GiNaC/ginac/numeric.h

/** @file numeric.h
 *
 *  Makes the interface to the underlying bignum package available. */

/*
 *  GiNaC Copyright (C) 1999-2006 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
 *  the Free Software Foundation; either version 2 of the License, or
 *  (at your option) any later version.
 *
 *  This program is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *  GNU General Public License for more details.
 *
 *  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., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
 */

#ifndef __GINAC_NUMERIC_H__
#define __GINAC_NUMERIC_H__

#include "basic.h"
#include "ex.h"

#include <stdexcept>
#include <vector>

#include <cln/complex.h>

#if defined(G__CINTVERSION) && !defined(__MAKECINT__)
// Cint @$#$! doesn't like forward declaring classes used for casting operators
// so we have to include the definition of cln::cl_N here, but it is enough to
// do so for the compiler, hence the !defined(__MAKECINT__).
  #include <cln/complex_class.h>
#endif

namespace GiNaC {

/** Function pointer to implement callbacks in the case 'Digits' gets changed.
 *  Main purpose of such callbacks is to adjust look-up tables of certain
 *  functions to the new precision. Parameter contains the signed difference
 *  between new Digits and old Digits. */
typedef void (* digits_changed_callback)(long);

/** This class is used to instantiate a global singleton object Digits
 *  which behaves just like Maple's Digits.  We need an object rather 
 *  than a dumber basic type since as a side-effect we let it change
 *  cl_default_float_format when it gets changed.  The only other
 *  meaningful thing to do with it is converting it to an unsigned,
 *  for temprary storing its value e.g.  The user must not create an
 *  own working object of this class!  Since C++ forces us to make the
 *  class definition visible in order to use an object we put in a
 *  flag which prevents other objects of that class to be created. */
class _numeric_digits
{
// member functions
public:
        _numeric_digits();
        _numeric_digits& operator=(long prec);
        operator long();
        void print(std::ostream& os) const;
        void add_callback(digits_changed_callback callback);
// member variables
private:
        long digits;                        ///< Number of decimal digits
        static bool too_late;               ///< Already one object present
        // Holds a list of functions that get called when digits is changed.
        std::vector<digits_changed_callback> callbacklist;
};


/** Exception class thrown when a singularity is encountered. */
class pole_error : public std::domain_error {
public:
        explicit pole_error(const std::string& what_arg, int degree);
        int degree() const;
private:
        int deg;
};


/** This class is a wrapper around CLN-numbers within the GiNaC class
 *  hierarchy. Objects of this type may directly be created by the user.*/
class numeric : public basic
{
        GINAC_DECLARE_REGISTERED_CLASS(numeric, basic)
        
// member functions
        
        // other constructors
public:
        numeric(int i);
        numeric(unsigned int i);
        numeric(long i);
        numeric(unsigned long i);
        numeric(long numer, long denom);
        numeric(double d);
        numeric(const char *);
        
        // functions overriding virtual functions from base classes
public:
        unsigned precedence() const {return 30;}
        bool info(unsigned inf) const;
        bool is_polynomial(const ex & var) const;
        int degree(const ex & s) const;
        int ldegree(const ex & s) const;
        ex coeff(const ex & s, int n = 1) const;
        bool has(const ex &other, unsigned options = 0) const;
        ex eval(int level = 0) const;
        ex evalf(int level = 0) const;
        ex subs(const exmap & m, unsigned options = 0) const { return subs_one_level(m, options); } // overwrites basic::subs() for performance reasons
        ex normal(exmap & repl, exmap & rev_lookup, int level = 0) const;
        ex to_rational(exmap & repl) const;
        ex to_polynomial(exmap & repl) const;
        numeric integer_content() const;
        ex smod(const numeric &xi) const;
        numeric max_coefficient() const;
        ex conjugate() const;
protected:
        /** Implementation of ex::diff for a numeric always returns 0.
         *  @see ex::diff */
        ex derivative(const symbol &s) const { return 0; }
        bool is_equal_same_type(const basic &other) const;
        unsigned calchash() const;
        
        // new virtual functions which can be overridden by derived classes
        // (none)
        
