metric tensors now silently replace their indices' dimensions with their
[ginac.git] / ginac / tensor.cpp
index 0d93e6529ea387c48a63963c16fd1fb5719da72d..0c36a68002423d712f4d8afa5ec903716ffba7e7 100644 (file)
@@ -3,7 +3,7 @@
  *  Implementation of GiNaC's special tensors. */
 
 /*
- *  GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
+ *  GiNaC Copyright (C) 1999-2002 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
@@ -20,6 +20,7 @@
  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
  */
 
+#include <iostream>
 #include <stdexcept>
 #include <vector>
 
@@ -34,7 +35,6 @@
 #include "print.h"
 #include "archive.h"
 #include "utils.h"
-#include "debugmsg.h"
 
 namespace GiNaC {
 
@@ -46,14 +46,9 @@ GINAC_IMPLEMENT_REGISTERED_CLASS(spinmetric, tensmetric)
 GINAC_IMPLEMENT_REGISTERED_CLASS(tensepsilon, tensor)
 
 //////////
-// default constructor, destructor, copy constructor assignment operator and helpers
+// default ctor, dtor, copy ctor, assignment operator and helpers
 //////////
 
-tensor::tensor(unsigned ti) : inherited(ti)
-{
-       debugmsg("tensor constructor from unsigned", LOGLEVEL_CONSTRUCT); \
-}
-
 DEFAULT_CTORS(tensor)
 DEFAULT_CTORS(tensdelta)
 DEFAULT_CTORS(tensmetric)
@@ -64,19 +59,16 @@ DEFAULT_DESTROY(tensepsilon)
 
 minkmetric::minkmetric() : pos_sig(false)
 {
-       debugmsg("minkmetric default constructor", LOGLEVEL_CONSTRUCT);
        tinfo_key = TINFO_minkmetric;
 }
 
 spinmetric::spinmetric()
 {
-       debugmsg("spinmetric default constructor", LOGLEVEL_CONSTRUCT);
        tinfo_key = TINFO_spinmetric;
 }
 
 minkmetric::minkmetric(bool ps) : pos_sig(ps)
 {
-       debugmsg("minkmetric constructor from bool", LOGLEVEL_CONSTRUCT);
        tinfo_key = TINFO_minkmetric;
 }
 
@@ -88,13 +80,11 @@ void minkmetric::copy(const minkmetric & other)
 
 tensepsilon::tensepsilon() : minkowski(false), pos_sig(false)
 {
-       debugmsg("tensepsilon default constructor", LOGLEVEL_CONSTRUCT);
        tinfo_key = TINFO_tensepsilon;
 }
 
 tensepsilon::tensepsilon(bool mink, bool ps) : minkowski(mink), pos_sig(ps)
 {
-       debugmsg("tensepsilon constructor from bool,bool", LOGLEVEL_CONSTRUCT);
        tinfo_key = TINFO_tensepsilon;
 }
 
@@ -118,7 +108,6 @@ DEFAULT_UNARCHIVE(tensepsilon)
 
 minkmetric::minkmetric(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
 {
-       debugmsg("minkmetric constructor from archive_node", LOGLEVEL_CONSTRUCT);
        n.find_bool("pos_sig", pos_sig);
 }
 
@@ -130,7 +119,6 @@ void minkmetric::archive(archive_node &n) const
 
 tensepsilon::tensepsilon(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
 {
-       debugmsg("tensepsilon constructor from archive_node", LOGLEVEL_CONSTRUCT);
        n.find_bool("minkowski", minkowski);
        n.find_bool("pos_sig", pos_sig);
 }
@@ -153,7 +141,7 @@ DEFAULT_COMPARE(spinmetric)
 
 int minkmetric::compare_same_type(const basic & other) const
 {
-       GINAC_ASSERT(is_of_type(other, minkmetric));
+       GINAC_ASSERT(is_a<minkmetric>(other));
        const minkmetric &o = static_cast<const minkmetric &>(other);
 
