HepLib Namespace Reference

HepLib namespace. More...

Namespaces
namespace	QGRAF
	namespace for generating Feynman diagrams or amplitudes.
namespace	SD
	namespace for Numerical integration with Sector Decomposition method

Classes
struct	AIOption
class	AsGamma
	class for AntiSymmetric Gamma object More...
class	DGamma
	class for Dirac Gamma object More...
class	Direct
	IBP reduction using Direc method. 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	Error
	class used to wrap error message More...
class	Exp2AMF
class	FCFormat
	class for FCFormat Output More...
class	Fermat
	interface to communicate with Fermat program More...
class	FIRE
	IBP reduction using FIRE program. More...
class	Form
	interface to communicate with Form program More...
class	FormFormat
	class for FormFormat Output More...
class	IBP
	IBP base class for IBP reduction. More...
class	Index
	class for index object More...
class	iSymbol
	class extended to GiNaC symbol class, pure imaginary symbol More...
class	KIRA
	IBP reduction using KIRA program. More...
class	Laporta
class	lstHelper
	class as lst Helper More...
class	MapFunction
	class to wrap map_function of GiNaC More...
class	MMAFormat
	class for Mathematica Format Output More...
class	Pair
	class for Pair object More...
class	Parser
	class to parse for string or file, helpful with Symbol class More...
class	Server
class	Solver
	IBP reduction using Solver method. More...
class	SUNF
	class for SUNF object More...
class	SUNF4
	class for SUNF4 object More...
class	SUNT
	class for SUNT object More...
class	Symbol
	class extended to GiNaC symbol class, represent a positive symbol More...
class	UKIRA
	IBP reduction using KIRA program with user-defined equations. More...
class	Vector
	class for vector object More...
class	XIntegral
	XIntegral Class, preface to SecDec. 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.
std::vector< std::string >	split (const std::string &s, char delimiter)
	split the string into serveral part, separated by the delimiter
string	now (bool use_date)
	date/time string
lst	gather_symbols (const ex &e)
	get all symbols from input expression
lst	gather_symbols (const exvector &ve)
	get all symbols from input expression
string	RunOS (const string &cmd)
	run symtem command and return the output as string
void	garRead (const string &garfn, map< string, ex > &resMap)
	garRead from file, and output in a map
ex	garRead (const string &garfn, const char *key)
	garRead from file, only the element w.r.t. key
ex	garRead (const string &garfn)
	garRead from file, only the element w.r.t. key "res", note inner check will be performed
void	garWrite (const string &garfn, const map< string, ex > &resMap)
	garWrite to write the string-key map to the archive
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
ex	str2ex (const string &expr, symtab stab)
	convert string to ex expression, using Parser internally
ex	str2ex (const string &expr)
	convert string to ex expression, using Parser internally
lst	str2lst (const string &expr, symtab stab)
	convert string to the lst, using Parser internally
lst	str2lst (const string &expr)
	convert string to the lst, using Parser internally
string	ex2str (const ex &expr)
	convert ex to output string, the defalut printer format will be used
string	ex2str (const exvector &expr)
	convert exvec to output string, the defalut printer format will be used
matrix	lst2mat (const lst &ls)
	convert 2Dim lst to matrix
string	ex2str (const exmap &expr)
	convert exmap to output string, the defalut printer format will be used
string	ex2str (const exset &expr)
	convert exset to output string, the defalut printer format will be used
string	file2str (string filename)
	read file content to string
void	str2file (const string &ostr, string filename)
	export string to a file
void	str2file (char *buff, FILE *fh)
vector< string >	file2strvec (string filename, bool skip_empty)
	read file content to string vector
ex	file2ex (string filename)
	read file content to ex
ex	file2ex (string filename, symtab st)
	read file content to ex
void	ex2file (const ex &expr, string filename)
	export expression file
void	ex2file (string filename, const ex &expr)
	export expression file
ex	q2ex (__float128 num)
	__float128 to ex
__float128	ex2q (ex num)
	ex of numeric to __float128
int	ex2int (ex num)
	ex to integer
lst	vec2lst (const exvector &ev)
	convert exvector to lst
exvector	lst2vec (const lst &alst)
	convert lst to exvector
lst	add2lst (const ex &expr)
	convert add to lst
lst	mul2lst (const ex &expr)
	convert mul to lst
lst	xlst (int bi, int ei)
	return a lst: x(bi), x(bi+1), ..., x(ei)
lst	xlst (int ei)
	return a lst: x(0), x(1), ..., x(ei)
ex	series_ex (ex const &expr_in, ex const &s0, int sn0)
	the series like Mathematica, include s^n
ex	series_ex (ex const &expr_in, symbol const &s0, int sn0)
	the series like Mathematica, include s^n
ex	diff_ex (ex const expr, ex const xp, unsigned nth, bool expand)
	the differential like Mathematica
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
ex	collect_ex (ex const &expr_in, std::function< bool(const ex &)> has_func, int opt)
	the collect function like Mathematica
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}, ... }
ex	EvalF (ex expr)
	the nuerical evaluation, Digits=100 will be used
ex	EvalL (ex expr)
ex	EvalQ (ex expr)
ex	EvalMP (ex expr)
ex	NN (ex expr, int digits)
	the nuerical evaluation
bool	xPositive (ex const expr)
	check the expr is xPositive, i.e., each x-monomial item is postive
int	xSign (ex const expr)
	the always sign for expr
void	let_op_append (ex &ex_in, const ex item)
	append item into expression
void	let_op_prepend (ex &ex_in, const ex item)
	preppend item into expression
void	let_op_remove_last (ex &ex_in)
	remove last from expression
void	let_op_remove_first (ex &ex_in)
	remove first from expression
void	let_op_append (ex &ex_in, int index, ex const item)
	append item into index-th of expression
void	let_op_append (lst &ex_in, int index, ex const item)
	append item into index-th of expression
void	let_op_append (ex &ex_in, int index1, int index2, ex const item)
	append item into index1-th.index2-th of expression
void	let_op_append (lst &ex_in, int index1, int index2, ex const item)
	append item into index1-th.index2-th of expression
void	let_op_prepend (ex &ex_in, int index, ex const item)
	prepend item into index-th of expression
void	let_op_prepend (lst &ex_in, int index, ex const item)
	prepend item into index-th of expression
void	let_op_prepend (ex &ex_in, int index1, int index2, ex const item)
	prepend item into index1-th.index2-th of expression
void	let_op_prepend (lst &ex_in, int index1, int index2, ex const item)
	prepend item into index1-th.index2-th of expression
void	let_op_remove_last (ex &ex_in, int index)
	remove the last in index-th of expression
void	let_op_remove_last (lst &ex_in, int index)
	remove the last in index-th of expression
void	let_op_remove_last (ex &ex_in, int index1, int index2)
	remove the last in index1-th.index2-th of expression
void	let_op_remove_last (lst &ex_in, int index1, int index2)
	remove the last in index1-th.index2-th of expression
void	let_op_remove_first (ex &ex_in, int index)
	remove the first in index-th of expression
void	let_op_remove_first (lst &ex_in, int index)
	remove the first in index-th of expression
void	let_op_remove_first (ex &ex_in, int index1, int index2)
	remove the first in index1-th.index2-th of expression
void	let_op_remove_first (lst &ex_in, int index1, int index2)
	remove the first in index1-th.index2-th of expression
void	let_op (ex &ex_in, int index1, int index2, const ex item)
	update index1-th.index2-th of expression with item
void	let_op (lst &ex_in, int index1, int index2, const ex item)
	update index1-th.index2-th of expression with item
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
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
ex	get_op (const ex ex_in, int index1, int index2)
	return index1-th.index2-th of expression
ex	get_op (const lst ex_in, int index1, int index2)
	return index1-th.index2-th of expression
ex	get_op (const ex ex_in, int index1, int index2, int index3)
	return index1-th.index2-th.index3-th of expression
ex	get_op (const lst ex_in, int index1, int index2, int index3)
	return index1-th.index2-th.index3-th of expression
int	CpuCores ()
	return the cpu cores using OpenMP
ex	normal_fermat (const ex &expr, bool dfactor)
	return the normalizatied expression, using fermat_numer_denom
ex	collect_factors (const ex &expr)
	a wrapper for collect_common_factors, catch errors
ex	exfactor (const ex &expr_in, int opt)
	factorize a expression
ex	exexpand (const ex &expr, int opt)
	factorize a expression
ex	exnormal (const ex &expr, int opt)
	normalize a expression
ex	exnd (const ex &expr, int opt)
	num_den a expression
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
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
ex	numer_denom_fermat (const ex &expr, bool dfactor)
	return the numerator and denominator after normalization
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
void	sort_lst_by (lst &ilst, int ki, bool less)
	sort the list in less order, or the reverse
void	sort_vec (exvector &ivec, bool less)
	sort the list in less order, or the reverse
void	sort_vec_by (exvector &ivec, int ki, bool less)
	sort the list in less order, or the reverse
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)
ex	ApartIR2ex (const ex &expr_in)
	convert ApartIR to ex
ex	ApartIR2F (const ex &expr_in)
	convert ApartIR to F(ps, ns), ns is like FIRE convention
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.
ex	Apart (const ex &expr_ino, const lst &vars_in, exmap smap)
	Apart on ex.
ex	Apart (const ex &expr_ino, const lst &loops, const lst &extps, exmap smap)
	Apart on ex.
ex	ApartIRC (const ex &expr_in)
	complete the ApartIR elements
ex	F2ex (const ex &expr_in)
	convert F(ps, ns) to normal ex, ns is like FIRE convention
void	ApartIBP (exvector &air_vec, AIOption aio)
	perform IBP reduction on the Aparted input
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
ex	AsGamma_mul_right (const ex &expr, const ex &pi_in)
ex	AsGamma_mul_left (const ex &expr, const ex &pi_in)
ex	AsGamma_to (const ex &expr)
ex	ncmul_expand (const ex &expr)
ex	GMatContract (const ex &expr_in, bool auto_tr)
	make contract on matrix, i.e., GMat(a,i1,i2)*GMat(b,i2,i3) -> GMat(a*b,i1,i3)
ex	Contract (const ex &ei)
ex	GMatOut (const ex &expr_in)
ex	GMatExpand (const ex &expr_in)
ex	GMatShift (const ex &expr, const ex &g, bool to_right)
ex	GMatSimplify (const ex &expr)
ex	GMatShift (const ex &expr)
ex	GMatECC (const ex &expr, int sign)
ex	GMatT (const ex &expr)
	REGISTER_FUNCTION (GMat, do_not_evalf_params().print_func< FCFormat >(&GMat_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
ex	GAS (const initializer_list< ex > &expr_lst, unsigned rl)
	function similar to GAD/GSD in FeynClac
ex	LC (ex pi1, ex pi2, ex pi3, ex pi4)
	function similar to LCD in FeynCalc
ex	form (const ex &iexpr, int verb)
	evalulate expr in form program, see also the form_trace_mode and form_expand_mode
ex	charge_conjugate (const ex &expr)
	make the charge conjugate operaton, M -> C^{-1} . M^T . C w.r.t. a GMat object
ex	gamma_transpose (const ex &expr)
	make the transpose operaton M --> M^T
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.
ex	sp (const ex &a, const ex &b)
	translated the vector dot a.b to a*b, useful in SecDec
ex	sp (const ex &a)
ex &	letSP (const ex &p1, const ex &p2)
	return the reference of p1.p2
ex &	letSP (const ex &p)
	return the reference of p.p
void	clearSP (const ex &p1, const ex &p2)
	delete the assignment of p1.p2
void	clearSP (const ex &p)
	delete the assignment of p.p
void	clearSP ()
	delete all assignment in SP_map
ex	SP2sp (const ex &exin)
	convert SP(a,b) to sp(a,b)
exmap	sp_map ()
	the SP_map with SP(a,b) replaced to sp(a,b)
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.
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)
lst	syms (const exvector &ev)
	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.
lst	LoopUF (const IBP &ibp, const ex &idx)
	UF function.
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.
pair< exmap, lst >	FindRules (vector< IBP * > fs, bool mi, std::function< lst(const IBP &, const ex &)> uf)
	Find Rules for Integral or Master Integral.
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
bool	GMat_using_cache = true
exmap	MapPreSP
int	_o_ = 0
slong	error_pass_dp = 100

