X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fidx.cpp;h=c539974d1e8c0f435b806a4116c8e6f597aef693;hp=480da0f24cde7b5c3e0d17892aa8d5c70727ed09;hb=69815a366be5ca81185386d94268d7e7dcce94e3;hpb=1bd972bf8e4eeeb8aec6081100876e81a7f18450 diff --git a/ginac/idx.cpp b/ginac/idx.cpp index 480da0f2..c539974d 100644 --- a/ginac/idx.cpp +++ b/ginac/idx.cpp @@ -3,7 +3,7 @@ * Implementation of GiNaC's indices. */ /* - * GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany + * GiNaC Copyright (C) 1999-2020 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 @@ -17,516 +17,558 @@ * * You should have received a copy of the GNU General Public License * along with this program; if not, write to the Free Software - * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA + * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA */ -#include - #include "idx.h" -#include "ex.h" +#include "symbol.h" #include "lst.h" #include "relational.h" +#include "operators.h" #include "archive.h" #include "utils.h" -#include "debugmsg.h" +#include "hash_seed.h" + +#include +#include +#include -#ifndef NO_NAMESPACE_GINAC namespace GiNaC { -#endif // ndef NO_NAMESPACE_GINAC -GINAC_IMPLEMENT_REGISTERED_CLASS(idx, basic) +GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(idx, basic, + print_func(&idx::do_print). + print_func(&idx::do_print_latex). + print_func(&idx::do_print_csrc). + print_func(&idx::do_print_tree)) + +GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(varidx, idx, + print_func(&varidx::do_print). + print_func(&varidx::do_print_latex). + print_func(&varidx::do_print_tree)) + +GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(spinidx, varidx, + print_func(&spinidx::do_print). + print_func(&spinidx::do_print_latex). + print_func(&spinidx::do_print_tree)) ////////// -// default constructor, destructor, copy constructor assignment operator and helpers +// default constructor ////////// -// public +idx::idx() {} -idx::idx() : inherited(TINFO_idx), symbolic(true), covariant(false) +varidx::varidx() : covariant(false) { - debugmsg("idx default constructor",LOGLEVEL_CONSTRUCT); - serial=next_serial++; - name=autoname_prefix()+ToString(serial); } -// protected +spinidx::spinidx() : dotted(false) +{ +} + +////////// +// other constructors +////////// + +idx::idx(const ex & v, const ex & d) : value(v), dim(d) +{ + if (is_dim_numeric()) + if (!dim.info(info_flags::posint)) + throw(std::invalid_argument("dimension of space must be a positive integer")); +} -void idx::copy(const idx & other) +varidx::varidx(const ex & v, const ex & d, bool cov) : inherited(v, d), covariant(cov) { - inherited::copy(other); - serial=other.serial; - symbolic=other.symbolic; - name=other.name; - value=other.value; - covariant=other.covariant; } -void idx::destroy(bool call_parent) +spinidx::spinidx(const ex & v, const ex & d, bool cov, bool dot) : inherited(v, d, cov), dotted(dot) { - if (call_parent) inherited::destroy(call_parent); } ////////// -// other constructors +// archiving ////////// -// public +void idx::read_archive(const archive_node& n, lst& sym_lst) +{ + inherited::read_archive(n, sym_lst); + n.find_ex("value", value, sym_lst); + n.find_ex("dim", dim, sym_lst); +} +GINAC_BIND_UNARCHIVER(idx); -/** Construct symbolic index, using an automatically generated unique name. - * - * @param cov Index is covariant (contravariant otherwise) - * @return newly constructed index */ -idx::idx(bool cov) : inherited(TINFO_idx), symbolic(true), covariant(cov) +void varidx::read_archive(const archive_node& n, lst& sym_lst) { - debugmsg("idx constructor from bool",LOGLEVEL_CONSTRUCT); - serial = next_serial++; - name = autoname_prefix()+ToString(serial); + inherited::read_archive(n, sym_lst); + n.find_bool("covariant", covariant); } +GINAC_BIND_UNARCHIVER(varidx); -/** Construct symbolic index with specified name. - * - * @param n Symbolic index name - * @param cov Index is covariant (contravariant otherwise) - * @return