X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Finifcns.h;h=0c1526c5aa2ddb859c662b1d6460b7c3f487ba59;hp=095abf7cd5427cf1428feaf5f8ba319009ae0677;hb=e5eeee53d814cedc12cd725e76b0eb87859cdd77;hpb=66c0f31c678e6c1938d637636b230ea376c157c1 diff --git a/ginac/inifcns.h b/ginac/inifcns.h index 095abf7c..0c1526c5 100644 --- a/ginac/inifcns.h +++ b/ginac/inifcns.h @@ -1,8 +1,9 @@ /** @file inifcns.h * - * Interface to GiNaC's initially known functions. - * - * GiNaC Copyright (C) 1999 Johannes Gutenberg University Mainz, Germany + * Interface to GiNaC's initially known functions. */ + +/* + * GiNaC Copyright (C) 1999-2011 Johannes Gutenberg University Mainz, Germany * * This program is free software; you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by @@ -16,14 +17,38 @@ * * You should have received a copy of the GNU General Public License * along with this program; if not, write to the Free Software - * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA + * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA */ -#ifndef __GINAC_INIFCNS_H__ -#define __GINAC_INIFCNS_H__ +#ifndef GINAC_INIFCNS_H +#define GINAC_INIFCNS_H + +#include "numeric.h" +#include "function.h" +#include "ex.h" + +namespace GiNaC { -#include -#include +/** Complex conjugate. */ +DECLARE_FUNCTION_1P(conjugate_function) + +/** Real part. */ +DECLARE_FUNCTION_1P(real_part_function) + +/** Imaginary part. */ +DECLARE_FUNCTION_1P(imag_part_function) + +/** Absolute value. */ +DECLARE_FUNCTION_1P(abs) + +/** Step function. */ +DECLARE_FUNCTION_1P(step) + +/** Complex sign. */ +DECLARE_FUNCTION_1P(csgn) + +/** Eta function: log(a*b) == log(a) + log(b) + eta(a, b). */ +DECLARE_FUNCTION_2P(eta) /** Sine. */ DECLARE_FUNCTION_1P(sin) @@ -76,9 +101,82 @@ DECLARE_FUNCTION_1P(Li2) /** Trilogarithm. */ DECLARE_FUNCTION_1P(Li3) -/** Gamma function. */ -DECLARE_FUNCTION_1P(gamma) +/** Derivatives of Riemann's Zeta-function. */ +DECLARE_FUNCTION_2P(zetaderiv) + +// overloading at work: we cannot use the macros here +/** Multiple zeta value including Riemann's zeta-function. */ +class zeta1_SERIAL { public: static unsigned serial; }; +template +inline function zeta(const T1& p1) { + return function(zeta1_SERIAL::serial, ex(p1)); +} +/** Alternating Euler sum or colored MZV. */ +class zeta2_SERIAL { public: static unsigned serial; }; +template +inline function zeta(const T1& p1, const T2& p2) { + return function(zeta2_SERIAL::serial, ex(p1), ex(p2)); +} +class zeta_SERIAL; +template<> inline bool is_the_function(const ex& x) +{ + return is_the_function(x) || is_the_function(x); +} +// overloading at work: we cannot use the macros here +/** Generalized multiple polylogarithm. */ +class G2_SERIAL { public: static unsigned serial; }; +template +inline function G(const T1& x, const T2& y) { + return function(G2_SERIAL::serial, ex(x), ex(y)); +} +/** Generalized multiple polylogarithm with explicit imaginary parts. */ +class G3_SERIAL { public: static unsigned serial; }; +template +inline function G(const T1& x, const T2& s, const T3& y) { + return function(G3_SERIAL::serial, ex(x), ex(s), ex(y)); +} +class G_SERIAL; +template<> inline bool is_the_function(const ex& x) +{ + return is_the_function(x) || is_the_function(x); +} + +/** Polylogarithm and multiple polylogarithm. */ +DECLARE_FUNCTION_2P(Li) + +/** Nielsen's generalized polylogarithm. */ +DECLARE_FUNCTION_3P(S) + +/** Harmonic polylogarithm. */ +DECLARE_FUNCTION_2P(H) + +/** Gamma-function. */ +DECLARE_FUNCTION_1P(lgamma) +DECLARE_FUNCTION_1P(tgamma) + +/** Beta-function. */ +DECLARE_FUNCTION_2P(beta) + +// overloading at work: we cannot use the macros here +/** Psi-function (aka digamma-function). */ +class psi1_SERIAL { public: static unsigned serial; }; +template +inline function psi(const T1 & p1) { + return function(psi1_SERIAL::serial, ex(p1)); +} +/** Derivatives of Psi-function (aka polygamma-functions). */ +class psi2_SERIAL { public: static unsigned serial; }; +template +inline function psi(const T1 & p1, const T2 & p2) { + return function(psi2_SERIAL::serial, ex(p1), ex(p2)); +} +class psi_SERIAL; +template<> inline bool is_the_function(const ex & x) +{ + return is_the_function(x) || is_the_function(x); +} + /** Factorial function. */ DECLARE_FUNCTION_1P(factorial) @@ -88,13 +186,30 @@ DECLARE_FUNCTION_2P(binomial) /** Order term function (for truncated power series). */ DECLARE_FUNCTION_1P(Order) -ex lsolve(ex const &eqns, ex const &symbols); +ex lsolve(const ex &eqns, const ex &symbols, unsigned options = solve_algo::automatic); -ex ncpower(ex const &basis, unsigned exponent); - -inline bool is_order_function(ex const & e) +/** Find a real root of real-valued function f(x) numerically within a given + * interval. The function must change sign across interval. Uses Newton- + * Raphson method combined with bisection in order to guarantee convergence. + * + * @param f Function f(x) + * @param x Symbol f(x) + * @param x1 lower interval limit + * @param x2 upper interval limit + * @exception runtime_error (if interval is invalid). */ +const numeric fsolve(const ex& f, const symbol& x, const numeric& x1, const numeric& x2); + +/** Check whether a function is the Order (O(n)) function. */ +inline bool is_order_function(const ex & e) { return is_ex_the_function(e, Order); } -#endif // ndef __GINAC_INIFCNS_H__ +/** Converts a given list containing parameters for H in Remiddi/Vermaseren notation into + * the corresponding GiNaC functions. + */ +ex convert_H_to_Li(const ex& parameterlst, const ex& arg); + +} // namespace GiNaC + +#endif // ndef GINAC_INIFCNS_H