        // non-virtual functions in this class
public:
        const numeric add(const numeric &other) const;
        const numeric sub(const numeric &other) const;
        const numeric mul(const numeric &other) const;
        const numeric div(const numeric &other) const;
        const numeric power(const numeric &other) const;
        const numeric & add_dyn(const numeric &other) const;
        const numeric & sub_dyn(const numeric &other) const;
        const numeric & mul_dyn(const numeric &other) const;
        const numeric & div_dyn(const numeric &other) const;
        const numeric & power_dyn(const numeric &other) const;
        const numeric & operator=(int i);
        const numeric & operator=(unsigned int i);
        const numeric & operator=(long i);
        const numeric & operator=(unsigned long i);
        const numeric & operator=(double d);
        const numeric & operator=(const char *s);
        const numeric inverse() const;
        numeric step() const;
        int csgn() const;
        int compare(const numeric &other) const;
        bool is_equal(const numeric &other) const;
        bool is_zero() const;
        bool is_positive() const;
        bool is_negative() const;
        bool is_integer() const;
        bool is_pos_integer() const;
        bool is_nonneg_integer() const;
        bool is_even() const;
        bool is_odd() const;
        bool is_prime() const;
        bool is_rational() const;
        bool is_real() const;
        bool is_cinteger() const;
        bool is_crational() const;
        bool operator==(const numeric &other) const;
        bool operator!=(const numeric &other) const;
        bool operator<(const numeric &other) const;
        bool operator<=(const numeric &other) const;
        bool operator>(const numeric &other) const;
        bool operator>=(const numeric &other) const;
        int to_int() const;
        long to_long() const;
        double to_double() const;
        cln::cl_N to_cl_N() const;
        const numeric real() const;
        const numeric imag() const;
        const numeric numer() const;
        const numeric denom() const;
        int int_length() const;
        // converting routines for interfacing with CLN:
        numeric(const cln::cl_N &z);

protected:
        void print_numeric(const print_context & c, const char *par_open, const char *par_close, const char *imag_sym, const char *mul_sym, unsigned level) const;
        void do_print(const print_context & c, unsigned level) const;
        void do_print_latex(const print_latex & c, unsigned level) const;
        void do_print_csrc(const print_csrc & c, unsigned level) const;
        void do_print_csrc_cl_N(const print_csrc_cl_N & c, unsigned level) const;
        void do_print_tree(const print_tree & c, unsigned level) const;
        void do_print_python_repr(const print_python_repr & c, unsigned level) const;

// member variables

protected:
        cln::cl_N value;
};


// global constants

extern const numeric I;
extern _numeric_digits Digits;

// global functions

const numeric exp(const numeric &x);
const numeric log(const numeric &x);
const numeric sin(const numeric &x);
const numeric cos(const numeric &x);
const numeric tan(const numeric &x);
const numeric asin(const numeric &x);
const numeric acos(const numeric &x);
const numeric atan(const numeric &x);
const numeric atan(const numeric &y, const numeric &x);
const numeric sinh(const numeric &x);
const numeric cosh(const numeric &x);
const numeric tanh(const numeric &x);
const numeric asinh(const numeric &x);
const numeric acosh(const numeric &x);
const numeric atanh(const numeric &x);
const numeric Li2(const numeric &x);
const numeric zeta(const numeric &x);
const numeric lgamma(const numeric &x);
const numeric tgamma(const numeric &x);
const numeric psi(const numeric &x);
const numeric psi(const numeric &n, const numeric &x);
const numeric factorial(const numeric &n);
const numeric doublefactorial(const numeric &n);
const numeric binomial(const numeric &n, const numeric &k);
const numeric bernoulli(const numeric &n);
const numeric fibonacci(const numeric &n);
const numeric isqrt(const numeric &x);
const numeric sqrt(const numeric &x);
const numeric abs(const numeric &x);
const numeric mod(const numeric &a, const numeric &b);
const numeric smod(const numeric &a, const numeric &b);
const numeric irem(const numeric &a, const numeric &b);
const numeric irem(const numeric &a, const numeric &b, numeric &q);
const numeric iquo(const numeric &a, const numeric &b);
const numeric iquo(const numeric &a, const numeric &b, numeric &r);
const numeric gcd(const numeric &a, const numeric &b);
const numeric lcm(const numeric &a, const numeric &b);

