones) are on the
-			// rightmost column.  For this to be efficient it turns out that
-			// the emptiest columns (i.e. the ones with most zeros) should be
-			// the ones on the right hand side.  Therefore we presort the
-			// columns of the matrix:
+			// rightmost column.  For this to be efficient, empirical tests
+			// have shown that the emptiest columns (i.e. the ones with most
+			// zeros) should be the ones on the right hand side -- although
+			// this might seem counter-intuitive (and in contradiction to some
+			// literature like the FORM manual).  Please go ahead and test it
+			// if you don't believe me!  Therefore we presort the columns of
+			// the matrix:
 			typedef std::pair<unsigned,unsigned> uintpair;
 			std::vector<uintpair> c_zeros;  // number of zeros in column
 			for (unsigned c=0; c<col; ++c) {
@@ -810,15 +783,15 @@ ex matrix::determinant(unsigned algo) const
 						++acc;
 				c_zeros.push_back(uintpair(acc,c));
 			}
-			sort(c_zeros.begin(),c_zeros.end());
+			std::sort(c_zeros.begin(),c_zeros.end());
 			std::vector<unsigned> pre_sort;
-			for (std::vector<uintpair>::iterator i=c_zeros.begin(); i!=c_zeros.end(); ++i)
+			for (std::vector<uintpair>::const_iterator i=c_zeros.begin(); i!=c_zeros.end(); ++i)
 				pre_sort.push_back(i->second);
 			std::vector<unsigned> pre_sort_test(pre_sort); // permutation_sign() modifies the vector so we make a copy here
 			int sign = permutation_sign(pre_sort_test.begin(), pre_sort_test.end());
 			exvector result(row*col);  // represents sorted matrix
 			unsigned c = 0;
-			for (std::vector<unsigned>::iterator i=pre_sort.begin();
+			for (std::vector<unsigned>::const_iterator i=pre_sort.begin();
 				 i!=pre_sort.end();
 				 ++i,++c) {
 				for (unsigned r=0; r<row; ++r)
@@ -874,10 +847,11 @@ ex matrix::charpoly(const symbol & lambda) const
 		throw (std::logic_error("matrix::charpoly(): matrix not square"));
 	
 	bool numeric_flag = true;
-	for (exvector::const_iterator r=m.begin(); r!=m.end(); ++r) {
-		if (!(*r).info(info_flags::numeric)) {
+	exvector::const_iterator r = m.begin(), rend = m.end();
+	while (r!=rend && numeric_flag==true) {
+		if (!r->info(info_flags::numeric))
 			numeric_flag = false;
-		}
+		++r;
 	}
 	
 	// The pure numeric case is traditionally rather common.  Hence, it is
@@ -924,7 +898,7 @@ matrix matrix::inverse(void) const
 	// First populate the identity matrix supposed to become the right hand side.
 	matrix identity(row,col);
 	for (unsigned i=0; i<row; ++i)
-		identity(i,i) = _ex1();
+		identity(i,i) = _ex1;
 	
 	// Populate a dummy matrix of variables, just because of compatibility with
 	// matrix::solve() which wants this (for compatibility with under-determined
@@ -984,9 +958,11 @@ matrix matrix::solve(const matrix & vars,
 	
 	// Gather some statistical information about the augmented matrix:
 	bool numeric_flag = true;
-	for (exvector::const_iterator r=aug.m.begin(); r!=aug.m.end(); ++r) {
-		if (!(*r).info(info_flags::numeric))
+	exvector::const_iterator r = aug.m.begin(), rend = aug.m.end();
+	while (r!=rend && numeric_flag==true) {
+		if (!r->info(info_flags::numeric))
 			numeric_flag = false;
+		++r;
 	}
 	
