/** @file idx.cpp
*
- * Implementation of GiNaC's indices.
- *
- * GiNaC Copyright (C) 1999 Johannes Gutenberg University Mainz, Germany
+ * Implementation of GiNaC's indices. */
+
+/*
+ * 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
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*/
+#include <iostream>
+#include <sstream>
#include <stdexcept>
#include "idx.h"
-#include "ex.h"
+#include "symbol.h"
#include "lst.h"
#include "relational.h"
+#include "operators.h"
+#include "archive.h"
#include "utils.h"
+namespace GiNaC {
+
+GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(idx, basic,
+ print_func<print_context>(&idx::do_print).
+ print_func<print_latex>(&idx::do_print_latex).
+ print_func<print_tree>(&idx::do_print_tree))
+
+GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(varidx, idx,
+ print_func<print_context>(&varidx::do_print).
+ // print_latex inherited from idx
+ print_func<print_tree>(&varidx::do_print_tree))
+
+GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(spinidx, varidx,
+ print_func<print_context>(&spinidx::do_print).
+ print_func<print_latex>(&spinidx::do_print_latex).
+ print_func<print_tree>(&spinidx::do_print_tree))
+
//////////
-// default constructor, destructor, copy constructor assignment operator and helpers
+// default constructor
//////////
-// public
+idx::idx() : inherited(TINFO_idx) {}
-idx::idx() : basic(TINFO_idx), symbolic(true), covariant(false)
+varidx::varidx() : covariant(false)
{
- debugmsg("idx default constructor",LOGLEVEL_CONSTRUCT);
- serial=next_serial++;
- name="index"+ToString(serial);
+ tinfo_key = TINFO_varidx;
}
-idx::~idx()
+spinidx::spinidx() : dotted(false)
{
- debugmsg("idx destructor",LOGLEVEL_DESTRUCT);
- destroy(0);
+ tinfo_key = TINFO_spinidx;
}
-idx::idx(idx const & other)
-{
- debugmsg("idx copy constructor",LOGLEVEL_CONSTRUCT);
- copy(other);
-}
+//////////
+// other constructors
+//////////
-idx const & idx::operator=(idx const & other)
+idx::idx(const ex & v, const ex & d) : inherited(TINFO_idx), value(v), dim(d)
{
- debugmsg("idx operator=",LOGLEVEL_ASSIGNMENT);
- if (this != &other) {
- destroy(1);
- copy(other);
- }
- return *this;
+ if (is_dim_numeric())
+ if (!dim.info(info_flags::posint))
+ throw(std::invalid_argument("dimension of space must be a positive integer"));
}
-// protected
-
-void idx::copy(idx const & other)
+varidx::varidx(const ex & v, const ex & d, bool cov) : inherited(v, d), covariant(cov)
{
- basic::copy(other);
- serial=other.serial;
- symbolic=other.symbolic;
- name=other.name;
- value=other.value;
- covariant=other.covariant;
+ tinfo_key = TINFO_varidx;
}
-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) basic::destroy(call_parent);
+ tinfo_key = TINFO_spinidx;
}
//////////
-// other constructors
+// archiving
//////////
-// public
+idx::idx(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst)
+{
+ n.find_ex("value", value, sym_lst);
+ n.find_ex("dim", dim, sym_lst);
+}
+
+varidx::varidx(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst)
+{
+ n.find_bool("covariant", covariant);
+}
-idx::idx(bool cov) : basic(TINFO_idx), symbolic(true), covariant(cov)
+spinidx::spinidx(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst)
{
- debugmsg("idx constructor from bool",LOGLEVEL_CONSTRUCT);
- serial=next_serial++;
- name="index"+ToString(serial);
+ n.find_bool("dotted", dotted);
}
-idx::idx(string const & n, bool cov) : basic(TINFO_idx),
