HepLib
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Namespaces | |
QGRAF | |
namespace for generating Feynman diagrams or amplitudes. | |
SD | |
namespace for Numerical integration with Sector Decomposition method | |
Classes | |
class | Symbol |
class extended to GiNaC symbol class, represent a positive symbol More... | |
class | iSymbol |
class extended to GiNaC symbol class, pure imaginary symbol More... | |
class | Error |
class used to wrap error message More... | |
class | lstHelper |
class as lst Helper More... | |
class | MapFunction |
class to wrap map_function of GiNaC More... | |
class | Parser |
class to parse for string or file, helpful with Symbol class More... | |
class | XIntegral |
XIntegral Class, preface to SecDec. More... | |
class | Fermat |
interface to communicate with Fermat program More... | |
class | Form |
interface to communicate with Form program More... | |
class | MMAFormat |
class for Mathematica Format Output More... | |
class | Server |
class | FormFormat |
class for FormFormat Output More... | |
class | FCFormat |
class for FCFormat Output More... | |
class | Index |
class for index object More... | |
class | Vector |
class for vector object More... | |
class | SUNT |
class for SUNT object More... | |
class | SUNF |
class for SUNF object More... | |
class | SUNF4 |
class for SUNF4 object More... | |
class | Pair |
class for Pair object More... | |
class | Eps |
class for Levi-Civita object https://onlinelibrary.wiley.com/doi/pdf/10.1002/9783527630097.app3 to make Tr(g5, g1, g2, g3, g4) is the same in both HepLib & FORM, require that Eps(a,b,c,d) = i_ * e_(a,b,c,d) (we use the convention as in FeynCalc, Tr[5,a,b,c,d]=(- i) 4 Eps(a,b,c,d)=4 eps_(a,b,c,d)), and Eps^{0123}=+1, and g5=i g^{0123}=(-i) Eps(a,b,c,d) gamma(a,b,c,d)/4! Eps is real in HepLib, while e_ is imaginary in FORM. More... | |
class | DGamma |
class for Dirac Gamma object More... | |
struct | AIOption |
class | IBP |
IBP base class for IBP reduction. More... | |
class | FIRE |
IBP reduction using FIRE program. More... | |
class | KIRA |
IBP reduction using KIRA program. More... | |
class | UKIRA |
IBP reduction using KIRA program with user-defined equations. More... | |
class | Direct |
IBP reduction using Direc method. More... | |
class | Laporta |
class | Solver |
IBP reduction using Solver method. More... | |
Typedefs | |
typedef vector< pair< ex, ex > > | epvec_t |
typedef pair< ex, epvec_t > | co_epvec_t |
typedef std::initializer_list< ex > | init_list |
typedef map< int, map< int, ex > > | SparseMatrix |
Functions | |
exvector | GiNaC_Parallel (int ntotal, std::function< ex(int)> f, const string &key) |
GiNaC Parallel Evaluation using fork. More... | |
std::vector< std::string > | split (const std::string &s, char delimiter) |
split the string into serveral part, separated by the delimiter More... | |
string | now (bool use_date) |
date/time string More... | |
lst | gather_symbols (const ex &e) |
get all symbols from input expression More... | |
lst | gather_symbols (const exvector &ve) |
get all symbols from input expression More... | |
string | RunOS (const string &cmd) |
run symtem command and return the output as string More... | |
void | garRead (const string &garfn, map< string, ex > &resMap) |
garRead from file, and output in a map More... | |
ex | garRead (const string &garfn, const char *key) |
garRead from file, only the element w.r.t. key More... | |
ex | garRead (const string &garfn) |
garRead from file, only the element w.r.t. key "res", note inner check will be performed More... | |
void | garWrite (const string &garfn, const map< string, ex > &resMap) |
garWrite to write the string-key map to the archive More... | |
void | garWrite (const string &garfn, const ex &res) |
garWrite to write the expression to the archive, with key: "res", including a check key will be written More... | |
ex | str2ex (const string &expr, symtab stab) |
convert string to ex expression, using Parser internally More... | |
ex | str2ex (const string &expr) |
convert string to ex expression, using Parser internally More... | |
lst | str2lst (const string &expr, symtab stab) |
convert string to the lst, using Parser internally More... | |
lst | str2lst (const string &expr) |
convert string to the lst, using Parser internally More... | |
string | ex2str (const ex &expr) |
convert ex to output string, the defalut printer format will be used More... | |
string | ex2str (const exvector &expr) |
convert exvec to output string, the defalut printer format will be used More... | |
matrix | lst2mat (const lst &ls) |
convert 2Dim lst to matrix More... | |
string | ex2str (const exmap &expr) |
convert exmap to output string, the defalut printer format will be used More... | |
string | ex2str (const exset &expr) |
convert exset to output string, the defalut printer format will be used More... | |
string | file2str (string filename) |
read file content to string More... | |
void | str2file (const string &ostr, string filename) |
export string to a file More... | |
void | str2file (char *buff, FILE *fh) |
vector< string > | file2strvec (string filename, bool skip_empty) |
read file content to string vector More... | |
ex | file2ex (string filename) |
read file content to ex More... | |
ex | file2ex (string filename, symtab st) |
read file content to ex More... | |
void | ex2file (const ex &expr, string filename) |
export expression file More... | |
void | ex2file (string filename, const ex &expr) |
export expression file More... | |
ex | q2ex (__float128 num) |
__float128 to ex More... | |
__float128 | ex2q (ex num) |
ex of numeric to __float128 More... | |
int | ex2int (ex num) |
ex to integer More... | |
lst | vec2lst (const exvector &ev) |
convert exvector to lst More... | |
exvector | lst2vec (const lst &alst) |
convert lst to exvector More... | |
lst | add2lst (const ex &expr) |
convert add to lst More... | |
lst | mul2lst (const ex &expr) |
convert mul to lst More... | |
