GiNaC/ginac/numeric.h

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

/*
 *  GiNaC Copyright (C) 1999-2000 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., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 */

#ifndef __GINAC_NUMERIC_H__
#define __GINAC_NUMERIC_H__

#include <strstream>
#include <ginac/basic.h>
#include <ginac/ex.h>

class cl_N;     // We want to include cln.h only in numeric.cpp in order to 
                // avoid namespace pollution and keep compile-time low.

#ifndef NO_GINAC_NAMESPACE
namespace GiNaC {
#endif // ndef NO_GINAC_NAMESPACE

#define HASHVALUE_NUMERIC 0x80000001U

/** This class is used to instantiate a global 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(ostream & os) const;
// member variables
private:
    long digits;
    static bool too_late;
};

/** 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)

// friends
    friend const numeric exp(const numeric & x);
    friend const numeric log(const numeric & x);
    friend const numeric sin(const numeric & x);
    friend const numeric cos(const numeric & x);
    friend const numeric tan(const numeric & x);
    friend const numeric asin(const numeric & x);
    friend const numeric acos(const numeric & x);
    friend const numeric atan(const numeric & x);
    friend const numeric atan(const numeric & y, const numeric & x);
    friend const numeric sinh(const numeric & x);
    friend const numeric cosh(const numeric & x);
    friend const numeric tanh(const numeric & x);
    friend const numeric asinh(const numeric & x);
    friend const numeric acosh(const numeric & x);
    friend const numeric atanh(const numeric & x);
    friend const numeric zeta(const numeric & x);
    friend const numeric bernoulli(const numeric & n);
    friend numeric abs(const numeric & x);
    friend numeric mod(const numeric & a, const numeric & b);
    friend numeric smod(const numeric & a, const numeric & b);
    friend numeric irem(const numeric & a, const numeric & b);
    friend numeric irem(const numeric & a, const numeric & b, numeric & q);
    friend numeric iquo(const numeric & a, const numeric & b);
    friend numeric iquo(const numeric & a, const numeric & b, numeric & r);
    friend numeric sqrt(const numeric & x);
    friend numeric isqrt(const numeric & x);
    friend numeric gcd(const numeric & a, const numeric & b);
    friend numeric lcm(const numeric & a, const numeric & b);

// member functions

    // default constructor, destructor, copy constructor assignment
    // operator and helpers
public:
    numeric();
    ~numeric();
    numeric(const numeric & other);
    const numeric & operator=(const numeric & other);
protected:
    void copy(const numeric & other);
    void destroy(bool call_parent);

    // other constructors
public:
    explicit numeric(int i);
    explicit numeric(unsigned int i);
    explicit numeric(long i);
    explicit numeric(unsigned long i);
    explicit numeric(long numer, long denom);
    explicit numeric(double d);
    explicit numeric(const char *);
    numeric(cl_N const & z);

    // functions overriding virtual functions from bases classes
public:
    basic * duplicate() const;
    void print(ostream & os, unsigned precedence=0) const;
    void printraw(ostream & os) const;
    void printtree(ostream & os, unsigned indent) const;
    void printcsrc(ostream & os, unsigned type, unsigned precedence=0) const;
    bool info(unsigned inf) const;
    ex evalf(int level=0) const;
    ex diff(const symbol & s) const;
    ex normal(lst &sym_lst, lst &repl_lst, int level=0) const;
    numeric integer_content(void) const;
    ex smod(const numeric &xi) const;
    numeric max_coefficient(void) const;
protected:
    int compare_same_type(const basic & other) const;
    bool is_equal_same_type(const basic & other) const;
    unsigned calchash(void) const {
        hashvalue=HASHVALUE_NUMERIC;
        return HASHVALUE_NUMERIC;
    }

    // new virtual functions which can be overridden by derived classes
    // (none)