// wrapper functions around member functions
inline const numeric pow(const numeric &x, const numeric &y)
{ return x.power(y); }

inline const numeric inverse(const numeric &x)
{ return x.inverse(); }

inline numeric step(const numeric &x)
{ return x.step(); }

inline int csgn(const numeric &x)
{ return x.csgn(); }

inline bool is_zero(const numeric &x)
{ return x.is_zero(); }

inline bool is_positive(const numeric &x)
{ return x.is_positive(); }

inline bool is_integer(const numeric &x)
{ return x.is_integer(); }

inline bool is_pos_integer(const numeric &x)
{ return x.is_pos_integer(); }

inline bool is_nonneg_integer(const numeric &x)
{ return x.is_nonneg_integer(); }

inline bool is_even(const numeric &x)
{ return x.is_even(); }

inline bool is_odd(const numeric &x)
{ return x.is_odd(); }

inline bool is_prime(const numeric &x)
{ return x.is_prime(); }

inline bool is_rational(const numeric &x)
{ return x.is_rational(); }

inline bool is_real(const numeric &x)
{ return x.is_real(); }

inline bool is_cinteger(const numeric &x)
{ return x.is_cinteger(); }

inline bool is_crational(const numeric &x)
{ return x.is_crational(); }

inline int to_int(const numeric &x)
{ return x.to_int(); }

inline long to_long(const numeric &x)
{ return x.to_long(); }

inline double to_double(const numeric &x)
{ return x.to_double(); }

inline const numeric real(const numeric &x)
{ return x.real(); }

inline const numeric imag(const numeric &x)
{ return x.imag(); }

inline const numeric numer(const numeric &x)
{ return x.numer(); }

inline const numeric denom(const numeric &x)
{ return x.denom(); }

// numeric evaluation functions for class constant objects:

ex PiEvalf();
ex EulerEvalf();
ex CatalanEvalf();


} // namespace GiNaC

#ifdef __MAKECINT__
#pragma link off defined_in cln/number.h;
#pragma link off defined_in cln/complex_class.h;
#endif