newly constructed index */ -idx::idx(const std::string & n, bool cov) : inherited(TINFO_idx), - symbolic(true), name(n), covariant(cov) +void spinidx::read_archive(const archive_node& n, lst& sym_lst) { - debugmsg("idx constructor from string,bool",LOGLEVEL_CONSTRUCT); - serial = next_serial++; + inherited::read_archive(n, sym_lst); + n.find_bool("dotted", dotted); } +GINAC_BIND_UNARCHIVER(spinidx); -/** Construct symbolic index with specified name. - * - * @param n Symbolic index name - * @param cov Index is covariant (contravariant otherwise) - * @return newly constructed index */ -idx::idx(const char * n, bool cov) : inherited(TINFO_idx), symbolic(true), name(n), covariant(cov) +void idx::archive(archive_node &n) const { - debugmsg("idx constructor from char*,bool",LOGLEVEL_CONSTRUCT); - serial = next_serial++; + inherited::archive(n); + n.add_ex("value", value); + n.add_ex("dim", dim); } -/** Construct numeric index with specified value. - * - * @param v Numeric index value - * @param cov Index is covariant (contravariant otherwise) - * @return newly constructed index */ -idx::idx(unsigned v, bool cov) : inherited(TINFO_idx), symbolic(false), value(v), covariant(cov) +void varidx::archive(archive_node &n) const +{ + inherited::archive(n); + n.add_bool("covariant", covariant); +} + +void spinidx::archive(archive_node &n) const { - debugmsg("idx constructor from unsigned,bool",LOGLEVEL_CONSTRUCT); - serial = 0; + inherited::archive(n); + n.add_bool("dotted", dotted); } ////////// -// archiving +// functions overriding virtual functions from base classes ////////// -/** Construct object from archive_node. */ -idx::idx(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst) +void idx::print_index(const print_context & c, unsigned level) const { - debugmsg("idx constructor from archive_node", LOGLEVEL_CONSTRUCT); - n.find_bool("symbolic", symbolic); - n.find_bool("covariant", covariant); - if (symbolic) { - serial = next_serial++; - if (!(n.find_string("name", name))) - name = autoname_prefix() + ToString(serial); - } else { - serial = 0; - n.find_unsigned("value", value); + bool need_parens = !(is_exactly_a(value) || is_a(value)); + if (need_parens) + c.s << "("; + value.print(c); + if (need_parens) + c.s << ")"; + if (c.options & print_options::print_index_dimensions) { + c.s << "["; + dim.print(c); + c.s << "]"; } } -/** Unarchive the object. */ -ex idx::unarchive(const archive_node &n, const lst &sym_lst) +void idx::do_print(const print_context & c, unsigned level) const { - ex s = (new idx(n, sym_lst))->setflag(status_flags::dynallocated); + c.s << "."; + print_index(c, level); +} - if (ex_to_idx(s).symbolic) { - // If idx is in sym_lst, return the existing idx - for (unsigned i=0; i(value).to_int(); else - n.add_unsigned("value", value); + value.print(c); + c.s << "]"; } -////////// -// functions overriding virtual functions from bases classes -////////// +void idx::do_print_tree(const print_tree & c, unsigned level) const +{ + c.s << std::string(level, ' ') << class_name() << " @" << this + << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec + << std::endl; + value.print(c, level + c.delta_indent); + dim.print(c, level + c.delta_indent); +} -// public +void varidx::do_print(const print_context & c, unsigned level) const +{ + if (covariant) + c.s << "."; + else + c.s << "~"; + print_index(c, level); +} -void idx::printraw(std::ostream & os) const +void varidx::do_print_tree(const print_tree & c, unsigned level) const { - debugmsg("idx printraw",LOGLEVEL_PRINT); + c.s << std::string(level, ' ') << class_name() << " @" << this + << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec + << (covariant ? ", covariant" : ", contravariant") + << std::endl; + value.print(c, level + c.delta_indent); + dim.print(c, level + c.delta_indent); +} - os << "idx("; +void spinidx::do_print(const print_context & c, unsigned level) const +{ + if (covariant) + c.s << "."; + else + c.s << "~"; + if (dotted) + c.s << "*"; + print_index(c, level); +} - if (symbolic) { - os << "symbolic,name=" << name; - } else { - os << "non symbolic,value=" << value; - } +void spinidx::do_print_latex(const print_latex & c, unsigned level) const +{ + if (dotted) + c.s << "\\dot{"; + else + c.s << "{"; + print_index(c, level); + c.s << "}"; +} - if (covariant) { - os << ",covariant"; - } else { - os << ",contravariant"; - } +void spinidx::do_print_tree(const print_tree & c, unsigned level) const +{ + c.s << std::string(level, ' ') << class_name() << " @" << this + << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec + << (covariant ? ", covariant" : ", contravariant") + << (dotted ? ", dotted" : ", undotted") + << std::endl; + value.print(c, level + c.delta_indent); + dim.print(c, level + c.delta_indent); +} - os << ",serial=" << serial; - os << ",hash=" << hashvalue << ",flags=" << flags; - os << ")"; +bool idx::info(unsigned inf) const +{ + switch(inf) { + case info_flags::idx: + case info_flags::has_indices: + return true; + } + return inherited::info(inf); } -void idx::printtree(std::ostream & os, unsigned indent) const +size_t idx::nops() const { - debugmsg("idx printtree",LOGLEVEL_PRINT); + // don't count the dimension as that is not really a sub-expression + return 1; +} - os << std::string(indent,' ') << "idx: "; +ex idx::op(size_t i) const +{ + GINAC_ASSERT(i == 0); + return value; +} - if (symbolic) { - os << "symbolic,name=" << name; - } else { - os << "non symbolic,value=" << value; +ex idx::map(map_function & f) const +{ + const ex &mapped_value = f(value); + if (are_ex_trivially_equal(value, mapped_value)) + return *this; + else { + idx *copy = duplicate(); + copy->clearflag(status_flags::hash_calculated); + copy->value = mapped_value; + return *copy; } +} - if (covariant) { - os << ",covariant"; - } else { - os << ",contravariant"; - } +/** Returns order relation between two indices of the same type. The order + * must be such that dummy indices lie next to each other. */ +int idx::compare_same_type(const basic & other) const +{ + GINAC_ASSERT(is_a(other)); + const idx &o = static_cast(other); - os << ", serial=" << serial - << ", hash=" << hashvalue - << " (0x" << std::hex << hashvalue << std::dec << ")" - << ", flags=" << flags << std::endl; + int cmpval = value.compare(o.value); + if (cmpval) + return cmpval; + return dim.compare(o.dim); } -void idx::print(std::ostream & os, unsigned upper_precedence) const +bool idx::match_same_type(const basic & other) const { - debugmsg("idx print",LOGLEVEL_PRINT); + GINAC_ASSERT(is_a(other)); + const idx &o = static_cast(other); - if (covariant) { - os << "_"; - } else { - os << "~"; - } - if (symbolic) { - os << name; - } else { - os << value; - } + return dim.is_equal(o.dim); } -bool idx::info(unsigned inf) const +int varidx::compare_same_type(const basic & other) const { - if (inf==info_flags::idx) return true; - return inherited::info(inf); + GINAC_ASSERT(is_a(other)); + const varidx &o = static_cast(other); + + int cmpval = inherited::compare_same_type(other); + if (cmpval) + return cmpval; + + // Check variance last so dummy indices will end up next to each other + if (covariant != o.covariant) + return covariant ? -1 : 1; + + return 0; } -ex idx::subs(const lst & ls, const lst & lr) const +bool varidx::match_same_type(const basic & other) const { - GINAC_ASSERT(ls.nops()==lr.nops()); -#ifdef DO_GINAC_ASSERT - for (unsigned i=0; i(other)); + const varidx &o = static_cast(other); - for (unsigned i=0; i(other)); + const spinidx &o = static_cast(other); -int idx::compare_same_type(const basic & other) const + // Check dottedness first so dummy indices will end up next to each other + if (dotted != o.dotted) + return dotted ? -1 : 1; + + int cmpval = inherited::compare_same_type(other); + if (cmpval) + return cmpval; + + return 0; +} + +bool spinidx::match_same_type(const basic & other) const { - GINAC_ASSERT(is_of_type(other,idx)); - const idx &o = static_cast(other); + GINAC_ASSERT(is_a(other)); + const spinidx &o = static_cast(other); - if (covariant!