Detailed Description

HepLib namespace.

namespace for IBP reduction

Typedef Documentation

co_epvec_t

typedef pair<ex,epvec_t> HepLib::co_epvec_t

Definition at line 1076 of file BASIC.cpp.

epvec_t

typedef vector<pair<ex,ex> > HepLib::epvec_t

Definition at line 1075 of file BASIC.cpp.

init_list

typedef std::initializer_list<ex> HepLib::init_list

Definition at line 47 of file BASIC.h.

SparseMatrix

typedef map<int,map<int,ex> > HepLib::SparseMatrix

Definition at line 178 of file Solver.cpp.

Function Documentation

A0()

ex HepLib::A0	(	const ex	m2,
		int	n,
		ex	d
	)

scalar integral A0, devided by (2pi)^(4-2ep)

Parameters

m2	mass squared
n	exponent for the propagator l^2-m^2

Returns

A0

Definition at line 17 of file ABCD.cpp.

ACSort() [1/2]

int HepLib::ACSort	(	int	n,
		ex	exs[]
	)

Definition at line 304 of file Functions.cpp.

ACSort() [2/2]

int HepLib::ACSort

(

lst &

exs

)

Definition at line 289 of file Functions.cpp.

add2lst()

lst HepLib::add2lst

(

const ex &

expr

)

convert add to lst

Parameters

expr	input expression

Returns

lst

Definition at line 921 of file BASIC.cpp.

add_collect_normal() [1/6]

ex HepLib::add_collect_normal	(	const ex &	e,
		ex const &	pats,
		int	opt
	)

Definition at line 2215 of file BASIC.cpp.

add_collect_normal() [2/6]

ex HepLib::add_collect_normal	(	const ex &	e,
		init_list const &	pats,
		int	opt
	)

Definition at line 2227 of file BASIC.cpp.

add_collect_normal() [3/6]

ex HepLib::add_collect_normal	(	const ex &	e,
		lst const &	pats,
		int	opt
	)

Definition at line 2221 of file BASIC.cpp.

add_collect_normal() [4/6]

ex HepLib::add_collect_normal	(	const exvector &	exv,
		ex const &	pats,
		int	opt
	)

Definition at line 2173 of file BASIC.cpp.

add_collect_normal() [5/6]

ex HepLib::add_collect_normal	(	const exvector &	exv,
		init_list const &	pats,
		int	opt
	)

Definition at line 2187 of file BASIC.cpp.

add_collect_normal() [6/6]

ex HepLib::add_collect_normal	(	const exvector &	exv,
		lst const &	pats,
		int	opt
	)

Definition at line 2201 of file BASIC.cpp.

air2pn()

ex HepLib::air2pn ( ex  air )

inline

Definition at line 89 of file Apart.cpp.

Apart() [1/3]

ex HepLib::Apart	(	const ex &	expr_ino,
		const lst &	loops,
		const lst &	extps,
		exmap	smap
	)

Apart on ex.

Parameters

expr_ino	input expression
loops	list of loop Vector
extps	list of external Vector
smap	the sign map

Returns

sum of coefficient * ApartIR

Definition at line 859 of file Apart.cpp.

Apart() [2/3]

ex HepLib::Apart	(	const ex &	expr_ino,
		const lst &	vars_in,
		exmap	smap
	)

Apart on ex.

Parameters

expr_ino	normal expresion, product of [ linear w.r.t. vars ]^n
vars_in	independent variables
smap	the sign map

Returns

sum of coefficient * ApartIR

Definition at line 616 of file Apart.cpp.

Apart() [3/3]

ex HepLib::Apart

(

const matrix &

mat

)

Apart on matrix.

Parameters

mat	each column: [c1,...,cn,c0,n] -> (c1 x1+...+cn xn+c0)^n

Returns

sum of coefficient * ApartIR

Definition at line 280 of file Apart.cpp.

ApartIBP() [1/3]

void HepLib::ApartIBP	(	exvector &	air_vec,
		AIOption	aio
	)

perform IBP reduction on the Aparted input

Parameters

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

Returns

nothing returned, the input air_vec will be updated

Definition at line 109 of file ApartIBP.cpp.

ApartIBP() [2/3]

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

Parameters

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

Returns

nothing returned, the input air_vec will be updated

Definition at line 614 of file ApartIBP.cpp.

ApartIBP() [3/3]

void HepLib::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  )

inline

Definition at line 596 of file HEP.h.

ApartIR2ex()

ex HepLib::ApartIR2ex

(

const ex &

expr_in

)

convert ApartIR to ex

Parameters

expr_in

expression contains ApartIR

Returns

ApartIR converted into normal ex

Definition at line 35 of file Apart.cpp.

ApartIR2F()

ex HepLib::ApartIR2F

(

const ex &

expr_in

)

convert ApartIR to F(ps, ns), ns is like FIRE convention

Parameters

expr_in

expression contains ApartIR

Returns

ApartIR converted into F(ps, ns)

Definition at line 61 of file Apart.cpp.

ApartIRC()

ex HepLib::ApartIRC

(

const ex &

expr_in

)

complete the ApartIR elements

Parameters

expr_in

input expression

Returns

ApartIR with complete matrix rank, ready for IBP reduction

Definition at line 914 of file Apart.cpp.

ApartRules()

exmap HepLib::ApartRules	(	const exvector &	airs,
		bool	irc
	)

Definition at line 156 of file Apart.cpp.

append_to() [1/2]

void HepLib::append_to ( const exvector &  exv, lst &  alst  )

inline

Definition at line 723 of file BASIC.h.

append_to() [2/2]

void HepLib::append_to ( const lst &  alst, exvector &  exv  )

inline

Definition at line 724 of file BASIC.h.

arg2map()

void HepLib::arg2map	(	int	argc,
		char **	argv,
		const char *	optstring,
		std::map< char, std::string > &	kv
	)

Definition at line 2337 of file BASIC.cpp.

as()

const Symbol HepLib::as

(

"as"

)

AsGamma_mul_left()

ex HepLib::AsGamma_mul_left	(	const ex &	expr,
		const ex &	pi_in
	)

Definition at line 277 of file AsGamma.cpp.

AsGamma_mul_right()

ex HepLib::AsGamma_mul_right	(	const ex &	expr,
		const ex &	pi_in
	)

Definition at line 264 of file AsGamma.cpp.

AsGamma_to()

ex HepLib::AsGamma_to

(

const ex &

expr

)

Definition at line 290 of file AsGamma.cpp.

CA()

const Symbol HepLib::CA

(

"CA"

)

ca_neg_pow_sub()

ex HepLib::ca_neg_pow_sub

(

const ex &

expr

)

Definition at line 1211 of file Basic.cpp.

CF()

const Symbol HepLib::CF

(

"CF"

)

charge_conjugate()

ex HepLib::charge_conjugate

(

const ex &

expr

)

make the charge conjugate operaton, M -> C^{-1} . M^T . C w.r.t. a GMat object

Parameters

expr	the input expression

Returns

returned charge conjugated expression

Definition at line 639 of file Form.cpp.