#endif // ndef __GINAC_NUMERIC_H__
1	cbauer	1.1	/** @file numeric.h
2			*
3	cbauer	1.4	* Makes the interface to the underlying bignum package available. */
4
5			/*
6	vollinga	1.72	* GiNaC Copyright (C) 1999-2006 Johannes Gutenberg University Mainz, Germany
7	cbauer	1.2	*
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.
12			*
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.
17			*
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	kreckel	1.70	* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
21	cbauer	1.2	*/
22	cbauer	1.1
23	cbauer	1.2	#ifndef __GINAC_NUMERIC_H__
24			#define __GINAC_NUMERIC_H__
25	cbauer	1.1
26	cbauer	1.21	#include "basic.h"
27			#include "ex.h"
28	cbauer	1.1
29	cbauer	1.63	#include <stdexcept>
30	vollinga	1.71	#include <vector>
31	cbauer	1.63
32	vollinga	1.68	#include <cln/complex.h>
33	kreckel	1.41
34			#if defined(G__CINTVERSION) && !defined(__MAKECINT__)
35			// Cint @$#$! doesn't like forward declaring classes used for casting operators
36			// so we have to include the definition of cln::cl_N here, but it is enough to
37			// do so for the compiler, hence the !defined(__MAKECINT__).
38			#include <cln/complex_class.h>
39			#endif
40	cbauer	1.1
41	cbauer	1.5	namespace GiNaC {
42
43	vollinga	1.71	/** Function pointer to implement callbacks in the case 'Digits' gets changed.
44			* Main purpose of such callbacks is to adjust look-up tables of certain
45			* functions to the new precision. Parameter contains the signed difference
46			* between new Digits and old Digits. */
47			typedef void (* digits_changed_callback)(long);
48
49	kreckel	1.48	/** This class is used to instantiate a global singleton object Digits
50			* which behaves just like Maple's Digits. We need an object rather
51			* than a dumber basic type since as a side-effect we let it change
52	cbauer	1.1	* cl_default_float_format when it gets changed. The only other
53			* meaningful thing to do with it is converting it to an unsigned,
54			* for temprary storing its value e.g. The user must not create an
55			* own working object of this class! Since C++ forces us to make the
56			* class definition visible in order to use an object we put in a
57			* flag which prevents other objects of that class to be created. */
58			class _numeric_digits
59			{
60			// member functions
61			public:
62	cbauer	1.38	_numeric_digits();
63			_numeric_digits& operator=(long prec);
64			operator long();
65	vollinga	1.71	void print(std::ostream& os) const;
66			void add_callback(digits_changed_callback callback);
67	cbauer	1.1	// member variables
68			private:
69	kreckel	1.48	long digits; ///< Number of decimal digits
70			static bool too_late; ///< Already one object present
71	vollinga	1.71	// Holds a list of functions that get called when digits is changed.
72			std::vector<digits_changed_callback> callbacklist;
73	cbauer	1.1	};
74
75	cbauer	1.63
76			/** Exception class thrown when a singularity is encountered. */
77			class pole_error : public std::domain_error {
78			public:
79			explicit pole_error(const std::string& what_arg, int degree);
80			int degree() const;
81			private:
82			int deg;
83			};
84
85
86	cbauer	1.1	/** This class is a wrapper around CLN-numbers within the GiNaC class
87			* hierarchy. Objects of this type may directly be created by the user.*/
88			class numeric : public basic
89			{
90	cbauer	1.38	GINAC_DECLARE_REGISTERED_CLASS(numeric, basic)
91	kreckel	1.48
92	cbauer	1.1	// member functions
93	kreckel	1.48
94	cbauer	1.63	// other constructors
95	cbauer	1.1	public:
96	kreckel	1.56	numeric(int i);
97			numeric(unsigned int i);
98			numeric(long i);
99			numeric(unsigned long i);
100			numeric(long numer, long denom);
101			numeric(double d);
102			numeric(const char *);
103	cbauer	1.38
104	cbauer	1.57	// functions overriding virtual functions from base classes
105	cbauer	1.1	public:
106	cbauer	1.63	unsigned precedence() const {return 30;}
107	cbauer	1.38	bool info(unsigned inf) const;
108	chrisd	1.77	bool is_polynomial(const ex & var) const;
109	cbauer	1.61	int degree(const ex & s) const;
110			int ldegree(const ex & s) const;
111			ex coeff(const ex & s, int n = 1) const;
112	chrisd	1.73	bool has(const ex &other, unsigned options = 0) const;
113	kreckel	1.47	ex eval(int level = 0) const;
114			ex evalf(int level = 0) const;
115	cbauer	1.64	ex subs(const exmap & m, unsigned options = 0) const { return subs_one_level(m, options); } // overwrites basic::subs() for performance reasons