=o.covariant) { - // different co/contravariant - return covariant ? -1 : 1; - } + if (dotted != o.dotted) + return false; + return inherited::match_same_type(other); +} - if ((!symbolic) && (!o.symbolic)) { - // non-symbolic, of equal type: compare values - if (value==o.value) { - return 0; - } - return value(other); + // First look for index substitutions + auto it = m.find(*this); + if (it != m.end()) { + + // Substitution index->index + if (is_a(it->second) || (options & subs_options::really_subs_idx)) + return it->second; + + // Otherwise substitute value + idx *i_copy = duplicate(); + i_copy->value = it->second; + i_copy->clearflag(status_flags::hash_calculated); + return *i_copy; + } - if (covariant != o.covariant) return false; - if (symbolic != o.symbolic) return false; - if (symbolic && o.symbolic) return serial==o.serial; - return value==o.value; -} + // None, substitute objects in value (not in dimension) + const ex &subsed_value = value.subs(m, options); + if (are_ex_trivially_equal(value, subsed_value)) + return *this; -unsigned idx::calchash(void) const + idx *i_copy = duplicate(); + i_copy->value = subsed_value; + i_copy->clearflag(status_flags::hash_calculated); + return *i_copy; +} + +/** Implementation of ex::diff() for an index always returns 0. + * + * @see ex::diff */ +ex idx::derivative(const symbol & s) const { - hashvalue=golden_ratio_hash(golden_ratio_hash(tinfo_key ^ serial)); - setflag(status_flags::hash_calculated); - return hashvalue; + return _ex0; } ////////// -// new virtual functions which can be overridden by derived classes +// new virtual functions ////////// -// public +bool idx::is_dummy_pair_same_type(const basic & other) const +{ + const idx &o = static_cast(other); + + // Only pure symbols form dummy pairs, "2n+1" doesn't + if (!is_a(value)) + return false; + + // Value must be equal, of course + if (!value.is_equal(o.value)) + return false; + + // Dimensions need not be equal but must be comparable (so we can + // determine the minimum dimension of contractions) + if (dim.is_equal(o.dim)) + return true; + + return is_exactly_a(dim) || is_exactly_a(o.dim); +} -/** Check whether the index forms a co-/contravariant pair with another - * index (i.e. same name/value but opposite co-/contravariance). */ -bool idx::is_co_contra_pair(const basic & other) const +bool varidx::is_dummy_pair_same_type(const basic & other) const { - // like is_equal_same_type(), but tests for different covariant status - GINAC_ASSERT(is_of_type(other,idx)); - const idx & o=static_cast(const_cast(other)); + const varidx &o = static_cast(other); + + // Variance must be opposite + if (covariant == o.covariant) + return false; - if (covariant==o.covariant) return false; - if (symbolic!=o.symbolic) return false; - if (symbolic && o.symbolic) return serial==o.serial; - return value==o.value; -} + return inherited::is_dummy_pair_same_type(other); +} -/** Toggle co-/contravariance of index. */ -ex idx::toggle_covariant(void) const +bool spinidx::is_dummy_pair_same_type(const basic & other) const { - idx * i_copy=static_cast(duplicate()); - i_copy->covariant = !i_copy->covariant; - i_copy->clearflag(status_flags::hash_calculated); - return i_copy->setflag(status_flags::dynallocated); + const spinidx &o = static_cast(other); + + // Dottedness must be the same + if (dotted != o.dotted) + return false; + + return inherited::is_dummy_pair_same_type(other); } + ////////// -// non-virtual functions in this class +// non-virtual functions ////////// -// private +ex idx::replace_dim(const ex & new_dim) const +{ + idx *i_copy = duplicate(); + i_copy->dim = new_dim; + i_copy->clearflag(status_flags::hash_calculated); + return *i_copy; +} -std::string & idx::autoname_prefix(void) +ex idx::minimal_dim(const idx & other) const { - static std::string * s = new std::string("index"); - return *s; + return GiNaC::minimal_dim(dim, other.dim); } -////////// -// static member variables -////////// +ex varidx::toggle_variance() const +{ + varidx *i_copy = duplicate(); + i_copy->covariant = !i_copy->covariant; + i_copy->clearflag(status_flags::hash_calculated); + return *i_copy; +} -// protected +ex spinidx::toggle_dot() const +{ + spinidx *i_copy = duplicate(); + i_copy->dotted = !i_copy->dotted; + i_copy->clearflag(status_flags::hash_calculated); + return *i_copy; +} -unsigned idx::next_serial=0; +ex spinidx::toggle_variance_dot() const +{ + spinidx *i_copy = duplicate(); + i_copy->covariant = !i_copy->covariant; + i_copy->dotted = !i_copy->dotted; + i_copy->clearflag(status_flags::hash_calculated); + return *i_copy; +} ////////// -// other functions +// global functions ////////// -/** Bring a vector of indices into a canonic order. This operation only makes - * sense if the object carrying these indices is either symmetric or totally - * antisymmetric with respect to the indices. - * - * @param iv Index vector - * @param antisymmetric Whether the object carrying the indices is antisymmetric (symmetric otherwise) - * @return the sign introduced by the reordering of the indices. For symmetric - * objects this is always +1. For antisymmetric objects this is either - * +1 or -1 or 0 (if two equal indices were encountered). If the index - * vector was unchanged this function returns INT_MAX. */ -int canonicalize_indices(exvector & iv, bool antisymmetric) -{ - if (iv.size()<2) { - // nothing do to for 0 or 1 indices - return INT_MAX; - } +bool is_dummy_pair(const idx & i1, const idx & i2) +{ + // The indices must be of exactly the same type + if (typeid(i1) != typeid(i2)) + return false; - bool something_changed=false; - int sig=1; - - // simple bubble sort algorithm should be sufficient for the small number of indices needed - exvector::const_iterator last_idx=iv.end(); - exvector::const_iterator next_to_last_idx=iv.end()-1; - for (exvector::iterator it1=iv.begin(); it1!=next_to_last_idx; ++it1) { - for (exvector::iterator it2=it1+1; it2!=last_idx; ++it2) { - int cmpval=(*it1).compare(*it2); - if (cmpval==1) { - iter_swap(it1,it2); - something_changed=true; - if (antisymmetric) sig=-sig; - } else if ((cmpval==0) && antisymmetric) { - something_changed=true; - sig=0; - } - } - } + // Same type, let the indices decide whether they are paired + return i1.is_dummy_pair_same_type(i2); +} - return something_changed ? sig : INT_MAX; -} - -/** Build a vector of indices as the set intersection of two other index - * vectors (i.e. the returned vector contains the indices which appear in - * both source vectors). */ -exvector idx_intersect(const exvector & iv1, const exvector & iv2) -{ - // Create union vector - exvector iv_union; - iv_union.reserve(iv1.size() + iv2.size()); - iv_union.insert(iv_union.end(), iv1.begin(), iv1.end()); - iv_union.insert(iv_union.end(), iv2.begin(), iv2.end()); - - // Sort it - canonicalize_indices(iv_union); - - // Look for duplicates - exvector iv_intersect; - exvector::const_iterator cit = iv_union.begin(), citend = iv_union.end(); - ex e; - if (cit != citend) - e = *cit++; - while (cit != citend) { - if (e.is_equal(*cit)) { - iv_intersect.push_back(e); - do { - cit++; - } while (cit != citend && e.is_equal(*cit)); - if (cit == citend) - break; - } - e = *cit++; - } - return iv_intersect; +bool is_dummy_pair(const ex & e1, const ex & e2) +{ + // The expressions must be indices + if (!is_a(e1) || !is_a(e2)) + return false; + + return is_dummy_pair(ex_to(e1), ex_to(e2)); } -/** Given a vector iv3 of three indices and a vector iv2 of two indices - * where iv2 is a subset of iv3, return the (free) index that is in iv3 - * but not in iv2 and the sign introduced by permuting that index to the - * front. - * - * @param iv3 Vector of 3 indices - * @param iv2 Vector of 2 indices, must be a subset of iv3 - * @param sig