X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fmatrix.cpp;h=4828bb9392db1e87666e382a77e5c4a5368f0cfb;hp=1a5d6953c3d994365d9d6b05a60ebf351119e7bd;hb=1b48bfdf43c8d104cb8b06147f27cb9efe42cb16;hpb=539de73dc25de63f2888f8696d73ac3fc83db45f

diff --git a/ginac/matrix.cpp b/ginac/matrix.cpp
index 1a5d6953..4828bb93 100644
--- a/ginac/matrix.cpp
+++ b/ginac/matrix.cpp
@@ -3,7 +3,7 @@
  *  Implementation of symbolic matrices */
 
 /*
- *  GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
+ *  GiNaC Copyright (C) 1999-2003 Johannes Gutenberg University Mainz, Germany
  *
  *  This program is free software; you can redistribute it and/or modify
  *  it under the terms of the GNU General Public License as published by
@@ -20,57 +20,43 @@
  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
  */
 
+#include <string>
+#include <iostream>
+#include <sstream>
 #include <algorithm>
 #include <map>
 #include <stdexcept>
 
 #include "matrix.h"
-#include "archive.h"
 #include "numeric.h"
 #include "lst.h"
 #include "idx.h"
 #include "indexed.h"
-#include "utils.h"
-#include "debugmsg.h"
+#include "add.h"
 #include "power.h"
 #include "symbol.h"
+#include "operators.h"
 #include "normal.h"
+#include "print.h"
+#include "archive.h"
+#include "utils.h"
 
 namespace GiNaC {
 
 GINAC_IMPLEMENT_REGISTERED_CLASS(matrix, basic)
 
 //////////
-// default ctor, dtor, copy ctor, assignment operator and helpers:
+// default constructor
 //////////
 
-// public
-
 /** 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());
-}
-
-// protected
-
-/** For use by copy ctor and assignment operator. */
-void matrix::copy(const matrix & other)
-{
-	inherited::copy(other);
-	row = other.row;
-	col = other.col;
-	m = other.m;  // STL's vector copying invoked here
-}
-
-void matrix::destroy(bool call_parent)
-{
-	if (call_parent) inherited::destroy(call_parent);
+	m.push_back(_ex0);
 }
 
 //////////
-// other ctors
+// other constructors
 //////////
 
 // public
@@ -82,27 +68,40 @@ void matrix::destroy(bool call_parent)
 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)
+  : 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.
+ *  If the list has more elements than the matrix, the excessive elements are
+ *  thrown away. */
+matrix::matrix(unsigned r, unsigned c, const lst & l)
+  : inherited(TINFO_matrix), row(r), col(c)
 {
-	debugmsg("matrix ctor from unsigned,unsigned,exvector",LOGLEVEL_CONSTRUCT);
+	m.resize(r*c, _ex0);
+
+	size_t i = 0;
+	for (lst::const_iterator it = l.begin(); it != l.end(); ++it, ++i) {
+		size_t x = i % c;
+		size_t y = i / c;
+		if (y >= r)
+			break; // matrix smaller than list: throw away excessive elements
+		m[y*c+x] = *it;
+	}
 }
 
 //////////
 // archiving
 //////////
 
-/** Construct object from archive_node. */
-matrix::matrix(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
+matrix::matrix(const archive_node &n, 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);
@@ -115,13 +114,6 @@ matrix::matrix(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst
 	}
 }
 