lst | xlst (int bi, int ei) |
return a lst: x(bi), x(bi+1), ..., x(ei) More... | |
lst | xlst (int ei) |
return a lst: x(0), x(1), ..., x(ei) More... | |
ex | series_ex (ex const &expr_in, ex const &s0, int sn0) |
the series like Mathematica, include s^n More... | |
ex | series_ex (ex const &expr_in, symbol const &s0, int sn0) |
the series like Mathematica, include s^n More... | |
ex | diff_ex (ex const expr, ex const xp, unsigned nth, bool expand) |
the differential like Mathematica More... | |
co_epvec_t | power_expand_2 (const co_epvec_t &co_epv, int n) |
pair< ex, epvec_t > | inner_expand_collect (ex const &expr_in, std::function< bool(const ex &)> has_func, int depth=0) |
ex | expand_ex (ex const &expr_in, std::function< bool(const ex &)> has_func) |
the expand like Mathematica More... | |
ex | collect_ex (ex const &expr_in, std::function< bool(const ex &)> has_func, int opt) |
the collect function like Mathematica More... | |
lst | collect_lst (ex const &expr_in, std::function< bool(const ex &)> has_func, int opt) |
the collect function like Mathematica, reture the lst { {c1,v1}, {c2,v2}, ... } More... | |
ex | EvalF (ex expr) |
the nuerical evaluation, Digits=100 will be used More... | |
ex | EvalL (ex expr) |
ex | EvalQ (ex expr) |
ex | EvalMP (ex expr) |
ex | NN (ex expr, int digits) |
the nuerical evaluation More... | |
bool | xPositive (ex const expr) |
check the expr is xPositive, i.e., each x-monomial item is postive More... | |
int | xSign (ex const expr) |
the always sign for expr More... | |
void | let_op_append (ex &ex_in, const ex item) |
append item into expression More... | |
void | let_op_prepend (ex &ex_in, const ex item) |
preppend item into expression More... | |
void | let_op_remove_last (ex &ex_in) |
remove last from expression More... | |
void | let_op_remove_first (ex &ex_in) |
remove first from expression More... | |
void | let_op_append (ex &ex_in, int index, ex const item) |
append item into index-th of expression More... | |
void | let_op_append (lst &ex_in, int index, ex const item) |
append item into index-th of expression More... | |
void | let_op_append (ex &ex_in, int index1, int index2, ex const item) |
append item into index1-th.index2-th of expression More... | |
void | let_op_append (lst &ex_in, int index1, int index2, ex const item) |
append item into index1-th.index2-th of expression More... | |
void | let_op_prepend (ex &ex_in, int index, ex const item) |
prepend item into index-th of expression More... | |
void | let_op_prepend (lst &ex_in, int index, ex const item) |
prepend item into index-th of expression More... | |
void | let_op_prepend (ex &ex_in, int index1, int index2, ex const item) |
prepend item into index1-th.index2-th of expression More... | |
void | let_op_prepend (lst &ex_in, int index1, int index2, ex const item) |
prepend item into index1-th.index2-th of expression More... | |
void | let_op_remove_last (ex &ex_in, int index) |
remove the last in index-th of expression More... | |
void | let_op_remove_last (lst &ex_in, int index) |
remove the last in index-th of expression More... | |
void | let_op_remove_last (ex &ex_in, int index1, int index2) |
remove the last in index1-th.index2-th of expression More... | |
void | let_op_remove_last (lst &ex_in, int index1, int index2) |
remove the last in index1-th.index2-th of expression More... | |
void | let_op_remove_first (ex &ex_in, int index) |
remove the first in index-th of expression More... | |
void | let_op_remove_first (lst &ex_in, int index) |
remove the first in index-th of expression More... | |
void | let_op_remove_first (ex &ex_in, int index1, int index2) |
remove the first in index1-th.index2-th of expression More... | |
void | let_op_remove_first (lst &ex_in, int index1, int index2) |
remove the first in index1-th.index2-th of expression More... | |
void | let_op (ex &ex_in, int index1, int index2, const ex item) |
update index1-th.index2-th of expression with item More... | |
void | let_op (lst &ex_in, int index1, int index2, const ex item) |
update index1-th.index2-th of expression with item More... | |
void | let_op (ex &ex_in, int index1, int index2, int index3, const ex item) |
update index1-th.index2-th.index3-th of expression with item More... | |
void | let_op (lst &ex_in, int index1, int index2, int index3, const ex item) |
update index1-th.index2-th.index3-th of expression with item More... | |
ex | get_op (const ex ex_in, int index1, int index2) |
return index1-th.index2-th of expression More... | |
ex | get_op (const lst ex_in, int index1, int index2) |
return index1-th.index2-th of expression More... | |
ex | get_op (const ex ex_in, int index1, int index2, int index3) |
return index1-th.index2-th.index3-th of expression More... | |
ex | get_op (const lst ex_in, int index1, int index2, int index3) |
return index1-th.index2-th.index3-th of expression More... | |
int | CpuCores () |
return the cpu cores using OpenMP More... | |
ex | normal_fermat (const ex &expr, bool dfactor) |
return the normalizatied expression, using fermat_numer_denom More... | |
ex | collect_factors (const ex &expr) |
a wrapper for collect_common_factors, catch errors More... | |
ex | exfactor (const ex &expr, int opt) |
factorize a expression More... | |
ex | exexpand (const ex &expr, int opt) |
factorize a expression More... | |
ex | exnormal (const ex &expr, int opt) |
normalize a expression More... | |
ex | exnd (const ex &expr, int opt) |
num_den a expression More... | |
ex | form_eval (const ex &expr) |
ex | inner_factor_form (const ex &expr) |
ex | factor_form (const ex &expr, bool nd) |
factorize a expression using FORM More... | |
void | garWrite (const exvector &exv, string garfn) |
void | garRead (exvector &exv, string garfn) |
ex | add_collect_normal (const exvector &exv, ex const &pats, int opt) |
ex | add_collect_normal (const exvector &exv, init_list const &pats, int opt) |
ex | add_collect_normal (const exvector &exv, lst const &pats, int opt) |
