#include "tensor.h"
#include "idx.h"
#include "indexed.h"
+#include "symmetry.h"
#include "relational.h"
#include "lst.h"
#include "numeric.h"
+#include "matrix.h"
#include "print.h"
#include "archive.h"
#include "utils.h"
GINAC_IMPLEMENT_REGISTERED_CLASS(tensdelta, tensor)
GINAC_IMPLEMENT_REGISTERED_CLASS(tensmetric, tensor)
GINAC_IMPLEMENT_REGISTERED_CLASS(minkmetric, tensmetric)
+GINAC_IMPLEMENT_REGISTERED_CLASS(spinmetric, tensmetric)
GINAC_IMPLEMENT_REGISTERED_CLASS(tensepsilon, tensor)
//////////
DEFAULT_CTORS(tensor)
DEFAULT_CTORS(tensdelta)
DEFAULT_CTORS(tensmetric)
+DEFAULT_COPY(spinmetric)
+DEFAULT_DESTROY(spinmetric)
DEFAULT_DESTROY(minkmetric)
DEFAULT_DESTROY(tensepsilon)
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);
DEFAULT_ARCHIVING(tensor)
DEFAULT_ARCHIVING(tensdelta)
DEFAULT_ARCHIVING(tensmetric)
+DEFAULT_ARCHIVING(spinmetric)
DEFAULT_UNARCHIVE(minkmetric)
DEFAULT_UNARCHIVE(tensepsilon)
}
//////////
-// functions overriding virtual functions from bases classes
+// functions overriding virtual functions from base classes
//////////
DEFAULT_COMPARE(tensor)
DEFAULT_COMPARE(tensdelta)
DEFAULT_COMPARE(tensmetric)
+DEFAULT_COMPARE(spinmetric)
int minkmetric::compare_same_type(const basic & other) const
{
return inherited::compare_same_type(other);
}
-DEFAULT_PRINT(tensdelta, "delta")
+DEFAULT_PRINT_LATEX(tensdelta, "delta", "\\delta")
DEFAULT_PRINT(tensmetric, "g")
-DEFAULT_PRINT(minkmetric, "eta")
-DEFAULT_PRINT(tensepsilon, "eps")
+DEFAULT_PRINT_LATEX(minkmetric, "eta", "\\eta")
+DEFAULT_PRINT_LATEX(spinmetric, "eps", "\\varepsilon")
+DEFAULT_PRINT_LATEX(tensepsilon, "eps", "\\varepsilon")
/** Automatic symbolic evaluation of an indexed delta tensor. */
ex tensdelta::eval_indexed(const basic & i) const
GINAC_ASSERT(i.nops() == 3);
GINAC_ASSERT(is_ex_of_type(i.op(0), tensdelta));
- 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));
// Trace of delta tensor is the dimension of the space
if (is_dummy_pair(i1, i2))
// 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();
+ int n1 = ex_to<numeric>(i1.get_value()).to_int(), n2 = ex_to<numeric>(i2.get_value()).to_int();
if (n1 == n2)
return _ex1();
else
GINAC_ASSERT(is_ex_of_type(i.op(1), varidx));
GINAC_ASSERT(is_ex_of_type(i.op(2), varidx));
- const varidx & i1 = ex_to_varidx(i.op(1));
- const varidx & i2 = ex_to_varidx(i.op(2));
+ const varidx & i1 = ex_to<varidx>(i.op(1));
+ const varidx & i2 = ex_to<varidx>(i.op(2));
// A metric tensor with one covariant and one contravariant index gets
// replaced by a delta tensor
GINAC_ASSERT(is_ex_of_type(i.op(1), varidx));
GINAC_ASSERT(is_ex_of_type(i.op(2), varidx));
- const varidx & i1 = ex_to_varidx(i.op(1));
- const varidx & i2 = ex_to_varidx(i.op(2));
+ const varidx & i1 = ex_to<varidx>(i.op(1));
+ const varidx & i2 = ex_to<varidx>(i.op(2));
// 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();
+ int n1 = ex_to<numeric>(i1.get_value()).to_int(), n2 = ex_to<numeric>(i2.get_value()).to_int();
if (n1 != n2)
return _ex0();
else if (n1 == 0)
return inherited::eval_indexed(i);
}
+/** 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(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));
+
+ 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();
+
+ // 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();
+ else if (n1 < n2)
+ return _ex1();
+ else
+ return _ex_1();
+ }
+
+ // No further simplifications
+ return i.hold();
+}
+
/** Automatic symbolic evaluation of an indexed epsilon tensor. */
ex tensepsilon::eval_indexed(const basic & i) const
{
GINAC_ASSERT(is_ex_of_type(i.op(0), tensepsilon));
// Convolutions are zero
- if (static_cast<const indexed &>(i).get_dummy_indices().size() != 0)
+ if (!(static_cast<const indexed &>(i).get_dummy_indices().empty()))
return _ex0();
// Numeric evaluation
std::vector<int> v;
v.reserve(i.nops() - 1);
for (unsigned j=1; j<i.nops(); j++)
- v.push_back(ex_to_numeric(ex_to_idx(i.op(j)).get_value()).to_int());
- int sign = permutation_sign(v);
+ v.push_back(ex_to<numeric>(ex_to<idx>(i.op(j)).get_value()).to_int());
+ int sign = permutation_sign(v.begin(), v.end());
// In a Minkowski space, check for covariant indices
if (minkowski) {
const ex & x = i.op(j);
if (!is_ex_of_type(x, varidx))
throw(std::runtime_error("indices of epsilon tensor in Minkowski space must be of type varidx"));
- if (ex_to_varidx(x).is_covariant())
- if (ex_to_idx(x).get_value().is_zero())
+ if (ex_to<varidx>(x).is_covariant())
+ if (ex_to<idx>(x).get_value().is_zero())
sign = (pos_sig ? -sign : sign);
else
sign = (pos_sig ? sign : -sign);
GINAC_ASSERT(is_ex_of_type(self->op(0), tensdelta));
// 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));
+ 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 (int i=1; i<other->nops(); i++) {
- const idx &other_idx = ex_to_idx(other->op(i));
+ 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 delta tensor and substitute