    // non-virtual functions in this class
public:
    numeric add(const numeric & other) const;
    numeric sub(const numeric & other) const;
    numeric mul(const numeric & other) const;
    numeric div(const numeric & other) 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);
    numeric inverse(void) const;
    int csgn(void) const;
    int compare(const numeric & other) const;
    bool is_equal(const numeric & other) const;
    bool is_zero(void) const;
    bool is_positive(void) const;
    bool is_negative(void) const;
    bool is_integer(void) const;
    bool is_pos_integer(void) const;
    bool is_nonneg_integer(void) const;
    bool is_even(void) const;
    bool is_odd(void) const;
    bool is_prime(void) const;
    bool is_rational(void) const;
    bool is_real(void) const;
    bool is_cinteger(void) const;
    bool is_crational(void) 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(void) const;
    long to_long(void) const;
    double to_double(void) const;
    numeric real(void) const;
    numeric imag(void) const;
    numeric numer(void) const;
    numeric denom(void) const;
    int int_length(void) const;

// member variables

protected:
    static unsigned precedence;
    cl_N *value;
};

// global constants

extern const numeric some_numeric;
extern const numeric I;
extern const type_info & typeid_numeric;
extern _numeric_digits Digits;

#define is_a_numeric_hash(x) ((x)==HASHVALUE_NUMERIC)
// may have to be changed to ((x)>=0x80000000U)

// 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 zeta(const numeric & x);
const numeric gamma(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);

numeric abs(const numeric & x);
numeric mod(const numeric & a, const numeric & b);
numeric smod(const numeric & a, const numeric & b);
numeric irem(const numeric & a, const numeric & b);
numeric irem(const numeric & a, const numeric & b, numeric & q);
numeric iquo(const numeric & a, const numeric & b);
numeric iquo(const numeric & a, const numeric & b, numeric & r);
numeric sqrt(const numeric & x);
numeric isqrt(const numeric & x);

numeric gcd(const numeric & a, const numeric & b);
numeric lcm(const numeric & a, const numeric & b);

/** Exception thrown by numeric members to signal failure */
struct numeric_fail
{
    int failval;
    numeric_fail(int n) { failval = n; }
};

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

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

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

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

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

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

// numeric evaluation functions for class constant objects:

ex PiEvalf(void);
ex EulerGammaEvalf(void);
ex CatalanEvalf(void);

// utility functions
inline const numeric &ex_to_numeric(const ex &e)
{
    return static_cast<const numeric &>(*e.bp);
}

#ifndef NO_GINAC_NAMESPACE
} // namespace GiNaC
#endif // ndef NO_GINAC_NAMESPACE