        if (pos_sig != o.pos_sig)
@@ -164,7 +152,7 @@ int minkmetric::compare_same_type(const basic & other) const
 
 int tensepsilon::compare_same_type(const basic & other) const
 {
-       GINAC_ASSERT(is_of_type(other, tensepsilon));
+       GINAC_ASSERT(is_a<tensepsilon>(other));
        const tensepsilon &o = static_cast<const tensepsilon &>(other);
 
        if (minkowski != o.minkowski)
@@ -184,24 +172,29 @@ DEFAULT_PRINT_LATEX(tensepsilon, "eps", "\\varepsilon")
 /** Automatic symbolic evaluation of an indexed delta tensor. */
 ex tensdelta::eval_indexed(const basic & i) const
 {
-       GINAC_ASSERT(is_of_type(i, indexed));
+       GINAC_ASSERT(is_a<indexed>(i));
        GINAC_ASSERT(i.nops() == 3);
-       GINAC_ASSERT(is_ex_of_type(i.op(0), tensdelta));
+       GINAC_ASSERT(is_a<tensdelta>(i.op(0)));
 
        const idx & i1 = ex_to<idx>(i.op(1));
        const idx & i2 = ex_to<idx>(i.op(2));
 
-       // Trace of delta tensor is the dimension of the space
-       if (is_dummy_pair(i1, i2))
-               return i1.get_dim();
+       // Trace of delta tensor is the (effective) dimension of the space
+       if (is_dummy_pair(i1, i2)) {
+               try {
+                       return i1.minimal_dim(i2);
+               } catch (std::exception &e) {
+                       return i.hold();
+               }
+       }
 
        // Numeric evaluation
        if (static_cast<const indexed &>(i).all_index_values_are(info_flags::integer)) {
                int n1 = ex_to<numeric>(i1.get_value()).to_int(), n2 = ex_to<numeric>(i2.get_value()).to_int();
                if (n1 == n2)
-                       return _ex1();
+                       return _ex1;
                else
-                       return _ex0();
+                       return _ex0;
        }
 
        // No further simplifications
@@ -211,15 +204,22 @@ ex tensdelta::eval_indexed(const basic & i) const
 /** Automatic symbolic evaluation of an indexed metric tensor. */
 ex tensmetric::eval_indexed(const basic & i) const
 {
-       GINAC_ASSERT(is_of_type(i, indexed));
+       GINAC_ASSERT(is_a<indexed>(i));
        GINAC_ASSERT(i.nops() == 3);
-       GINAC_ASSERT(is_ex_of_type(i.op(0), tensmetric));
-       GINAC_ASSERT(is_ex_of_type(i.op(1), varidx));
-       GINAC_ASSERT(is_ex_of_type(i.op(2), varidx));
+       GINAC_ASSERT(is_a<tensmetric>(i.op(0)));
+       GINAC_ASSERT(is_a<varidx>(i.op(1)));
+       GINAC_ASSERT(is_a<varidx>(i.op(2)));
 
        const varidx & i1 = ex_to<varidx>(i.op(1));
        const varidx & i2 = ex_to<varidx>(i.op(2));
 
+       // The dimension of the indices must be equal, otherwise we use the minimal
+       // dimension
+       if (!i1.get_dim().is_equal(i2.get_dim())) {
+               ex min_dim = i1.minimal_dim(i2);
+               return i.subs(lst(i1 == i1.replace_dim(min_dim), i2 == i2.replace_dim(min_dim)));
+       }
+
        // A metric tensor with one covariant and one contravariant index gets
        // replaced by a delta tensor
        if (i1.is_covariant() != i2.is_covariant())
@@ -232,11 +232,11 @@ ex tensmetric::eval_indexed(const basic & i) const
 /** Automatic symbolic evaluation of an indexed Lorentz metric tensor. */
 ex minkmetric::eval_indexed(const basic & i) const
 {
-       GINAC_ASSERT(is_of_type(i, indexed));
+       GINAC_ASSERT(is_a<indexed>(i));
        GINAC_ASSERT(i.nops() == 3);
-       GINAC_ASSERT(is_ex_of_type(i.op(0), minkmetric));
-       GINAC_ASSERT(is_ex_of_type(i.op(1), varidx));
-       GINAC_ASSERT(is_ex_of_type(i.op(2), varidx));
+       GINAC_ASSERT(is_a<minkmetric>(i.op(0)));
+       GINAC_ASSERT(is_a<varidx>(i.op(1)));
+       GINAC_ASSERT(is_a<varidx>(i.op(2)));
 