- symbolic(true), name(n), covariant(cov)
+void idx::archive(archive_node &n) const
{
- debugmsg("idx constructor from string,bool",LOGLEVEL_CONSTRUCT);
- serial=next_serial++;
+ inherited::archive(n);
+ n.add_ex("value", value);
+ n.add_ex("dim", dim);
}
-idx::idx(char const * n, bool cov) : basic(TINFO_idx),
- symbolic(true), name(n), covariant(cov)
+void varidx::archive(archive_node &n) const
{
- debugmsg("idx constructor from char*,bool",LOGLEVEL_CONSTRUCT);
- serial=next_serial++;
+ inherited::archive(n);
+ n.add_bool("covariant", covariant);
}
-idx::idx(unsigned const v, bool cov) : basic(TINFO_idx),
- symbolic(false), value(v), covariant(cov)
+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);
}
+DEFAULT_UNARCHIVE(idx)
+DEFAULT_UNARCHIVE(varidx)
+DEFAULT_UNARCHIVE(spinidx)
//////////
-// functions overriding virtual functions from bases classes
+// functions overriding virtual functions from base classes
//////////
-// public
-
-basic * idx::duplicate() const
+void idx::print_index(const print_context & c, unsigned level) const
{
- debugmsg("idx duplicate",LOGLEVEL_DUPLICATE);
- return new idx(*this);
+ bool need_parens = !(is_exactly_a<numeric>(value) || is_a<symbol>(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 << "]";
+ }
}
-void idx::printraw(ostream & os) const
+void idx::do_print(const print_context & c, unsigned level) const
{
- debugmsg("idx printraw",LOGLEVEL_PRINT);
-
- os << "idx(";
+ c.s << ".";
+ print_index(c, level);
+}
- if (symbolic) {
- os << "symbolic,name=" << name;
- } else {
- os << "non symbolic,value=" << value;
- }
+void idx::do_print_latex(const print_latex & c, unsigned level) const
+{
+ c.s << "{";
+ print_index(c, level);
+ c.s << "}";
+}
- if (covariant) {
- os << ",covariant";
- } else {
- os << ",contravariant";
- }
+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);
+}
- os << ",serial=" << serial;
- os << ",hash=" << hashvalue << ",flags=" << flags;
- os << ")";
+void varidx::do_print(const print_context & c, unsigned level) const
+{
+ if (covariant)
+ c.s << ".";
+ else
+ c.s << "~";
+ print_index(c, level);
}
-void idx::printtree(ostream & os, unsigned indent) const
+void varidx::do_print_tree(const print_tree & c, unsigned level) const
{
- debugmsg("idx printtree",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 << string(indent,' ') << "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
- << ", hash=" << hashvalue << " (0x" << hex << hashvalue << dec << ")"
- << ", flags=" << flags << endl;
+bool idx::info(unsigned inf) const
+{
+ if (inf == info_flags::idx)
+ return true;
+ return inherited::info(inf);
}
-void idx::print(ostream & os, unsigned upper_precedence) const
+size_t idx::nops() const
{
- debugmsg("idx print",LOGLEVEL_PRINT);
+ // don't count the dimension as that is not really a sub-expression
+ return 1;
+}
- if (covariant) {
- os << "_";
- } else {
- os << "~";
- }
- if (symbolic) {
- os << name;
- } else {
- os << value;
- }
+ex idx::op(size_t i) const
+{
+ GINAC_ASSERT(i == 0);
+ return value;
}
-bool idx::info(unsigned inf) const
+ex idx::map(map_function & f) const
{
- if (inf==info_flags::idx) return true;
- return basic::info(inf);
+ idx *copy = duplicate();
+ copy->setflag(status_flags::dynallocated);
+ copy->clearflag(status_flags::hash_calculated);
+ copy->value = f(value);
+ return *copy;
}
-ex idx::subs(lst const & ls, lst const & lr) const
+/** 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
{
