* Implementation of the Zeta-function and some related stuff. */
/*
- * GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2003 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
#include <stdexcept>
#include "inifcns.h"
-#include "ex.h"
#include "constant.h"
#include "numeric.h"
#include "power.h"
#include "symbol.h"
+#include "operators.h"
#include "utils.h"
-#ifndef NO_NAMESPACE_GINAC
namespace GiNaC {
-#endif // ndef NO_NAMESPACE_GINAC
//////////
// Riemann's Zeta-function
static ex zeta1_evalf(const ex & x)
{
- BEGIN_TYPECHECK
- TYPECHECK(x,numeric)
- END_TYPECHECK(zeta(x))
-
- return zeta(ex_to_numeric(x));
+ if (is_exactly_a<numeric>(x)) {
+ try {
+ return zeta(ex_to<numeric>(x));
+ } catch (const dunno &e) { }
+ }
+
+ return zeta(x).hold();
}
static ex zeta1_eval(const ex & x)
{
- if (x.info(info_flags::numeric)) {
- numeric y = ex_to_numeric(x);
- // trap integer arguments:
- if (y.is_integer()) {
- if (y.is_zero())
- return -_ex1_2();
- if (x.is_equal(_ex1()))
- throw(std::domain_error("zeta(1): infinity"));
- if (x.info(info_flags::posint)) {
- if (x.info(info_flags::odd))
- return zeta(x).hold();
- else
- return abs(bernoulli(y))*pow(Pi,x)*pow(_num2(),y-_num1())/factorial(y);
- } else {
- if (x.info(info_flags::odd))
- return -bernoulli(_num1()-y)/(_num1()-y);
- else
- return _num0();
- }
- }
- }
- return zeta(x).hold();
+ if (x.info(info_flags::numeric)) {
+ const numeric &y = ex_to<numeric>(x);
+ // trap integer arguments:
+ if (y.is_integer()) {
+ if (y.is_zero())
+ return _ex_1_2;
+ if (y.is_equal(_num1))
+ throw(std::domain_error("zeta(1): infinity"));
+ if (y.info(info_flags::posint)) {
+ if (y.info(info_flags::odd))
+ return zeta(x).hold();
+ else
+ return abs(bernoulli(y))*pow(Pi,y)*pow(_num2,y-_num1)/factorial(y);
+ } else {
+ if (y.info(info_flags::odd))
+ return -bernoulli(_num1-y)/(_num1-y);
+ else
+ return _ex0;
+ }
+ }
+ // zeta(float)
+ if (y.info(info_flags::numeric) && !y.info(info_flags::crational))
+ return zeta1_evalf(x);
+ }
+ return zeta(x).hold();
}
static ex zeta1_deriv(const ex & x, unsigned deriv_param)
{
- GINAC_ASSERT(deriv_param==0);
-
- return zeta(_ex1(), x);
+ GINAC_ASSERT(deriv_param==0);
+
+ return zeta(_ex1, x);
}
-const unsigned function_index_zeta1 =
- function::register_new(function_options("zeta").
- eval_func(zeta1_eval).
- evalf_func(zeta1_evalf).
- derivative_func(zeta1_deriv).
- overloaded(2));
+unsigned zeta1_SERIAL::serial =
+ function::register_new(function_options("zeta").
+ eval_func(zeta1_eval).
+ evalf_func(zeta1_evalf).
+ derivative_func(zeta1_deriv).
+ latex_name("\\zeta").
+ overloaded(2));
//////////
// Derivatives of Riemann's Zeta-function zeta(0,x)==zeta(x)
static ex zeta2_eval(const ex & n, const ex & x)
{
- if (n.info(info_flags::numeric)) {
- // zeta(0,x) -> zeta(x)
- if (n.is_zero())
- return zeta(x);
- }
-
- return zeta(n, x).hold();
+ if (n.info(info_flags::numeric)) {
+ // zeta(0,x) -> zeta(x)
+ if (n.is_zero())
+ return zeta(x);
+ }
+
+ return zeta(n, x).hold();
}
static ex zeta2_deriv(const ex & n, const ex & x, unsigned deriv_param)
{
- GINAC_ASSERT(deriv_param<2);
-
- if (deriv_param==0) {
- // d/dn zeta(n,x)
- throw(std::logic_error("cannot diff zeta(n,x) with respect to n"));
- }
- // d/dx psi(n,x)
- return zeta(n+1,x);
+ GINAC_ASSERT(deriv_param<2);
+
+ if (deriv_param==0) {
+ // d/dn zeta(n,x)
+ throw(std::logic_error("cannot diff zeta(n,x) with respect to n"));
+ }
+ // d/dx psi(n,x)
+ return zeta(n+1,x);
}
-const unsigned function_index_zeta2 =
- function::register_new(function_options("zeta").
- eval_func(zeta2_eval).
- derivative_func(zeta2_deriv).
- overloaded(2));
+unsigned zeta2_SERIAL::serial =
+ function::register_new(function_options("zeta").
+ eval_func(zeta2_eval).
+ derivative_func(zeta2_deriv).
+ latex_name("\\zeta").
+ overloaded(2));
-#ifndef NO_NAMESPACE_GINAC
} // namespace GiNaC
-#endif // ndef NO_NAMESPACE_GINAC