116	cbauer	1.65	ex normal(exmap & repl, exmap & rev_lookup, int level = 0) const;
117	cbauer	1.67	ex to_rational(exmap & repl) const;
118			ex to_polynomial(exmap & repl) const;
119	cbauer	1.63	numeric integer_content() const;
120	cbauer	1.38	ex smod(const numeric &xi) const;
121	cbauer	1.63	numeric max_coefficient() const;
122	vollinga	1.68	ex conjugate() const;
123	cbauer	1.1	protected:
124	kreckel	1.48	/** Implementation of ex::diff for a numeric always returns 0.
125			* @see ex::diff */
126	kreckel	1.59	ex derivative(const symbol &s) const { return 0; }
127	kreckel	1.48	bool is_equal_same_type(const basic &other) const;
128	cbauer	1.63	unsigned calchash() const;
129	kreckel	1.48
130	cbauer	1.38	// new virtual functions which can be overridden by derived classes
131			// (none)
132	kreckel	1.48
133	cbauer	1.38	// non-virtual functions in this class
134	cbauer	1.1	public:
135	kreckel	1.48	const numeric add(const numeric &other) const;
136			const numeric sub(const numeric &other) const;
137			const numeric mul(const numeric &other) const;
138			const numeric div(const numeric &other) const;
139			const numeric power(const numeric &other) const;
140			const numeric & add_dyn(const numeric &other) const;
141			const numeric & sub_dyn(const numeric &other) const;
142			const numeric & mul_dyn(const numeric &other) const;
143			const numeric & div_dyn(const numeric &other) const;
144			const numeric & power_dyn(const numeric &other) const;
145	cbauer	1.38	const numeric & operator=(int i);
146			const numeric & operator=(unsigned int i);
147			const numeric & operator=(long i);
148			const numeric & operator=(unsigned long i);
149			const numeric & operator=(double d);
150	kreckel	1.48	const numeric & operator=(const char *s);
151	cbauer	1.63	const numeric inverse() const;
152	chrisd	1.76	numeric step() const;
153	cbauer	1.63	int csgn() const;
154	kreckel	1.48	int compare(const numeric &other) const;
155			bool is_equal(const numeric &other) const;
156	cbauer	1.63	bool is_zero() const;
157			bool is_positive() const;
158			bool is_negative() const;
159			bool is_integer() const;
160			bool is_pos_integer() const;
161			bool is_nonneg_integer() const;
162			bool is_even() const;
163			bool is_odd() const;
164			bool is_prime() const;
165			bool is_rational() const;
166			bool is_real() const;
167			bool is_cinteger() const;
168			bool is_crational() const;
169	kreckel	1.48	bool operator==(const numeric &other) const;
170			bool operator!=(const numeric &other) const;
171			bool operator<(const numeric &other) const;
172			bool operator<=(const numeric &other) const;
173			bool operator>(const numeric &other) const;
174			bool operator>=(const numeric &other) const;
175	cbauer	1.63	int to_int() const;
176			long to_long() const;
177			double to_double() const;
178			cln::cl_N to_cl_N() const;
179			const numeric real() const;
180			const numeric imag() const;
181			const numeric numer() const;
182			const numeric denom() const;
183			int int_length() const;
184	kreckel	1.41	// converting routines for interfacing with CLN:
185	kreckel	1.48	numeric(const cln::cl_N &z);
186	cbauer	1.66
187			protected:
188			void print_numeric(const print_context & c, const char par_open, const char par_close, const char imag_sym, const char mul_sym, unsigned level) const;
189			void do_print(const print_context & c, unsigned level) const;
190			void do_print_latex(const print_latex & c, unsigned level) const;
191			void do_print_csrc(const print_csrc & c, unsigned level) const;
192			void do_print_csrc_cl_N(const print_csrc_cl_N & c, unsigned level) const;
193			void do_print_tree(const print_tree & c, unsigned level) const;
194			void do_print_python_repr(const print_python_repr & c, unsigned level) const;
195	cbauer	1.1
196			// member variables
197
198			protected:
199	vollinga	1.68	cln::cl_N value;
200	cbauer	1.1	};
201
202	cbauer	1.63
203	cbauer	1.1	// global constants
204
205			extern const numeric I;
206			extern _numeric_digits Digits;
207
208			// global functions
209
210	kreckel	1.48	const numeric exp(const numeric &x);
211			const numeric log(const numeric &x);
212			const numeric sin(const numeric &x);
213			const numeric cos(const numeric &x);
214			const numeric tan(const numeric &x);
215			const numeric asin(const numeric &x);
216			const numeric acos(const numeric &x);
217			const numeric atan(const numeric &x);
218			const numeric atan(const numeric &y, const numeric &x);