- ASSERT(ls.nops()==lr.nops());
-#ifdef DOASSERT
- for (int i=0; i<ls.nops(); i++) {
- ASSERT(is_ex_exactly_of_type(ls.op(i),symbol)||
- is_ex_of_type(ls.op(i),idx));
- }
-#endif // def DOASSERT
+ GINAC_ASSERT(is_a<idx>(other));
+ const idx &o = static_cast<const idx &>(other);
- for (int i=0; i<ls.nops(); i++) {
- if (is_equal(*(ls.op(i)).bp)) {
- return lr.op(i);
- }
- }
- return *this;
+ int cmpval = value.compare(o.value);
+ if (cmpval)
+ return cmpval;
+ return dim.compare(o.dim);
}
-// protected
-
-int idx::compare_same_type(basic const & other) const
+bool idx::match_same_type(const basic & other) const
{
- ASSERT(is_of_type(other,idx));
- idx const & o=static_cast<idx const &>
- (const_cast<basic &>(other));
+ GINAC_ASSERT(is_a<idx>(other));
+ const idx &o = static_cast<const idx &>(other);
- if (covariant!=o.covariant) {
- // different co/contravariant
- return covariant ? -1 : 1;
- }
- if ((!symbolic) && (!o.symbolic)) {
- // non-symbolic, of equal type: compare values
- if (value==o.value) {
- return 0;
- }
- return value<o.value ? -1 : 1;
- }
- if (symbolic && o.symbolic) {
- // both symbolic: compare serials
- if (serial==o.serial) {
- return 0;
- }
- return serial<o.serial ? -1 : 1;
- }
- // one symbolic, one value: value is sorted first
- return o.symbolic ? -1 : 1;
+ return dim.is_equal(o.dim);
}
-bool idx::is_equal_same_type(basic const & other) const
+int varidx::compare_same_type(const basic & other) const
{
- ASSERT(is_of_type(other,idx));
- idx const & o=static_cast<idx const &>
- (const_cast<basic &>(other));
+ GINAC_ASSERT(is_a<varidx>(other));
+ const varidx &o = static_cast<const varidx &>(other);
+
+ int cmpval = inherited::compare_same_type(other);
+ if (cmpval)
+ return cmpval;
- if (covariant!=o.covariant) return false;
- if (symbolic!=o.symbolic) return false;
- if (symbolic && o.symbolic) return serial==o.serial;
- return value==o.value;
-}
+ // Check variance last so dummy indices will end up next to each other
+ if (covariant != o.covariant)
+ return covariant ? -1 : 1;
-unsigned idx::calchash(void) const
+ return 0;
+}
+
+bool varidx::match_same_type(const basic & other) const
{
- hashvalue=golden_ratio_hash(golden_ratio_hash(tinfo_key ^ serial));
- setflag(status_flags::hash_calculated);
- return hashvalue;
+ GINAC_ASSERT(is_a<varidx>(other));
+ const varidx &o = static_cast<const varidx &>(other);
+
+ if (covariant != o.covariant)
+ return false;
+
+ return inherited::match_same_type(other);
}
-//////////
-// new virtual functions which can be overridden by derived classes
-//////////
+int spinidx::compare_same_type(const basic & other) const
+{
+ GINAC_ASSERT(is_a<spinidx>(other));
+ const spinidx &o = static_cast<const spinidx &>(other);
+
+ // 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;
-// public
+ return 0;
+}
-bool idx::is_co_contra_pair(basic const & other) const
+bool spinidx::match_same_type(const basic & other) const
{
- // like is_equal_same_type(), but tests for different covariant status
- ASSERT(is_of_type(other,idx));
- idx const & o=static_cast<idx const &>
- (const_cast<basic &>(other));
+ GINAC_ASSERT(is_a<spinidx>(other));
+ const spinidx &o = static_cast<const spinidx &>(other);
- if (covariant==o.covariant) return false;
- if (symbolic!=o.symbolic) return false;
- if (symbolic && o.symbolic) return serial==o.serial;
- return value==o.value;
-}
+ if (dotted != o.dotted)
+ return false;
+ return inherited::match_same_type(other);
