X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fidx.h;h=1ce32d2be0156128c70875e7aa93b404706c2ad4;hp=8b991ac1ffad1ef843863c14c2e153ad432a2915;hb=274c1632d78ec31575c4b3b328d75ad95a7855aa;hpb=e58227e1112f989f3b5417e497a61d53fc2971fa diff --git a/ginac/idx.h b/ginac/idx.h index 8b991ac1..1ce32d2b 100644 --- a/ginac/idx.h +++ b/ginac/idx.h @@ -23,102 +23,239 @@ #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) - // default constructor, destructor, copy constructor assignment operator and helpers -public: - idx(); - ~idx(); - idx (const idx & other); - const idx & operator=(const idx & other); -protected: - void copy(const idx & other); - void destroy(bool call_parent); - // 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 bases classes + // functions overriding virtual functions from base classes public: - basic * duplicate() const; - void printraw(std::ostream & os) const; - void printtree(std::ostream & os, unsigned indent) const; - void print(std::ostream & os, unsigned upper_precedence=0) const; + void print(const print_context & c, unsigned level = 0) const; bool info(unsigned inf) const; + unsigned nops() const; + ex & let_op(int i); + ex evalf(int level = 0) const; + ex subs(const lst & ls, const lst & lr, bool no_pattern = false) const; + protected: - int compare_same_type(const basic & other) const; - bool is_equal_same_type(const basic & other) const; - unsigned calchash(void) const; - ex subs(const lst & ls, const lst & lr) const; + ex derivative(const symbol & s) const; + bool match_same_type(const basic & other) const; - // new virtual functions which can be overridden by derived classes + // new virtual functions in this class public: - virtual bool is_co_contra_pair(const basic & other) const; - virtual ex toggle_covariant(void) const; + /** 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: - /** Check whether index is symbolic (not numeric). */ - bool is_symbolic(void) const {return symbolic;} + /** Get value of index. */ + ex get_value(void) const {return value;} + + /** Check whether the index is numeric. */ + bool is_numeric(void) const {return is_exactly_a(value);} + + /** Check whether the index is symbolic. */ + bool is_symbolic(void) const {return !is_exactly_a(value);} + + /** Get dimension of index space. */ + ex get_dim(void) const {return dim;} + + /** Check whether the dimension is numeric. */ + bool is_dim_numeric(void) const {return is_exactly_a(dim);} + + /** Check whether the dimension is symbolic. */ + bool is_dim_symbolic(void) const {return !is_exactly_a(dim);} + +protected: + ex value; /**< Expression that constitutes the index (numeric or symbolic name) */ + ex dim; /**< Dimension of space (can be symbolic or numeric) */ +}; + + +/** 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); - /** Get numeric value of index. Undefined for symbolic indices. */ - unsigned get_value(void) const {return value;} + // functions overriding virtual functions from base classes +public: + void print(const print_context & c, unsigned level = 0) const; + bool is_dummy_pair_same_type(const basic & other) const; - /** Check whether index is covariant (not contravariant). */ +protected: + bool match_same_type(const basic & other) const; + + // non-virtual functions in this class +public: + /** Check whether the index is covariant. */ bool is_covariant(void) const {return covariant;} - void setname(const std::string & n) {name=n;} - std::string getname(void) const {return name;} + /** Check whether the index is contravariant (not covariant). */ + bool is_contravariant(void) const {return !covariant;} -private: - std::string & autoname_prefix(void); + /** Make a new index with the same value but the opposite variance. */ + ex toggle_variance(void) 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 covariant; /**< x.mu, default is contravariant: x~mu */ }; + +/** 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: + void print(const print_context & c, unsigned level = 0) const; + bool is_dummy_pair_same_type(const basic & other) const; + +protected: + bool match_same_type(const basic & other) const; + + // non-virtual functions in this class +public: + /** Check whether the index is dotted. */ + bool is_dotted(void) const {return dotted;} + + /** Check whether the index is not dotted. */ + bool is_undotted(void) const {return !dotted;} + + /** Make a new index with the same value and variance but the opposite + * dottedness. */ + ex toggle_dot(void) const; + + /** Make a new index with the same value but opposite variance and + * dottedness. */ + ex toggle_variance_dot(void) const; + + // member variables +protected: + bool dotted; +}; + + // utility functions -inline const idx &ex_to_idx(const ex &e) + +/** Specialization of is_exactly_a(obj) for idx objects. */ +template<> inline bool is_exactly_a(const basic & obj) +{ + return obj.tinfo()==TINFO_idx; +} + +/** Specialization of is_exactly_a(obj) for varidx objects. */ +template<> inline bool is_exactly_a(const basic & obj) +{ + return obj.tinfo()==TINFO_varidx; +} + +/** Specialization of is_exactly_a(obj) for spinidx objects. */ +template<> inline bool is_exactly_a(const basic & obj) { - return static_cast(*e.bp); + return obj.tinfo()==TINFO_spinidx; } -// global functions +/** Check whether two indices form a dummy pair. */ +bool is_dummy_pair(const idx & i1, const idx & i2); -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); +/** 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) +{ + find_free_and_dummy(v.begin(), v.end(), out_free, out_dummy); +} + +/** 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 unsigned 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 unsigned 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(); +} -#ifndef NO_NAMESPACE_GINAC } // namespace GiNaC -#endif // ndef NO_NAMESPACE_GINAC #endif // ndef __GINAC_IDX_H__