        const varidx & i1 = ex_to<varidx>(i.op(1));
        const varidx & i2 = ex_to<varidx>(i.op(2));
@@ -245,11 +245,11 @@ ex minkmetric::eval_indexed(const basic & i) const
        if (static_cast<const indexed &>(i).all_index_values_are(info_flags::nonnegint)) {
                int n1 = ex_to<numeric>(i1.get_value()).to_int(), n2 = ex_to<numeric>(i2.get_value()).to_int();
                if (n1 != n2)
-                       return _ex0();
+                       return _ex0;
                else if (n1 == 0)
-                       return pos_sig ? _ex_1() : _ex1();
+                       return pos_sig ? _ex_1 : _ex1;
                else
-                       return pos_sig ? _ex1() : _ex_1();
+                       return pos_sig ? _ex1 : _ex_1;
        }
 
        // Perform the usual evaluations of a metric tensor
@@ -259,28 +259,28 @@ ex minkmetric::eval_indexed(const basic & i) const
 /** Automatic symbolic evaluation of an indexed metric tensor. */
 ex spinmetric::eval_indexed(const basic & i) const
 {
-       GINAC_ASSERT(is_of_type(i, indexed));
+       GINAC_ASSERT(is_a<indexed>(i));
        GINAC_ASSERT(i.nops() == 3);
-       GINAC_ASSERT(is_ex_of_type(i.op(0), spinmetric));
-       GINAC_ASSERT(is_ex_of_type(i.op(1), spinidx));
-       GINAC_ASSERT(is_ex_of_type(i.op(2), spinidx));
+       GINAC_ASSERT(is_a<spinmetric>(i.op(0)));
+       GINAC_ASSERT(is_a<spinidx>(i.op(1)));
+       GINAC_ASSERT(is_a<spinidx>(i.op(2)));
 
        const spinidx & i1 = ex_to<spinidx>(i.op(1));
        const spinidx & i2 = ex_to<spinidx>(i.op(2));
 
        // Convolutions are zero
        if (!(static_cast<const indexed &>(i).get_dummy_indices().empty()))
-               return _ex0();
+               return _ex0;
 
        // Numeric evaluation
        if (static_cast<const indexed &>(i).all_index_values_are(info_flags::nonnegint)) {
                int n1 = ex_to<numeric>(i1.get_value()).to_int(), n2 = ex_to<numeric>(i2.get_value()).to_int();
                if (n1 == n2)
-                       return _ex0();
+                       return _ex0;
                else if (n1 < n2)
-                       return _ex1();
+                       return _ex1;
                else
-                       return _ex_1();
+                       return _ex_1;
        }
 
        // No further simplifications
@@ -290,13 +290,13 @@ ex spinmetric::eval_indexed(const basic & i) const
 /** Automatic symbolic evaluation of an indexed epsilon tensor. */
 ex tensepsilon::eval_indexed(const basic & i) const
 {
-       GINAC_ASSERT(is_of_type(i, indexed));
+       GINAC_ASSERT(is_a<indexed>(i));
        GINAC_ASSERT(i.nops() > 1);
-       GINAC_ASSERT(is_ex_of_type(i.op(0), tensepsilon));
+       GINAC_ASSERT(is_a<tensepsilon>(i.op(0)));
 
        // Convolutions are zero
        if (!(static_cast<const indexed &>(i).get_dummy_indices().empty()))
-               return _ex0();
+               return _ex0;
 
