X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Ftensor.cpp;h=0c36a68002423d712f4d8afa5ec903716ffba7e7;hp=9d5feb63c4051dbe5c9d65ee3a0398fd5ada7c96;hb=b8b8cfbb72bfa59b01371f67f542914cf55f2ab9;hpb=539de73dc25de63f2888f8696d73ac3fc83db45f;ds=sidebyside diff --git a/ginac/tensor.cpp b/ginac/tensor.cpp index 9d5feb63..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 @@ -20,16 +20,21 @@ * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */ +#include #include +#include #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" -#include "debugmsg.h" namespace GiNaC { @@ -37,46 +42,33 @@ 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) ////////// -// default constructor, destructor, copy constructor assignment operator and helpers +// default ctor, dtor, copy ctor, assignment operator and helpers ////////// -#define DEFAULT_CTORS(classname) \ -classname::classname() : inherited(TINFO_##classname) \ -{ \ - debugmsg(#classname " default constructor", LOGLEVEL_CONSTRUCT); \ -} \ -void classname::copy(const classname & other) \ -{ \ - inherited::copy(other); \ -} \ -void classname::destroy(bool call_parent) \ -{ \ - if (call_parent) \ - inherited::destroy(call_parent); \ -} - -tensor::tensor(unsigned ti) : inherited(ti) -{ - debugmsg("tensor constructor from unsigned", LOGLEVEL_CONSTRUCT); \ -} - DEFAULT_CTORS(tensor) DEFAULT_CTORS(tensdelta) DEFAULT_CTORS(tensmetric) -DEFAULT_CTORS(tensepsilon) +DEFAULT_COPY(spinmetric) +DEFAULT_DESTROY(spinmetric) +DEFAULT_DESTROY(minkmetric) +DEFAULT_DESTROY(tensepsilon) minkmetric::minkmetric() : pos_sig(false) { - debugmsg("minkmetric default constructor", LOGLEVEL_CONSTRUCT); tinfo_key = TINFO_minkmetric; } +spinmetric::spinmetric() +{ + tinfo_key = TINFO_spinmetric; +} + minkmetric::minkmetric(bool ps) : pos_sig(ps) { - debugmsg("minkmetric constructor from bool", LOGLEVEL_CONSTRUCT); tinfo_key = TINFO_minkmetric; } @@ -86,71 +78,70 @@ void minkmetric::copy(const minkmetric & other) pos_sig = other.pos_sig; } -void minkmetric::destroy(bool call_parent) +tensepsilon::tensepsilon() : minkowski(false), pos_sig(false) { - if (call_parent) - inherited::destroy(call_parent); + tinfo_key = TINFO_tensepsilon; +} + +tensepsilon::tensepsilon(bool mink, bool ps) : minkowski(mink), pos_sig(ps) +{ + tinfo_key = TINFO_tensepsilon; +} + +void tensepsilon::copy(const tensepsilon & other) +{ + inherited::copy(other); + minkowski = other.minkowski; + pos_sig = other.pos_sig; } ////////// // archiving ////////// -#define DEFAULT_ARCHIVING(classname) \ -classname::classname(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst) \ -{ \ - debugmsg(#classname " constructor from archive_node", LOGLEVEL_CONSTRUCT); \ -} \ -ex classname::unarchive(const archive_node &n, const lst &sym_lst) \ -{ \ - return (new classname(n, sym_lst))->setflag(status_flags::dynallocated); \ -} \ -void classname::archive(archive_node &n) const \ -{ \ - inherited::archive(n); \ -} - DEFAULT_ARCHIVING(tensor) DEFAULT_ARCHIVING(tensdelta) DEFAULT_ARCHIVING(tensmetric) -DEFAULT_ARCHIVING(tensepsilon) +DEFAULT_ARCHIVING(spinmetric) +DEFAULT_UNARCHIVE(minkmetric) +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); } -ex minkmetric::unarchive(const archive_node &n, const lst &sym_lst) +void minkmetric::archive(archive_node &n) const { - return (new minkmetric(n, sym_lst))->setflag(status_flags::dynallocated); + inherited::archive(n); + n.add_bool("pos_sig", pos_sig); } -void minkmetric::archive(archive_node &n) const +tensepsilon::tensepsilon(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst) +{ + n.find_bool("minkowski", minkowski); + n.find_bool("pos_sig", pos_sig); +} + +void tensepsilon::archive(archive_node &n) const { inherited::archive(n); + n.add_bool("minkowski", minkowski); n.add_bool("pos_sig", pos_sig); } ////////// -// functions overriding virtual functions from bases classes +// functions overriding virtual functions from base classes ////////// -#define DEFAULT_COMPARE(classname) \ -int classname::compare_same_type(const basic & other) const \ -{ \ - /* by default, two tensors of the same class are always identical */ \ - return 0; \ -} - DEFAULT_COMPARE(tensor) DEFAULT_COMPARE(tensdelta) DEFAULT_COMPARE(tensmetric) -DEFAULT_COMPARE(tensepsilon) +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) @@ -159,43 +150,52 @@ int minkmetric::compare_same_type(const basic & other) const return inherited::compare_same_type(other); } -void tensdelta::print(std::ostream & os, unsigned upper_precedence) const +int tensepsilon::compare_same_type(const basic & other) const { - debugmsg("tensdelta print",LOGLEVEL_PRINT); - os << "delta"; -} - -void tensmetric::print(std::ostream & os, unsigned upper_precedence) const -{ - debugmsg("tensmetric print",LOGLEVEL_PRINT); - os << "g"; -} + GINAC_ASSERT(is_a(other)); + const tensepsilon &o = static_cast(other); -void minkmetric::print(std::ostream & os, unsigned upper_precedence) const -{ - debugmsg("minkmetric print",LOGLEVEL_PRINT); - os << "eta"; + if (minkowski != o.minkowski) + return minkowski ? -1 : 1; + else if (pos_sig != o.pos_sig) + return pos_sig ? -1 : 1; + else + return inherited::compare_same_type(other); } -void tensepsilon::print(std::ostream & os, unsigned upper_precedence) const -{ - debugmsg("tensepsilon print",LOGLEVEL_PRINT); - os << "eps"; -} +DEFAULT_PRINT_LATEX(tensdelta, "delta", "\\delta") +DEFAULT_PRINT(tensmetric, "g") +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(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_idx(i.op(1)); - const idx & i2 = ex_to_idx(i.op(2)); + const idx & i1 = ex_to(i.op(1)); + const idx & i2 = ex_to(i.op(2)); + + // 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(); + } + } - // Trace of delta tensor is the dimension of the space - if (is_dummy_pair(i1, i2)) - return i1.get_dim(); + // 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; + else + return _ex0; + } // No further simplifications return i.hold(); @@ -204,14 +204,21 @@ 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)); - - const varidx & i1 = ex_to_varidx(i.op(1)); - const varidx & i2 = ex_to_varidx(i.op(2)); + 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 @@ -225,63 +232,137 @@ 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_varidx(i.op(1)); - const varidx & i2 = ex_to_varidx(i.op(2)); + const varidx & i1 = ex_to(i.op(1)); + const varidx & i2 = ex_to(i.op(2)); // Numeric evaluation if (static_cast(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(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 return inherited::eval_indexed(i); } -/** Contraction of an indexed delta tensor with something else. */ -bool tensdelta::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const +/** Automatic symbolic evaluation of an indexed metric tensor. */ +ex spinmetric::eval_indexed(const basic & i) 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)); + GINAC_ASSERT(is_a(i)); + GINAC_ASSERT(i.nops() == 3); + GINAC_ASSERT(is_a(i.op(0))); + GINAC_ASSERT(is_a(i.op(1))); + GINAC_ASSERT(is_a(i.op(2))); - // 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 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; + + // 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; + 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_a(i)); + GINAC_ASSERT(i.nops() > 1); + GINAC_ASSERT(is_a(i.op(0))); + + // Convolutions are zero + if (!(static_cast(i).get_dummy_indices().empty())) + return _ex0; + + // Numeric evaluation + if (static_cast(i).all_index_values_are(info_flags::nonnegint)) { + + // Get sign of index permutation (the indices should already be in + // 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).is_covariant()) + if (ex_to(x).get_value().is_zero()) + sign = (pos_sig ? -sign : sign); + else + sign = (pos_sig ? sign : -sign); + } + } + + return sign; + } + + // No further simplifications + return i.hold(); +} + +bool tensor::replace_contr_index(exvector::iterator self, exvector::iterator other) const +{ + // 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 (int i=1; inops(); i++) { - const idx &other_idx = ex_to_idx(other->op(i)); + 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 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 - self_idx = &ex_to_idx(self->op(2)); - free_idx = &ex_to_idx(self->op(1)); + // 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; goto again; } @@ -289,33 +370,97 @@ 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_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; + + // 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_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))); + + // Contractions between spinor metrics + if (is_ex_of_type(other->op(0), spinmetric)) { + 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)); + const idx &other_i2 = ex_to(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_exactly_of_type(other->op(0), tensdelta)) + 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)); + const idx *self_idx = &ex_to(self->op(1)); + const idx *free_idx = &ex_to(self->op(2)); bool first_index_tried = false; + int sign = 1; again: if (self_idx->is_symbolic()) { - for (int i=1; inops(); i++) { - const idx &other_idx = ex_to_idx(other->op(i)); + 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(); + *self = (static_cast(self_idx)->is_covariant() ? sign : -sign); *other = other->subs(other_idx == *free_idx); return true; } @@ -325,15 +470,46 @@ again: 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(self->op(2)); + free_idx = &ex_to(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_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()) { + + // 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), 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; + return true; + } + + return false; +} + ////////// // global functions ////////// @@ -343,7 +519,7 @@ ex delta_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 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) @@ -351,7 +527,7 @@ 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(), i1, i2); + return indexed(tensmetric(), sy_symm(), i1, i2); } ex lorentz_g(const ex & i1, const ex & i2, bool pos_sig) @@ -359,17 +535,59 @@ 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(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")); + + 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")); - if (!ex_to_idx(i1).get_dim().is_equal(_ex2()) || !ex_to_idx(i2).get_dim().is_equal(_ex2())) - throw(std::invalid_argument("index dimension of epsilon tensor must match number of indices")); - return indexed(tensepsilon(), indexed::antisymmetric, i1, 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)) + throw(std::runtime_error("index dimension of epsilon tensor must match number of indices")); + + 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(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)) + throw(std::runtime_error("index dimension of epsilon tensor must match number of indices")); + + 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(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)) + 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); } } // namespace GiNaC