X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fidx.h;h=e38bf20baaf587dac2b430d82fbc6ac4bce48f69;hp=3c8ec34e904655bc0c40e6dcd88daa7af41f8fc8;hb=8cffcdf13d817a47f217f1a1043317d95969e070;hpb=1bd972bf8e4eeeb8aec6081100876e81a7f18450;ds=sidebyside diff --git a/ginac/idx.h b/ginac/idx.h index 3c8ec34e..e38bf20b 100644 --- a/ginac/idx.h +++ b/ginac/idx.h @@ -3,7 +3,7 @@ * Interface to GiNaC's indices. */ /* - * GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany + * GiNaC Copyright (C) 1999-2019 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 @@ -17,96 +17,261 @@ * * 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 */ -#ifndef __GINAC_IDX_H__ -#define __GINAC_IDX_H__ +#ifndef GINAC_IDX_H +#define GINAC_IDX_H -#include -//#include -#include "basic.h" #include "ex.h" +#include "numeric.h" -#ifndef NO_NAMESPACE_GINAC namespace GiNaC { -#endif // ndef NO_NAMESPACE_GINAC - -/** This class holds one index of an indexed object. Indices can be symbolic - * (e.g. "mu", "i") or numeric (unsigned integer), and they can be contravariant - * (the default) or covariant. */ +/** This class holds one index of an indexed object. Indices can + * theoretically consist of any symbolic expression but they are usually + * only just a symbol (e.g. "mu", "i") or numeric (integer). Indices belong + * to a space with a certain numeric or symbolic dimension. */ class idx : public basic { GINAC_DECLARE_REGISTERED_CLASS(idx, basic) // other constructors public: - explicit idx(bool cov); - explicit idx(const std::string & n, bool cov=false); - explicit idx(const char * n, bool cov=false); - explicit idx(unsigned v, bool cov=false); + /** Construct index with given value and dimension. + * + * @param v Value of index (numeric or symbolic) + * @param dim Dimension of index space (numeric or symbolic) + * @return newly constructed index */ + explicit idx(const ex & v, const ex & dim); + + // functions overriding virtual functions from base classes +public: + bool info(unsigned inf) const override; + size_t nops() const override; + ex op(size_t i) const override; + ex map(map_function & f) const override; + ex evalf() const override; + ex subs(const exmap & m, unsigned options = 0) const override; + void archive(archive_node& n) const override; + void read_archive(const archive_node& n, lst& syms) override; +protected: + ex derivative(const symbol & s) const override; + bool match_same_type(const basic & other) const override; + unsigned calchash() const override; + + // new virtual functions in this class +public: + /** Check whether the index forms a dummy index pair with another index + * of the same type. */ + virtual bool is_dummy_pair_same_type(const basic & other) const; + + // non-virtual functions in this class +public: + /** Get value of index. */ + ex get_value() const {return value;} + + /** Check whether the index is numeric. */ + bool is_numeric() const {return is_exactly_a(value);} + + /** Check whether the index is symbolic. */ + bool is_symbolic() const {return !is_exactly_a(value);} + + /** Get dimension of index space. */ + ex get_dim() const {return dim;} + + /** Check whether the dimension is numeric. */ + bool is_dim_numeric() const {return is_exactly_a(dim);} + + /** Check whether the dimension is symbolic. */ + bool is_dim_symbolic() const {return !is_exactly_a(dim);} + + /** Make a new index with the same value but a different dimension. */ + ex replace_dim(const ex & new_dim) const; + + /** Return the minimum of the dimensions of this and another index. + * If this is undecidable, throw an exception. */ + ex minimal_dim(const idx & other) const; - // functions overriding virtual functions from bases classes +protected: + void print_index(const print_context & c, unsigned level) const; + void do_print(const print_context & c, unsigned level) const; + void do_print_csrc(const print_csrc & c, unsigned level) const; + void do_print_latex(const print_latex & c, unsigned level) const; + void do_print_tree(const print_tree & c, unsigned level) const; + +protected: + ex value; /**< Expression that constitutes the index (numeric