ex | add_collect_normal (const ex &e, ex const &pats, int opt) |
ex | add_collect_normal (const ex &e, lst const &pats, int opt) |
ex | add_collect_normal (const ex &e, init_list const &pats, int opt) |
bool | has_w (const ex &e) |
void | subs_w (exmap &repl) |
void | subs_w (lst &repl) |
void | ReShare (const ex &e) |
void | ReShare (const lst &es) |
void | ReShare (const ex &e1, const ex &e2) |
void | ReShare (const ex &e1, const ex &e2, const ex &e3) |
void | ReShare (const exvector &ev) |
void | ReShare (const exvector &ev1, const exvector &ev2) |
ex | nextprime (const ex &n) |
ex | nextprime (int n) |
ex | Rationalize (const ex &e, int dn) |
void | set_precision (long prec, bool push) |
void | reset_precision () |
long | get_precision () |
void | arg2map (int argc, char **argv, const char *optstring, std::map< char, std::string > &kv) |
bool | has_symbol (const ex &e) |
ex | subs (const ex &e, init_list sl) |
bool | has_any (ex expr, lst ps) |
bool | has_all (ex expr, lst ps) |
bool | is_equal_any (ex expr, lst ps) |
bool | match_any (ex expr, lst ps) |
bool | match_all (ex expr, lst ps) |
vector< std::string > | split (const string &s, char delimiter) |
bool | file_remove (string fn) |
bool | file_exists (string fn) |
bool | key_exists (const exmap &map, const ex &key) |
bool | dir_exists (string dir) |
void | garWrite (const map< string, ex > &resMap, const string &garfn) |
void | garWrite (const ex &res, const string &garfn) |
string | in2str (int i) |
ex | expand_ex (const ex &expr) |
ex | expand_ex (ex const &expr, lst const &pats) |
ex | expand_ex (ex const &expr, ex const &pat) |
ex | collect_ex (const ex &expr, init_list const &pats, int opt=o_none) |
ex | collect_ex (const ex &expr, lst const &pats, int opt=o_none) |
ex | collect_ex (const ex &expr, ex const &pat, int opt=o_none) |
lst | collect_lst (const ex &expr, init_list const &pats, int opt=o_none) |
lst | collect_lst (const ex &expr, lst const &pats, int opt=o_none) |
lst | collect_lst (const ex &expr, ex const &pat, int opt=o_none) |
ex | fermat_eval (const ex &expr) |
return the numerator and denominator after normalization More... | |
ex | numer_denom_fermat (const ex &expr, bool dfactor) |
return the numerator and denominator after normalization More... | |
ex | numer_fermat (const ex &expr) |
ex | fermat_numer_denom (const ex &expr, bool dfactor=false) |
ex | fermat_normal (const ex &expr, bool dfactor=false) |
ex | normal_flint (const ex &expr, int opt=o_flint) |
ex | factor_flint (const ex &e, bool nd=true) |
ex | form_factor (const ex &expr, bool nd=true) |
std::function< GiNaC::function(const ex &)> | GiNaC_Function_1 (const string name) |
std::function< GiNaC::function(const ex &, const ex &)> | GiNaC_Function_2 (const string name) |
std::function< GiNaC::function(const ex &, const ex &, const ex &)> | GiNaC_Function_3 (const string name) |
std::function< GiNaC::function(const ex &, const ex &, const ex &, const ex &)> | GiNaC_Function_4 (const string name) |
bool | isFunction (const ex &e, string func_name) |
bool | isFunction (const ex &e, string func_name, int nargs) |
bool | has_function (const ex &expr) |
void | PreTree (const ex &e, std::function< void(const ex &)> f) |
void | PostTree (const ex &e, std::function< void(const ex &)> f) |
void | string_replace_all (string &str, const string &from, const string &to) |
void | string_trim (string &str) |
bool | string_start_with (const string &fstr, const string &sstr) |
bool | string_end_with (const string &fstr, const string &estr) |
bool | string_contain (const string &fstr, const string &mstr) |
void | Combinations (int n, int m, std::function< void(const int *)> f) |
void | CombinationsR (int n, int m, std::function< void(const int *)> f) |
void | Permutations (int n, std::function< void(const int *)> f) |
void | Permutations (int n, int m, std::function< void(const int *)> f) |
void | PermutationsR (int n, int m, std::function< void(const int *)> f) |
bool | isSorted (const lst &exs) |
bool | isSorted (int n, const ex exs[]) |
int | ACSort (lst &exs) |
int | ACSort (int n, ex exs[]) |
long long | node_number (const ex &expr, int level=0) |
bool | ex_less (const ex &a, const ex &b) |
void | sort_lst (lst &ilst, bool less) |
sort the list in less order, or the reverse More... | |
void | sort_lst_by (lst &ilst, int ki, bool less) |
sort the list in less order, or the reverse More... | |
void | sort_vec (exvector &ivec, bool less) |
sort the list in less order, or the reverse More... | |
void | sort_vec_by (exvector &ivec, int ki, bool less) |
sort the list in less order, or the reverse More... | |
void | append_to (const exvector &exv, lst &alst) |
void | append_to (const lst &alst, exvector &exv) |
lst | CoPat (const ex &e, std::function< bool(const ex &)> f) |
void | garWrite (string garfn, const exvector &exv) |
void | garRead (string garfn, exvector &exv) |
numeric | RationalReconstruct (numeric a, numeric p) |
numeric | mulInv (numeric a, numeric b) |
numeric | ChineseRemainder (std::vector< numeric > a, std::vector< numeric > n) |
numeric | RationalReconstruct (vector< numeric > aa, vector< numeric > pp) |
ex | Thiele (const exvector &keys, const exvector &values, const ex &d) |
ex | Newton (const exvector &keys, const exvector &values, const ex &d, const ex factor=1) |
matrix | fermat_Redrowech (const matrix &mat) |
matrix | fermat_Redrowech_Sparse (const matrix &mat) |
ex | fermat_Det (const matrix &mat) |
ex | fermat_Det_Sparse (const matrix &mat) |
matrix | fermat_inv (const matrix &mat) |
matrix | fermat_mul (const matrix &m1, const matrix &m2) |
matrix | fermat_pow (const matrix &mat_in, int n) |
void | fermat_mat (const matrix &mat_in, const string &name) |
matrix | fermat_mat (const string &name) |
void | fermat_eval (const string &fcmd="@[**]") |
ex | A0 (const ex m2, int n, ex d) |
scalar integral A0, devided by (2pi)^(4-2ep) More... | |
ex | ApartIR2ex (const ex &expr_in) |
convert ApartIR to ex More... | |