219			const numeric sinh(const numeric &x);
220			const numeric cosh(const numeric &x);
221			const numeric tanh(const numeric &x);
222			const numeric asinh(const numeric &x);
223			const numeric acosh(const numeric &x);
224			const numeric atanh(const numeric &x);
225			const numeric Li2(const numeric &x);
226			const numeric zeta(const numeric &x);
227			const numeric lgamma(const numeric &x);
228			const numeric tgamma(const numeric &x);
229			const numeric psi(const numeric &x);
230			const numeric psi(const numeric &n, const numeric &x);
231			const numeric factorial(const numeric &n);
232			const numeric doublefactorial(const numeric &n);
233			const numeric binomial(const numeric &n, const numeric &k);
234			const numeric bernoulli(const numeric &n);
235			const numeric fibonacci(const numeric &n);
236			const numeric isqrt(const numeric &x);
237			const numeric sqrt(const numeric &x);
238			const numeric abs(const numeric &x);
239			const numeric mod(const numeric &a, const numeric &b);
240			const numeric smod(const numeric &a, const numeric &b);
241			const numeric irem(const numeric &a, const numeric &b);
242			const numeric irem(const numeric &a, const numeric &b, numeric &q);
243			const numeric iquo(const numeric &a, const numeric &b);
244			const numeric iquo(const numeric &a, const numeric &b, numeric &r);
245			const numeric gcd(const numeric &a, const numeric &b);
246			const numeric lcm(const numeric &a, const numeric &b);
247	cbauer	1.1
248			// wrapper functions around member functions
249	kreckel	1.48	inline const numeric pow(const numeric &x, const numeric &y)
250	kreckel	1.16	{ return x.power(y); }
251
252	kreckel	1.48	inline const numeric inverse(const numeric &x)
253	cbauer	1.1	{ return x.inverse(); }
254	kreckel	1.6
255	chrisd	1.76	inline numeric step(const numeric &x)
256	chrisd	1.74	{ return x.step(); }
257
258	kreckel	1.48	inline int csgn(const numeric &x)
259	kreckel	1.6	{ return x.csgn(); }
260	cbauer	1.1
261	kreckel	1.48	inline bool is_zero(const numeric &x)
262	cbauer	1.1	{ return x.is_zero(); }
263
264	kreckel	1.48	inline bool is_positive(const numeric &x)
265	cbauer	1.1	{ return x.is_positive(); }
266
267	kreckel	1.48	inline bool is_integer(const numeric &x)
268	cbauer	1.1	{ return x.is_integer(); }
269
270	kreckel	1.48	inline bool is_pos_integer(const numeric &x)
271	cbauer	1.1	{ return x.is_pos_integer(); }
272
273	kreckel	1.48	inline bool is_nonneg_integer(const numeric &x)
274	cbauer	1.1	{ return x.is_nonneg_integer(); }
275
276	kreckel	1.48	inline bool is_even(const numeric &x)
277	cbauer	1.1	{ return x.is_even(); }
278
279	kreckel	1.48	inline bool is_odd(const numeric &x)
280	cbauer	1.1	{ return x.is_odd(); }
281
282	kreckel	1.48	inline bool is_prime(const numeric &x)
283	cbauer	1.1	{ return x.is_prime(); }
284
285	kreckel	1.48	inline bool is_rational(const numeric &x)
286	cbauer	1.1	{ return x.is_rational(); }
287
288	kreckel	1.48	inline bool is_real(const numeric &x)
289	cbauer	1.1	{ return x.is_real(); }
290
291	kreckel	1.48	inline bool is_cinteger(const numeric &x)
292	kreckel	1.14	{ return x.is_cinteger(); }
293
294	kreckel	1.48	inline bool is_crational(const numeric &x)
295	kreckel	1.14	{ return x.is_crational(); }
296	kreckel	1.42
297	kreckel	1.48	inline int to_int(const numeric &x)
298	kreckel	1.42	{ return x.to_int(); }
299
300	kreckel	1.48	inline long to_long(const numeric &x)
301	kreckel	1.42	{ return x.to_long(); }
302
303	kreckel	1.48	inline double to_double(const numeric &x)
304	kreckel	1.42	{ return x.to_double(); }
305	kreckel	1.14
306	kreckel	1.48	inline const numeric real(const numeric &x)
307	cbauer	1.1	{ return x.real(); }
308
309	kreckel	1.48	inline const numeric imag(const numeric &x)
310	cbauer	1.1	{ return x.imag(); }
311
312	kreckel	1.48	inline const numeric numer(const numeric &x)
313	cbauer	1.1	{ return x.numer(); }
314
315	kreckel	1.48	inline const numeric denom(const numeric &x)
316	cbauer	1.1	{ return x.denom(); }
317
318	kreckel	1.11	// numeric evaluation functions for class constant objects:
319
320	cbauer	1.63	ex PiEvalf();
321			ex EulerEvalf();
322			ex CatalanEvalf();
323	cbauer	1.1
324	kreckel	1.23
325	cbauer	1.5	} // namespace GiNaC
326	kreckel	1.41
327			#ifdef __MAKECINT__
328			#pragma link off defined_in cln/number.h;
329			#pragma link off defined_in cln/complex_class.h;
330			#endif
331	cbauer	1.1
332	cbauer	1.2	#endif // ndef __GINAC_NUMERIC_H__
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