-/** Unarchive the object. */
-ex matrix::unarchive(const archive_node &n, const lst &sym_lst)
-{
-	return (new matrix(n, sym_lst))->setflag(status_flags::dynallocated);
-}
-
-/** Archive the object. */
 void matrix::archive(archive_node &n) const
 {
 	inherited::archive(n);
@@ -134,96 +126,90 @@ 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(std::ostream & os, unsigned upper_precedence) const
+void matrix::print(const print_context & c, unsigned level) const
 {
-	debugmsg("matrix print",LOGLEVEL_PRINT);
-	os << "[[ ";
-	for (unsigned r=0; r<row-1; ++r) {
-		os << "[[";
-		for (unsigned c=0; c<col-1; ++c)
-			os << m[r*col+c] << ",";
-		os << m[col*(r+1)-1] << "]], ";
-	}
-	os << "[[";
-	for (unsigned c=0; c<col-1; ++c)
-		os << m[(row-1)*col+c] << ",";
-	os << m[row*col-1] << "]] ]]";
-}
+	if (is_a<print_tree>(c)) {
+
+		inherited::print(c, level);
+
+	} else {
+
+		if (is_a<print_python_repr>(c))
+			c.s << class_name() << '(';
+
+		if (is_a<print_latex>(c))
+			c.s << "\\left(\\begin{array}{" << std::string(col,'c') << "}";
+		else
+			c.s << "[";
+
+		for (unsigned ro=0; ro<row; ++ro) {
+			if (!is_a<print_latex>(c))
+				c.s << "[";
+			for (unsigned co=0; co<col; ++co) {
+				m[ro*col+co].print(c);
+				if (co<col-1) {
+					if (is_a<print_latex>(c))
+						c.s << "&";
+					else
+						c.s << ",";
+				} else {
+					if (!is_a<print_latex>(c))
+						c.s << "]";
+				}
+			}
+			if (ro<row-1) {
+				if (is_a<print_latex>(c))
+					c.s << "\\\\";
+				else
+					c.s << ",";
+			}
+		}
+
+		if (is_a<print_latex>(c))
+			c.s << "\\end{array}\\right)";
+		else
+			c.s << "]";
+
+		if (is_a<print_python_repr>(c))
+			c.s << ')';
 
-void matrix::printraw(std::ostream & os) const
-{
-	debugmsg("matrix printraw",LOGLEVEL_PRINT);
-	os << class_name() << "(" << row << "," << col <<",";
-	for (unsigned r=0; r<row-1; ++r) {
-		os << "(";
-		for (unsigned c=0; c<col-1; ++c)
-			os << m[r*col+c] << ",";
-		os << m[col*(r-1)-1] << "),";
 	}
-	os << "(";
-	for (unsigned c=0; c<col-1; ++c)
-		os << m[(row-1)*col+c] << ",";
-	os << m[row*col-1] << "))";
 }
 
 /** nops is defined to be rows x columns. */
-unsigned matrix::nops() const
+size_t matrix::nops() const
 {
-	return row*col;
+	return static_cast<size_t>(row) * static_cast<size_t>(col);
 }
 
 /** returns matrix entry at position (i/col, i%col). */
-ex matrix::op(int i) const
+ex matrix::op(size_t i) const
 {
-	return m[i];
-}
-
-/** returns matrix entry at position (i/col, i%col). */
-ex & matrix::let_op(int i)
-{
-	GINAC_ASSERT(i>=0);
 	GINAC_ASSERT(i<nops());
 	
 	return m[i];
 }
 
-/** expands the elements of a matrix entry by entry. */
-ex matrix::expand(unsigned options) const
+/** returns writable matrix entry at position (i/col, i%col). */
+ex & matrix::let_op(size_t i)
 {
-	exvector tmp(row*col);
-	for (unsigned i=0; i<row*col; ++i)
-		tmp[i] = m[i].expand(options);
-	
-	return matrix(row, col, tmp);
-}
-
-/** Search ocurrences.  A matrix 'has' an expression if it is the expression
- *  itself or one of the elements 'has' it. */
-bool matrix::has(const ex & other) const
-{
-	GINAC_ASSERT(other.bp!=0);
-	
-	// tautology: it is the expression itself
-	if (is_equal(*other.bp)) return true;
-	
-	// search all the elements
-	for (exvector::const_iterator r=m.begin(); r!=m.end(); ++r)
-		if ((*r).has(other)) return true;
+	GINAC_ASSERT(i<nops());
 	
-	return false;
+	ensure_if_modifiable();
+	return m[i];
 }
 
 /** 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;
@@ -240,49 +226,25 @@ ex matrix::eval(int level) const
 			m2[r*col+c] = m[r*col+c].eval(level);
 	
 	return (new matrix(row, col, m2))->setflag(status_flags::dynallocated |
-											   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);
+											   status_flags::evaluated);
 }
 