ex | ApartIR2F (const ex &expr_in) |
convert ApartIR to F(ps, ns), ns is like FIRE convention More... | |
ex | air2pn (ex air) |
ex | pn2mat (ex ps, ex ns, ex vars) |
bool | is_subset (const ex &e1, const ex &e2) |
ex | pn2p (ex pn) |
exmap | ApartRules (const exvector &airs, bool irc) |
ex | Apart (const matrix &mat) |
Apart on matrix. More... | |
ex | Apart (const ex &expr_ino, const lst &vars_in, exmap smap) |
Apart on ex. More... | |
ex | Apart (const ex &expr_ino, const lst &loops, const lst &extps, exmap smap) |
Apart on ex. More... | |
ex | ApartIRC (const ex &expr_in) |
complete the ApartIR elements More... | |
ex | F2ex (const ex &expr_in) |
convert F(ps, ns) to normal ex, ns is like FIRE convention More... | |
void | ApartIBP (exvector &air_vec, AIOption aio) |
perform IBP reduction on the Aparted input More... | |
void | ApartIBP (exvector &air_vec, int IBPmethod, const lst &loops, const lst &exts, const lst &cut_props, std::function< lst(const IBP &, const ex &)> uf) |
perform IBP reduction on the Aparted input More... | |
ex | MatrixContract (const ex &expr_in) |
make contract on matrix, i.e., Matrix(a,i1,i2)*Matrix(b,i2,i3) -> Matrix(a*b,i1,i3) More... | |
REGISTER_FUNCTION (Matrix, do_not_evalf_params().print_func< FCFormat >(&Matrix_fc_print).conjugate_func(mat_conj).set_return_type(return_types::commutative)) bool IsZero(const ex &e) | |
ex | ToCF (const ex &e) |
ex | ca_neg_pow_sub (const ex &expr) |
ex | ToCACF (const ex &e) |
ex | HomCACF (const ex &e) |
ex | DoColor (const ex &expr, const ex &pref, int method) |
REGISTER_FUNCTION (TR, do_not_evalf_params(). conjugate_func(tr_conj). print_func< FormFormat >(&TR_form_print). print_func< FCFormat >(&TR_fc_print). set_return_type(return_types::commutative). expl_derivative_func(expl_TR_diff)) | |
REGISTER_FUNCTION (TTR, do_not_evalf_params(). conjugate_func(ttr_conj). print_func< FormFormat >(&TTR_form_print). print_func< FCFormat >(&TTR_fc_print)) | |
REGISTER_FUNCTION (HF, do_not_evalf_params()) | |
ex | GAS (const ex &expr, unsigned rl) |
function similar to GAD/GSD in FeynClac More... | |
ex | LC (ex pi1, ex pi2, ex pi3, ex pi4) |
function similar to LCD in FeynCalc More... | |
ex | form (const ex &iexpr, int verb) |
evalulate expr in form program, see also the form_trace_mode and form_expand_mode More... | |
ex | charge_conjugate (const ex &expr) |
make the charge conjugate operaton, M -> C^{-1} . M^T . C w.r.t. a Matrix object More... | |
ex | SP (const ex &a, bool use_map=false) |
ex | SP (const ex &a, const ex &b, bool use_map) |
Function similar to SPD/FVD in FeynCalc. More... | |
ex | sp (const ex &a, const ex &b) |
translated the vector dot a.b to a*b, useful in SecDec More... | |
ex | sp (const ex &a) |
ex & | letSP (const ex &p1, const ex &p2) |
return the reference of p1.p2 More... | |
ex & | letSP (const ex &p) |
return the reference of p.p More... | |
void | clearSP (const ex &p1, const ex &p2) |
delete the assignment of p1.p2 More... | |
void | clearSP (const ex &p) |
delete the assignment of p.p More... | |
void | clearSP () |
delete all assignment in SP_map More... | |
ex | SP2sp (const ex &exin) |
convert SP(a,b) to sp(a,b) More... | |
exmap | sp_map () |
the SP_map with SP(a,b) replaced to sp(a,b) More... | |
ex | GAS (const Vector &p, unsigned rl=0) |
ex | GAS (const Index &i, unsigned rl=0) |
ex | UnContract (const ex expr, const lst &loop_ps, const lst &ext_ps=lst{}) |
ex | TIR (const ex &expr_in, const lst &loop_ps, const lst &ext_ps) |
Tensor Index Reduction, note that we only handle numerator. More... | |
void | ApartIBP (int IBPmethod, exvector &io_vec, const lst &loops, const lst &exts, const lst &cut_props=lst{}, std::function< lst(const IBP &, const ex &)> uf=LoopUF) |
bool | IsZero (const ex &e) |
REGISTER_FUNCTION (a, do_not_evalf_params().print_func< print_dflt >(a_print)) void IBP | |
exmap | SortPermutation (const ex &in_expr, const lst &xs) |
Sort for all permuations, and return xs w.r.t. 1st permutation. More... | |
lst | LoopUF (const IBP &ibp, const ex &idx) |
UF function. More... | |
lst | UF (const ex &props, const ex &ns, const ex &loops, const ex &tloops, const ex &lsubs, const ex &tsubs) |
UF function, from FIRE.m. More... | |
pair< exmap, lst > | FindRules (vector< IBP * > fs, bool mi, std::function< lst(const IBP &, const ex &)> uf) |
Find Rules for Integral or Master Integral. More... | |
ex | GPolynomial (const IBP &ibp) |
void | GPermutation (const ex &uf, const lst &xs) |
pair< exmap, lst > | FindRules (IBP &ibp, bool mi=true, std::function< lst(const IBP &, const ex &)> uf=LoopUF) |
const Symbol | NA ("NA") |
const Symbol | NF ("NF") |
const Symbol | TF ("TF") |
const Symbol | CA ("CA") |
const Symbol | CF ("CF") |
const Symbol | gs ("gs") |
const Symbol | as ("as") |
const Symbol | mu ("mu") |
const Symbol | nL ("nL") |
const Symbol | nH ("nH") |
const Symbol | eps ("eps") |
const Symbol | vs ("vs") |
const Symbol | vz ("vz") |
const Symbol | epz ("epz") |
const Symbol | NaN ("NaN") |
const Symbol | ep ("ep") |
const Symbol | d ("d") |
const Symbol | iet ("iet") |
const iSymbol | iEpsilon ("iEpsilon") |
MMAFormat | mout (cout) |
FCFormat | fcout (cout) |
Variables | |
const char * | ErrColor = RED |
const char * | WarnColor = MAGENTA |
const char * | Color_HighLight = WHITE |
std::stack< cln::float_format_t > | cln_prec_stack |
std::stack< long > | digits_stack |
string | Version = "1.5 @2024-04-28" |
unsigned | nopat = GiNaC::subs_options::no_pattern |
const int | o_none = (_o_++) |
const int | o_normal = (_o_++) |
const int | o_fermat = (_o_++) |
const int | o_fermatfD = (_o_++) |
const int | o_fermatN = (_o_++) |
const int | o_form = (_o_++) |
const int | o_flint = (_o_++) |
const int | o_flintf = (_o_++) |
const int | o_flintfD = (_o_++) |
const int | o_normal_fermat = (_o_++) |
const int | o_normal_form = (_o_++) |
const int | o_fermat_form = (_o_++) |
bool | In_GiNaC_Parallel = false |
int | GiNaC_Parallel_Process = -1 |