 	// Here is the heuristics in case this routine has to decide:
@@ -1133,7 +1109,7 @@ ex matrix::determinant_minor(void) const
 			Pkey.push_back(i);
 		unsigned fc = 0;  // controls logic for our strange flipper counter
 		do {
-			det = _ex0();
+			det = _ex0;
 			for (unsigned r=0; r<n-c; ++r) {
 				// maybe there is nothing to do?
 				if (m[Pkey[r]*n+c].is_zero())
@@ -1213,12 +1189,12 @@ int matrix::gauss_elimination(const bool det)
 				}
 				// fill up left hand side with zeros
 				for (unsigned c=0; c<=r1; ++c)
-					this->m[r2*n+c] = _ex0();
+					this->m[r2*n+c] = _ex0;
 			}
 			if (det) {
 				// save space by deleting no longer needed elements
 				for (unsigned c=r0+1; c<n; ++c)
-					this->m[r0*n+c] = _ex0();
+					this->m[r0*n+c] = _ex0;
 			}
 			++r0;
 		}
@@ -1260,12 +1236,12 @@ int matrix::division_free_elimination(const bool det)
 					this->m[r2*n+c] = (this->m[r0*n+r1]*this->m[r2*n+c] - this->m[r2*n+r1]*this->m[r0*n+c]).expand();
 				// fill up left hand side with zeros
 				for (unsigned c=0; c<=r1; ++c)
-					this->m[r2*n+c] = _ex0();
+					this->m[r2*n+c] = _ex0;
 			}
 			if (det) {
 				// save space by deleting no longer needed elements
 				for (unsigned c=r0+1; c<n; ++c)
-					this->m[r0*n+c] = _ex0();
+					this->m[r0*n+c] = _ex0;
 			}
 			++r0;
 		}
@@ -1333,13 +1309,13 @@ int matrix::fraction_free_elimination(const bool det)
 	matrix tmp_n(*this);
 	matrix tmp_d(m,n);  // for denominators, if needed
 	lst srl;  // symbol replacement list
-	exvector::iterator it = this->m.begin();
-	exvector::iterator tmp_n_it = tmp_n.m.begin();
-	exvector::iterator tmp_d_it = tmp_d.m.begin();
-	for (; it!= this->m.end(); ++it, ++tmp_n_it, ++tmp_d_it) {
-		(*tmp_n_it) = (*it).normal().to_rational(srl);
-		(*tmp_d_it) = (*tmp_n_it).denom();
-		(*tmp_n_it) = (*tmp_n_it).numer();
+	exvector::const_iterator cit = this->m.begin(), citend = this->m.end();
+	exvector::iterator tmp_n_it = tmp_n.m.begin(), tmp_d_it = tmp_d.m.begin();
+	while (cit != citend) {
+		ex nd = cit->normal().to_rational(srl).numer_denom();
+		++cit;
+		*tmp_n_it++ = nd.op(0);
+		*tmp_d_it++ = nd.op(1);
 	}
 	
 	unsigned r0 = 0;
@@ -1373,7 +1349,7 @@ int matrix::fraction_free_elimination(const bool det)
 				}
 				// fill up left hand side with zeros
 				for (unsigned c=0; c<=r1; ++c)
-					tmp_n.m[r2*n+c] = _ex0();
+					tmp_n.m[r2*n+c] = _ex0;
 			}
 			if ((r1<n-1)&&(r0<m-1)) {
 				// compute next iteration's divisor
@@ -1382,8 +1358,8 @@ int matrix::fraction_free_elimination(const bool det)
 				if (det) {
 					// save space by deleting no longer needed elements
 					for (unsigned c=0; c<n; ++c) {
-						tmp_n.m[r0*n+c] = _ex0();
-						tmp_d.m[r0*n+c] = _ex1();
+						tmp_n.m[r0*n+c] = _ex0;
+						tmp_d.m[r0*n+c] = _ex1;
 					}
 				}
 			}
@@ -1391,11 +1367,11 @@ int matrix::fraction_free_elimination(const bool det)
 		}
 	}
 	// repopulate *this matrix:
-	it = this->m.begin();
+	exvector::iterator it = this->m.begin(), itend = this->m.end();
 	tmp_n_it = tmp_n.m.begin();
 	tmp_d_it = tmp_d.m.begin();
-	for (; it!= this->m.end(); ++it, ++tmp_n_it, ++tmp_d_it)
-		(*it) = ((*tmp_n_it)/(*tmp_d_it)).subs(srl);
+	while (it != itend)
+		*it++ = ((*tmp_n_it++)/(*tmp_d_it++)).subs(srl);
 	
 	return sign;
 }
@@ -1423,12 +1399,12 @@ int matrix::pivot(unsigned ro, unsigned co, bool symbolic)
 			++k;
 	} else {
 		// search largest element in column co beginning at row ro
-		GINAC_ASSERT(is_ex_of_type(this->m[k*col+co],numeric));
+		GINAC_ASSERT(is_a<numeric>(this->m[k*col+co]));
 		unsigned kmax = k+1;
-		numeric mmax = abs(ex_to_numeric(m[kmax*col+co]));
+		numeric mmax = abs(ex_to<numeric>(m[kmax*col+co]));
 		while (kmax<row) {
-			GINAC_ASSERT(is_ex_of_type(this->m[kmax*col+co],numeric));
-			numeric tmp = ex_to_numeric(this->m[kmax*col+co]);
+			GINAC_ASSERT(is_a<numeric>(this->m[kmax*col+co]));
+			numeric tmp = ex_to<numeric>(this->m[kmax*col+co]);
 			if (abs(tmp) > mmax) {
 				mmax = tmp;
 				k = kmax;
@@ -1468,7 +1444,7 @@ ex lst_to_matrix(const lst & l)
 			if (l.op(i).nops() > j)
 				m(i, j) = l.op(i).op(j);
 			else
-				m(i, j) = _ex0();
+				m(i, j) = _ex0;
 	return m;
 }