+}
-bool idx::is_symbolic(void) const
+unsigned idx::calchash() const
{
- return symbolic;
+ unsigned v = golden_ratio_hash(tinfo());
+ v = rotate_left(v);
+ v ^= value.gethash();
+ v = rotate_left(v);
+ v ^= dim.gethash();
+
+ // Store calculated hash value only if object is already evaluated
+ if (flags & status_flags::evaluated) {
+ setflag(status_flags::hash_calculated);
+ hashvalue = v;
+ }
+
+ return v;
}
-unsigned idx::get_value(void) const
+/** By default, basic::evalf would evaluate the index value but we don't want
+ * a.1 to become a.(1.0). */
+ex idx::evalf(int level) const
{
- return value;
+ return *this;
}
-bool idx::is_covariant(void) const
+ex idx::subs(const exmap & m, unsigned options) const
{
- return covariant;
+ // First look for index substitutions
+ exmap::const_iterator it = m.find(*this);
+ if (it != m.end()) {
+
+ // Substitution index->index
+ if (is_a<idx>(it->second))
+ 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->setflag(status_flags::dynallocated);
+ }
+
+ // 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;
+
+ idx *i_copy = duplicate();
+ i_copy->value = subsed_value;
+ i_copy->clearflag(status_flags::hash_calculated);
+ return i_copy->setflag(status_flags::dynallocated);
}
-ex idx::toggle_covariant(void) const
+/** Implementation of ex::diff() for an index always returns 0.
+ *
+ * @see ex::diff */
+ex idx::derivative(const symbol & s) const
{
- idx * i_copy=static_cast<idx *>(duplicate());
- i_copy->covariant = !i_copy->covariant;
- i_copy->clearflag(status_flags::hash_calculated);
- return i_copy->setflag(status_flags::dynallocated);
+ return _ex0;
}
//////////
-// non-virtual functions in this class
+// new virtual functions
//////////
-// none
+bool idx::is_dummy_pair_same_type(const basic & other) const
+{
+ const idx &o = static_cast<const idx &>(other);
-//////////
-// static member variables
-//////////
+ // Only pure symbols form dummy pairs, "2n+1" doesn't
+ if (!is_a<symbol>(value))
+ return false;
-// protected
+ // 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 (dim < o.dim || dim > o.dim || (is_exactly_a<numeric>(dim) && is_a<symbol>(o.dim)) || (is_a<symbol>(dim) && is_exactly_a<numeric>(o.dim)));
+}
+
+bool varidx::is_dummy_pair_same_type(const basic & other) const
+{
+ const varidx &o = static_cast<const varidx &>(other);
+
+ // Variance must be opposite
+ if (covariant == o.covariant)
+ return false;
+
+ return inherited::is_dummy_pair_same_type(other);
+}
+
+bool spinidx::is_dummy_pair_same_type(const basic & other) const
+{
+ const spinidx &o = static_cast<const spinidx &>(other);
+
+ // Dottedness must be the same
+ if (dotted != o.dotted)
+ return false;
+
+ return inherited::is_dummy_pair_same_type(other);
+}
-unsigned idx::next_serial=0;
//////////
-// global constants
+// non-virtual functions
//////////
-const idx some_idx;
-type_info const & typeid_idx=typeid(some_idx);
+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->setflag(status_flags::dynallocated);
+}
+
+ex idx::minimal_dim(const idx & other) const
+{
+ return GiNaC::minimal_dim(dim, other.dim);
+}
+
+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->setflag(status_flags::dynallocated);
+}
+
+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->setflag(status_flags::dynallocated);
+}
+
+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->setflag(status_flags::dynallocated);
+}
//////////
-// other functions
+// global functions