        // Numeric evaluation
        if (static_cast<const indexed &>(i).all_index_values_are(info_flags::nonnegint)) {
@@ -330,15 +330,9 @@ ex tensepsilon::eval_indexed(const basic & i) const
        return i.hold();
 }
 
-/** Contraction of an indexed delta tensor with something else. */
-bool tensdelta::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
+bool tensor::replace_contr_index(exvector::iterator self, exvector::iterator other) const
 {
-       GINAC_ASSERT(is_ex_of_type(*self, indexed));
-       GINAC_ASSERT(is_ex_of_type(*other, indexed));
-       GINAC_ASSERT(self->nops() == 3);
-       GINAC_ASSERT(is_ex_of_type(self->op(0), tensdelta));
-
-       // Try to contract first index
+       // Try to contract the first index
        const idx *self_idx = &ex_to<idx>(self->op(1));
        const idx *free_idx = &ex_to<idx>(self->op(2));
        bool first_index_tried = false;
@@ -349,18 +343,24 @@ again:
                        const idx &other_idx = ex_to<idx>(other->op(i));
                        if (is_dummy_pair(*self_idx, other_idx)) {
 
-                               // Contraction found, remove delta tensor and substitute
-                               // index in second object
-                               *self = _ex1();
-                               *other = other->subs(other_idx == *free_idx);
-                               return true;
+                               // Contraction found, remove this tensor and substitute the
+                               // index in the second object
+                               try {
+                                       // minimal_dim() throws an exception when index dimensions are not comparable
+                                       ex min_dim = self_idx->minimal_dim(other_idx);
+                                       *self = _ex1;
+                                       *other = other->subs(other_idx == free_idx->replace_dim(min_dim));
+                                       return true;
+                               } catch (std::exception &e) {
+                                       return false;
+                               }
                        }
                }
        }
 
        if (!first_index_tried) {
 
-               // No contraction with first index found, try second index
+               // No contraction with the first index found, try the second index
                self_idx = &ex_to<idx>(self->op(2));
                free_idx = &ex_to<idx>(self->op(1));
                first_index_tried = true;
@@ -370,58 +370,44 @@ again:
        return false;
 }
 
+/** Contraction of an indexed delta tensor with something else. */
+bool tensdelta::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
+{
+       GINAC_ASSERT(is_a<indexed>(*self));
+       GINAC_ASSERT(is_a<indexed>(*other));
+       GINAC_ASSERT(self->nops() == 3);
+       GINAC_ASSERT(is_a<tensdelta>(self->op(0)));
+
+       // Replace the dummy index with this tensor's other index and remove
+       // the tensor (this is valid for contractions with all other tensors)
+       return replace_contr_index(self, other);
+}
+
 /** Contraction of an indexed metric tensor with something else. */
 bool tensmetric::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() == 3);
-       GINAC_ASSERT(is_ex_of_type(self->op(0), tensmetric));
+       GINAC_ASSERT(is_a<tensmetric>(self->op(0)));
 
        // If contracting with the delta tensor, let the delta do it
        // (don't raise/lower delta indices)
        if (is_ex_of_type(other->op(0), tensdelta))
                return false;
 
-       // Try to contract first index
-       const idx *self_idx = &ex_to<idx>(self->op(1));
-       const idx *free_idx = &ex_to<idx>(self->op(2));
-       bool first_index_tried = false;
-
-again:
-       if (self_idx->is_symbolic()) {
-               for (unsigned i=1; i<other->nops(); i++) {
-                       const idx &other_idx = ex_to<idx>(other->op(i));
-                       if (is_dummy_pair(*self_idx, other_idx)) {
-
-                               // Contraction found, remove metric tensor and substitute
-                               // index in second object
-                               *self = _ex1();
-                               *other = other->subs(other_idx == *free_idx);
-                               return true;
-                       }
-               }
-       }
-
-       if (!first_index_tried) {
-
-               // No contraction with first index found, try second index
-               self_idx = &ex_to<idx>(self->op(2));
-               free_idx = &ex_to<idx>(self->op(1));
-               first_index_tried = true;
-               goto again;
-       }
-
-       return false;
+       // Replace the dummy index with this tensor's other index and remove
+       // the tensor (this is valid for contractions with all other tensors)
+       return replace_contr_index(self, other);
 }
 