#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	kreckel	1.17	* GiNaC Copyright (C) 1999-2000 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			* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
21			*/
22	cbauer	1.1
23	cbauer	1.2	#ifndef __GINAC_NUMERIC_H__
24			#define __GINAC_NUMERIC_H__
25	cbauer	1.1
26			#include <strstream>
27	cbauer	1.3	#include <ginac/basic.h>
28	cbauer	1.5	#include <ginac/ex.h>
29	cbauer	1.1
30			class cl_N; // We want to include cln.h only in numeric.cpp in order to
31			// avoid namespace pollution and keep compile-time low.
32
33	frink	1.12	#ifndef NO_GINAC_NAMESPACE
34	cbauer	1.5	namespace GiNaC {
35	frink	1.12	#endif // ndef NO_GINAC_NAMESPACE
36	cbauer	1.5
37			#define HASHVALUE_NUMERIC 0x80000001U
38
39	cbauer	1.1	/** This class is used to instantiate a global object Digits which
40			* behaves just like Maple's Digits. We need an object rather than a
41			* dumber basic type since as a side-effect we let it change
42			* cl_default_float_format when it gets changed. The only other
43			* meaningful thing to do with it is converting it to an unsigned,
44			* for temprary storing its value e.g. The user must not create an
45			* own working object of this class! Since C++ forces us to make the
46			* class definition visible in order to use an object we put in a
47			* flag which prevents other objects of that class to be created. */
48			class _numeric_digits
49			{
50			// member functions
51			public:
52			_numeric_digits();
53			_numeric_digits& operator=(long prec);
54			operator long();
55			void print(ostream & os) const;
56			// member variables
57			private:
58			long digits;
59			static bool too_late;
60			};
61
62			/** This class is a wrapper around CLN-numbers within the GiNaC class
63			* hierarchy. Objects of this type may directly be created by the user.*/
64			class numeric : public basic
65			{
66	cbauer	1.18	GINAC_DECLARE_REGISTERED_CLASS(numeric, basic)
67
68	cbauer	1.1	// friends
69	kreckel	1.20	friend const numeric exp(const numeric & x);
70			friend const numeric log(const numeric & x);
71			friend const numeric sin(const numeric & x);
72			friend const numeric cos(const numeric & x);
73			friend const numeric tan(const numeric & x);
74			friend const numeric asin(const numeric & x);
75			friend const numeric acos(const numeric & x);
76			friend const numeric atan(const numeric & x);
77			friend const numeric atan(const numeric & y, const numeric & x);
78			friend const numeric sinh(const numeric & x);
79			friend const numeric cosh(const numeric & x);
80			friend const numeric tanh(const numeric & x);
81			friend const numeric asinh(const numeric & x);
82			friend const numeric acosh(const numeric & x);
83			friend const numeric atanh(const numeric & x);
84			friend const numeric zeta(const numeric & x);
85			friend const numeric bernoulli(const numeric & n);
86	kreckel	1.16	friend numeric abs(const numeric & x);
87			friend numeric mod(const numeric & a, const numeric & b);
88			friend numeric smod(const numeric & a, const numeric & b);
89			friend numeric irem(const numeric & a, const numeric & b);
90			friend numeric irem(const numeric & a, const numeric & b, numeric & q);
91			friend numeric iquo(const numeric & a, const numeric & b);
92			friend numeric iquo(const numeric & a, const numeric & b, numeric & r);
93			friend numeric sqrt(const numeric & x);
94			friend numeric isqrt(const numeric & x);
95			friend numeric gcd(const numeric & a, const numeric & b);
96			friend numeric lcm(const numeric & a, const numeric & b);
97	cbauer	1.1
98			// member functions
99
100			// default constructor, destructor, copy constructor assignment
101			// operator and helpers
102			public:
103			numeric();
104			~numeric();
105	kreckel	1.16	numeric(const numeric & other);
106			const numeric & operator=(const numeric & other);
107	cbauer	1.1	protected:
108	kreckel	1.16	void copy(const numeric & other);
109	cbauer	1.1	void destroy(bool call_parent);
110
111			// other constructors
112			public:
113			explicit numeric(int i);
114			explicit numeric(unsigned int i);
115			explicit numeric(long i);
116			explicit numeric(unsigned long i);
117			explicit numeric(long numer, long denom);
118			explicit numeric(double d);