-ex matrix::subs(const lst & ls, const lst & lr) const
+ex matrix::subs(const exmap & mp, unsigned options) const
 {
 	exvector m2(row * col);
 	for (unsigned r=0; r<row; ++r)
 		for (unsigned c=0; c<col; ++c)
-			m2[r*col+c] = m[r*col+c].subs(ls, lr);
+			m2[r*col+c] = m[r*col+c].subs(mp, options);
 
-	return matrix(row, col, m2);
+	return matrix(row, col, m2).subs_one_level(mp, options);
 }
 
 // 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())
@@ -304,11 +266,21 @@ 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);
 
@@ -319,7 +291,7 @@ 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) {
 
@@ -329,7 +301,7 @@ 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);
@@ -343,7 +315,7 @@ 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);
@@ -353,8 +325,8 @@ 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"));
@@ -367,7 +339,7 @@ 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)
@@ -381,28 +353,77 @@ ex matrix::eval_indexed(const basic & i) const
 	return i.hold();
 }
 
+/** Sum of two indexed matrices. */
+ex matrix::add_indexed(const ex & self, const ex & other) const
+{
+	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_a<matrix>(other.op(0))) {
+		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));
+
+		if (self.nops() == 2 && other.nops() == 2) { // vector + vector
+
+			if (self_matrix.row == other_matrix.row)
+				return indexed(self_matrix.add(other_matrix), self.op(1));
+			else if (self_matrix.row == other_matrix.col)
+				return indexed(self_matrix.add(other_matrix.transpose()), self.op(1));
+
+		} else if (self.nops() == 3 && other.nops() == 3) { // matrix + matrix
+
+			if (self.op(1).is_equal(other.op(1)) && self.op(2).is_equal(other.op(2)))
+				return indexed(self_matrix.add(other_matrix), self.op(1), self.op(2));
+			else if (self.op(1).is_equal(other.op(2)) && self.op(2).is_equal(other.op(1)))
+				return indexed(self_matrix.add(other_matrix.transpose()), self.op(1), self.op(2));
+
+		}
+	}
+
+	// Don't know what to do, return unevaluated sum
+	return self + other;
+}
+
+/** Product of an indexed matrix with a number. */
+ex matrix::scalar_mul_indexed(const ex & self, const numeric & other) const
+{
+	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));
+
+	if (self.nops() == 2)
+		return indexed(self_matrix.mul(other), self.op(1));
+	else // self.nops() == 3
+		return indexed(self_matrix.mul(other), self.op(1), self.op(2));
+}
+
 /** 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))
+	if (!is_a<matrix>(other->op(0)))
 		return false;
 
 	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) {
@@ -421,7 +442,7 @@ 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
@@ -432,7 +453,7 @@ 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;
 			}
 
@@ -442,7 +463,7 @@ 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;
 			}
 		}
@@ -452,28 +473,28 @@ 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;
 		}
 	}
@@ -494,13 +515,13 @@ bool matrix::contract_with(exvector::iterator self, exvector::iterator other, ex
 matrix matrix::add(const matrix & other) const
 {
 	if (col != other.col || row != other.row)
-		throw (std::logic_error("matrix::add(): incompatible matrices"));
+		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);
 }
@@ -512,13 +533,13 @@ matrix matrix::add(const matrix & other) const
 matrix matrix::sub(const matrix & other) const
 {
 	if (col != other.col || row != other.row)
-		throw (std::logic_error("matrix::sub(): incompatible matrices"));
+		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);
 }
@@ -530,7 +551,7 @@ matrix matrix::sub(const matrix & other) const
 matrix matrix::mul(const matrix & other) const
 {
 	if (this->cols() != other.rows())
-		throw (std::logic_error("matrix::mul(): incompatible matrices"));
+		throw std::logic_error("matrix::mul(): incompatible matrices");
 	
 	exvector prod(this->rows()*other.cols());
 	