map< string, int > | GiNaC_Parallel_Verb |
map< string, int > | GiNaC_Parallel_NP |
int | GiNaC_Parallel_Batch = 0 |
map< string, int > | GiNaC_Parallel_NB |
map< string, bool > | GiNaC_Parallel_RM |
map< string, bool > | GiNaC_Parallel_ReWR |
map< string, string > | GiNaC_Parallel_PRE |
bool | using_cache = true |
long long | cache_limit = -1 |
int | fermat_using_array = 0 |
map< ex, long long, ex_is_less > | fermat_weight |
int | NNDigits = 100 |
ex | w = wild() |
ex | w0 = wild(0) |
ex | w1 = wild(1) |
ex | w2 = wild(2) |
ex | w3 = wild(3) |
ex | w4 = wild(4) |
ex | w5 = wild(5) |
ex | w6 = wild(6) |
ex | w7 = wild(7) |
ex | w8 = wild(8) |
ex | w9 = wild(9) |
string | InstallPrefix = install_prefix() |
string | INC_FLAGS = "-I'"+InstallPrefix+"/include' " + "@INC_FLAGS@" |
string | LIB_FLAGS = "-L'"+InstallPrefix+"/lib' -Wl,-rpath,'"+InstallPrefix+"'/lib " + "@LIB_FLAGS@" |
const iSymbol | iEpsilon |
const ex | iEpsilonN = I*pow(ex(10), -50) |
int | Verbose = 0 |
string | PRE = " " |
bool | Debug = false |
MMAFormat | mout |
const Symbol | NA |
const Symbol | NF |
const Symbol | TF |
const Symbol | CA |
const Symbol | CF |
const Symbol | gs |
const Symbol | as |
const Symbol | mu |
const Symbol | nL |
const Symbol | nH |
const Symbol | iet |
const Symbol | d |
const Symbol | ep |
const Symbol | eps |
const Symbol | vs |
const Symbol | vz |
const Symbol | epz |
const Symbol | NaN |
exmap | SP_map |
int | form_trace_mode = form_trace_auto |
const int | form_trace_auto = 0 |
const int | form_trace_all = 1 |
const int | form_trace_each_all = 2 |
const int | form_trace_each_each = 3 |
int | form_expand_mode = form_expand_tr |
const int | form_expand_none = 0 |
const int | form_expand_tr = 1 |
const int | form_expand_ci = 2 |
const int | form_expand_li = 3 |
const int | form_expand_all = 4 |
bool | Apart_using_fermat = true |
bool | form_using_su3 = false |
bool | form_using_dim4 = false |
bool | form_using_gamma5 = false |
FCFormat | fcout |
exmap | MapPreSP |
int | _o_ = 0 |
slong | error_pass_dp = 100 |
typedef pair<ex,epvec_t> HepLib::co_epvec_t |
typedef vector<pair<ex,ex> > HepLib::epvec_t |
typedef std::initializer_list<ex> HepLib::init_list |
typedef map<int,map<int,ex> > HepLib::SparseMatrix |
Definition at line 178 of file Solver.cpp.
ex HepLib::A0 | ( | const ex | m2, |
int | n, | ||
ex | d | ||
) |
int HepLib::ACSort | ( | int | n, |
ex | exs[] | ||
) |
Definition at line 304 of file Functions.cpp.
int HepLib::ACSort | ( | lst & | exs | ) |
Definition at line 289 of file Functions.cpp.
lst HepLib::add2lst | ( | const ex & | expr | ) |
ex HepLib::add_collect_normal | ( | const ex & | e, |
ex const & | pats, | ||
int | opt | ||
) |
ex HepLib::add_collect_normal | ( | const ex & | e, |
init_list const & | pats, | ||
int | opt | ||
) |
ex HepLib::add_collect_normal | ( | const ex & | e, |
lst const & | pats, | ||
int | opt | ||
) |
ex HepLib::add_collect_normal | ( | const exvector & | exv, |
ex const & | pats, | ||
int | opt | ||
) |
ex HepLib::add_collect_normal | ( | const exvector & | exv, |
init_list const & | pats, | ||
int | opt | ||
) |
ex HepLib::add_collect_normal | ( | const exvector & | exv, |
lst const & | pats, | ||
int | opt | ||
) |
ex HepLib::Apart | ( | const ex & | expr_ino, |
const lst & | loops, | ||
const lst & | extps, | ||
exmap | smap | ||
) |
ex HepLib::Apart | ( | const ex & | expr_ino, |
const lst & | vars_in, | ||
exmap | smap | ||
) |
ex HepLib::Apart | ( | const matrix & | mat | ) |
void HepLib::ApartIBP | ( | exvector & | air_vec, |
AIOption | aio | ||
) |
perform IBP reduction on the Aparted input
IBPmethod | ibp method used, 0-No IBP, 1-FIRE, 2-KIRA |
air_vec | vector contains aparted input, ApartIRC will be call internally |
aio | AIOption for ApartIBP input |
Definition at line 109 of file ApartIBP.cpp.
void HepLib::ApartIBP | ( | exvector & | air_vec, |
int | IBPmethod, | ||
const lst & | loops, | ||
const lst & | exts, | ||
const lst & | cut_props, | ||
std::function< lst(const IBP &, const ex &)> | uf | ||
) |
perform IBP reduction on the Aparted input
IBPmethod | ibp method used, 0-No IBP, 1-FIRE, 2-KIRA |
air_vec | vector contains aparted input, ApartIRC will be call internally |
loops | loop vectors |
exts | external vectors |
cut_props | cut propagators, default is { } |
uf | the function to compute UF polynomial |
Definition at line 614 of file ApartIBP.cpp.
ex HepLib::ApartIR2ex | ( | const ex & | expr_in | ) |
ex HepLib::ApartIR2F | ( | const ex & | expr_in | ) |
ex HepLib::ApartIRC | ( | const ex & | expr_in | ) |
exmap HepLib::ApartRules | ( | const exvector & | airs, |
bool | irc | ||
) |
|
inline |
|
inline |
void HepLib::arg2map | ( | int | argc, |
char ** | argv, | ||
const char * | optstring, | ||
std::map< char, std::string > & | kv | ||
) |
const Symbol HepLib::as | ( | "as" | ) |
const Symbol HepLib::CA | ( | "CA" | ) |
const Symbol HepLib::CF | ( | "CF" | ) |
ex HepLib::charge_conjugate | ( | const ex & | expr | ) |
numeric HepLib::ChineseRemainder | ( | std::vector< numeric > | a, |
std::vector< numeric > | n | ||
) |
Definition at line 53 of file Rational.cpp.
void HepLib::clearSP | ( | const ex & | p | ) |
void HepLib::clearSP | ( | const ex & | p1, |
const ex & | p2 | ||
) |
|
inline |
|
inline |
ex HepLib::collect_ex | ( | ex const & | expr_in, |
std::function< bool(const ex &)> | has_func, | ||
int | opt | ||
) |
ex HepLib::collect_factors | ( | const ex & | expr | ) |
|
inline |
|
inline |
lst HepLib::collect_lst | ( | ex const & | expr_in, |
std::function< bool(const ex &)> | has_func, | ||
int | opt | ||
) |
the collect function like Mathematica, reture the lst { {c1,v1}, {c2,v2}, ... }
expr_in | input expression |
has_func | only collect the element e, when has_func(e) is true |
opt | 0: do nothing, 1: using exnormal, 2: using exfactor on the coefficient |
void HepLib::Combinations | ( | int | n, |
int | m, | ||
std::function< void(const int *)> | f | ||
) |
Definition at line 184 of file Functions.cpp.