ChineseRemainder()

numeric HepLib::ChineseRemainder	(	std::vector< numeric >	a,
		std::vector< numeric >	n
	)

Definition at line 53 of file Rational.cpp.

clearSP() [1/3]

void HepLib::clearSP

(

)

delete all assignment in SP_map

Definition at line 293 of file Pair.cpp.

clearSP() [2/3]

void HepLib::clearSP

(

const ex &

p

)

delete the assignment of p.p

Parameters

p	vector/index

Definition at line 284 of file Pair.cpp.

clearSP() [3/3]

void HepLib::clearSP	(	const ex &	p1,
		const ex &	p2
	)

delete the assignment of p1.p2

Parameters

p1	the 1st vector/index
p2	the 2nd vector/index

Definition at line 274 of file Pair.cpp.

collect_ex() [1/4]

ex HepLib::collect_ex ( const ex &  expr, ex const &  pat, int  opt = o_none  )

inline

Definition at line 429 of file BASIC.h.

collect_ex() [2/4]

ex HepLib::collect_ex ( const ex &  expr, init_list const &  pats, int  opt = o_none  )

inline

Definition at line 415 of file BASIC.h.

collect_ex() [3/4]

ex HepLib::collect_ex ( const ex &  expr, lst const &  pats, int  opt = o_none  )

inline

Definition at line 422 of file BASIC.h.

collect_ex() [4/4]

ex HepLib::collect_ex	(	ex const &	expr_in,
		std::function< bool(const ex &)>	has_func,
		int	opt
	)

the collect function like Mathematica

Parameters

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

Returns

the collected expression

Definition at line 1202 of file BASIC.cpp.

collect_factors()

ex HepLib::collect_factors

(

const ex &

expr

)

a wrapper for collect_common_factors, catch errors

Parameters

expr	the input expression

Returns

collect_common_factors result

Definition at line 1841 of file BASIC.cpp.

collect_lst() [1/4]

lst HepLib::collect_lst ( const ex &  expr, ex const &  pat, int  opt = o_none  )

inline

Definition at line 449 of file BASIC.h.

collect_lst() [2/4]

lst HepLib::collect_lst ( const ex &  expr, init_list const &  pats, int  opt = o_none  )

inline

Definition at line 435 of file BASIC.h.

collect_lst() [3/4]

lst HepLib::collect_lst ( const ex &  expr, lst const &  pats, int  opt = o_none  )

inline

Definition at line 442 of file BASIC.h.

collect_lst() [4/4]

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}, ... }

Parameters

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

Returns

the collected expression in lst

Definition at line 1222 of file BASIC.cpp.

Combinations()

void HepLib::Combinations	(	int	n,
		int	m,
		std::function< void(const int *)>	f
	)

Definition at line 184 of file Functions.cpp.

CombinationsR()

void HepLib::CombinationsR	(	int	n,
		int	m,
		std::function< void(const int *)>	f
	)

Definition at line 197 of file Functions.cpp.

Contract()

ex HepLib::Contract

(

const ex &

ei

)

Definition at line 757 of file Basic.cpp.

CoPat()

lst HepLib::CoPat ( const ex &  e, std::function< bool(const ex &)>  f  )

inline

Definition at line 725 of file BASIC.h.

CpuCores()

int HepLib::CpuCores

(

)

return the cpu cores using OpenMP

Returns

the cpu cores

Definition at line 1820 of file BASIC.cpp.

d()

const Symbol HepLib::d

(

"d"

)

diff_ex()

ex HepLib::diff_ex	(	ex const	expr,
		ex const	xp,
		unsigned	nth,
		bool	expand
	)

the differential like Mathematica

Parameters

expr	input expression
xp	the variable, can be an expression, will replace by a symbol and back again
nth	nth-derivative
expand	true to call collect_ex before diff

Returns

the corresponding nth-derivative

Definition at line 1063 of file BASIC.cpp.

dir_exists()

bool HepLib::dir_exists ( string  dir )

inline

Definition at line 297 of file BASIC.h.

DoColor()

ex HepLib::DoColor	(	const ex &	expr,
		const ex &	pref,
		int	method
	)

Definition at line 1289 of file Basic.cpp.

ep()

const Symbol HepLib::ep

(

"ep"

)

eps()

const Symbol HepLib::eps

(

"eps"

)

epz()

const Symbol HepLib::epz

(

"epz"

)

EvalF()

ex HepLib::EvalF

(

ex

expr

)

the nuerical evaluation, Digits=100 will be used

Parameters

expr	input expression

Returns

the nuerical expression

Definition at line 1245 of file BASIC.cpp.

EvalL()

ex HepLib::EvalL

(

ex

expr

)

Definition at line 1256 of file BASIC.cpp.

EvalMP()

ex HepLib::EvalMP

(

ex

expr

)

Definition at line 1266 of file BASIC.cpp.

EvalQ()

ex HepLib::EvalQ

(

ex

expr

)

Definition at line 1261 of file BASIC.cpp.

ex2file() [1/2]

void HepLib::ex2file	(	const ex &	expr,
		string	filename
	)

export expression file

Parameters

expr	the input expression
filename	file name

Returns

the file content in ex

Definition at line 845 of file BASIC.cpp.

ex2file() [2/2]

void HepLib::ex2file	(	string	filename,
		const ex &	expr
	)

export expression file

Parameters

filename	file name
expr	the input expression

Returns

the file content in ex

Definition at line 858 of file BASIC.cpp.

ex2int()

int HepLib::ex2int

(

ex

num

)

ex to integer

Parameters

num	an integer in ex

Returns

the integer for the number

Definition at line 893 of file BASIC.cpp.

ex2q()

__float128 HepLib::ex2q

(

ex

num

)

ex of numeric to __float128

Parameters

num	a ex number

Returns

a __float128 object for the number

Definition at line 879 of file BASIC.cpp.

ex2str() [1/4]

string HepLib::ex2str

(

const ex &

expr

)

convert ex to output string, the defalut printer format will be used

Parameters

expr	a expression

Returns

the output string

Definition at line 715 of file BASIC.cpp.

ex2str() [2/4]

string HepLib::ex2str

(

const exmap &

expr

)

convert exmap to output string, the defalut printer format will be used

Parameters

expr	a exvec expression

Returns

the output string

Definition at line 753 of file BASIC.cpp.

ex2str() [3/4]

string HepLib::ex2str

(

const exset &

expr

)

convert exset to output string, the defalut printer format will be used

Parameters

expr	a exvec expression

Returns

the output string

Definition at line 764 of file BASIC.cpp.

ex2str() [4/4]

string HepLib::ex2str

(

const exvector &

expr

)

convert exvec to output string, the defalut printer format will be used

Parameters

expr	a exvec expression

Returns

the output string

Definition at line 726 of file BASIC.cpp.

ex_less()

bool HepLib::ex_less	(	const ex &	a,
		const ex &	b
	)

Definition at line 10 of file Sort.cpp.

exexpand()

ex HepLib::exexpand	(	const ex &	expr,
		int	opt
	)

factorize a expression

Parameters

expr	the input expression
opt	1 to use FORM, otherwise using GiNaC for factorization

Returns

factorized result

Definition at line 1877 of file BASIC.cpp.

exfactor()

ex HepLib::exfactor	(	const ex &	expr_in,
		int	opt
	)

factorize a expression

Parameters

expr	the input expression
opt	1 to use FORM, otherwise using GiNaC for factorization

Returns

factorized result

Definition at line 1854 of file BASIC.cpp.

exnd()

ex HepLib::exnd	(	const ex &	expr,
		int	opt
	)

num_den a expression

Parameters

expr	the input expression
opt	1 to use factor_form, 2 to use Fermat, otherwise using GiNaC for numer_denom

Returns

lst of { num, den }

Definition at line 1932 of file BASIC.cpp.

exnormal()

ex HepLib::exnormal	(	const ex &	expr,
		int	opt
	)

normalize a expression

Parameters

expr	the input expression
opt	1 to use Fermat, otherwise using GiNaC for normalization

Returns

factorized result

Definition at line 1916 of file BASIC.cpp.

expand_ex() [1/4]

ex HepLib::expand_ex ( const ex &  expr )

inline

Definition at line 398 of file BASIC.h.

expand_ex() [2/4]

ex HepLib::expand_ex ( ex const &  expr, ex const &  pat  )

inline

Definition at line 409 of file BASIC.h.

expand_ex() [3/4]

ex HepLib::expand_ex ( ex const &  expr, lst const &  pats  )

inline

Definition at line 402 of file BASIC.h.

expand_ex() [4/4]

ex HepLib::expand_ex	(	ex const &	expr_in,
		std::function< bool(const ex &)>	has_func
	)

the expand like Mathematica

Parameters

expr_in	input expression
has_func	only expand the element e, when has_func(e) is true

Returns

the expanded expression

Definition at line 1188 of file BASIC.cpp.

F2ex()

ex HepLib::F2ex

(

const ex &

expr_in

)

convert F(ps, ns) to normal ex, ns is like FIRE convention

Parameters

expr_in

expression contains F

Returns

F(ps, ns) converted into normal expression

Definition at line 87 of file ApartIBP.cpp.

factor_flint()

ex HepLib::factor_flint	(	const ex &	e,
		bool	nd = true
	)

factor_form()

ex HepLib::factor_form	(	const ex &	expr,
		bool	nd
	)

factorize a expression using FORM

Parameters

expr	the input expression

Returns

factorized result

Definition at line 2048 of file BASIC.cpp.

fcout()

FCFormat HepLib::fcout

(

cout

)

fermat_Det()

ex HepLib::fermat_Det

(

const matrix &

mat

)

Definition at line 650 of file Fermat.cpp.

fermat_Det_Sparse()

ex HepLib::fermat_Det_Sparse

(

const matrix &

mat

)

Definition at line 757 of file Fermat.cpp.

fermat_eval() [1/2]

ex HepLib::fermat_eval

(

const ex &

expr

)

return the numerator and denominator after normalization

Parameters

expr	the input expression

Returns

fermat evaluated expression

Definition at line 317 of file Fermat.cpp.

fermat_eval() [2/2]

void HepLib::fermat_eval

(

const string &

fcmd = "@[**]"

)

Definition at line 1343 of file Fermat.cpp.

fermat_inv()

matrix HepLib::fermat_inv

(

const matrix &

mat

)

Definition at line 880 of file Fermat.cpp.

fermat_mat() [1/2]

void HepLib::fermat_mat	(	const matrix &	mat_in,
		const string &	name
	)