@@ -546,7 +567,79 @@ matrix matrix::mul(const matrix & other) const
 }
 
 
-/** operator() to access elements.
+/** Product of matrix and scalar. */
+matrix matrix::mul(const numeric & other) const
+{
+	exvector prod(row * col);
+
+	for (unsigned r=0; r<row; ++r)
+		for (unsigned c=0; c<col; ++c)
+			prod[r*col+c] = m[r*col+c] * other;
+
+	return matrix(row, col, prod);
+}
+
+
+/** Product of matrix and scalar expression. */
+matrix matrix::mul_scalar(const ex & other) const
+{
+	if (other.return_type() != return_types::commutative)
+		throw std::runtime_error("matrix::mul_scalar(): non-commutative scalar");
+
+	exvector prod(row * col);
+
+	for (unsigned r=0; r<row; ++r)
+		for (unsigned c=0; c<col; ++c)
+			prod[r*col+c] = m[r*col+c] * other;
+
+	return matrix(row, col, prod);
+}
+
+
+/** Power of a matrix.  Currently handles integer exponents only. */
+matrix matrix::pow(const ex & expn) const
+{
+	if (col!=row)
+		throw (std::logic_error("matrix::pow(): matrix not square"));
+	
+	if (is_exactly_a<numeric>(expn)) {
+		// 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 b = ex_to<numeric>(expn);
+			matrix A(row,col);
+			if (expn.info(info_flags::negative)) {
+				b *= -1;
+				A = this->inverse();
+			} else {
+				A = *this;
+			}
+			matrix C(row,col);
+			for (unsigned r=0; r<row; ++r)
+				C(r,r) = _ex1;
+			if (b.is_zero())
+				return C;
+			// 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!=_num1) {
+				if (b.is_odd()) {
+					C = C.mul(A);
+					--b;
+				}
+				b /= _num2;  // still integer.
+				A = A.mul(A);
+			}
+			return A.mul(C);
+		}
+	}
+	throw (std::runtime_error("matrix::pow(): don't know how to handle exponent"));
+}
+
+
+/** operator() to access elements for reading.
  *
  *  @param ro row of element
  *  @param co column of element
@@ -560,23 +653,24 @@ const ex & matrix::operator() (unsigned ro, unsigned co) const
 }
 
 
-/** Set individual elements manually.
+/** operator() to access elements for writing.
  *
+ *  @param ro row of element
+ *  @param co column of element
  *  @exception range_error (index out of range) */
-matrix & matrix::set(unsigned ro, unsigned co, ex value)
+ex & matrix::operator() (unsigned ro, unsigned co)
 {
 	if (ro>=row || co>=col)
-		throw (std::range_error("matrix::set(): index out of range"));
-    
+		throw (std::range_error("matrix::operator(): index out of range"));
+
 	ensure_if_modifiable();
-	m[ro*col+co] = value;
-	return *this;
+	return m[ro*col+co];
 }
 
 
 /** Transposed of an m x n matrix, producing a new n x m matrix object that
  *  represents the transposed. */
-matrix matrix::transpose(void) const
+matrix matrix::transpose() const
 {
 	exvector trans(this->cols()*this->rows());
 	
@@ -587,7 +681,6 @@ matrix matrix::transpose(void) const
 	return matrix(this->cols(),this->rows(),trans);
 }
 
