X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Finifcns.h;h=b8349d1bba898d93e292debc4aef6ecbc313639d;hp=6a7efbe610a24930690b1462eb42f02427585f9a;hb=83a7ee99a947cbbf331018b803ad6be43a9ccd45;hpb=0117bd6ef4af029934703940d59e1c70866937b0 diff --git a/ginac/inifcns.h b/ginac/inifcns.h index 6a7efbe6..b8349d1b 100644 --- a/ginac/inifcns.h +++ b/ginac/inifcns.h @@ -3,7 +3,7 @@ * Interface to GiNaC's initially known functions. */ /* - * GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany + * GiNaC Copyright (C) 1999-2008 Johannes Gutenberg University Mainz, Germany * * This program is free software; you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by @@ -17,20 +17,33 @@ * * 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__ +#include "numeric.h" #include "function.h" #include "ex.h" namespace GiNaC { +/** 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) @@ -88,18 +101,56 @@ DECLARE_FUNCTION_1P(Li2) /** Trilogarithm. */ DECLARE_FUNCTION_1P(Li3) +/** Derivatives of Riemann's Zeta-function. */ +DECLARE_FUNCTION_2P(zetaderiv) + // overloading at work: we cannot use the macros here -/** Riemann's Zeta-function. */ -extern const unsigned function_index_zeta1; -inline function zeta(const ex & p1) { - return function(function_index_zeta1, p1); +/** 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)); } -/** Derivatives of Riemann's Zeta-function. */ -extern const unsigned function_index_zeta2; -inline function zeta(const ex & p1, const ex & p2) { - return function(function_index_zeta2, p1, p2); +/** 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) @@ -109,14 +160,21 @@ DECLARE_FUNCTION_2P(beta) // overloading at work: we cannot use the macros here /** Psi-function (aka digamma-function). */ -extern const unsigned function_index_psi1; -inline function psi(const ex & p1) { - return function(function_index_psi1, p1); +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). */ -extern const unsigned function_index_psi2; -inline function psi(const ex & p1, const ex & p2) { - return function(function_index_psi2, p1, p2); +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. */ @@ -128,43 +186,30 @@ DECLARE_FUNCTION_2P(binomial) /** Order term function (for truncated power series). */ DECLARE_FUNCTION_1P(Order) -/** Inert partial differentiation operator. */ -DECLARE_FUNCTION_2P(Derivative) - -ex lsolve(const ex &eqns, const ex &symbols); - -/** Power of non-commutative basis. */ -ex ncpow(const ex & basis, unsigned exponent); - -/** Symmetrize expression over a set of objects (symbols, indices). */ -ex symmetrize(const ex & e, exvector::const_iterator first, exvector::const_iterator last); - -/** Symmetrize expression over a set of objects (symbols, indices). */ -inline ex symmetrize(const ex & e, const exvector & v) -{ - return symmetrize(e, v.begin(), v.end()); -} - -/** Symmetrize expression over a list of objects (symbols, indices). */ -ex symmetrize(const ex & e, const lst & l); - -/** Antisymmetrize expression over a set of objects (symbols, indices). */ -ex antisymmetrize(const ex & e, exvector::const_iterator first, exvector::const_iterator last); - -/** Antisymmetrize expression over a set of objects (symbols, indices). */ -inline ex antisymmetrize(const ex & e, const exvector & v) -{ - return antisymmetrize(e, v.begin(), v.end()); -} - -/** Antisymmetrize expression over a list of objects (symbols, indices). */ -ex antisymmetrize(const ex & e, const lst & l); +ex lsolve(const ex &eqns, const ex &symbols, unsigned options = solve_algo::automatic); +/** 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); } +/** 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__