void HepLib::CombinationsR | ( | int | n, |
int | m, | ||
std::function< void(const int *)> | f | ||
) |
Definition at line 197 of file Functions.cpp.
|
inline |
int HepLib::CpuCores | ( | ) |
const Symbol HepLib::d | ( | "d" | ) |
ex HepLib::diff_ex | ( | ex const | expr, |
ex const | xp, | ||
unsigned | nth, | ||
bool | expand | ||
) |
ex HepLib::DoColor | ( | const ex & | expr, |
const ex & | pref, | ||
int | method | ||
) |
const Symbol HepLib::ep | ( | "ep" | ) |
const Symbol HepLib::eps | ( | "eps" | ) |
const Symbol HepLib::epz | ( | "epz" | ) |
ex HepLib::EvalF | ( | ex | expr | ) |
void HepLib::ex2file | ( | const ex & | expr, |
string | filename | ||
) |
void HepLib::ex2file | ( | string | filename, |
const ex & | expr | ||
) |
int HepLib::ex2int | ( | ex | num | ) |
__float128 HepLib::ex2q | ( | ex | num | ) |
string HepLib::ex2str | ( | const ex & | expr | ) |
string HepLib::ex2str | ( | const exmap & | expr | ) |
string HepLib::ex2str | ( | const exset & | expr | ) |
string HepLib::ex2str | ( | const exvector & | expr | ) |
ex HepLib::exexpand | ( | const ex & | expr, |
int | opt | ||
) |
ex HepLib::exfactor | ( | const ex & | expr, |
int | opt | ||
) |
ex HepLib::exnd | ( | const ex & | expr, |
int | opt | ||
) |
ex HepLib::exnormal | ( | const ex & | expr, |
int | opt | ||
) |
|
inline |
|
inline |
ex HepLib::expand_ex | ( | ex const & | expr_in, |
std::function< bool(const ex &)> | has_func | ||
) |
ex HepLib::F2ex | ( | const ex & | expr_in | ) |
convert F(ps, ns) to normal ex, ns is like FIRE convention
expr_in | expression contains F |
Definition at line 87 of file ApartIBP.cpp.
ex HepLib::factor_flint | ( | const ex & | e, |
bool | nd = true |
||
) |
ex HepLib::factor_form | ( | const ex & | expr, |
bool | nd | ||
) |
FCFormat HepLib::fcout | ( | cout | ) |
ex HepLib::fermat_Det | ( | const matrix & | mat | ) |
Definition at line 650 of file Fermat.cpp.
ex HepLib::fermat_Det_Sparse | ( | const matrix & | mat | ) |
Definition at line 757 of file Fermat.cpp.
ex HepLib::fermat_eval | ( | const ex & | expr | ) |
return the numerator and denominator after normalization
expr | the input expression |
Definition at line 317 of file Fermat.cpp.
void HepLib::fermat_eval | ( | const string & | fcmd = "@[**]" | ) |
Definition at line 1343 of file Fermat.cpp.
matrix HepLib::fermat_inv | ( | const matrix & | mat | ) |
Definition at line 880 of file Fermat.cpp.
void HepLib::fermat_mat | ( | const matrix & | mat_in, |
const string & | name | ||
) |
Definition at line 1224 of file Fermat.cpp.
matrix HepLib::fermat_mat | ( | const string & | name | ) |
Definition at line 1301 of file Fermat.cpp.
matrix HepLib::fermat_mul | ( | const matrix & | m1, |
const matrix & | m2 | ||
) |
Definition at line 987 of file Fermat.cpp.
|
inline |
|
inline |
matrix HepLib::fermat_pow | ( | const matrix & | mat_in, |
int | n | ||
) |
Definition at line 1112 of file Fermat.cpp.
matrix HepLib::fermat_Redrowech | ( | const matrix & | mat | ) |
Definition at line 409 of file Fermat.cpp.
matrix HepLib::fermat_Redrowech_Sparse | ( | const matrix & | mat | ) |
Definition at line 516 of file Fermat.cpp.
ex HepLib::file2ex | ( | string | filename | ) |
ex HepLib::file2ex | ( | string | filename, |
symtab | st | ||
) |
string HepLib::file2str | ( | string | filename | ) |
vector< string > HepLib::file2strvec | ( | string | filename, |
bool | skip_empty | ||
) |
ex HepLib::form | ( | const ex & | iexpr, |
int | verb | ||
) |
|
inline |
ex HepLib::garRead | ( | const string & | garfn | ) |
ex HepLib::garRead | ( | const string & | garfn, |
const char * | key | ||
) |
void HepLib::garRead | ( | const string & | garfn, |
map< string, ex > & | resMap | ||
) |
|
inline |
|
inline |
void HepLib::garWrite | ( | const exvector & | exv, |
string | garfn | ||
) |
|
inline |
void HepLib::garWrite | ( | const string & | garfn, |
const ex & | res | ||
) |
void HepLib::garWrite | ( | const string & | garfn, |
const map< string, ex > & | resMap | ||
) |
|
inline |
ex HepLib::GAS | ( | const ex & | expr, |
unsigned | rl | ||
) |
function similar to GAD/GSD in FeynClac
expr | momentum/index or 1,5,6,7 |
rl | the represent line number |
Definition at line 246 of file DGamma.cpp.
lst HepLib::gather_symbols | ( | const ex & | e | ) |
lst HepLib::gather_symbols | ( | const exvector & | ve | ) |
ex HepLib::get_op | ( | const ex | ex_in, |
int | index1, | ||
int | index2 | ||
) |
ex HepLib::get_op | ( | const ex | ex_in, |
int | index1, | ||
int | index2, | ||
int | index3 | ||
) |
ex HepLib::get_op | ( | const lst | ex_in, |
int | index1, | ||
int | index2 | ||
) |
ex HepLib::get_op | ( | const lst | ex_in, |
int | index1, | ||
int | index2, | ||
int | index3 | ||
) |
|
inline |
|
inline |
|
inline |
|
inline |
exvector HepLib::GiNaC_Parallel | ( | int | ntotal, |
std::function< ex(int)> | f, | ||
const string & | key | ||
) |
GiNaC Parallel Evaluation using fork.