-
 /** Determinant of square matrix.  This routine doesn't actually calculate the
  *  determinant, it only implements some heuristics about which algorithm to
  *  run.  If all the elements of the matrix are elements of an integral domain
@@ -612,9 +705,10 @@ 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))
@@ -622,6 +716,7 @@ 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:
@@ -674,7 +769,7 @@ 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)
@@ -686,10 +781,13 @@ 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) {
@@ -699,14 +797,15 @@ 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);
-			int sign = permutation_sign(pre_sort);
+			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)
@@ -728,7 +827,7 @@ ex matrix::determinant(unsigned algo) const
  *
  *  @return    the sum of diagonal elements
  *  @exception logic_error (matrix not square) */
-ex matrix::trace(void) const
+ex matrix::trace() const
 {
 	if (row != col)
 		throw (std::logic_error("matrix::trace(): matrix not square"));
@@ -762,16 +861,18 @@ 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
 	// trapped and we use Leverrier's algorithm which goes as row^3 for
 	// every coefficient.  The expensive part is the matrix multiplication.
 	if (numeric_flag) {
+
 		matrix B(*this);
 		ex c = B.trace();
 		ex poly = power(lambda,row)-c*power(lambda,row-1);
@@ -779,20 +880,22 @@ ex matrix::charpoly(const symbol & lambda) const
 			for (unsigned j=0; j<row; ++j)
 				B.m[j*col+j] -= c;
 			B = this->mul(B);
-			c = B.trace()/ex(i+1);
+			c = B.trace() / ex(i+1);
 			poly -= c*power(lambda,row-i-1);
 		}
 		if (row%2)
 			return -poly;
 		else
 			return poly;
-	}
+
+	} else {
 	
-	matrix M(*this);
-	for (unsigned r=0; r<col; ++r)
-		M.m[r*col+r] -= lambda;
+		matrix M(*this);
+		for (unsigned r=0; r<col; ++r)
+			M.m[r*col+r] -= lambda;
 	
-	return M.determinant().collect(lambda);
+		return M.determinant().collect(lambda);
+	}
 }
 
 
@@ -801,55 +904,37 @@ ex matrix::charpoly(const symbol & lambda) const
  *  @return    the inverted matrix
  *  @exception logic_error (matrix not square)
  *  @exception runtime_error (singular matrix) */
-matrix matrix::inverse(void) const
+matrix matrix::inverse() const
 {
 	if (row != col)
 		throw (std::logic_error("matrix::inverse(): matrix not square"));
 	
-	// NOTE: the Gauss-Jordan elimination used here can in principle be
-	// replaced by two clever calls to gauss_elimination() and some to
-	// transpose().  Wouldn't be more efficient (maybe less?), just more
-	// orthogonal.
-	matrix tmp(row,col);
-	// set tmp to the unit matrix
-	for (unsigned i=0; i<col; ++i)
-		tmp.m[i*col+i] = _ex1();
+	// This routine actually doesn't do anything fancy at all.  We compute the
+	// inverse of the matrix A by solving the system A * A^{-1} == Id.
 	
-	// create a copy of this matrix
-	matrix cpy(*this);
-	for (unsigned r1=0; r1<row; ++r1) {
-		int indx = cpy.pivot(r1, r1);
-		if (indx == -1) {
+	// 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;
+	
+	// Populate a dummy matrix of variables, just because of compatibility with
+	// matrix::solve() which wants this (for compatibility with under-determined
+	// systems of equations).
+	matrix vars(row,col);
+	for (unsigned r=0; r<row; ++r)
+		for (unsigned c=0; c<col; ++c)
+			vars(r,c) = symbol();
+	
+	matrix sol(row,col);
+	try {
+		sol = this->solve(vars,identity);
+	} catch (const std::runtime_error & e) {
+	    if (e.what()==std::string("matrix::solve(): inconsistent linear system"))
 			throw (std::runtime_error("matrix::inverse(): singular matrix"));
-		}
-		if (indx != 0) {  // swap rows r and indx of matrix tmp
-			for (unsigned i=0; i<col; ++i)
-				tmp.m[r1*col+i].swap(tmp.m[indx*col+i]);
-		}
-		ex a1 = cpy.m[r1*col+r1];
-		for (unsigned c=0; c<col; ++c) {
-			cpy.m[r1*col+c] /= a1;
-			tmp.m[r1*col+c] /= a1;
-		}
-		for (unsigned r2=0; r2<row; ++r2) {
-			if (r2 != r1) {
-				if (!cpy.m[r2*col+r1].is_zero()) {
-					ex a2 = cpy.m[r2*col+r1];
-					// yes, there is something to do in this column
-					for (unsigned c=0; c<col; ++c) {
-						cpy.m[r2*col+c] -= a2 * cpy.m[r1*col+c];
-						if (!cpy.m[r2*col+c].info(info_flags::numeric))
-							cpy.m[r2*col+c] = cpy.m[r2*col+c].normal();
-						tmp.m[r2*col+c] -= a2 * tmp.m[r1*col+c];
-						if (!tmp.m[r2*col+c].info(info_flags::numeric))
-							tmp.m[r2*col+c] = tmp.m[r2*col+c].normal();
-					}
-				}
-			}
-		}
+		else
+			throw;
 	}
-	
-	return tmp;
+	return sol;
 }
 