Definition at line 1224 of file Fermat.cpp.

fermat_mat() [2/2]

matrix HepLib::fermat_mat

(

const string &

name

)

Definition at line 1301 of file Fermat.cpp.

fermat_mul()

matrix HepLib::fermat_mul	(	const matrix &	m1,
		const matrix &	m2
	)

Definition at line 987 of file Fermat.cpp.

fermat_normal()

ex HepLib::fermat_normal ( const ex &  expr, bool  dfactor = false  )

inline

Definition at line 465 of file BASIC.h.

fermat_numer_denom()

ex HepLib::fermat_numer_denom ( const ex &  expr, bool  dfactor = false  )

inline

Definition at line 461 of file BASIC.h.

fermat_pow()

matrix HepLib::fermat_pow	(	const matrix &	mat_in,
		int	n
	)

Definition at line 1112 of file Fermat.cpp.

fermat_Redrowech()

matrix HepLib::fermat_Redrowech

(

const matrix &

mat

)

Definition at line 409 of file Fermat.cpp.

fermat_Redrowech_Sparse()

matrix HepLib::fermat_Redrowech_Sparse

(

const matrix &

mat

)

Definition at line 516 of file Fermat.cpp.

file2ex() [1/2]

ex HepLib::file2ex

(

string

filename

)

read file content to ex

Parameters

filename

file name

Returns

the file content in ex

Definition at line 825 of file BASIC.cpp.

file2ex() [2/2]

ex HepLib::file2ex	(	string	filename,
		symtab	st
	)

read file content to ex

Parameters

filename	file name
st	symtab

Returns

the file content in ex

Definition at line 835 of file BASIC.cpp.

file2str()

string HepLib::file2str

(

string

filename

)

read file content to string

Parameters

filename

file name

Returns

the file content in string

Definition at line 775 of file BASIC.cpp.

file2strvec()

vector< string > HepLib::file2strvec	(	string	filename,
		bool	skip_empty
	)

read file content to string vector

Parameters

filename	file name
skip_empty	skip blank lines

Returns

the file content in string vector, lines in vector

Definition at line 809 of file BASIC.cpp.

file_exists()

bool HepLib::file_exists ( string  fn )

inline

Definition at line 289 of file BASIC.h.

file_remove()

bool HepLib::file_remove ( string  fn )

inline

Definition at line 285 of file BASIC.h.

FindRules() [1/2]

pair< exmap, lst > HepLib::FindRules ( IBP &  ibp, bool  mi = true, std::function< lst(const IBP &, const ex &)>  uf = LoopUF  )

inline

Definition at line 235 of file IBP.h.

FindRules() [2/2]

pair< exmap, lst > HepLib::FindRules	(	vector< IBP * >	fs,
		bool	mi,
		std::function< lst(const IBP &, const ex &)>	uf
	)

Find Rules for Integral or Master Integral.

Parameters

fs	vector of IBP pointer object
mi	true for Master Integals
uf	the function to compute the UF polynomial

Returns

rules replacement and left integrals or left master integrals

Definition at line 574 of file IBP.cpp.

form()

ex HepLib::form	(	const ex &	iexpr,
		int	verb
	)

evalulate expr in form program, see also the form_trace_mode and form_expand_mode

Parameters

expr	the input expression
verb	for verb output

Returns

result with index contract, trace performed, etc.

Definition at line 565 of file Form.cpp.

form_eval()

ex HepLib::form_eval

(

const ex &

expr

)

Definition at line 1938 of file BASIC.cpp.

form_factor()

ex HepLib::form_factor ( const ex &  expr, bool  nd = true  )

inline

Definition at line 472 of file BASIC.h.

gamma_transpose()

ex HepLib::gamma_transpose

(

const ex &

expr

)

make the transpose operaton M --> M^T

Parameters

expr	the input expression

Returns

returned transposed expression

Definition at line 685 of file Form.cpp.

garRead() [1/5]

ex HepLib::garRead

(

const string &

garfn

)

garRead from file, only the element w.r.t. key "res", note inner check will be performed

Parameters

garfn

ginac archive filename

Returns

the expression w.r.t. key "res"

Definition at line 623 of file BASIC.cpp.

garRead() [2/5]

ex HepLib::garRead	(	const string &	garfn,
		const char *	key
	)

garRead from file, only the element w.r.t. key

Parameters

garfn	ginac archive filename
key	the archive key, note (const char *) type, match unarchive_ex in GiNaC

Returns

the expression w.r.t. key

Definition at line 609 of file BASIC.cpp.

garRead() [3/5]

void HepLib::garRead	(	const string &	garfn,
		map< string, ex > &	resMap
	)

garRead from file, and output in a map

Parameters

garfn	ginac archive filename
resMap	will be update, a string key map

Definition at line 591 of file BASIC.cpp.

garRead() [4/5]

void HepLib::garRead	(	exvector &	exv,
		string	garfn
	)

Definition at line 2154 of file BASIC.cpp.

garRead() [5/5]

void HepLib::garRead ( string  garfn, exvector &  exv  )

inline

Definition at line 866 of file BASIC.h.

garWrite() [1/6]

void HepLib::garWrite ( const ex &  res, const string &  garfn  )

inline

Definition at line 326 of file BASIC.h.

garWrite() [2/6]

void HepLib::garWrite	(	const exvector &	exv,
		string	garfn
	)

Definition at line 2143 of file BASIC.cpp.

garWrite() [3/6]

void HepLib::garWrite ( const map< string, ex > &  resMap, const string &  garfn  )

inline

Definition at line 324 of file BASIC.h.

garWrite() [4/6]

void HepLib::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

Parameters

garfn	ginac archive filename for output
res	the output expression

Definition at line 654 of file BASIC.cpp.

garWrite() [5/6]

void HepLib::garWrite	(	const string &	garfn,
		const map< string, ex > &	resMap
	)

garWrite to write the string-key map to the archive

Parameters

garfn	ginac archive filename for output
resMap	a key-valued map

Definition at line 639 of file BASIC.cpp.

garWrite() [6/6]

void HepLib::garWrite ( string  garfn, const exvector &  exv  )

inline

Definition at line 864 of file BASIC.h.

GAS() [1/4]

ex HepLib::GAS	(	const ex &	expr,
		unsigned	rl
	)

function similar to GAD/GSD in FeynClac

Parameters

expr	momentum/index or 1,5,6,7
rl	the represent line number

Returns

expanded/translasted to Dirac Gamma objects

Definition at line 280 of file DGamma.cpp.

GAS() [2/4]

ex HepLib::GAS ( const Index &  i, unsigned  rl = 0  )

inline

Definition at line 566 of file HEP.h.

GAS() [3/4]

ex HepLib::GAS	(	const initializer_list< ex > &	expr_lst,
		unsigned	rl
	)

function similar to GAD/GSD in FeynClac

Parameters

expr	momentum/index or 1,5,6,7
rl	the represent line number

Returns

expanded/translasted to Dirac Gamma objects

Definition at line 323 of file DGamma.cpp.

GAS() [4/4]

ex HepLib::GAS ( const Vector &  p, unsigned  rl = 0  )

inline

Definition at line 565 of file HEP.h.

gather_symbols() [1/2]

lst HepLib::gather_symbols

(

const ex &

e

)

get all symbols from input expression

Parameters

e	input expression

Returns

all symbols in the input

Definition at line 539 of file BASIC.cpp.

gather_symbols() [2/2]

lst HepLib::gather_symbols

(

const exvector &

ve

)

get all symbols from input expression

Parameters

ve	input expression vector

Returns

all symbols in the input

Definition at line 554 of file BASIC.cpp.

get_op() [1/4]

ex HepLib::get_op	(	const ex	ex_in,
		int	index1,
		int	index2
	)

return index1-th.index2-th of expression

Parameters

ex_in	input expression will be update
index1	the index
index2	the index

Returns

the element

Definition at line 1606 of file BASIC.cpp.

get_op() [2/4]

ex HepLib::get_op	(	const ex	ex_in,
		int	index1,
		int	index2,
		int	index3
	)

return index1-th.index2-th.index3-th of expression

Parameters

ex_in	input expression will be update
index1	the index
index2	the index
index3	the index

Returns

the element

Definition at line 1629 of file BASIC.cpp.

get_op() [3/4]

ex HepLib::get_op	(	const lst	ex_in,
		int	index1,
		int	index2
	)

return index1-th.index2-th of expression

Parameters

ex_in	input expression will be update
index1	the index
index2	the index

Returns

the element

Definition at line 1617 of file BASIC.cpp.

get_op() [4/4]

ex HepLib::get_op	(	const lst	ex_in,
		int	index1,
		int	index2,
		int	index3
	)

return index1-th.index2-th.index3-th of expression

Parameters

ex_in	input expression will be update
index1	the index
index2	the index
index3	the index

Returns

the element

Definition at line 1641 of file BASIC.cpp.

get_precision()

long HepLib::get_precision

(

)

Definition at line 2333 of file BASIC.cpp.

GiNaC_Function_1()

std::function< GiNaC::function(const ex &)> HepLib::GiNaC_Function_1 ( const string  name )

inline

Definition at line 600 of file BASIC.h.

GiNaC_Function_2()

std::function< GiNaC::function(const ex &, const ex &)> HepLib::GiNaC_Function_2 ( const string  name )

inline

Definition at line 607 of file BASIC.h.

GiNaC_Function_3()

std::function< GiNaC::function(const ex &, const ex &, const ex &)> HepLib::GiNaC_Function_3 ( const string  name )

inline

Definition at line 614 of file BASIC.h.

GiNaC_Function_4()

std::function< GiNaC::function(const ex &, const ex &, const ex &, const ex &)> HepLib::GiNaC_Function_4 ( const string  name )

inline

Definition at line 621 of file BASIC.h.

GiNaC_Parallel()

exvector HepLib::GiNaC_Parallel	(	int	ntotal,
		std::function< ex(int)>	f,
		const string &	key
	)

GiNaC Parallel Evaluation using fork.