ntotal | the number of total items, 0 for non-parallel version |
f | function to be applied on the index, from 0 to (ntotal-1) |
key | key used in archive file name and display message |
rm | default true, and false will keep the archive file |
pre | the pre-string in the print message |
void HepLib::GPermutation | ( | const ex & | uf, |
const lst & | xs | ||
) |
const Symbol HepLib::gs | ( | "gs" | ) |
const iSymbol HepLib::iEpsilon | ( | "iEpsilon" | ) |
const Symbol HepLib::iet | ( | "iet" | ) |
pair<ex,epvec_t> HepLib::inner_expand_collect | ( | ex const & | expr_in, |
std::function< bool(const ex &)> | has_func, | ||
int | depth = 0 |
||
) |
|
inline |
|
inline |
|
inline |
bool HepLib::isSorted | ( | const lst & | exs | ) |
Definition at line 273 of file Functions.cpp.
bool HepLib::isSorted | ( | int | n, |
const ex | exs[] | ||
) |
Definition at line 281 of file Functions.cpp.
bool HepLib::IsZero | ( | const ex & | e | ) |
|
inline |
ex HepLib::LC | ( | ex | pi1, |
ex | pi2, | ||
ex | pi3, | ||
ex | pi4 | ||
) |
void HepLib::let_op | ( | ex & | ex_in, |
int | index1, | ||
int | index2, | ||
const ex | item | ||
) |
void HepLib::let_op | ( | ex & | ex_in, |
int | index1, | ||
int | index2, | ||
int | index3, | ||
const ex | item | ||
) |
void HepLib::let_op | ( | lst & | ex_in, |
int | index1, | ||
int | index2, | ||
const ex | item | ||
) |
void HepLib::let_op | ( | lst & | ex_in, |
int | index1, | ||
int | index2, | ||
int | index3, | ||
const ex | item | ||
) |
void HepLib::let_op_append | ( | ex & | ex_in, |
const ex | item | ||
) |
void HepLib::let_op_append | ( | ex & | ex_in, |
int | index, | ||
ex const | item | ||
) |
void HepLib::let_op_append | ( | ex & | ex_in, |
int | index1, | ||
int | index2, | ||
ex const | item | ||
) |
void HepLib::let_op_append | ( | lst & | ex_in, |
int | index, | ||
ex const | item | ||
) |
void HepLib::let_op_append | ( | lst & | ex_in, |
int | index1, | ||
int | index2, | ||
ex const | item | ||
) |
void HepLib::let_op_prepend | ( | ex & | ex_in, |
const ex | item | ||
) |
void HepLib::let_op_prepend | ( | ex & | ex_in, |
int | index, | ||
ex const | item | ||
) |
void HepLib::let_op_prepend | ( | ex & | ex_in, |
int | index1, | ||
int | index2, | ||
ex const | item | ||
) |
void HepLib::let_op_prepend | ( | lst & | ex_in, |
int | index, | ||
ex const | item | ||
) |
void HepLib::let_op_prepend | ( | lst & | ex_in, |
int | index1, | ||
int | index2, | ||
ex const | item | ||
) |
void HepLib::let_op_remove_first | ( | ex & | ex_in | ) |
void HepLib::let_op_remove_first | ( | ex & | ex_in, |
int | index | ||
) |
void HepLib::let_op_remove_first | ( | ex & | ex_in, |
int | index1, | ||
int | index2 | ||
) |
void HepLib::let_op_remove_first | ( | lst & | ex_in, |
int | index | ||
) |
void HepLib::let_op_remove_first | ( | lst & | ex_in, |
int | index1, | ||
int | index2 | ||
) |
void HepLib::let_op_remove_last | ( | ex & | ex_in | ) |
void HepLib::let_op_remove_last | ( | ex & | ex_in, |
int | index | ||
) |
void HepLib::let_op_remove_last | ( | ex & | ex_in, |
int | index1, | ||
int | index2 | ||
) |
void HepLib::let_op_remove_last | ( | lst & | ex_in, |
int | index | ||
) |
void HepLib::let_op_remove_last | ( | lst & | ex_in, |
int | index1, | ||
int | index2 | ||
) |
ex & HepLib::letSP | ( | const ex & | p | ) |
ex & HepLib::letSP | ( | const ex & | p1, |
const ex & | p2 | ||
) |
lst HepLib::LoopUF | ( | const IBP & | ibp, |
const ex & | idx | ||
) |
matrix HepLib::lst2mat | ( | const lst & | ls | ) |
exvector HepLib::lst2vec | ( | const lst & | alst | ) |
ex HepLib::MatrixContract | ( | const ex & | expr_in | ) |
MMAFormat HepLib::mout | ( | cout | ) |
const Symbol HepLib::mu | ( | "mu" | ) |
lst HepLib::mul2lst | ( | const ex & | expr | ) |
numeric HepLib::mulInv | ( | numeric | a, |
numeric | b | ||
) |
Definition at line 31 of file Rational.cpp.
const Symbol HepLib::NA | ( | "NA" | ) |
const Symbol HepLib::NaN | ( | "NaN" | ) |
ex HepLib::Newton | ( | const exvector & | keys, |
const exvector & | values, | ||
const ex & | d, | ||
const ex | factor = 1 |
||
) |
Definition at line 105 of file Rational.cpp.
const Symbol HepLib::NF | ( | "NF" | ) |
const Symbol HepLib::nH | ( | "nH" | ) |
const Symbol HepLib::nL | ( | "nL" | ) |
ex HepLib::NN | ( | ex | expr, |
int | digits | ||
) |
long long HepLib::node_number | ( | const ex & | expr, |
int | level = 0 |
||
) |
ex HepLib::normal_fermat | ( | const ex & | expr, |
bool | dfactor | ||
) |
ex HepLib::normal_flint | ( | const ex & | expr, |
int | opt = o_flint |
||
) |
string HepLib::now | ( | bool | use_date | ) |
ex HepLib::numer_denom_fermat | ( | const ex & | expr, |
bool | dfactor | ||
) |
return the numerator and denominator after normalization
expr | the input expression |
dfactor | true for factorize on the denominator |
Definition at line 23 of file Fermat.cpp.
ex HepLib::numer_fermat | ( | const ex & | expr | ) |
Definition at line 170 of file Fermat.cpp.
void HepLib::Permutations | ( | int | n, |
int | m, | ||
std::function< void(const int *)> | f | ||
) |
Definition at line 220 of file Functions.cpp.
void HepLib::Permutations | ( | int | n, |
std::function< void(const int *)> | f | ||
) |
Definition at line 213 of file Functions.cpp.
void HepLib::PermutationsR | ( | int | n, |
int | m, | ||
std::function< void(const int *)> | f | ||
) |
Definition at line 268 of file Functions.cpp.
|
inline |
co_epvec_t HepLib::power_expand_2 | ( | const co_epvec_t & | co_epv, |
int | n | ||
) |
|
inline |
ex HepLib::q2ex | ( | __float128 | num | ) |
numeric HepLib::RationalReconstruct | ( | numeric | a, |
numeric | p | ||
) |
Definition at line 8 of file Rational.cpp.
numeric HepLib::RationalReconstruct | ( | vector< numeric > | aa, |
vector< numeric > | pp | ||
) |
Definition at line 66 of file Rational.cpp.
