* 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
*
* 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)
/** 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<typename T1>
+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<typename T1, typename T2>
+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<zeta_SERIAL>(const ex& x)
+{
+ return is_the_function<zeta1_SERIAL>(x) || is_the_function<zeta2_SERIAL>(x);
}
+// overloading at work: we cannot use the macros here
+/** Generalized multiple polylogarithm. */
+class G2_SERIAL { public: static unsigned serial; };
+template<typename T1, typename T2>
+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<typename T1, typename T2, typename T3>
+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<G_SERIAL>(const ex& x)
+{
+ return is_the_function<G2_SERIAL>(x) || is_the_function<G3_SERIAL>(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)
// 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<typename T1>
+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<typename T1, typename T2>
+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<psi_SERIAL>(const ex & x)
+{
+ return is_the_function<psi1_SERIAL>(x) || is_the_function<psi2_SERIAL>(x);
}
/** Factorial function. */
/** 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);
+ex lsolve(const ex &eqns, const ex &symbols, unsigned options = solve_algo::automatic);
-/** 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());
-}
-
-/** 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());
-}
-
-/** Symmetrize expression by cyclic permuation over a set of objects
- * (symbols, indices). */
-ex symmetrize_cyclic(const ex & e, exvector::const_iterator first, exvector::const_iterator last);
-
-/** Symmetrize expression by cyclic permutation over a set of objects
- * (symbols, indices). */
-inline ex symmetrize_cyclic(const ex & e, const exvector & v)
-{
- return symmetrize(e, v.begin(), v.end());
-}
+/** 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__
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