Parameters

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

Returns

return the ntotal-element vector, i.e., [f(0), ..., f(ntotal-1)]

Definition at line 260 of file BASIC.cpp.

GMatContract()

ex HepLib::GMatContract	(	const ex &	expr_in,
		bool	auto_tr
	)

make contract on matrix, i.e., GMat(a,i1,i2)*GMat(b,i2,i3) -> GMat(a*b,i1,i3)

Parameters

expr_in	expression contains GMat
auto_tr	automatic transpose to avoid index conflict

Returns

contracted expression

Definition at line 629 of file Basic.cpp.

GMatECC()

ex HepLib::GMatECC	(	const ex &	expr,
		int	sign
	)

Definition at line 1080 of file Basic.cpp.

GMatExpand()

ex HepLib::GMatExpand

(

const ex &

expr_in

)

Definition at line 823 of file Basic.cpp.

GMatOut()

ex HepLib::GMatOut

(

const ex &

expr_in

)

Definition at line 799 of file Basic.cpp.

GMatShift() [1/2]

ex HepLib::GMatShift

(

const ex &

expr

)

Definition at line 1032 of file Basic.cpp.

GMatShift() [2/2]

ex HepLib::GMatShift	(	const ex &	expr,
		const ex &	g,
		bool	to_right
	)

Definition at line 925 of file Basic.cpp.

GMatSimplify()

ex HepLib::GMatSimplify

(

const ex &

expr

)

Definition at line 987 of file Basic.cpp.

GMatT()

ex HepLib::GMatT

(

const ex &

expr

)

Definition at line 1140 of file Basic.cpp.

GPermutation()

void HepLib::GPermutation	(	const ex &	uf,
		const lst &	xs
	)

Definition at line 1042 of file IBP.cpp.

GPolynomial()

ex HepLib::GPolynomial

(

const IBP &

ibp

)

Definition at line 1004 of file IBP.cpp.

gs()

const Symbol HepLib::gs

(

"gs"

)

has_all()

bool HepLib::has_all ( ex  expr, lst  ps  )

inline

Definition at line 59 of file BASIC.h.

has_any()

bool HepLib::has_any ( ex  expr, lst  ps  )

inline

Definition at line 55 of file BASIC.h.

has_function()

bool HepLib::has_function ( const ex &  expr )

inline

Definition at line 668 of file BASIC.h.

has_symbol()

bool HepLib::has_symbol

(

const ex &

e

)

Definition at line 2353 of file BASIC.cpp.

has_w()

bool HepLib::has_w

(

const ex &

e

)

Definition at line 2233 of file BASIC.cpp.

HomCACF()

ex HepLib::HomCACF

(

const ex &

e

)

Definition at line 1247 of file Basic.cpp.

iEpsilon()

const iSymbol HepLib::iEpsilon

(

"iEpsilon"

)

iet()

const Symbol HepLib::iet

(

"iet"

)

in2str()

string HepLib::in2str ( int  i )

inline

Definition at line 346 of file BASIC.h.

inner_expand_collect()

pair< ex, epvec_t > HepLib::inner_expand_collect	(	ex const &	expr_in,
		std::function< bool(const ex &)>	has_func,
		int	depth = 0
	)

Definition at line 1121 of file BASIC.cpp.

inner_factor_form()

ex HepLib::inner_factor_form

(

const ex &

expr

)

Definition at line 1984 of file BASIC.cpp.

is_equal_any()

bool HepLib::is_equal_any ( ex  expr, lst  ps  )

inline

Definition at line 64 of file BASIC.h.

is_subset()

bool HepLib::is_subset ( const ex &  e1, const ex &  e2  )

inline

Definition at line 130 of file Apart.cpp.

isFunction() [1/2]

bool HepLib::isFunction ( const ex &  e, string  func_name  )

inline

Definition at line 658 of file BASIC.h.

isFunction() [2/2]

bool HepLib::isFunction ( const ex &  e, string  func_name, int  nargs  )

inline

Definition at line 661 of file BASIC.h.

isSorted() [1/2]

bool HepLib::isSorted

(

const lst &

exs

)

Definition at line 273 of file Functions.cpp.

isSorted() [2/2]

bool HepLib::isSorted	(	int	n,
		const ex	exs[]
	)

Definition at line 281 of file Functions.cpp.

IsZero()

bool HepLib::IsZero

(

const ex &

e

)

key_exists()

bool HepLib::key_exists ( const exmap &  map, const ex &  key  )

inline

Definition at line 293 of file BASIC.h.

LC()

ex HepLib::LC	(	ex	pi1,
		ex	pi2,
		ex	pi3,
		ex	pi4
	)

function similar to LCD in FeynCalc

Parameters

pi1	vector/index in the 1st position
pi2	vector/index in the 2nd position
pi3	vector/index in the 3rd position
pi4	vector/index in the 4th position

Returns

expanded/translated to Eps objects

Definition at line 179 of file Eps.cpp.

let_op() [1/4]

void HepLib::let_op	(	ex &	ex_in,
		int	index1,
		int	index2,
		const ex	item
	)

update index1-th.index2-th of expression with item

Parameters

ex_in	input expression will be update
index1	the index
index2	the index
item	the new item

Definition at line 1560 of file BASIC.cpp.

let_op() [2/4]

void HepLib::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

Parameters

ex_in	input expression will be update
index1	the index
index2	the index
index3	the index
item	the new item

Definition at line 1583 of file BASIC.cpp.

let_op() [3/4]

void HepLib::let_op	(	lst &	ex_in,
		int	index1,
		int	index2,
		const ex	item
	)

update index1-th.index2-th of expression with item

Parameters

ex_in	input expression will be update
index1	the index
index2	the index
item	the new item

Definition at line 1571 of file BASIC.cpp.

let_op() [4/4]

void HepLib::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

Parameters

ex_in	input expression will be update
index1	the index
index2	the index
index3	the index
item	the new item

Definition at line 1595 of file BASIC.cpp.

let_op_append() [1/5]

void HepLib::let_op_append	(	ex &	ex_in,
		const ex	item
	)

append item into expression

Parameters

ex_in	input expression will be update
item	element to be appended to ex_in

Definition at line 1324 of file BASIC.cpp.

let_op_append() [2/5]

void HepLib::let_op_append	(	ex &	ex_in,
		int	index,
		ex const	item
	)

append item into index-th of expression

Parameters

ex_in	input expression will be update
index	the index, index-th should be lst, and item will be append into it
item	element to be appended to index-th of ex_in

Definition at line 1367 of file BASIC.cpp.

let_op_append() [3/5]

void HepLib::let_op_append	(	ex &	ex_in,
		int	index1,
		int	index2,
		ex const	item
	)

append item into index1-th.index2-th of expression

Parameters

ex_in	input expression will be update
index1	the first index
index2	the second index
item	element to be appended to index1-th.index2-th of ex_in

Definition at line 1392 of file BASIC.cpp.

let_op_append() [4/5]

void HepLib::let_op_append	(	lst &	ex_in,
		int	index,
		ex const	item
	)

append item into index-th of expression

Parameters

ex_in	input expression will be update
index	the index, index-th should be lst, and item will be append into it
item	element to be appended to index-th of ex_in

Definition at line 1379 of file BASIC.cpp.

let_op_append() [5/5]

void HepLib::let_op_append	(	lst &	ex_in,
		int	index1,
		int	index2,
		ex const	item
	)

append item into index1-th.index2-th of expression

Parameters

ex_in	input expression will be update
index1	the first index
index2	the second index
item	element to be appended to index1-th.index2-th of ex_in

Definition at line 1405 of file BASIC.cpp.

let_op_prepend() [1/5]

void HepLib::let_op_prepend	(	ex &	ex_in,
		const ex	item
	)

preppend item into expression

Parameters

ex_in	input expression will be update
item	element to be prepended to ex_in

Definition at line 1335 of file BASIC.cpp.

let_op_prepend() [2/5]

void HepLib::let_op_prepend	(	ex &	ex_in,
		int	index,
		ex const	item
	)

prepend item into index-th of expression

Parameters

ex_in	input expression will be update
index	the index, index-th should be lst, and item will be append into it
item	element to be prepended to index-th of ex_in

Definition at line 1417 of file BASIC.cpp.

let_op_prepend() [3/5]

void HepLib::let_op_prepend	(	ex &	ex_in,
		int	index1,
		int	index2,
		ex const	item
	)

prepend item into index1-th.index2-th of expression

Parameters

ex_in	input expression will be update
index1	the first index
index2	the second index
item	element to be prepend to index1-th.index2-th of ex_in

Definition at line 1442 of file BASIC.cpp.

let_op_prepend() [4/5]

void HepLib::let_op_prepend	(	lst &	ex_in,
		int	index,
		ex const	item
	)

prepend item into index-th of expression

Parameters

ex_in	input expression will be update
index	the index, index-th should be lst, and item will be append into it
item	element to be prepended to index-th of ex_in

Definition at line 1429 of file BASIC.cpp.

let_op_prepend() [5/5]

void HepLib::let_op_prepend	(	lst &	ex_in,
		int	index1,
		int	index2,
		ex const	item
	)

prepend item into index1-th.index2-th of expression

Parameters

ex_in	input expression will be update
index1	the first index
index2	the second index
item	element to be prepend to index1-th.index2-th of ex_in

Definition at line 1455 of file BASIC.cpp.

let_op_remove_first() [1/5]

void HepLib::let_op_remove_first

(

ex &

ex_in

)

remove first from expression

Parameters

ex_in

input lst and will be update, first element will be remove

Definition at line 1355 of file BASIC.cpp.

let_op_remove_first() [2/5]

void HepLib::let_op_remove_first	(	ex &	ex_in,
		int	index
	)

remove the first in index-th of expression

Parameters

ex_in	input expression will be update
index	the index

Definition at line 1512 of file BASIC.cpp.