HepLib::REGISTER_FUNCTION | ( | a | , |
do_not_evalf_params().print_func< print_dflt >(a_print) | |||
) |
HepLib::REGISTER_FUNCTION | ( | HF | , |
do_not_evalf_params() | |||
) |
HepLib::REGISTER_FUNCTION | ( | Matrix | , |
do_not_evalf_params().print_func< FCFormat > &Matrix_fc_print.conjugate_func(mat_conj).set_return_type(return_types::commutative) | |||
) | const & |
HepLib::REGISTER_FUNCTION | ( | TR | , |
do_not_evalf_params(). conjugate_func(tr_conj). print_func< FormFormat > &TR_form_print. print_func< FCFormat > &TR_fc_print. set_return_type(return_types::commutative). expl_derivative_func(expl_TR_diff) | |||
) |
HepLib::REGISTER_FUNCTION | ( | TTR | , |
do_not_evalf_params(). conjugate_func(ttr_conj). print_func< FormFormat > &TTR_form_print. print_func< FCFormat > & | TTR_fc_print | ||
) |
void HepLib::ReShare | ( | const ex & | e1, |
const ex & | e2, | ||
const ex & | e3 | ||
) |
void HepLib::ReShare | ( | const exvector & | ev1, |
const exvector & | ev2 | ||
) |
string HepLib::RunOS | ( | const string & | cmd | ) |
ex HepLib::series_ex | ( | ex const & | expr_in, |
ex const & | s0, | ||
int | sn0 | ||
) |
ex HepLib::series_ex | ( | ex const & | expr_in, |
symbol const & | s0, | ||
int | sn0 | ||
) |
void HepLib::sort_lst | ( | lst & | ilst, |
bool | less | ||
) |
void HepLib::sort_lst_by | ( | lst & | ilst, |
int | ki, | ||
bool | less | ||
) |
void HepLib::sort_vec | ( | exvector & | ivec, |
bool | less | ||
) |
void HepLib::sort_vec_by | ( | exvector & | ivec, |
int | ki, | ||
bool | less | ||
) |
exmap HepLib::SortPermutation | ( | const ex & | in_expr, |
const lst & | xs | ||
) |
ex HepLib::sp | ( | const ex & | a, |
const ex & | b | ||
) |
ex HepLib::SP | ( | const ex & | a, |
const ex & | b, | ||
bool | use_map | ||
) |
ex HepLib::SP2sp | ( | const ex & | exin | ) |
exmap HepLib::sp_map | ( | ) |
std::vector<std::string> HepLib::split | ( | const std::string & | s, |
char | delimiter | ||
) |
vector<std::string> HepLib::split | ( | const string & | s, |
char | delimiter | ||
) |
ex HepLib::str2ex | ( | const string & | expr | ) |
ex HepLib::str2ex | ( | const string & | expr, |
symtab | stab | ||
) |
void HepLib::str2file | ( | const string & | ostr, |
string | filename | ||
) |
lst HepLib::str2lst | ( | const string & | expr | ) |
lst HepLib::str2lst | ( | const string & | expr, |
symtab | stab | ||
) |
bool HepLib::string_contain | ( | const string & | fstr, |
const string & | mstr | ||
) |
Definition at line 180 of file Functions.cpp.
bool HepLib::string_end_with | ( | const string & | fstr, |
const string & | estr | ||
) |
Definition at line 172 of file Functions.cpp.
void HepLib::string_replace_all | ( | string & | str, |
const string & | from, | ||
const string & | to | ||
) |
Definition at line 148 of file Functions.cpp.
bool HepLib::string_start_with | ( | const string & | fstr, |
const string & | sstr | ||
) |
Definition at line 164 of file Functions.cpp.
void HepLib::string_trim | ( | string & | str | ) |
Definition at line 156 of file Functions.cpp.
const Symbol HepLib::TF | ( | "TF" | ) |
ex HepLib::Thiele | ( | const exvector & | keys, |
const exvector & | values, | ||
const ex & | d | ||
) |
Definition at line 81 of file Rational.cpp.
ex HepLib::TIR | ( | const ex & | expr_in, |
const lst & | loop_ps, | ||
const lst & | ext_ps | ||
) |
lst HepLib::UF | ( | const ex & | props, |
const ex & | ns, | ||
const ex & | loops, | ||
const ex & | tloops, | ||
const ex & | lsubs, | ||
const ex & | tsubs | ||
) |
ex HepLib::UnContract | ( | const ex | expr, |
const lst & | loop_ps, | ||
const lst & | ext_ps = lst{} |
||
) |
lst HepLib::vec2lst | ( | const exvector & | ev | ) |
const Symbol HepLib::vs | ( | "vs" | ) |
const Symbol HepLib::vz | ( | "vz" | ) |
lst HepLib::xlst | ( | int | bi, |
int | ei | ||
) |
lst HepLib::xlst | ( | int | ei | ) |
bool HepLib::xPositive | ( | ex const | expr | ) |
int HepLib::xSign | ( | ex const | expr | ) |
const Symbol HepLib::as("as") |
const Symbol HepLib::CA("CA") |
const Symbol HepLib::CF("CF") |
const Symbol HepLib::d("d") |
const Symbol HepLib::ep("ep") |
const Symbol HepLib::eps("eps") |
const Symbol HepLib::epz("epz") |
FCFormat HepLib::fcout(cout) |
int HepLib::form_expand_mode = form_expand_tr |
int HepLib::form_trace_mode = form_trace_auto |
const Symbol HepLib::gs("gs") |
const iSymbol HepLib::iEpsilon("iEpsilon") |
const Symbol HepLib::iet("iet") |
string HepLib::INC_FLAGS = "-I'"+InstallPrefix+"/include' " + "@INC_FLAGS@" |
string HepLib::LIB_FLAGS = "-L'"+InstallPrefix+"/lib' -Wl,-rpath,'"+InstallPrefix+"'/lib " + "@LIB_FLAGS@" |
MMAFormat HepLib::mout(cout) |
const Symbol HepLib::mu("mu") |
const Symbol HepLib::NA("NA") |
const Symbol HepLib::NaN("NaN") |
const Symbol HepLib::NF("NF") |
const Symbol HepLib::nH("nH") |
const Symbol HepLib::nL("nL") |
const Symbol HepLib::TF("TF") |
const Symbol HepLib::vs("vs") |
const Symbol HepLib::vz("vz") |