Returns the sign introduced by permuting the free index to the - * front if the object carrying the indices was antisymmetric (if - * it's symmetric, you can just ignore the returned value). - * @return the free index (the one that is in iv3 but not in iv2) */ -ex permute_free_index_to_front(const exvector & iv3, const exvector & iv2, int * sig) -{ - // match (return value,iv2) to iv3 by permuting indices - // iv3 is always cyclic - - GINAC_ASSERT(iv3.size()==3); - GINAC_ASSERT(iv2.size()==2); - - *sig=1; - -#define TEST_PERMUTATION(A,B,C,P) \ - if ((iv3[B].is_equal(iv2[0]))&&(iv3[C].is_equal(iv2[1]))) { \ - *sig=P; \ - return iv3[A]; \ - } - - TEST_PERMUTATION(0,1,2, 1); - TEST_PERMUTATION(0,2,1, -1); - TEST_PERMUTATION(1,0,2, -1); - TEST_PERMUTATION(1,2,0, 1); - TEST_PERMUTATION(2,0,1, 1); - TEST_PERMUTATION(2,1,0, -1); - throw(std::logic_error("permute_free_index_to_front(): no valid permutation found")); -} - -/** Substitute one index in a vector of expressions. - * - * @param v Vector to substitute in (will be modified) - * @param is Index being substituted - * @param ir Index to replace by - * @return number of performed substitutions */ -unsigned subs_index_in_exvector(exvector & v, const ex & is, const ex & ir) -{ - exvector::iterator it; - unsigned replacements=0; - unsigned current_replacements; - - GINAC_ASSERT(is_ex_of_type(is,idx)); - GINAC_ASSERT(is_ex_of_type(ir,idx)); - - for (it=v.begin(); it!=v.end(); ++it) { - current_replacements=count_index(*it,is); - if (current_replacements>0) { - (*it)=(*it).subs(is==ir); - } - replacements += current_replacements; +void find_free_and_dummy(exvector::const_iterator it, exvector::const_iterator itend, exvector & out_free, exvector & out_dummy) +{ + out_free.clear(); + out_dummy.clear(); + + // No indices? Then do nothing + if (it == itend) + return; + + // Only one index? Then it is a free one if it's not numeric + if (itend - it == 1) { + if (ex_to(*it).is_symbolic()) + out_free.push_back(*it); + return; } - return replacements; -} -/** Count number of times a given index appears in the index vector of an - * indexed object. - * - * @param e Indexed object - * @param i Index to look for - * @return number of times the index was found */ -unsigned count_index(const ex & e, const ex & i) -{ - exvector idxv=e.get_indices(); - unsigned count=0; - for (exvector::const_iterator cit=idxv.begin(); cit!=idxv.end(); ++cit) { - if ((*cit).is_equal(i)) count++; + // Sort index vector. This will cause dummy indices come to lie next + // to each other (because the sort order is defined to guarantee this). + exvector v(it, itend); + shaker_sort(v.begin(), v.end(), ex_is_less(), ex_swap()); + + // Find dummy pairs and free indices + it = v.begin(); itend = v.end(); + auto last = it++; + while (it != itend) { + if (is_dummy_pair(*it, *last)) { + out_dummy.push_back(*last); + it++; + if (it == itend) + return; + } else { + if (!it->is_equal(*last) && ex_to(*last).is_symbolic()) + out_free.push_back(*last); + } + last = it++; } - return count; + if (ex_to(*last).is_symbolic()) + out_free.push_back(*last); } -/** Substitute multiple indices in an expression. - * - * @param e Expression to substitute in - * @param idxv_subs Vector of indices being substituted - * @param idxv_repl Vector of indices to replace by (1:1 correspondence to idxv_subs) - * @return expression with substituted indices */ -ex subs_indices(const ex & e, const exvector & idxv_subs, const exvector & idxv_repl) -{ - GINAC_ASSERT(idxv_subs.size()==idxv_repl.size()); - ex res=e; - for (unsigned i=0; i(dim1) && !is_a(dim2))) + return dim1; + else if (dim1 > dim2 || (!is_a(dim1) && is_exactly_a(dim2))) + return dim2; + else { + std::ostringstream s; + s << "minimal_dim(): index dimensions " << dim1 << " and " << dim2 << " cannot be ordered"; + throw (std::runtime_error(s.str())); } - return res; } -#ifndef NO_NAMESPACE_GINAC } // namespace GiNaC -#endif // ndef NO_NAMESPACE_GINAC