let_op_remove_first() [3/5]

void HepLib::let_op_remove_first	(	ex &	ex_in,
		int	index1,
		int	index2
	)

remove the first in index1-th.index2-th of expression

Parameters

ex_in	input expression will be update
index1	the index
index2	the index

Definition at line 1535 of file BASIC.cpp.

let_op_remove_first() [4/5]

void HepLib::let_op_remove_first	(	lst &	ex_in,
		int	index
	)

remove the first in index-th of expression

Parameters

ex_in	input expression will be update
index	the index

Definition at line 1523 of file BASIC.cpp.

let_op_remove_first() [5/5]

void HepLib::let_op_remove_first	(	lst &	ex_in,
		int	index1,
		int	index2
	)

remove the first in index1-th.index2-th of expression

Parameters

ex_in	input expression will be update
index1	the index
index2	the index

Definition at line 1547 of file BASIC.cpp.

let_op_remove_last() [1/5]

void HepLib::let_op_remove_last

(

ex &

ex_in

)

remove last from expression

Parameters

ex_in

input lst and will be update, last element will be remove

Definition at line 1345 of file BASIC.cpp.

let_op_remove_last() [2/5]

void HepLib::let_op_remove_last	(	ex &	ex_in,
		int	index
	)

remove the last in index-th of expression

Parameters

ex_in	input expression will be update
index	the index

Definition at line 1466 of file BASIC.cpp.

let_op_remove_last() [3/5]

void HepLib::let_op_remove_last	(	ex &	ex_in,
		int	index1,
		int	index2
	)

remove the last in index1-th.index2-th of expression

Parameters

ex_in	input expression will be update
index1	the index
index2	the index

Definition at line 1489 of file BASIC.cpp.

let_op_remove_last() [4/5]

void HepLib::let_op_remove_last	(	lst &	ex_in,
		int	index
	)

remove the last in index-th of expression

Parameters

ex_in	input expression will be update
index	the index

Definition at line 1477 of file BASIC.cpp.

let_op_remove_last() [5/5]

void HepLib::let_op_remove_last	(	lst &	ex_in,
		int	index1,
		int	index2
	)

remove the last in index1-th.index2-th of expression

Parameters

ex_in	input expression will be update
index1	the index
index2	the index

Definition at line 1501 of file BASIC.cpp.

letSP() [1/2]

ex & HepLib::letSP

(

const ex &

p

)

return the reference of p.p

Parameters

p	the vector/index

Returns

the refernce of p.p in SP_map, can be used in assignment

Definition at line 263 of file Pair.cpp.

letSP() [2/2]

ex & HepLib::letSP	(	const ex &	p1,
		const ex &	p2
	)

return the reference of p1.p2

Parameters

p1	the 1st vector/index
p2	the 2nd vector/index

Returns

the refernce of p1.p2 in SP_map, can be used in assignment

Definition at line 252 of file Pair.cpp.

LoopUF()

lst HepLib::LoopUF	(	const IBP &	ibp,
		const ex &	idx
	)

UF function.

Parameters

IBP	the IBP object
idx	exponent for the internal Propagator

Returns

lst of {U, F, sign}

Definition at line 318 of file IBP.cpp.

lst2mat()

matrix HepLib::lst2mat

(

const lst &

ls

)

convert 2Dim lst to matrix

Parameters

ls	a 2Dim lst

Returns

the matrix

Definition at line 737 of file BASIC.cpp.

lst2vec()

exvector HepLib::lst2vec

(

const lst &

alst

)

convert lst to exvector

Parameters

alst

input lst

Returns

exvector

Definition at line 911 of file BASIC.cpp.

match_all()

bool HepLib::match_all ( ex  expr, lst  ps  )

inline

Definition at line 73 of file BASIC.h.

match_any()

bool HepLib::match_any ( ex  expr, lst  ps  )

inline

Definition at line 69 of file BASIC.h.

mout()

MMAFormat HepLib::mout

(

cout

)

mu()

const Symbol HepLib::mu

(

"mu"

)

mul2lst()

lst HepLib::mul2lst

(

const ex &

expr

)

convert mul to lst

Parameters

expr	input expression

Returns

lst

Definition at line 933 of file BASIC.cpp.

mulInv()

numeric HepLib::mulInv	(	numeric	a,
		numeric	b
	)

Definition at line 31 of file Rational.cpp.

NA()

const Symbol HepLib::NA

(

"NA"

)

NaN()

const Symbol HepLib::NaN

(

"NaN"

)

ncmul_expand()

ex HepLib::ncmul_expand

(

const ex &

expr

)

Definition at line 600 of file Basic.cpp.

Newton()

ex HepLib::Newton	(	const exvector &	keys,
		const exvector &	values,
		const ex &	d,
		const ex	factor = 1
	)

Definition at line 106 of file Rational.cpp.

nextprime() [1/2]

ex HepLib::nextprime

(

const ex &

n

)

Definition at line 2284 of file BASIC.cpp.

nextprime() [2/2]

ex HepLib::nextprime

(

int

n

)

Definition at line 2288 of file BASIC.cpp.

NF()

const Symbol HepLib::NF

(

"NF"

)

nH()

const Symbol HepLib::nH

(

"nH"

)

nL()

const Symbol HepLib::nL

(

"nL"

)

NN()

ex HepLib::NN	(	ex	expr,
		int	digits
	)

the nuerical evaluation

Parameters

expr	input expression
digits	precision digits

Returns

the nuerical expression

Definition at line 1278 of file BASIC.cpp.

node_number()

long long HepLib::node_number	(	const ex &	expr,
		int	level = 0
	)

normal_fermat()

ex HepLib::normal_fermat	(	const ex &	expr,
		bool	dfactor
	)

return the normalizatied expression, using fermat_numer_denom

Parameters

expr	the input expression
dfactor	true for factorize on the denominator

Returns

the normalized expression: numer/denom

Definition at line 1831 of file BASIC.cpp.

normal_flint()

ex HepLib::normal_flint	(	const ex &	expr,
		int	opt = o_flint
	)

now()

string HepLib::now

(

bool

use_date

)

date/time string

Parameters

use_date

defualt true to include the date in the string

Returns

return date/time string

Definition at line 525 of file BASIC.cpp.

numer_denom_fermat()

ex HepLib::numer_denom_fermat	(	const ex &	expr,
		bool	dfactor
	)

return the numerator and denominator after normalization

Parameters

expr	the input expression
dfactor	true for factorize on the denominator

Returns

a list of { numer, denom }

Definition at line 23 of file Fermat.cpp.

numer_fermat()

ex HepLib::numer_fermat

(

const ex &

expr

)

Definition at line 170 of file Fermat.cpp.

Permutations() [1/2]

void HepLib::Permutations	(	int	n,
		int	m,
		std::function< void(const int *)>	f
	)

Definition at line 220 of file Functions.cpp.

Permutations() [2/2]

void HepLib::Permutations	(	int	n,
		std::function< void(const int *)>	f
	)

Definition at line 213 of file Functions.cpp.

PermutationsR()

void HepLib::PermutationsR	(	int	n,
		int	m,
		std::function< void(const int *)>	f
	)

Definition at line 268 of file Functions.cpp.

pn2mat()

ex HepLib::pn2mat ( ex  ps, ex  ns, ex  vars  )

inline

Definition at line 109 of file Apart.cpp.

pn2p()

ex HepLib::pn2p ( ex  pn )

inline

Definition at line 145 of file Apart.cpp.

PostTree()

void HepLib::PostTree ( const ex &  e, std::function< void(const ex &)>  f  )

inline

Definition at line 679 of file BASIC.h.

power_expand_2()

co_epvec_t HepLib::power_expand_2	(	const co_epvec_t &	co_epv,
		int	n
	)

Definition at line 1077 of file BASIC.cpp.

PreTree()

void HepLib::PreTree ( const ex &  e, std::function< void(const ex &)>  f  )

inline

Definition at line 676 of file BASIC.h.

q2ex()

ex HepLib::q2ex

(

__float128

num

)

__float128 to ex

Parameters

num	a __float128 number

Returns

a ex object for the number

Definition at line 867 of file BASIC.cpp.

Rationalize()

ex HepLib::Rationalize	(	const ex &	e,
		int	dn
	)

Definition at line 2293 of file BASIC.cpp.

RationalReconstruct() [1/2]

numeric HepLib::RationalReconstruct	(	numeric	a,
		numeric	p
	)

Definition at line 8 of file Rational.cpp.

RationalReconstruct() [2/2]

numeric HepLib::RationalReconstruct	(	vector< numeric >	aa,
		vector< numeric >	pp
	)

Definition at line 66 of file Rational.cpp.

REGISTER_FUNCTION() [1/5]

HepLib::REGISTER_FUNCTION	(	a	,
		do_not_evalf_params().print_func< print_dflt >(a_print)
	)

Definition at line 20 of file IBP.cpp.

REGISTER_FUNCTION() [2/5]

HepLib::REGISTER_FUNCTION	(	GMat	,
		do_not_evalf_params().print_func< FCFormat > &GMat_fc_print.conjugate_func(mat_conj).set_return_type(return_types::commutative)
	)		const &

Definition at line 1159 of file Basic.cpp.

REGISTER_FUNCTION() [3/5]

HepLib::REGISTER_FUNCTION	(	HF	,
		do_not_evalf_params()
	)

REGISTER_FUNCTION() [4/5]

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)
	)

REGISTER_FUNCTION() [5/5]

HepLib::REGISTER_FUNCTION	(	TTR	,
		do_not_evalf_params(). conjugate_func(ttr_conj). print_func< FormFormat > &TTR_form_print. print_func< FCFormat > &	TTR_fc_print
	)

reset_precision()

void HepLib::reset_precision

(

)

Definition at line 2323 of file BASIC.cpp.

ReShare() [1/6]

void HepLib::ReShare

(

const ex &

e

)

Definition at line 2250 of file BASIC.cpp.

