X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Ftensor.cpp;h=07605e7a77cfa7ad87d33c67528ac54bb41fd0e2;hp=f6379bd0b7d95bc3ce24ced1d525f7f42f512f19;hb=c1285bb62f3a86454ca26260cf8b4352238a1fc5;hpb=27d6204effdef95a00af461fff98024e290dbaa7 diff --git a/ginac/tensor.cpp b/ginac/tensor.cpp index f6379bd0..07605e7a 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) 1999-2003 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 @@ -20,6 +20,7 @@ * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */ +#include #include #include @@ -28,83 +29,74 @@ #include "indexed.h" #include "symmetry.h" #include "relational.h" +#include "operators.h" #include "lst.h" #include "numeric.h" #include "matrix.h" -#include "print.h" #include "archive.h" #include "utils.h" -#include "debugmsg.h" namespace GiNaC { GINAC_IMPLEMENT_REGISTERED_CLASS(tensor, basic) -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) + +GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(tensdelta, tensor, + print_func(&tensdelta::do_print). + print_func(&tensdelta::do_print_latex)) + +GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(tensmetric, tensor, + print_func(&tensmetric::do_print). + print_func(&tensmetric::do_print)) + +GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(minkmetric, tensmetric, + print_func(&minkmetric::do_print). + print_func(&minkmetric::do_print_latex)) + +GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(spinmetric, tensmetric, + print_func(&spinmetric::do_print). + print_func(&spinmetric::do_print_latex)) + +GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(tensepsilon, tensor, + print_func(&tensepsilon::do_print). + print_func(&tensepsilon::do_print_latex)) ////////// -// default constructor, destructor, copy constructor assignment operator and helpers +// constructors ////////// -tensor::tensor(unsigned ti) : inherited(ti) +tensor::tensor() : inherited(TINFO_tensor) { - debugmsg("tensor constructor from unsigned", LOGLEVEL_CONSTRUCT); \ + setflag(status_flags::evaluated | status_flags::expanded); } -DEFAULT_CTORS(tensor) -DEFAULT_CTORS(tensdelta) -DEFAULT_CTORS(tensmetric) -DEFAULT_COPY(spinmetric) -DEFAULT_DESTROY(spinmetric) -DEFAULT_DESTROY(minkmetric) -DEFAULT_DESTROY(tensepsilon) +DEFAULT_CTOR(tensdelta) +DEFAULT_CTOR(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; } -void minkmetric::copy(const minkmetric & other) -{ - inherited::copy(other); - pos_sig = other.pos_sig; -} - 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; } -void tensepsilon::copy(const tensepsilon & other) -{ - inherited::copy(other); - minkowski = other.minkowski; - pos_sig = other.pos_sig; -} - ////////// // archiving ////////// @@ -116,9 +108,8 @@ DEFAULT_ARCHIVING(spinmetric) DEFAULT_UNARCHIVE(minkmetric) DEFAULT_UNARCHIVE(tensepsilon) -minkmetric::minkmetric(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst) +minkmetric::minkmetric(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst) { - debugmsg("minkmetric constructor from archive_node", LOGLEVEL_CONSTRUCT); n.find_bool("pos_sig", pos_sig); } @@ -128,9 +119,8 @@ void minkmetric::archive(archive_node &n) const n.add_bool("pos_sig", pos_sig); } -tensepsilon::tensepsilon(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst) +tensepsilon::tensepsilon(const archive_node &n, 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); } @@ -191,9 +181,24 @@ ex tensdelta::eval_indexed(const basic & i) const 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(); + // 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); + exmap m; + m[i1] = i1.replace_dim(min_dim); + m[i2] = i2.replace_dim(min_dim); + return i.subs(m, subs_options::no_pattern); + } + + // 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)) { @@ -220,6 +225,16 @@ ex tensmetric::eval_indexed(const basic & i) const 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); + exmap m; + m[i1] = i1.replace_dim(min_dim); + m[i2] = i2.replace_dim(min_dim); + return i.subs(m, subs_options::no_pattern); + } + // A metric tensor with one covariant and one contravariant index gets // replaced by a delta tensor if (i1.is_covariant() != i2.is_covariant()) @@ -305,15 +320,15 @@ ex tensepsilon::eval_indexed(const basic & i) const // a canonic order but we can't assume what exactly that order is) std::vector v; v.reserve(i.nops() - 1); - for (unsigned j=1; j(ex_to(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) { - for (unsigned j=1; j(x)) throw(std::runtime_error("indices of epsilon tensor in Minkowski space must be of type varidx")); if (ex_to(x).is_covariant()) if (ex_to(x).get_value().is_zero()) @@ -330,37 +345,37 @@ 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_a(*self)); - GINAC_ASSERT(is_a(*other)); - GINAC_ASSERT(self->nops() == 3); - GINAC_ASSERT(is_a(self->op(0))); - - // 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; again: if (self_idx->is_symbolic()) { - for (unsigned i=1; inops(); i++) { + for (size_t i=1; inops(); i++) { 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); + *other = other->subs(other_idx == free_idx->replace_dim(min_dim)); + *self = _ex1; // *other is assigned first because assigning *self invalidates free_idx + 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; @@ -370,6 +385,19 @@ 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 { @@ -380,39 +408,12 @@ bool tensmetric::contract_with(exvector::iterator self, exvector::iterator other // 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)) + if (is_a(other->op(0))) 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 + return replace_contr_index(self, other); } /** Contraction of an indexed spinor metric with something else. */ @@ -424,7 +425,7 @@ bool spinmetric::contract_with(exvector::iterator self, exvector::iterator other GINAC_ASSERT(is_a(self->op(0))); // Contractions between spinor metrics - if (is_ex_of_type(other->op(0), spinmetric)) { + if (is_a(other->op(0))) { const idx &self_i1 = ex_to(self->op(1)); const idx &self_i2 = ex_to(self->op(2)); const idx &other_i1 = ex_to(other->op(1)); @@ -457,7 +458,7 @@ bool spinmetric::contract_with(exvector::iterator self, exvector::iterator other // 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)) + if (is_a(other->op(0))) return false; // Try to contract first index @@ -468,14 +469,15 @@ bool spinmetric::contract_with(exvector::iterator self, exvector::iterator other again: if (self_idx->is_symbolic()) { - for (unsigned i=1; inops(); i++) { + for (size_t 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 = (static_cast(self_idx)->is_covariant() ? sign : -sign); + // index in second object (assign *self last because this + // invalidates free_idx) *other = other->subs(other_idx == *free_idx); + *self = (static_cast(self_idx)->is_covariant() ? sign : -sign); return true; } } @@ -500,63 +502,27 @@ bool tensepsilon::contract_with(exvector::iterator self, exvector::iterator othe GINAC_ASSERT(is_a(*self)); GINAC_ASSERT(is_a(*other)); GINAC_ASSERT(is_a(self->op(0))); - unsigned num = self->nops() - 1; + size_t num = self->nops() - 1; - if (is_ex_exactly_of_type(other->op(0), tensepsilon) && num+1 == other->nops()) { + if (is_exactly_a(other->op(0)) && num+1 == other->nops()) { // Contraction of two epsilon tensors is a determinant - ex dim = ex_to(self->op(1)).get_dim(); + bool variance = is_a(self->op(1)); matrix M(num, num); - for (int i=0; iop(i+1), other->op(j+1), pos_sig); - else + else if (variance) M(i, j) = metric_tensor(self->op(i+1), other->op(j+1)); + else + 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; 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; - } - } - } - } -#endif } return false; @@ -568,7 +534,7 @@ bool tensepsilon::contract_with(exvector::iterator self, exvector::iterator othe ex delta_tensor(const ex & i1, const ex & i2) { - if (!is_ex_of_type(i1, idx) || !is_ex_of_type(i2, idx)) + if (!is_a(i1) || !is_a(i2)) throw(std::invalid_argument("indices of delta tensor must be of type idx")); return indexed(tensdelta(), sy_symm(), i1, i2); @@ -576,7 +542,7 @@ ex delta_tensor(const ex & i1, const ex & i2) ex metric_tensor(const ex & i1, const ex & i2) { - if (!is_ex_of_type(i1, varidx) || !is_ex_of_type(i2, varidx)) + if (!is_a(i1) || !is_a(i2)) throw(std::invalid_argument("indices of metric tensor must be of type varidx")); return indexed(tensmetric(), sy_symm(), i1, i2); @@ -584,7 +550,7 @@ ex metric_tensor(const ex & i1, const ex & 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)) + if (!is_a(i1) || !is_a(i2)) throw(std::invalid_argument("indices of metric tensor must be of type varidx")); return indexed(minkmetric(pos_sig), sy_symm(), i1, i2); @@ -592,7 +558,7 @@ ex lorentz_g(const ex & i1, const ex & i2, bool pos_sig) ex spinor_metric(const ex & i1, const ex & i2) { - if (!is_ex_of_type(i1, spinidx) || !is_ex_of_type(i2, spinidx)) + if (!is_a(i1) || !is_a(i2)) throw(std::invalid_argument("indices of spinor metric must be of type spinidx")); if (!ex_to(i1).get_dim().is_equal(2) || !ex_to(i2).get_dim().is_equal(2)) throw(std::runtime_error("index dimension for spinor metric must be 2")); @@ -602,7 +568,7 @@ ex spinor_metric(const ex & i1, const ex & i2) ex epsilon_tensor(const ex & i1, const ex & i2) { - if (!is_ex_of_type(i1, idx) || !is_ex_of_type(i2, idx)) + if (!is_a(i1) || !is_a(i2)) throw(std::invalid_argument("indices of epsilon tensor must be of type idx")); ex dim = ex_to(i1).get_dim(); @@ -616,7 +582,7 @@ ex epsilon_tensor(const ex & i1, const ex & 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)) + if (!is_a(i1) || !is_a(i2) || !is_a(i3)) throw(std::invalid_argument("indices of epsilon tensor must be of type idx")); ex dim = ex_to(i1).get_dim(); @@ -630,7 +596,7 @@ ex epsilon_tensor(const ex & i1, const ex & i2, const ex & 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)) + if (!is_a(i1) || !is_a(i2) || !is_a(i3) || !is_a(i4)) throw(std::invalid_argument("indices of Lorentz epsilon tensor must be of type varidx")); ex dim = ex_to(i1).get_dim(); @@ -642,16 +608,4 @@ ex lorentz_eps(const ex & i1, const ex & i2, const ex & i3, const ex & i4, bool 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