119	cbauer	1.19	explicit numeric(const char *);
120	cbauer	1.1	numeric(cl_N const & z);
121
122			// functions overriding virtual functions from bases classes
123			public:
124			basic * duplicate() const;
125	kreckel	1.14	void print(ostream & os, unsigned precedence=0) const;
126	cbauer	1.1	void printraw(ostream & os) const;
127			void printtree(ostream & os, unsigned indent) const;
128			void printcsrc(ostream & os, unsigned type, unsigned precedence=0) const;
129			bool info(unsigned inf) const;
130			ex evalf(int level=0) const;
131	cbauer	1.19	ex diff(const symbol & s) const;
132	cbauer	1.1	ex normal(lst &sym_lst, lst &repl_lst, int level=0) const;
133			numeric integer_content(void) const;
134	kreckel	1.16	ex smod(const numeric &xi) const;
135	cbauer	1.1	numeric max_coefficient(void) const;
136			protected:
137	cbauer	1.19	int compare_same_type(const basic & other) const;
138			bool is_equal_same_type(const basic & other) const;
139	cbauer	1.1	unsigned calchash(void) const {
140			hashvalue=HASHVALUE_NUMERIC;
141			return HASHVALUE_NUMERIC;
142			}
143
144			// new virtual functions which can be overridden by derived classes
145			// (none)
146
147			// non-virtual functions in this class
148			public:
149	kreckel	1.16	numeric add(const numeric & other) const;
150			numeric sub(const numeric & other) const;
151			numeric mul(const numeric & other) const;
152			numeric div(const numeric & other) const;
153			numeric power(const numeric & other) const;
154			const numeric & add_dyn(const numeric & other) const;
155			const numeric & sub_dyn(const numeric & other) const;
156			const numeric & mul_dyn(const numeric & other) const;
157			const numeric & div_dyn(const numeric & other) const;
158			const numeric & power_dyn(const numeric & other) const;
159			const numeric & operator=(int i);
160			const numeric & operator=(unsigned int i);
161			const numeric & operator=(long i);
162			const numeric & operator=(unsigned long i);
163			const numeric & operator=(double d);
164	cbauer	1.19	const numeric & operator=(const char * s);
165	cbauer	1.1	numeric inverse(void) const;
166	kreckel	1.6	int csgn(void) const;
167	kreckel	1.16	int compare(const numeric & other) const;
168			bool is_equal(const numeric & other) const;
169	cbauer	1.1	bool is_zero(void) const;
170			bool is_positive(void) const;
171			bool is_negative(void) const;
172			bool is_integer(void) const;
173			bool is_pos_integer(void) const;
174			bool is_nonneg_integer(void) const;
175			bool is_even(void) const;
176			bool is_odd(void) const;
177			bool is_prime(void) const;
178			bool is_rational(void) const;
179			bool is_real(void) const;
180	kreckel	1.13	bool is_cinteger(void) const;
181			bool is_crational(void) const;
182	kreckel	1.16	bool operator==(const numeric & other) const;
183			bool operator!=(const numeric & other) const;
184			bool operator<(const numeric & other) const;
185			bool operator<=(const numeric & other) const;
186			bool operator>(const numeric & other) const;
187			bool operator>=(const numeric & other) const;
188	cbauer	1.1	int to_int(void) const;
189	kreckel	1.20	long to_long(void) const;
190	cbauer	1.1	double to_double(void) const;
191			numeric real(void) const;
192			numeric imag(void) const;
193			numeric numer(void) const;
194			numeric denom(void) const;
195			int int_length(void) const;
196
197			// member variables
198
199			protected:
200			static unsigned precedence;
201			cl_N *value;
202			};
203
204			// global constants
205
206			extern const numeric some_numeric;
207			extern const numeric I;
208	cbauer	1.19	extern const type_info & typeid_numeric;
209	cbauer	1.1	extern _numeric_digits Digits;
210
211			#define is_a_numeric_hash(x) ((x)==HASHVALUE_NUMERIC)
212			// may have to be changed to ((x)>=0x80000000U)
213
214			// global functions
215
216	kreckel	1.20	const numeric exp(const numeric & x);
217			const numeric log(const numeric & x);
218			const numeric sin(const numeric & x);
219			const numeric cos(const numeric & x);
220			const numeric tan(const numeric & x);
221			const numeric asin(const numeric & x);
222			const numeric acos(const numeric & x);
223			const numeric atan(const numeric & x);
224			const numeric atan(const numeric & y, const numeric & x);