ReShare() [2/6]

void HepLib::ReShare	(	const ex &	e1,
		const ex &	e2
	)

Definition at line 2260 of file BASIC.cpp.

ReShare() [3/6]

void HepLib::ReShare	(	const ex &	e1,
		const ex &	e2,
		const ex &	e3
	)

Definition at line 2266 of file BASIC.cpp.

ReShare() [4/6]

void HepLib::ReShare

(

const exvector &

ev

)

Definition at line 2273 of file BASIC.cpp.

ReShare() [5/6]

void HepLib::ReShare	(	const exvector &	ev1,
		const exvector &	ev2
	)

Definition at line 2278 of file BASIC.cpp.

ReShare() [6/6]

void HepLib::ReShare

(

const lst &

es

)

Definition at line 2255 of file BASIC.cpp.

RunOS()

string HepLib::RunOS

(

const string &

cmd

)

run symtem command and return the output as string

Parameters

cmd	symtem command

Returns

the command output

Definition at line 571 of file BASIC.cpp.

series_ex() [1/2]

ex HepLib::series_ex	(	ex const &	expr_in,
		ex const &	s0,
		int	sn0
	)

the series like Mathematica, include s^n

Parameters

expr_in	input expression
s0	the variable
sn0	expanded upto sn0 order, include s0^sn0

Returns

the corresponding series

Definition at line 968 of file BASIC.cpp.

series_ex() [2/2]

ex HepLib::series_ex	(	ex const &	expr_in,
		symbol const &	s0,
		int	sn0
	)

the series like Mathematica, include s^n

Parameters

expr_in	input expression
s0	the variable
sn0	expanded upto sn0 order, include s0^sn0

Returns

the corresponding series

Definition at line 980 of file BASIC.cpp.

set_precision()

void HepLib::set_precision	(	long	prec,
		bool	push
	)

Definition at line 2314 of file BASIC.cpp.

sort_lst()

void HepLib::sort_lst	(	lst &	ilst,
		bool	less
	)

sort the list in less order, or the reverse

Parameters

ilst	input lst, will be updated after call
less	true for less order

Definition at line 79 of file Sort.cpp.

sort_lst_by()

void HepLib::sort_lst_by	(	lst &	ilst,
		int	ki,
		bool	less
	)

sort the list in less order, or the reverse

Parameters

ilst	input lst, will be updated after call
ki	the sort key is at .op(n)
less	true for less order

Definition at line 91 of file Sort.cpp.

sort_vec()

void HepLib::sort_vec	(	exvector &	ivec,
		bool	less
	)

sort the list in less order, or the reverse

Parameters

ivec	input exvector, will be updated after call
less	true for less order

Definition at line 54 of file Sort.cpp.

sort_vec_by()

void HepLib::sort_vec_by	(	exvector &	ivec,
		int	ki,
		bool	less
	)

sort the list in less order, or the reverse

Parameters

ivec	input exvector, will be updated after call
ki	the sort key is at .op(n)
less	true for less order

Definition at line 67 of file Sort.cpp.

SortPermutation()

exmap HepLib::SortPermutation	(	const ex &	in_expr,
		const lst &	xs
	)

Sort for all permuations, and return xs w.r.t. 1st permutation.

Parameters

in_expr	the input expression, as the sort key, no need of polynormial of xs
xs	the permutation list

Returns

x-replacement

Definition at line 204 of file IBP.cpp.

sp() [1/2]

ex HepLib::sp

(

const ex &

a

)

Definition at line 241 of file Pair.cpp.

SP() [1/2]

ex HepLib::SP	(	const ex &	a,
		bool	use_map = false
	)

Definition at line 166 of file Pair.cpp.

sp() [2/2]

ex HepLib::sp	(	const ex &	a,
		const ex &	b
	)

translated the vector dot a.b to a*b, useful in SecDec

Parameters

a	the 1st vector argument or a symbol
b	the 2nd vector or a symbol

Returns

expression with vector name left only

Definition at line 237 of file Pair.cpp.

SP() [2/2]

ex HepLib::SP	(	const ex &	a,
		const ex &	b,
		bool	use_map
	)

Function similar to SPD/FVD in FeynCalc.

Parameters

a	the 1st vector/index
b	the 2nd vector/index
use_map	true for apply the SP_map in the function call

Returns

expanded/translated Pair objects

Definition at line 175 of file Pair.cpp.

SP2sp()

ex HepLib::SP2sp

(

const ex &

exin

)

convert SP(a,b) to sp(a,b)

Parameters

exin	the input expression

Returns

expression with SP(a,b) replaced to sp(a,b)

Definition at line 302 of file Pair.cpp.

sp_map()

exmap HepLib::sp_map

(

)

the SP_map with SP(a,b) replaced to sp(a,b)

Returns

the SP_map with SP(a,b) replaced to sp(a,b)

Definition at line 318 of file Pair.cpp.

split() [1/2]

std::vector< std::string > HepLib::split	(	const std::string &	s,
		char	delimiter
	)

split the string into serveral part, separated by the delimiter

Parameters

s	the input string
delimiter	the char delimiter

Returns

return separated string vector

Definition at line 499 of file BASIC.cpp.

split() [2/2]

vector< std::string > HepLib::split	(	const string &	s,
		char	delimiter
	)

str2ex() [1/2]

ex HepLib::str2ex

(

const string &

expr

)

convert string to ex expression, using Parser internally

Parameters

expr	expression in string format

Returns

the parsed expression

Definition at line 681 of file BASIC.cpp.

str2ex() [2/2]

ex HepLib::str2ex	(	const string &	expr,
		symtab	stab
	)

convert string to ex expression, using Parser internally

Parameters

expr	expression in string format
stab	the symtab

Returns

the parsed expression

Definition at line 670 of file BASIC.cpp.

str2file() [1/2]

void HepLib::str2file	(	char *	buff,
		FILE *	fh
	)

Definition at line 795 of file BASIC.cpp.

str2file() [2/2]

void HepLib::str2file	(	const string &	ostr,
		string	filename
	)

export string to a file

Parameters

ostr	the input string
filename	output file name

Definition at line 787 of file BASIC.cpp.

str2lst() [1/2]

lst HepLib::str2lst

(

const string &

expr

)

convert string to the lst, using Parser internally

Parameters

expr	a lst in string format

Returns

the parsed expression

Definition at line 704 of file BASIC.cpp.

str2lst() [2/2]

lst HepLib::str2lst	(	const string &	expr,
		symtab	stab
	)

convert string to the lst, using Parser internally

Parameters

expr	a lst in string format
stab	the symtab

Returns

the parsed expression

Definition at line 693 of file BASIC.cpp.

string_contain()

bool HepLib::string_contain	(	const string &	fstr,
		const string &	mstr
	)

Definition at line 180 of file Functions.cpp.

string_end_with()

bool HepLib::string_end_with	(	const string &	fstr,
		const string &	estr
	)

Definition at line 172 of file Functions.cpp.

string_replace_all()

void HepLib::string_replace_all	(	string &	str,
		const string &	from,
		const string &	to
	)

Definition at line 148 of file Functions.cpp.

string_start_with()

bool HepLib::string_start_with	(	const string &	fstr,
		const string &	sstr
	)

Definition at line 164 of file Functions.cpp.

string_trim()

void HepLib::string_trim

(

string &

str

)

Definition at line 156 of file Functions.cpp.

subs()

ex HepLib::subs ( const ex &  e, init_list  sl  )

inline

Definition at line 51 of file BASIC.h.

subs_w() [1/2]

void HepLib::subs_w

(

exmap &

repl

)

Definition at line 2238 of file BASIC.cpp.

subs_w() [2/2]

void HepLib::subs_w

(

lst &

repl

)

Definition at line 2243 of file BASIC.cpp.

syms()

lst HepLib::syms ( const exvector &  ev )

inline

Definition at line 61 of file FIRE.cpp.

TF()

const Symbol HepLib::TF

(

"TF"

)

Thiele()

ex HepLib::Thiele	(	const exvector &	keys,
		const exvector &	values,
		const ex &	d
	)

Definition at line 81 of file Rational.cpp.

TIR()

ex HepLib::TIR	(	const ex &	expr_in,
		const lst &	loop_ps,
		const lst &	ext_ps
	)

Tensor Index Reduction, note that we only handle numerator.

Parameters

expr_in	expression
loop_ps	lst contains loop vectors
ext_ps	lst constains external vectors

Returns

TIR result

Definition at line 119 of file TIR.cpp.

ToCACF()

ex HepLib::ToCACF

(

const ex &

e

)

Definition at line 1220 of file Basic.cpp.

ToCF()

ex HepLib::ToCF

(

const ex &

e

)

Definition at line 1185 of file Basic.cpp.

UF()

lst HepLib::UF	(	const ex &	props,
		const ex &	ns,
		const ex &	loops,
		const ex &	tloops,
		const ex &	lsubs,
		const ex &	tsubs
	)

UF function, from FIRE.m.

Parameters

ps	the list of propagator
ns	the list of exponent
loops	the list of loop momenta
tloops	the list of transverse/quasi momenta
lsubs	the replacements for loops
tsubs	the replacements for tloops

Returns

lst of {U1, U2, F, sign}

Definition at line 428 of file IBP.cpp.

