X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Ftensor.cpp;h=0c36a68002423d712f4d8afa5ec903716ffba7e7;hp=d294c72303006c916356586ade3269212d9a48e6;hb=b8b8cfbb72bfa59b01371f67f542914cf55f2ab9;hpb=834bacb25c9427fb03b8f9b34605738fb59202e1 diff --git a/ginac/tensor.cpp b/ginac/tensor.cpp index d294c723..0c36a680 100644 --- a/ginac/tensor.cpp +++ b/ginac/tensor.cpp @@ -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 #include #include @@ -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(other)); const minkmetric &o = static_cast(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(other)); const tensepsilon &o = static_cast(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(i)); GINAC_ASSERT(i.nops() == 3); - GINAC_ASSERT(is_ex_of_type(i.op(0), tensdelta)); + GINAC_ASSERT(is_a(i.op(0))); const idx & i1 = ex_to(i.op(1)); const idx & i2 = ex_to(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(i).all_index_values_are(info_flags::integer)) { int n1 = ex_to(i1.get_value()).to_int(), n2 = ex_to(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(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(i.op(0))); + GINAC_ASSERT(is_a(i.op(1))); + GINAC_ASSERT(is_a(i.op(2))); const varidx & i1 = ex_to(i.op(1)); const varidx & i2 = ex_to(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(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(i.op(0))); + GINAC_ASSERT(is_a(i.op(1))); + GINAC_ASSERT(is_a(i.op(2))); const varidx & i1 = ex_to(i.op(1)); const varidx & i2 = ex_to(i.op(2)); @@ -245,11 +245,11 @@ ex minkmetric::eval_indexed(const basic & i) const if (static_cast(i).all_index_values_are(info_flags::nonnegint)) { int n1 = ex_to(i1.get_value()).to_int(), n2 = ex_to(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(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(i.op(0))); + GINAC_ASSERT(is_a(i.op(1))); + GINAC_ASSERT(is_a(i.op(2))); const spinidx & i1 = ex_to(i.op(1)); const spinidx & i2 = ex_to(i.op(2)); // Convolutions are zero if (!(static_cast(i).get_dummy_indices().empty())) - return _ex0(); + return _ex0; // Numeric evaluation if (static_cast(i).all_index_values_are(info_flags::nonnegint)) { int n1 = ex_to(i1.get_value()).to_int(), n2 = ex_to(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(i)); GINAC_ASSERT(i.nops() > 1); - GINAC_ASSERT(is_ex_of_type(i.op(0), tensepsilon)); + GINAC_ASSERT(is_a(i.op(0))); // Convolutions are zero if (!(static_cast(i).get_dummy_indices().empty())) - return _ex0(); + return _ex0; // Numeric evaluation if (static_cast(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(self->op(1)); const idx *free_idx = &ex_to(self->op(2)); bool first_index_tried = false; @@ -349,18 +343,24 @@ again: const idx &other_idx = ex_to(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(self->op(2)); free_idx = &ex_to(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(*self)); + GINAC_ASSERT(is_a(*other)); + GINAC_ASSERT(self->nops() == 3); + GINAC_ASSERT(is_a(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(*self)); + GINAC_ASSERT(is_a(*other)); GINAC_ASSERT(self->nops() == 3); - GINAC_ASSERT(is_ex_of_type(self->op(0), tensmetric)); + GINAC_ASSERT(is_a(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(self->op(1)); - const idx *free_idx = &ex_to(self->op(2)); - bool first_index_tried = false; - -again: - if (self_idx->is_symbolic()) { - for (unsigned i=1; inops(); i++) { - const idx &other_idx = ex_to(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(self->op(2)); - free_idx = &ex_to(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(*self)); + GINAC_ASSERT(is_a(*other)); GINAC_ASSERT(self->nops() == 3); - GINAC_ASSERT(is_ex_of_type(self->op(0), spinmetric)); + GINAC_ASSERT(is_a(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), spinmetric)); + GINAC_ASSERT(is_a(*self)); + GINAC_ASSERT(is_a(*other)); + GINAC_ASSERT(is_a(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(self->op(1)).get_dim(); matrix M(num, num); - for (int i=0; iop(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; iop(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(*ait) && ait->return_type() == return_types::commutative && ex_to(*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; jop(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(i1).get_dim(); if (!dim.is_equal(ex_to(i2).get_dim())) throw(std::invalid_argument("all indices of epsilon tensor must have the same dimension")); - if (!ex_to(i1).get_dim().is_equal(_ex2())) + if (!ex_to(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(i1).get_dim(); if (!dim.is_equal(ex_to(i2).get_dim()) || !dim.is_equal(ex_to(i3).get_dim())) throw(std::invalid_argument("all indices of epsilon tensor must have the same dimension")); - if (!ex_to(i1).get_dim().is_equal(_ex3())) + if (!ex_to(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(i1).get_dim(); if (!dim.is_equal(ex_to(i2).get_dim()) || !dim.is_equal(ex_to(i3).get_dim()) || !dim.is_equal(ex_to(i4).get_dim())) throw(std::invalid_argument("all indices of epsilon tensor must have the same dimension")); - if (!ex_to(i1).get_dim().is_equal(_ex4())) + if (!ex_to(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(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