 /** Contraction of an indexed spinor metric with something else. */
 bool spinmetric::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() == 3);
-       GINAC_ASSERT(is_ex_of_type(self->op(0), spinmetric));
+       GINAC_ASSERT(is_a<spinmetric>(self->op(0)));
 
        // Contractions between spinor metrics
        if (is_ex_of_type(other->op(0), spinmetric)) {
@@ -432,25 +418,25 @@ bool spinmetric::contract_with(exvector::iterator self, exvector::iterator other
 
                if (is_dummy_pair(self_i1, other_i1)) {
                        if (is_dummy_pair(self_i2, other_i2))
-                               *self = _ex2();
+                               *self = _ex2;
                        else
                                *self = delta_tensor(self_i2, other_i2);
-                       *other = _ex1();
+                       *other = _ex1;
                        return true;
                } else if (is_dummy_pair(self_i1, other_i2)) {
                        if (is_dummy_pair(self_i2, other_i1))
-                               *self = _ex_2();
+                               *self = _ex_2;
                        else
                                *self = -delta_tensor(self_i2, other_i1);
-                       *other = _ex1();
+                       *other = _ex1;
                        return true;
                } else if (is_dummy_pair(self_i2, other_i1)) {
                        *self = -delta_tensor(self_i1, other_i2);
-                       *other = _ex1();
+                       *other = _ex1;
                        return true;
                } else if (is_dummy_pair(self_i2, other_i2)) {
                        *self = delta_tensor(self_i1, other_i1);
-                       *other = _ex1();
+                       *other = _ex1;
                        return true;
                }
        }
@@ -497,9 +483,9 @@ again:
 /** Contraction of epsilon tensor with something else. */
 bool tensepsilon::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_ex_of_type(self->op(0), tensepsilon));
+       GINAC_ASSERT(is_a<indexed>(*self));
+       GINAC_ASSERT(is_a<indexed>(*other));
+       GINAC_ASSERT(is_a<tensepsilon>(self->op(0)));
        unsigned num = self->nops() - 1;
 
        if (is_ex_exactly_of_type(other->op(0), tensepsilon) && num+1 == other->nops()) {
@@ -507,51 +493,18 @@ bool tensepsilon::contract_with(exvector::iterator self, exvector::iterator othe
                // Contraction of two epsilon tensors is a determinant
                ex dim = ex_to<idx>(self->op(1)).get_dim();
                matrix M(num, num);
-               for (int i=0; i<num; i++)
-                       for (int j=0; j<num; j++)
-                               M(i, j) = delta_tensor(self->op(i+1), other->op(j+1));
-               int sign = minkowski ? -1 : 1;
-               *self = sign * M.determinant().simplify_indexed();
-               *other = _ex1();
-               return true;
-
-       } else if (other->return_type() == return_types::commutative) {
-
-#if 0
-               // This handles eps.i.j.k * p.j * p.k = 0
-               // Maybe something like this should go to simplify_indexed() because
-               // such relations are true for any antisymmetric tensors...
-               exvector c;
-
-               // Handle all indices of the epsilon tensor
                for (int i=0; i<num; i++) {
-                       ex idx = self->op(i+1);
-
-                       // Look whether there's a contraction with this index
-                       exvector::const_iterator ait, aitend = v.end();
-                       for (ait = v.begin(); ait != aitend; ait++) {
-                               if (ait == self)
-                                       continue;
-                               if (is_a<indexed>(*ait) && ait->return_type() == return_types::commutative && ex_to<indexed>(*ait).has_dummy_index_for(idx) && ait->nops() == 2) {
-
-                                       // Yes, did we already have another contraction with the same base expression?
-                                       ex base = ait->op(0);
-                                       if (std::find_if(c.begin(), c.end(), bind2nd(ex_is_equal(), base)) == c.end()) {
-
-                                               // No, add the base expression to the list
-                                               c.push_back(base);
-
-                                       } else {
-
-                                               // Yes, the contraction is zero
-                                               *self = _ex0();
-                                               *other = _ex0();
-                                               return true;
-                                       }
-                               }
+                       for (int j=0; j<num; j++) {
+                               if (minkowski)
+                                       M(i, j) = lorentz_g(self->op(i+1), other->op(j+1), pos_sig);
+                               else
+                                       M(i, j) = metric_tensor(self->op(i+1), other->op(j+1));
                        }
                }
-#endif
+               int sign = minkowski ? -1 : 1;
+               *self = sign * M.determinant().simplify_indexed();
+               *other = _ex1;
+               return true;
        }
 
