Data Structures | Macros | Typedefs | Enumerations | Functions | Variables
coeffs.h File Reference

Coefficient rings, fields and other domains suitable for Singular polynomials. More...

#include <misc/auxiliary.h>
#include <omalloc/omalloc.h>
#include <misc/sirandom.h>
#include <reporter/reporter.h>
#include <reporter/s_buff.h>
#include <factory/factory.h>
#include <coeffs/si_gmp.h>
#include <coeffs/Enumerator.h>
#include <coeffs/numstats.h>

Go to the source code of this file.

Data Structures

struct  GFInfo
 Creation data needed for finite fields. More...
 
struct  LongComplexInfo
 
struct  coeffs
 

Macros

#define FREE_RNUMBER(x)   omFreeBin((void *)x, rnumber_bin)
 
#define ALLOC_RNUMBER()   (number)omAllocBin(rnumber_bin)
 
#define ALLOC0_RNUMBER()   (number)omAlloc0Bin(rnumber_bin)
 
#define n_New(n, r)   nNew(n)
 
#define n_Test(a, r)   n_DBTest(a, __FILE__, __LINE__, r)
 BOOLEAN n_Test(number a, const coeffs r) More...
 

Typedefs

typedef number(* numberfunc) (number a, number b, const coeffs r)
 
typedef number(* nMapFunc) (number a, const coeffs src, const coeffs dst)
 maps "a", which lives in src, into dst More...
 
typedef IEnumerator< number > ICoeffsEnumerator
 Abstract interface for an enumerator of number coefficients for an object, e.g. a polynomial. More...
 
typedef void(* nCoeffsEnumeratorFunc) (ICoeffsEnumerator &numberCollectionEnumerator, number &output, const coeffs r)
 goes over coeffs given by the ICoeffsEnumerator and changes them. Additionally returns a number; More...
 

Enumerations

enum  n_coeffType {
  n_unknown =0, n_Zp, n_Q, n_R,
  n_GF, n_long_R, n_polyExt, n_algExt,
  n_transExt, n_long_C, n_Z, n_Zn,
  n_Znm, n_Z2m, n_CF
}
 
enum  n_coeffRep {
  n_rep_unknown =0, n_rep_int, n_rep_gap_rat, n_rep_gap_gmp,
  n_rep_poly, n_rep_rat_fct, n_rep_gmp, n_rep_float,
  n_rep_gmp_float, n_rep_gmp_complex, n_rep_gf
}
 

Functions

static FORCE_INLINE n_coeffType getCoeffType (const coeffs r)
 Returns the type of coeffs domain. More...
 
coeffs nInitChar (n_coeffType t, void *parameter)
 one-time initialisations for new coeffs in case of an error return NULL More...
 
static FORCE_INLINE coeffs nCopyCoeff (const coeffs r)
 "copy" coeffs, i.e. increment ref More...
 
void nKillChar (coeffs r)
 undo all initialisations More...
 
static FORCE_INLINE void nSetChar (const coeffs r)
 initialisations after each ring change More...
 
void nNew (number *a)
 
static FORCE_INLINE int n_GetChar (const coeffs r)
 Return the characteristic of the coeff. domain. More...
 
static FORCE_INLINE number n_Copy (number n, const coeffs r)
 return a copy of 'n' More...
 
static FORCE_INLINE void n_Delete (number *p, const coeffs r)
 delete 'p' More...
 
static FORCE_INLINE BOOLEAN n_Equal (number a, number b, const coeffs r)
 TRUE iff 'a' and 'b' represent the same number; they may have different representations. More...
 
static FORCE_INLINE BOOLEAN n_IsZero (number n, const coeffs r)
 TRUE iff 'n' represents the zero element. More...
 
static FORCE_INLINE BOOLEAN n_IsOne (number n, const coeffs r)
 TRUE iff 'n' represents the one element. More...
 
static FORCE_INLINE BOOLEAN n_IsMOne (number n, const coeffs r)
 TRUE iff 'n' represents the additive inverse of the one element, i.e. -1. More...
 
