3 * Interface to GiNaC's initially known functions. */
6 * GiNaC Copyright (C) 1999-2007 Johannes Gutenberg University Mainz, Germany
8 * This program is free software; you can redistribute it and/or modify
9 * it under the terms of the GNU General Public License as published by
10 * the Free Software Foundation; either version 2 of the License, or
11 * (at your option) any later version.
13 * This program is distributed in the hope that it will be useful,
14 * but WITHOUT ANY WARRANTY; without even the implied warranty of
15 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
16 * GNU General Public License for more details.
18 * You should have received a copy of the GNU General Public License
19 * along with this program; if not, write to the Free Software
20 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
23 #ifndef __GINAC_INIFCNS_H__
24 #define __GINAC_INIFCNS_H__
32 /** Complex conjugate. */
33 DECLARE_FUNCTION_1P(conjugate_function)
36 DECLARE_FUNCTION_1P(real_part_function)
38 /** Imaginary part. */
39 DECLARE_FUNCTION_1P(imag_part_function)
41 /** Absolute value. */
42 DECLARE_FUNCTION_1P(abs)
45 DECLARE_FUNCTION_1P(step)
48 DECLARE_FUNCTION_1P(csgn)
50 /** Eta function: log(a*b) == log(a) + log(b) + eta(a, b). */
51 DECLARE_FUNCTION_2P(eta)
54 DECLARE_FUNCTION_1P(sin)
57 DECLARE_FUNCTION_1P(cos)
60 DECLARE_FUNCTION_1P(tan)
62 /** Exponential function. */
63 DECLARE_FUNCTION_1P(exp)
65 /** Natural logarithm. */
66 DECLARE_FUNCTION_1P(log)
68 /** Inverse sine (arc sine). */
69 DECLARE_FUNCTION_1P(asin)
71 /** Inverse cosine (arc cosine). */
72 DECLARE_FUNCTION_1P(acos)
74 /** Inverse tangent (arc tangent). */
75 DECLARE_FUNCTION_1P(atan)
77 /** Inverse tangent with two arguments. */
78 DECLARE_FUNCTION_2P(atan2)
80 /** Hyperbolic Sine. */
81 DECLARE_FUNCTION_1P(sinh)
83 /** Hyperbolic Cosine. */
84 DECLARE_FUNCTION_1P(cosh)
86 /** Hyperbolic Tangent. */
87 DECLARE_FUNCTION_1P(tanh)
89 /** Inverse hyperbolic Sine (area hyperbolic sine). */
90 DECLARE_FUNCTION_1P(asinh)
92 /** Inverse hyperbolic Cosine (area hyperbolic cosine). */
93 DECLARE_FUNCTION_1P(acosh)
95 /** Inverse hyperbolic Tangent (area hyperbolic tangent). */
96 DECLARE_FUNCTION_1P(atanh)
99 DECLARE_FUNCTION_1P(Li2)
102 DECLARE_FUNCTION_1P(Li3)
104 /** Derivatives of Riemann's Zeta-function. */
105 DECLARE_FUNCTION_2P(zetaderiv)
107 // overloading at work: we cannot use the macros here
108 /** Multiple zeta value including Riemann's zeta-function. */
109 class zeta1_SERIAL { public: static unsigned serial; };
110 template<typename T1>
111 inline function zeta(const T1& p1) {
112 return function(zeta1_SERIAL::serial, ex(p1));
114 /** Alternating Euler sum or colored MZV. */
115 class zeta2_SERIAL { public: static unsigned serial; };
116 template<typename T1, typename T2>
117 inline function zeta(const T1& p1, const T2& p2) {
118 return function(zeta2_SERIAL::serial, ex(p1), ex(p2));
121 template<> inline bool is_the_function<zeta_SERIAL>(const ex& x)
123 return is_the_function<zeta1_SERIAL>(x) || is_the_function<zeta2_SERIAL>(x);
126 // overloading at work: we cannot use the macros here
127 /** Generalized multiple polylogarithm. */
128 class G2_SERIAL { public: static unsigned serial; };
129 template<typename T1, typename T2>
130 inline function G(const T1& x, const T2& y) {
131 return function(G2_SERIAL::serial, ex(x), ex(y));
133 /** Generalized multiple polylogarithm with explicit imaginary parts. */
134 class G3_SERIAL { public: static unsigned serial; };
135 template<typename T1, typename T2, typename T3>
136 inline function G(const T1& x, const T2& s, const T3& y) {
137 return function(G3_SERIAL::serial, ex(x), ex(s), ex(y));
140 template<> inline bool is_the_function<G_SERIAL>(const ex& x)
142 return is_the_function<G2_SERIAL>(x) || is_the_function<G3_SERIAL>(x);
145 /** Polylogarithm and multiple polylogarithm. */
146 DECLARE_FUNCTION_2P(Li)
148 /** Nielsen's generalized polylogarithm. */
149 DECLARE_FUNCTION_3P(S)
151 /** Harmonic polylogarithm. */
152 DECLARE_FUNCTION_2P(H)
154 /** Gamma-function. */
155 DECLARE_FUNCTION_1P(lgamma)
156 DECLARE_FUNCTION_1P(tgamma)
158 /** Beta-function. */
159 DECLARE_FUNCTION_2P(beta)
161 // overloading at work: we cannot use the macros here
162 /** Psi-function (aka digamma-function). */
163 class psi1_SERIAL { public: static unsigned serial; };
164 template<typename T1>
165 inline function psi(const T1 & p1) {
166 return function(psi1_SERIAL::serial, ex(p1));
168 /** Derivatives of Psi-function (aka polygamma-functions). */
169 class psi2_SERIAL { public: static unsigned serial; };
170 template<typename T1, typename T2>
171 inline function psi(const T1 & p1, const T2 & p2) {
172 return function(psi2_SERIAL::serial, ex(p1), ex(p2));
175 template<> inline bool is_the_function<psi_SERIAL>(const ex & x)
177 return is_the_function<psi1_SERIAL>(x) || is_the_function<psi2_SERIAL>(x);
180 /** Factorial function. */
181 DECLARE_FUNCTION_1P(factorial)
183 /** Binomial function. */
184 DECLARE_FUNCTION_2P(binomial)
186 /** Order term function (for truncated power series). */
187 DECLARE_FUNCTION_1P(Order)
189 ex lsolve(const ex &eqns, const ex &symbols, unsigned options = solve_algo::automatic);
191 /** Find a real root of real-valued function f(x) numerically within a given
192 * interval. The function must change sign across interval. Uses Newton-
193 * Raphson method combined with bisection in order to guarantee convergence.
195 * @param f Function f(x)
196 * @param x Symbol f(x)
197 * @param x1 lower interval limit
198 * @param x2 upper interval limit
199 * @exception runtime_error (if interval is invalid). */
200 const numeric fsolve(const ex& f, const symbol& x, const numeric& x1, const numeric& x2);
202 /** Check whether a function is the Order (O(n)) function. */
203 inline bool is_order_function(const ex & e)
205 return is_ex_the_function(e, Order);
208 /** Converts a given list containing parameters for H in Remiddi/Vermaseren notation into
209 * the corresponding GiNaC functions.
211 ex convert_H_to_Li(const ex& parameterlst, const ex& arg);
215 #endif // ndef __GINAC_INIFCNS_H__