or symbolic name) */ + ex dim; /**< Dimension of space (can be symbolic or numeric) */ +}; +GINAC_DECLARE_UNARCHIVER(idx); + + +/** This class holds an index with a variance (co- or contravariant). There + * is an associated metric tensor that can be used to raise/lower indices. */ +class varidx : public idx +{ + GINAC_DECLARE_REGISTERED_CLASS(varidx, idx) + + // other constructors +public: + /** Construct index with given value, dimension and variance. + * + * @param v Value of index (numeric or symbolic) + * @param dim Dimension of index space (numeric or symbolic) + * @param covariant Make covariant index (default is contravariant) + * @return newly constructed index */ + varidx(const ex & v, const ex & dim, bool covariant = false); + + // functions overriding virtual functions from base classes +public: + bool is_dummy_pair_same_type(const basic & other) const override; + void archive(archive_node& n) const override; + void read_archive(const archive_node& n, lst& syms) override; +protected: + bool match_same_type(const basic & other) const override; + + // non-virtual functions in this class public: - void printraw(std::ostream & os) const; - void printtree(std::ostream & os, unsigned indent) const; - void print(std::ostream & os, unsigned upper_precedence=0) const; - bool info(unsigned inf) const; + /** Check whether the index is covariant. */ + bool is_covariant() const {return covariant;} + + /** Check whether the index is contravariant (not covariant). */ + bool is_contravariant() const {return !covariant;} + + /** Make a new index with the same value but the opposite variance. */ + ex toggle_variance() const; + +protected: + void do_print(const print_context & c, unsigned level) const; + void do_print_tree(const print_tree & c, unsigned level) const; + + // member variables protected: - bool is_equal_same_type(const basic & other) const; - unsigned calchash(void) const; - ex subs(const lst & ls, const lst & lr) const; + bool covariant; /**< x.mu, default is contravariant: x~mu */ +}; +GINAC_DECLARE_UNARCHIVER(varidx); + - // new virtual functions which can be overridden by derived classes +/** This class holds a spinor index that can be dotted or undotted and that + * also has a variance. This is used in the Weyl-van-der-Waerden formalism + * where the dot indicates complex conjugation. There is an associated + * (asymmetric) metric tensor that can be used to raise/lower spinor + * indices. */ +class spinidx : public varidx +{ + GINAC_DECLARE_REGISTERED_CLASS(spinidx, varidx) + + // other constructors +public: + /** Construct index with given value, dimension, variance and dot. + * + * @param v Value of index (numeric or symbolic) + * @param dim Dimension of index space (numeric or symbolic) + * @param covariant Make covariant index (default is contravariant) + * @param dotted Make covariant dotted (default is undotted) + * @return newly constructed index */ + spinidx(const ex & v, const ex & dim = 2, bool covariant = false, bool dotted = false); + + // functions overriding virtual functions from base classes public: - virtual bool is_co_contra_pair(const basic & other) const; - virtual ex toggle_covariant(void) const; + bool is_dummy_pair_same_type(const basic & other) const override; + // complex conjugation + ex conjugate() const override { return toggle_dot(); } + void archive(archive_node& n) const override; + void read_archive(const archive_node& n, lst& syms) override; +protected: + bool match_same_type(const basic & other) const override; // non-virtual functions in this class public: - /** Check whether index is symbolic (not numeric). */ - bool is_symbolic(void) const {return symbolic;} + /** Check whether the index is dotted. */ + bool is_dotted() const {return dotted;} - /** Get numeric value of index. Undefined for symbolic indices. */ - unsigned get_value(void) const {return value;} + /** Check whether the index is not dotted. */ + bool is_undotted() const {return !dotted;} - /** Check whether index is covariant (not contravariant). */ - bool is_covariant(void) const {return covariant;} + /** Make a