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));
+ self_idx = &ex_to<idx>(self->op(2));
+ free_idx = &ex_to<idx>(self->op(1));
first_index_tried = true;
goto again;
}
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));
+ 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 (int i=1; i<other->nops(); i++) {
- const idx &other_idx = ex_to_idx(other->op(i));
+ 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
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));
+ self_idx = &ex_to<idx>(self->op(2));
+ free_idx = &ex_to<idx>(self->op(1));
first_index_tried = true;
goto again;
}
return false;
}
+/** 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(self->nops() == 3);
+ GINAC_ASSERT(is_ex_of_type(self->op(0), spinmetric));
+
+ // Contractions between spinor metrics
+ if (is_ex_of_type(other->op(0), spinmetric)) {
+ const idx &self_i1 = ex_to<idx>(self->op(1));
+ const idx &self_i2 = ex_to<idx>(self->op(2));
+ const idx &other_i1 = ex_to<idx>(other->op(1));
+ const idx &other_i2 = ex_to<idx>(other->op(2));
+
+ if (is_dummy_pair(self_i1, other_i1)) {
+ if (is_dummy_pair(self_i2, other_i2))
+ *self = _ex2();
+ else
+ *self = delta_tensor(self_i2, other_i2);
+ *other = _ex1();
+ return true;
+ } else if (is_dummy_pair(self_i1, other_i2)) {
+ if (is_dummy_pair(self_i2, other_i1))
+ *self = _ex_2();
+ else
+ *self = -delta_tensor(self_i2, other_i1);
+ *other = _ex1();
+ return true;
+ } else if (is_dummy_pair(self_i2, other_i1)) {
+ *self = -delta_tensor(self_i1, other_i2);
+ *other = _ex1();
+ return true;
+ } else if (is_dummy_pair(self_i2, other_i2)) {
+ *self = delta_tensor(self_i1, other_i1);
+ *other = _ex1();
+ return true;
+ }
+ }
+
+ // 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;
+ int sign = 1;
+
+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 = (static_cast<const spinidx *>(self_idx)->is_covariant() ? sign : -sign);
+ *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;
+ sign = -sign;
+ goto again;
+ }
+
+ return false;
+}
+
+/** 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));
+ 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));
+ 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;
+ }
+ }
+ }
+ }
+#endif
+ }
+
+ return false;
+}
+
//////////
// global functions
//////////
if (!is_ex_of_type(i1, idx) || !is_ex_of_type(i2, idx))
throw(std::invalid_argument("indices of delta tensor must be of type idx"));
- return indexed(tensdelta(), indexed::symmetric, i1, i2);
+ return indexed(tensdelta(), sy_symm(), i1, i2);
}
ex metric_tensor(const ex & i1, const ex & 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"));
- return indexed(tensmetric(), indexed::symmetric, i1, i2);
+ return indexed(tensmetric(), sy_symm(), i1, i2);
}
ex lorentz_g(const ex & i1, const ex & i2, bool pos_sig)
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"));
- return indexed(minkmetric(pos_sig), indexed::symmetric, i1, i2);
+ return indexed(minkmetric(pos_sig), sy_symm(), i1, i2);
+}
+
+ex spinor_metric(const ex & i1, const ex & i2)
+{
+ if (!is_ex_of_type(i1, spinidx) || !is_ex_of_type(i2, spinidx))
+ throw(std::invalid_argument("indices of spinor metric must be of type spinidx"));
+ if (!ex_to<idx>(i1).get_dim().is_equal(2) || !ex_to<idx>(i2).get_dim().is_equal(2))
+ throw(std::runtime_error("index dimension for spinor metric must be 2"));
+
+ return indexed(spinmetric(), sy_anti(), i1, i2);
}
ex epsilon_tensor(const ex & i1, const ex & i2)
if (!is_ex_of_type(i1, idx) || !is_ex_of_type(i2, idx))
throw(std::invalid_argument("indices of epsilon tensor must be of type idx"));
- ex dim = ex_to_idx(i1).get_dim();
- if (!dim.is_equal(ex_to_idx(i2).get_dim()))
+ 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(), indexed::antisymmetric, i1, i2);
+ return indexed(tensepsilon(), sy_anti(), i1, i2);
}
ex epsilon_tensor(const ex & i1, const ex & i2, const ex & i3)
if (!is_ex_of_type(i1, idx) || !is_ex_of_type(i2, idx) || !is_ex_of_type(i3, idx))
throw(std::invalid_argument("indices of epsilon tensor must be of type idx"));
- 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()))
+ 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(), indexed::antisymmetric, i1, i2, i3);
+ return indexed(tensepsilon(), sy_anti(), i1, i2, i3);
}
ex lorentz_eps(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 Lorentz epsilon tensor must be of type varidx"));
- 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()))
+ 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), indexed::antisymmetric, i1, i2, i3, i4);
+ 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();
+ 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), indexed::antisymmetric, i1, i2, i3, i4);
+ return indexed(tensepsilon(true, pos_sig), sy_anti(), i1, i2, i3, i4);
}
} // namespace GiNaC
git://www.ginac.de / ginac.git / blobdiff