* 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
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*/
+#include <iostream>
#include <stdexcept>
#include <vector>
#include "print.h"
#include "archive.h"
#include "utils.h"
-#include "debugmsg.h"
namespace GiNaC {
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)
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;
}
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;
}
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);
}
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);
}
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)
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)
/** 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));
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
/** 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));
/** 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));
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
/** 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
/** 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)) {
/** 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_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), tensdelta));
+ GINAC_ASSERT(is_a<tensdelta>(self->op(0)));
// Try to contract first index
const idx *self_idx = &ex_to<idx>(self->op(1));
// Contraction found, remove delta tensor and substitute
// index in second object
- *self = _ex1();
+ *self = _ex1;
*other = other->subs(other_idx == *free_idx);
return true;
}
/** 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)
// Contraction found, remove metric tensor and substitute
// index in second object
- *self = _ex1();
+ *self = _ex1;
*other = other->subs(other_idx == *free_idx);
return true;
}
/** 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)) {
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;
}
}
/** 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), spinmetric));
+ 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()) {
// 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));
+ for (int i=0; i<num; i++) {
+ 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));
+ }
+ }
int sign = minkowski ? -1 : 1;
*self = sign * M.determinant().simplify_indexed();
- *other = _ex1();
+ *other = _ex1;
return true;
+
+ } else if (other->return_type() == return_types::commutative) {
+
+#if 1
+ // This handles eps.i.j.k * p.j * p.k = 0 and related cases.
+ // Actually, simplify_indexed() can handle most of them on its own
+ // but one specific case that is not covered there is
+ // eps~mu.nu~i~j * p.mu * p~nu
+ // because of the difference in variance in the dummy indices mu
+ // and nu. Eventually, simplify_indexed() should be extended to
+ // handle this case, and this hack removed.
+ 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;
+ }
+ }
+ }
+ }
+#endif
}
return false;
{
if (!is_ex_of_type(i1, varidx) || !is_ex_of_type(i2, varidx))
throw(std::invalid_argument("indices of metric tensor must be of type varidx"));
+ 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 metric tensor must have the same dimension"));
return indexed(tensmetric(), sy_symm(), i1, i2);
}
{
if (!is_ex_of_type(i1, varidx) || !is_ex_of_type(i2, varidx))
throw(std::invalid_argument("indices of metric tensor must be of type varidx"));
+ 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 metric tensor must have the same dimension"));
return indexed(minkmetric(pos_sig), sy_symm(), i1, 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);
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);
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);
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