        return false;
@@ -603,7 +556,7 @@ ex epsilon_tensor(const ex & i1, const ex & i2)
        ex dim = ex_to<idx>(i1).get_dim();
        if (!dim.is_equal(ex_to<idx>(i2).get_dim()))
                throw(std::invalid_argument("all indices of epsilon tensor must have the same dimension"));
-       if (!ex_to<idx>(i1).get_dim().is_equal(_ex2()))
+       if (!ex_to<idx>(i1).get_dim().is_equal(_ex2))
                throw(std::runtime_error("index dimension of epsilon tensor must match number of indices"));
 
        return indexed(tensepsilon(), sy_anti(), i1, i2);
@@ -617,7 +570,7 @@ ex epsilon_tensor(const ex & i1, const ex & i2, const ex & i3)
        ex dim = ex_to<idx>(i1).get_dim();
        if (!dim.is_equal(ex_to<idx>(i2).get_dim()) || !dim.is_equal(ex_to<idx>(i3).get_dim()))
                throw(std::invalid_argument("all indices of epsilon tensor must have the same dimension"));
-       if (!ex_to<idx>(i1).get_dim().is_equal(_ex3()))
+       if (!ex_to<idx>(i1).get_dim().is_equal(_ex3))
                throw(std::runtime_error("index dimension of epsilon tensor must match number of indices"));
 
        return indexed(tensepsilon(), sy_anti(), i1, i2, i3);
@@ -631,22 +584,10 @@ ex lorentz_eps(const ex & i1, const ex & i2, const ex & i3, const ex & i4, bool
        ex dim = ex_to<idx>(i1).get_dim();
        if (!dim.is_equal(ex_to<idx>(i2).get_dim()) || !dim.is_equal(ex_to<idx>(i3).get_dim()) || !dim.is_equal(ex_to<idx>(i4).get_dim()))
                throw(std::invalid_argument("all indices of epsilon tensor must have the same dimension"));
-       if (!ex_to<idx>(i1).get_dim().is_equal(_ex4()))
+       if (!ex_to<idx>(i1).get_dim().is_equal(_ex4))
                throw(std::runtime_error("index dimension of epsilon tensor must match number of indices"));
 
        return indexed(tensepsilon(true, pos_sig), sy_anti(), i1, i2, i3, i4);
 }
 
-ex eps0123(const ex & i1, const ex & i2, const ex & i3, const ex & i4, bool pos_sig)
-{
-       if (!is_ex_of_type(i1, varidx) || !is_ex_of_type(i2, varidx) || !is_ex_of_type(i3, varidx) || !is_ex_of_type(i4, varidx))
-               throw(std::invalid_argument("indices of epsilon tensor must be of type varidx"));
-
-       ex dim = ex_to<idx>(i1).get_dim();
-       if (dim.is_equal(4))
-               return lorentz_eps(i1, i2, i3, i4, pos_sig);
-       else
-               return indexed(tensepsilon(true, pos_sig), sy_anti(), i1, i2, i3, i4);
-}
-
 } // namespace GiNaC