new index with the same value and variance but the opposite + * dottedness. */ + ex toggle_dot() const; - void setname(const std::string & n) {name=n;} - std::string getname(void) const {return name;} + /** Make a new index with the same value but opposite variance and + * dottedness. */ + ex toggle_variance_dot() const; -private: - std::string & autoname_prefix(void); +protected: + void do_print(const print_context & c, unsigned level) const; + void do_print_latex(const print_latex & c, unsigned level) const; + void do_print_tree(const print_tree & c, unsigned level) const; // member variables protected: - unsigned serial; /**< Unique serial number for comparing symbolic indices */ - bool symbolic; /**< Is index symbolic? */ - std::string name; /**< Symbolic name (if symbolic == true) */ - unsigned value; /**< Numeric value (if symbolic == false) */ - static unsigned next_serial; - bool covariant; /**< x_mu, default is contravariant: x~mu */ + bool dotted; }; +GINAC_DECLARE_UNARCHIVER(spinidx); + // utility functions -inline const idx &ex_to_idx(const ex &e) + +/** Check whether two indices form a dummy pair. */ +bool is_dummy_pair(const idx & i1, const idx & i2); + +/** Check whether two expressions form a dummy index pair. */ +bool is_dummy_pair(const ex & e1, const ex & e2); + +/** Given a vector of indices, split them into two vectors, one containing + * the free indices, the other containing the dummy indices (numeric + * indices are neither free nor dummy ones). + * + * @param it Pointer to start of index vector + * @param itend Pointer to end of index vector + * @param out_free Vector of free indices (returned, sorted) + * @param out_dummy Vector of dummy indices (returned, sorted) */ +void find_free_and_dummy(exvector::const_iterator it, exvector::const_iterator itend, exvector & out_free, exvector & out_dummy); + +/** Given a vector of indices, split them into two vectors, one containing + * the free indices, the other containing the dummy indices (numeric + * indices are neither free nor dummy ones). + * + * @param v Index vector + * @param out_free Vector of free indices (returned, sorted) + * @param out_dummy Vector of dummy indices (returned, sorted) */ +inline void find_free_and_dummy(const exvector & v, exvector & out_free, exvector & out_dummy) { - return static_cast(*e.bp); + find_free_and_dummy(v.begin(), v.end(), out_free, out_dummy); } -// global functions +/** Given a vector of indices, find the dummy indices. + * + * @param v Index vector + * @param out_dummy Vector of dummy indices (returned, sorted) */ +inline void find_dummy_indices(const exvector & v, exvector & out_dummy) +{ + exvector free_indices; + find_free_and_dummy(v.begin(), v.end(), free_indices, out_dummy); +} + +/** Count the number of dummy index pairs in an index vector. */ +inline size_t count_dummy_indices(const exvector & v) +{ + exvector free_indices, dummy_indices; + find_free_and_dummy(v.begin(), v.end(), free_indices, dummy_indices); + return dummy_indices.size(); +} + +/** Count the number of dummy index pairs in an index vector. */ +inline size_t count_free_indices(const exvector & v) +{ + exvector free_indices, dummy_indices; + find_free_and_dummy(v.begin(), v.end(), free_indices, dummy_indices); + return free_indices.size(); +} -int canonicalize_indices(exvector & iv, bool antisymmetric=false); -exvector idx_intersect(const exvector & iv1, const exvector & iv2); -ex permute_free_index_to_front(const exvector & iv3, const exvector & iv2, int * sig); -unsigned subs_index_in_exvector(exvector & v, const ex & is, const ex & ir); -ex subs_indices(const ex & e, const exvector & idxv_contra, const exvector & idxv_co); -unsigned count_index(const ex & e, const ex & i); +/** Return the minimum of two index dimensions. If this is undecidable, + * throw an exception. Numeric dimensions are always considered "smaller" + * than symbolic dimensions. */ +ex minimal_dim(const ex & dim1, const ex & dim2); -#ifndef NO_NAMESPACE_GINAC } // namespace GiNaC -#endif // ndef NO_NAMESPACE_GINAC -#endif // ndef __GINAC_IDX_H__ +#endif // ndef GINAC_IDX_H