 
@@ -890,9 +975,11 @@ 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:
@@ -912,8 +999,10 @@ matrix matrix::solve(const matrix & vars,
 	switch(algo) {
 		case solve_algo::gauss:
 			aug.gauss_elimination();
+			break;
 		case solve_algo::divfree:
 			aug.division_free_elimination();
+			break;
 		case solve_algo::bareiss:
 		default:
 			aug.fraction_free_elimination();
@@ -936,19 +1025,18 @@ matrix matrix::solve(const matrix & vars,
 				// assign solutions for vars between fnz+1 and
 				// last_assigned_sol-1: free parameters
 				for (unsigned c=fnz; c<last_assigned_sol-1; ++c)
-					sol.set(c,co,vars.m[c*p+co]);
+					sol(c,co) = vars.m[c*p+co];
 				ex e = aug.m[r*(n+p)+n+co];
 				for (unsigned c=fnz; c<n; ++c)
 					e -= aug.m[r*(n+p)+c]*sol.m[c*p+co];
-				sol.set(fnz-1,co,
-						(e/(aug.m[r*(n+p)+(fnz-1)])).normal());
+				sol(fnz-1,co) = (e/(aug.m[r*(n+p)+(fnz-1)])).normal();
 				last_assigned_sol = fnz;
 			}
 		}
 		// assign solutions for vars between 1 and
 		// last_assigned_sol-1: free parameters
 		for (unsigned ro=0; ro<last_assigned_sol-1; ++ro)
-			sol.set(ro,co,vars(ro,co));
+			sol(ro,co) = vars(ro,co);
 	}
 	
 	return sol;
@@ -967,7 +1055,7 @@ matrix matrix::solve(const matrix & vars,
  *
  *  @return the determinant as a new expression (in expanded form)
  *  @see matrix::determinant() */
-ex matrix::determinant_minor(void) const
+ex matrix::determinant_minor() const
 {
 	// for small matrices the algorithm does not make any sense:
 	const unsigned n = this->cols();
@@ -992,9 +1080,9 @@ ex matrix::determinant_minor(void) const
 	//     for (unsigned r=0; r<minorM.rows(); ++r) {
 	//         for (unsigned c=0; c<minorM.cols(); ++c) {
 	//             if (r<r1)
-	//                 minorM.set(r,c,m[r*col+c+1]);
+	//                 minorM(r,c) = m[r*col+c+1];
 	//             else
-	//                 minorM.set(r,c,m[(r+1)*col+c+1]);
+	//                 minorM(r,c) = m[(r+1)*col+c+1];
 	//         }
 	//     }
 	//     // recurse down and care for sign:
@@ -1038,7 +1126,7 @@ 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())
@@ -1118,12 +1206,12 @@ 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;
 		}
@@ -1165,12 +1253,12 @@ 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;
 		}
@@ -1200,7 +1288,7 @@ int matrix::fraction_free_elimination(const bool det)
 	//
 	// Bareiss (fraction-free) elimination in addition divides that element
 	// by m[k-1](k-1,k-1) for k>1, where it can be shown by means of the
-	// Sylvester determinant that this really divides m[k+1](r,c).
+	// Sylvester identity that this really divides m[k+1](r,c).
 	//
 	// We also allow rational functions where the original prove still holds.
 	// However, we must care for numerator and denominator separately and
@@ -1238,13 +1326,13 @@ 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;
@@ -1278,7 +1366,7 @@ 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
@@ -1287,8 +1375,8 @@ 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;
 					}
 				}
 			}
@@ -1296,11 +1384,11 @@ 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, subs_options::no_pattern);
 	
 	return sign;
 }
@@ -1328,12 +1416,12 @@ 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_exactly_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_exactly_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;
@@ -1357,27 +1445,94 @@ int matrix::pivot(unsigned ro, unsigned co, bool symbolic)
 	return k;
 }
 