UnContract()

ex HepLib::UnContract	(	const ex	expr,
		const lst &	loop_ps,
		const lst &	ext_ps = lst{}
	)

Definition at line 43 of file TIR.cpp.

vec2lst()

lst HepLib::vec2lst

(

const exvector &

ev

)

convert exvector to lst

Parameters

exvec

input exvector

Returns

lst

Definition at line 902 of file BASIC.cpp.

vs()

const Symbol HepLib::vs

(

"vs"

)

vz()

const Symbol HepLib::vz

(

"vz"

)

xlst() [1/2]

lst HepLib::xlst	(	int	bi,
		int	ei
	)

return a lst: x(bi), x(bi+1), ..., x(ei)

Parameters

bi	start index
ei	end index

Returns

the x lst

Definition at line 946 of file BASIC.cpp.

xlst() [2/2]

lst HepLib::xlst

(

int

ei

)

return a lst: x(0), x(1), ..., x(ei)

Parameters

ei

end index

Returns

the x lst

Definition at line 957 of file BASIC.cpp.

xPositive()

bool HepLib::xPositive

(

ex const

expr

)

check the expr is xPositive, i.e., each x-monomial item is postive

Parameters

expr	input expression

Returns

xPositive or not

Definition at line 1290 of file BASIC.cpp.

xSign()

int HepLib::xSign

(

ex const

expr

)

the always sign for expr

Parameters

expr	input expression

Returns

1 for xPositive exprs, -1 when -expr is xPositive, 0 for others

Definition at line 1312 of file BASIC.cpp.

Variable Documentation

_o_

int HepLib::_o_ = 0

Definition at line 106 of file Init.cpp.

Apart_using_fermat

bool HepLib::Apart_using_fermat = true

Definition at line 212 of file Init.cpp.

as

const Symbol HepLib::as("as")

CA

const Symbol HepLib::CA("CA")

cache_limit

long long HepLib::cache_limit = -1

Definition at line 157 of file Init.cpp.

CF

const Symbol HepLib::CF("CF")

cln_prec_stack

std::stack< cln::float_format_t > HepLib::cln_prec_stack

Definition at line 362 of file Init.cpp.

Color_HighLight

const char * HepLib::Color_HighLight = WHITE

Definition at line 248 of file BASIC.cpp.

d

const Symbol HepLib::d("d")

Debug

bool HepLib::Debug = false

Definition at line 144 of file Init.cpp.

digits_stack

std::stack< long > HepLib::digits_stack

Definition at line 363 of file Init.cpp.

ep

const Symbol HepLib::ep("ep")

eps

const Symbol HepLib::eps("eps")

epz

const Symbol HepLib::epz("epz")

ErrColor

const char * HepLib::ErrColor = RED

Definition at line 246 of file BASIC.cpp.

error_pass_dp

slong HepLib::error_pass_dp = 100

Definition at line 351 of file Init.cpp.

fcout

FCFormat HepLib::fcout(cout)

fermat_using_array

int HepLib::fermat_using_array = 0

Definition at line 154 of file Init.cpp.

fermat_weight

map< ex, long long, ex_is_less > HepLib::fermat_weight

Definition at line 155 of file Init.cpp.

form_expand_all

const int HepLib::form_expand_all = 4

Definition at line 210 of file Init.cpp.

form_expand_ci

const int HepLib::form_expand_ci = 2

Definition at line 208 of file Init.cpp.

form_expand_li

const int HepLib::form_expand_li = 3

Definition at line 209 of file Init.cpp.

form_expand_mode

int HepLib::form_expand_mode = form_expand_tr

Definition at line 211 of file Init.cpp.

form_expand_none

const int HepLib::form_expand_none = 0

Definition at line 206 of file Init.cpp.

form_expand_tr

const int HepLib::form_expand_tr = 1

Definition at line 207 of file Init.cpp.

form_trace_all

const int HepLib::form_trace_all = 1

Definition at line 201 of file Init.cpp.

form_trace_auto

const int HepLib::form_trace_auto = 0

Definition at line 200 of file Init.cpp.

form_trace_each_all

const int HepLib::form_trace_each_all = 2

Definition at line 202 of file Init.cpp.

form_trace_each_each

const int HepLib::form_trace_each_each = 3

Definition at line 203 of file Init.cpp.

form_trace_mode

int HepLib::form_trace_mode = form_trace_auto

Definition at line 204 of file Init.cpp.

form_using_dim4

bool HepLib::form_using_dim4 = false

Definition at line 214 of file Init.cpp.

form_using_gamma5

bool HepLib::form_using_gamma5 = false

Definition at line 215 of file Init.cpp.

form_using_su3

bool HepLib::form_using_su3 = false

Definition at line 213 of file Init.cpp.

GiNaC_Parallel_Batch

int HepLib::GiNaC_Parallel_Batch = 0

Definition at line 149 of file Init.cpp.

GiNaC_Parallel_NB

map< string, int > HepLib::GiNaC_Parallel_NB

Definition at line 150 of file Init.cpp.

GiNaC_Parallel_NP

map< string, int > HepLib::GiNaC_Parallel_NP

Definition at line 147 of file Init.cpp.

GiNaC_Parallel_PRE

map< string, string > HepLib::GiNaC_Parallel_PRE

Definition at line 152 of file Init.cpp.

GiNaC_Parallel_Process

int HepLib::GiNaC_Parallel_Process = -1

Definition at line 146 of file Init.cpp.

GiNaC_Parallel_ReWR

map< string, bool > HepLib::GiNaC_Parallel_ReWR

Definition at line 153 of file Init.cpp.

GiNaC_Parallel_RM

map< string, bool > HepLib::GiNaC_Parallel_RM

Definition at line 151 of file Init.cpp.

GiNaC_Parallel_Verb

map< string, int > HepLib::GiNaC_Parallel_Verb

Definition at line 148 of file Init.cpp.

GMat_using_cache

bool HepLib::GMat_using_cache = true

Definition at line 160 of file Init.cpp.

gs

const Symbol HepLib::gs("gs")

iEpsilon

const iSymbol HepLib::iEpsilon("iEpsilon")

iEpsilonN

const ex HepLib::iEpsilonN = I*pow(ex(10), -50)

Definition at line 141 of file Init.cpp.

iet

const Symbol HepLib::iet("iet")

In_GiNaC_Parallel

bool HepLib::In_GiNaC_Parallel = false

Definition at line 145 of file Init.cpp.

INC_FLAGS

string HepLib::INC_FLAGS = "-I'"+InstallPrefix+"/include' " + "@INC_FLAGS@"

Definition at line 165 of file Init.cpp.

InstallPrefix

string HepLib::InstallPrefix = install_prefix()

Definition at line 164 of file Init.cpp.

LIB_FLAGS

string HepLib::LIB_FLAGS = "-L'"+InstallPrefix+"/lib' -Wl,-rpath,'"+InstallPrefix+"'/lib " + "@LIB_FLAGS@"

Definition at line 166 of file Init.cpp.

MapPreSP

exmap HepLib::MapPreSP

Definition at line 342 of file Init.cpp.

mout

MMAFormat HepLib::mout(cout)

mu

const Symbol HepLib::mu("mu")

NA

const Symbol HepLib::NA("NA")

NaN

const Symbol HepLib::NaN("NaN")

NF

const Symbol HepLib::NF("NF")

nH

const Symbol HepLib::nH("nH")

nL

const Symbol HepLib::nL("nL")

NNDigits

int HepLib::NNDigits = 100

Definition at line 158 of file Init.cpp.

nopat

unsigned HepLib::nopat = GiNaC::subs_options::no_pattern

Definition at line 91 of file Init.cpp.

o_fermat

const int HepLib::o_fermat = (_o_++)

Definition at line 109 of file Init.cpp.

o_fermat_form

const int HepLib::o_fermat_form = (_o_++)

Definition at line 118 of file Init.cpp.

o_fermatfD

const int HepLib::o_fermatfD = (_o_++)

Definition at line 110 of file Init.cpp.

o_fermatN

const int HepLib::o_fermatN = (_o_++)

Definition at line 111 of file Init.cpp.

o_flint

const int HepLib::o_flint = (_o_++)

Definition at line 113 of file Init.cpp.

o_flintf

const int HepLib::o_flintf = (_o_++)

Definition at line 114 of file Init.cpp.

o_flintfD

const int HepLib::o_flintfD = (_o_++)

Definition at line 115 of file Init.cpp.

o_form

const int HepLib::o_form = (_o_++)

Definition at line 112 of file Init.cpp.

o_none

const int HepLib::o_none = (_o_++)

Definition at line 107 of file Init.cpp.

o_normal

const int HepLib::o_normal = (_o_++)

Definition at line 108 of file Init.cpp.

o_normal_fermat

const int HepLib::o_normal_fermat = (_o_++)

Definition at line 116 of file Init.cpp.

o_normal_form

const int HepLib::o_normal_form = (_o_++)

Definition at line 117 of file Init.cpp.

PRE

string HepLib::PRE = " "

Definition at line 143 of file Init.cpp.

SP_map

exmap HepLib::SP_map

Definition at line 184 of file Init.cpp.

TF

const Symbol HepLib::TF("TF")

using_cache

bool HepLib::using_cache = true

Definition at line 156 of file Init.cpp.

Verbose

int HepLib::Verbose = 0

Definition at line 142 of file Init.cpp.

Version

string HepLib::Version = "1.5 @2024-04-28"

Definition at line 85 of file Init.cpp.

vs

const Symbol HepLib::vs("vs")

vz

const Symbol HepLib::vz("vz")

w

ex HepLib::w = wild()

Definition at line 93 of file Init.cpp.

w0

ex HepLib::w0 = wild(0)

Definition at line 499 of file BASIC.h.

w1

ex HepLib::w1 = wild(1)

Definition at line 499 of file BASIC.h.

w2

ex HepLib::w2 = wild(2)

Definition at line 499 of file BASIC.h.

w3

ex HepLib::w3 = wild(3)

Definition at line 499 of file BASIC.h.

w4

ex HepLib::w4 = wild(4)

Definition at line 499 of file BASIC.h.

w5

ex HepLib::w5 = wild(5)

Definition at line 499 of file BASIC.h.

w6

ex HepLib::w6 = wild(6)

Definition at line 499 of file BASIC.h.

w7

ex HepLib::w7 = wild(7)

Definition at line 499 of file BASIC.h.

w8

ex HepLib::w8 = wild(8)

Definition at line 499 of file BASIC.h.

w9

ex HepLib::w9 = wild(9)

Definition at line 499 of file BASIC.h.

WarnColor

const char * HepLib::WarnColor = MAGENTA

Definition at line 247 of file BASIC.cpp.