//////////
-int canonicalize_indices(exvector & iv, bool antisymmetric)
-{
- if (iv.size()<2) {
- // nothing do to for 0 or 1 indices
- return INT_MAX;
- }
-
- 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;
- }
- }
- }
- return something_changed ? sig : INT_MAX;
-}
-
-exvector idx_intersect(exvector const & iv1, exvector const & iv2)
-{
- // build a vector of symbolic indices contained in iv1 and iv2 simultaneously
- // assumes (but does not test) that each index occurs at most twice
- exvector iv_intersect;
- for (exvector::const_iterator cit1=iv1.begin(); cit1!=iv1.end(); ++cit1) {
- ASSERT(is_ex_of_type(*cit1,idx));
- if (ex_to_idx(*cit1).is_symbolic()) {
- for (exvector::const_iterator cit2=iv2.begin(); cit2!=iv2.end(); ++cit2) {
- ASSERT(is_ex_of_type(*cit2,idx));
- if ((*cit1).is_equal(*cit2)) {
- iv_intersect.push_back(*cit1);
- break;
- }
- }
- }
- }
- return iv_intersect;
-}
-
-#define TEST_PERMUTATION(A,B,C,P) \
- if ((iv3[B].is_equal(iv2[0]))&&(iv3[C].is_equal(iv2[1]))) { \
- if (antisymmetric) *sig=P; \
- return iv3[A]; \
- }
-
-ex permute_free_index_to_front(exvector const & iv3, exvector const & iv2,
- bool antisymmetric, int * sig)
-{
- // match (return value,iv2) to iv3 by permuting indices
- // iv3 is always cyclic
-
- ASSERT(iv3.size()==3);
- ASSERT(iv2.size()==2);
-
- *sig=1;
-
- 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"));
-}
-
-unsigned subs_index_in_exvector(exvector & v, ex const & is, ex const & ir)
-{
- exvector::iterator it;
- unsigned replacements=0;
- unsigned current_replacements;
-
- ASSERT(is_ex_of_type(is,idx));
- 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;
- }
- return replacements;
-}
-
-unsigned count_index(ex const & e, ex const & 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++;
- }
- return count;
-}
-
-ex subs_indices(ex const & e, exvector const & idxv_subs,
- exvector const & idxv_repl)
-{
- ASSERT(idxv_subs.size()==idxv_repl.size());
- ex res=e;
- for (unsigned i=0; i<idxv_subs.size(); ++i) {
- res=res.subs(idxv_subs[i]==idxv_repl[i]);
- }
- return res;
+bool is_dummy_pair(const idx & i1, const idx & i2)
+{
+ // The indices must be of exactly the same type
+ if (i1.tinfo() != i2.tinfo())
+ return false;
+
+ // Same type, let the indices decide whether they are paired
+ return i1.is_dummy_pair_same_type(i2);
}
+bool is_dummy_pair(const ex & e1, const ex & e2)
+{
+ // The expressions must be indices
+ if (!is_a<idx>(e1) || !is_a<idx>(e2))
+ return false;
+ return is_dummy_pair(ex_to<idx>(e1), ex_to<idx>(e2));
+}
+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<idx>(*it).is_symbolic())
+ out_free.push_back(*it);
+ return;
+ }
+
+ // 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();
+ exvector::const_iterator 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<idx>(*last).is_symbolic())
+ out_free.push_back(*last);
+ }
+ last = it++;
+ }
+ if (ex_to<idx>(*last).is_symbolic())
+ out_free.push_back(*last);
+}
+
+ex minimal_dim(const ex & dim1, const ex & dim2)
+{
+ if (dim1.is_equal(dim2) || dim1 < dim2 || (is_exactly_a<numeric>(dim1) && is_a<symbol>(dim2)))
+ return dim1;
+ else if (dim1 > dim2 || (is_a<symbol>(dim1) && is_exactly_a<numeric>(dim2)))
+ return dim2;
+ else {
+ std::ostringstream s;
+ s << "minimal_dim(): index dimensions " << dim1 << " and " << dim2 << " cannot be ordered";
+ throw (std::runtime_error(s.str()));
+ }
+}
+} // namespace GiNaC
git://www.ginac.de / ginac.git / blobdiff