static FORCE_INLINE BOOLEAN n_GreaterZero (number n, const coeffs r)
 ordered fields: TRUE iff 'n' is positive; in Z/pZ: TRUE iff 0 < m <= roundedBelow(p/2), where m is the long representing n in C: TRUE iff (Im(n) != 0 and Im(n) >= 0) or (Im(n) == 0 and Re(n) >= 0) in K(a)/<p(a)>: TRUE iff (n != 0 and (LC(n) > 0 or deg(n) > 0)) in K(t_1, ..., t_n): TRUE iff (LC(numerator(n) is a constant and > 0) or (LC(numerator(n) is not a constant) in Z/2^kZ: TRUE iff 0 < n <= 2^(k-1) in Z/mZ: TRUE iff the internal mpz is greater than zero in Z: TRUE iff n > 0 More...
 
static FORCE_INLINE BOOLEAN n_Greater (number a, number b, const coeffs r)
 ordered fields: TRUE iff 'a' is larger than 'b'; in Z/pZ: TRUE iff la > lb, where la and lb are the long's representing More...
 
static FORCE_INLINE BOOLEAN n_IsUnit (number n, const coeffs r)
 TRUE iff n has a multiplicative inverse in the given coeff field/ring r. More...
 
static FORCE_INLINE coeffs n_CoeffRingQuot1 (number c, const coeffs r)
 
static FORCE_INLINE int n_DivComp (number a, number b, const coeffs r)
 
static FORCE_INLINE number n_GetUnit (number n, const coeffs r)
 in Z: 1 in Z/kZ (where k is not a prime): largest divisor of n (taken in Z) that is co-prime with k in Z/2^kZ: largest odd divisor of n (taken in Z) other cases: not implemented More...
 
static FORCE_INLINE number n_Init (long i, const coeffs r)
 a number representing i in the given coeff field/ring r More...
 
static FORCE_INLINE number n_InitMPZ (mpz_t n, const coeffs r)
 conversion of a GMP integer to number More...
 
static FORCE_INLINE long n_Int (number &n, const coeffs r)
 conversion of n to an int; 0 if not possible in Z/pZ: the representing int lying in (-p/2 .. p/2] More...
 
static FORCE_INLINE void n_MPZ (mpz_t result, number &n, const coeffs r)
 conversion of n to a GMP integer; 0 if not possible More...
 
static FORCE_INLINE number n_InpNeg (number n, const coeffs r)
 in-place negation of n MUST BE USED: n = n_InpNeg(n) (no copy is returned) More...
 
static FORCE_INLINE number n_Invers (number a, const coeffs r)
 return the multiplicative inverse of 'a'; raise an error if 'a' is not invertible More...
 
static FORCE_INLINE int n_Size (number n, const coeffs r)
 return a non-negative measure for the complexity of n; return 0 only when n represents zero; (used for pivot strategies in matrix computations with entries from r) More...
 
static FORCE_INLINE void n_Normalize (number &n, const coeffs r)
 inplace-normalization of n; produces some canonical representation of n; More...
 
static FORCE_INLINE void n_WriteLong (number &n, const coeffs r)
 write to the output buffer of the currently used reporter More...
 
static FORCE_INLINE void n_WriteShort (number &n, const coeffs r)
 write to the output buffer of the currently used reporter in a shortest possible way, e.g. in K(a): a2 instead of a^2 More...
 
static FORCE_INLINE void n_Write (number &n, const coeffs r, const BOOLEAN bShortOut=TRUE)
 
static FORCE_INLINE const char * n_Read (const char *s, number *a, const coeffs r)
 !!! Recommendation: This method is too cryptic to be part of the user- !!! interface. As defined here, it is merely a helper !!! method for parsing number input strings. More...
 
static FORCE_INLINE number n_GetDenom (number &n, const coeffs r)
 return the denominator of n (if elements of r are by nature not fractional, result is 1) More...
 
static FORCE_INLINE number n_GetNumerator (number &n, const coeffs r)
 return the numerator of n (if elements of r are by nature not fractional, result is n) More...
 