225			const numeric sinh(const numeric & x);
226			const numeric cosh(const numeric & x);
227			const numeric tanh(const numeric & x);
228			const numeric asinh(const numeric & x);
229			const numeric acosh(const numeric & x);
230			const numeric atanh(const numeric & x);
231			const numeric zeta(const numeric & x);
232			const numeric gamma(const numeric & x);
233			const numeric psi(const numeric & x);
234			const numeric psi(const numeric & n, const numeric & x);
235			const numeric factorial(const numeric & n);
236			const numeric doublefactorial(const numeric & n);
237			const numeric binomial(const numeric & n, const numeric & k);
238			const numeric bernoulli(const numeric & n);
239			const numeric fibonacci(const numeric & n);
240	kreckel	1.16
241			numeric abs(const numeric & x);
242			numeric mod(const numeric & a, const numeric & b);
243			numeric smod(const numeric & a, const numeric & b);
244			numeric irem(const numeric & a, const numeric & b);
245			numeric irem(const numeric & a, const numeric & b, numeric & q);
246			numeric iquo(const numeric & a, const numeric & b);
247			numeric iquo(const numeric & a, const numeric & b, numeric & r);
248			numeric sqrt(const numeric & x);
249			numeric isqrt(const numeric & x);
250	cbauer	1.1
251	kreckel	1.16	numeric gcd(const numeric & a, const numeric & b);
252			numeric lcm(const numeric & a, const numeric & b);
253	cbauer	1.1
254			/** Exception thrown by numeric members to signal failure */
255			struct numeric_fail
256			{
257			int failval;
258			numeric_fail(int n) { failval = n; }
259			};
260
261			// wrapper functions around member functions
262	kreckel	1.16	inline numeric pow(const numeric & x, const numeric & y)
263			{ return x.power(y); }
264
265			inline numeric inverse(const numeric & x)
266	cbauer	1.1	{ return x.inverse(); }
267	kreckel	1.6
268	kreckel	1.16	inline bool csgn(const numeric & x)
269	kreckel	1.6	{ return x.csgn(); }
270	cbauer	1.1
271	kreckel	1.16	inline bool is_zero(const numeric & x)
272	cbauer	1.1	{ return x.is_zero(); }
273
274	kreckel	1.16	inline bool is_positive(const numeric & x)
275	cbauer	1.1	{ return x.is_positive(); }
276
277	kreckel	1.16	inline bool is_integer(const numeric & x)
278	cbauer	1.1	{ return x.is_integer(); }
279
280	kreckel	1.16	inline bool is_pos_integer(const numeric & x)
281	cbauer	1.1	{ return x.is_pos_integer(); }
282
283	kreckel	1.16	inline bool is_nonneg_integer(const numeric & x)
284	cbauer	1.1	{ return x.is_nonneg_integer(); }
285
286	kreckel	1.16	inline bool is_even(const numeric & x)
287	cbauer	1.1	{ return x.is_even(); }
288
289	kreckel	1.16	inline bool is_odd(const numeric & x)
290	cbauer	1.1	{ return x.is_odd(); }
291
292	kreckel	1.16	inline bool is_prime(const numeric & x)
293	cbauer	1.1	{ return x.is_prime(); }
294
295	kreckel	1.16	inline bool is_rational(const numeric & x)
296	cbauer	1.1	{ return x.is_rational(); }
297
298	kreckel	1.16	inline bool is_real(const numeric & x)
299	cbauer	1.1	{ return x.is_real(); }
300
301	kreckel	1.16	inline bool is_cinteger(const numeric & x)
302	kreckel	1.14	{ return x.is_cinteger(); }
303
304	kreckel	1.16	inline bool is_crational(const numeric & x)
305	kreckel	1.14	{ return x.is_crational(); }
306
307	kreckel	1.16	inline numeric real(const numeric & x)
308	cbauer	1.1	{ return x.real(); }
309
310	kreckel	1.16	inline numeric imag(const numeric & x)
311	cbauer	1.1	{ return x.imag(); }
312
313	kreckel	1.16	inline numeric numer(const numeric & x)
314	cbauer	1.1	{ return x.numer(); }
315
316	kreckel	1.16	inline numeric denom(const numeric & x)
317	cbauer	1.1	{ return x.denom(); }
318
319	kreckel	1.11	// numeric evaluation functions for class constant objects:
320
321	cbauer	1.1	ex PiEvalf(void);
322			ex EulerGammaEvalf(void);
323			ex CatalanEvalf(void);
324
325	cbauer	1.5	// utility functions
326			inline const numeric &ex_to_numeric(const ex &e)
327			{
328	kreckel	1.14	return static_cast<const numeric &>(*e.bp);
329	cbauer	1.5	}
330	cbauer	1.1
331	frink	1.12	#ifndef NO_GINAC_NAMESPACE
332	cbauer	1.5	} // namespace GiNaC
333	frink	1.12	#endif // ndef NO_GINAC_NAMESPACE
334	cbauer	1.1
335	cbauer	1.2	#endif // ndef __GINAC_NUMERIC_H__
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