-/** Convert list of lists to matrix. */
-ex lst_to_matrix(const ex &l)
+ex lst_to_matrix(const lst & l)
 {
-	if (!is_ex_of_type(l, lst))
-		throw(std::invalid_argument("argument to lst_to_matrix() must be a lst"));
-	
+	lst::const_iterator itr, itc;
+
 	// Find number of rows and columns
-	unsigned rows = l.nops(), cols = 0, i, j;
-	for (i=0; i<rows; i++)
-		if (l.op(i).nops() > cols)
-			cols = l.op(i).nops();
-	
+	size_t rows = l.nops(), cols = 0;
+	for (itr = l.begin(); itr != l.end(); ++itr) {
+		if (!is_a<lst>(*itr))
+			throw (std::invalid_argument("lst_to_matrix: argument must be a list of lists"));
+		if (itr->nops() > cols)
+			cols = itr->nops();
+	}
+
 	// Allocate and fill matrix
-	matrix &m = *new matrix(rows, cols);
-	for (i=0; i<rows; i++)
-		for (j=0; j<cols; j++)
-			if (l.op(i).nops() > j)
-				m.set(i, j, l.op(i).op(j));
-			else
-				m.set(i, j, ex(0));
-	return m;
+	matrix &M = *new matrix(rows, cols);
+	M.setflag(status_flags::dynallocated);
+
+	unsigned i;
+	for (itr = l.begin(), i = 0; itr != l.end(); ++itr, ++i) {
+		unsigned j;
+		for (itc = ex_to<lst>(*itr).begin(), j = 0; itc != ex_to<lst>(*itr).end(); ++itc, ++j)
+			M(i, j) = *itc;
+	}
+
+	return M;
+}
+
+ex diag_matrix(const lst & l)
+{
+	lst::const_iterator it;
+	size_t dim = l.nops();
+
+	// Allocate and fill matrix
+	matrix &M = *new matrix(dim, dim);
+	M.setflag(status_flags::dynallocated);
+
+	unsigned i;
+	for (it = l.begin(), i = 0; it != l.end(); ++it, ++i)
+		M(i, i) = *it;
+
+	return M;
+}
+
+ex unit_matrix(unsigned r, unsigned c)
+{
+	matrix &Id = *new matrix(r, c);
+	Id.setflag(status_flags::dynallocated);
+	for (unsigned i=0; i<r && i<c; i++)
+		Id(i,i) = _ex1;
+
+	return Id;
+}
+
+ex symbolic_matrix(unsigned r, unsigned c, const std::string & base_name, const std::string & tex_base_name)
+{
+	matrix &M = *new matrix(r, c);
+	M.setflag(status_flags::dynallocated | status_flags::evaluated);
+
+	bool long_format = (r > 10 || c > 10);
+	bool single_row = (r == 1 || c == 1);
+
+	for (unsigned i=0; i<r; i++) {
+		for (unsigned j=0; j<c; j++) {
+			std::ostringstream s1, s2;
+			s1 << base_name;
+			s2 << tex_base_name << "_{";
+			if (single_row) {
+				if (c == 1) {
+					s1 << i;
+					s2 << i << '}';
+				} else {
+					s1 << j;
+					s2 << j << '}';
+				}
+			} else {
+				if (long_format) {
+					s1 << '_' << i << '_' << j;
+					s2 << i << ';' << j << "}";
+				} else {
+					s1 << i << j;
+					s2 << i << j << '}';
+				}
+			}
+			M(i, j) = symbol(s1.str(), s2.str());
+		}
+	}
+
+	return M;
 }
 
 } // namespace GiNaC