static FORCE_INLINE number n_Div (number a, number b, const coeffs r)
 return the quotient of 'a' and 'b', i.e., a/b; raises an error if 'b' is not invertible in r exception in Z: raises an error if 'a' is not divisible by 'b' always: n_Div(a,b,r)*b+n_IntMod(a,b,r)==a More...
 
static FORCE_INLINE number n_ExactDiv (number a, number b, const coeffs r)
 assume that there is a canonical subring in cf and we know that division is possible for these a and b in the subring, n_ExactDiv performs it, may skip additional tests. Can always be substituted by n_Div at the cost of larger computing time. More...
 
static FORCE_INLINE number n_IntMod (number a, number b, const coeffs r)
 for r a field, return n_Init(0,r) always: n_Div(a,b,r)*b+n_IntMod(a,b,r)==a n_IntMod(a,b,r) >=0 More...
 
static FORCE_INLINE void n_Power (number a, int b, number *res, const coeffs r)
 fill res with the power a^b More...
 
static FORCE_INLINE number n_Mult (number a, number b, const coeffs r)
 return the product of 'a' and 'b', i.e., a*b More...
 
static FORCE_INLINE void n_InpMult (number &a, number b, const coeffs r)
 multiplication of 'a' and 'b'; replacement of 'a' by the product a*b More...
 
static FORCE_INLINE void n_InpAdd (number &a, number b, const coeffs r)
 addition of 'a' and 'b'; replacement of 'a' by the sum a+b More...
 
static FORCE_INLINE number n_Add (number a, number b, const coeffs r)
 return the sum of 'a' and 'b', i.e., a+b More...
 
static FORCE_INLINE number n_Sub (number a, number b, const coeffs r)
 return the difference of 'a' and 'b', i.e., a-b More...
 
static FORCE_INLINE number n_Gcd (number a, number b, const coeffs r)
 in Z: return the gcd of 'a' and 'b' in Z/nZ, Z/2^kZ: computed as in the case Z in Z/pZ, C, R: not implemented in Q: return the gcd of the numerators of 'a' and 'b' in K(a)/<p(a)>: not implemented in K(t_1, ..., t_n): not implemented More...
 
static FORCE_INLINE number n_SubringGcd (number a, number b, const coeffs r)
 
static FORCE_INLINE number n_ExtGcd (number a, number b, number *s, number *t, const coeffs r)
 beware that ExtGCD is only relevant for a few chosen coeff. domains and may perform something unexpected in some cases... More...
 
static FORCE_INLINE number n_XExtGcd (number a, number b, number *s, number *t, number *u, number *v, const coeffs r)
 
static FORCE_INLINE number n_EucNorm (number a, const coeffs r)
 
static FORCE_INLINE number n_Ann (number a, const coeffs r)
 if r is a ring with zero divisors, return an annihilator!=0 of b otherwise return NULL More...
 
static FORCE_INLINE number n_QuotRem (number a, number b, number *q, const coeffs r)
 
static FORCE_INLINE number n_Lcm (number a, number b, const coeffs r)
 in Z: return the lcm of 'a' and 'b' in Z/nZ, Z/2^kZ: computed as in the case Z in Z/pZ, C, R: not implemented in K(a)/<p(a)>: not implemented in K(t_1, ..., t_n): not implemented More...
 
static FORCE_INLINE number n_NormalizeHelper (number a, number b, const coeffs r)
 assume that r is a quotient field (otherwise, return 1) for arguments (a1/a2,b1/b2) return (lcm(a1,b2)/1) More...
 
static FORCE_INLINE nMapFunc n_SetMap (const coeffs src, const coeffs dst)
 set the mapping function pointers for translating numbers from src to dst More...
 
static FORCE_INLINE BOOLEAN n_DBTest (number n, const char *filename, const int linenumber, const coeffs r)
 test whether n is a correct number; only used if LDEBUG is defined More...
 
static FORCE_INLINE void n_CoeffWrite (const coeffs r, BOOLEAN details=TRUE)
 output the coeff description More...
 
static FORCE_INLINE BOOLEAN nCoeff_is_Ring_2toM (const coeffs r)
 
static FORCE_INLINE BOOLEAN nCoeff_is_Ring_ModN (const coeffs r)
 
static FORCE_INLINE BOOLEAN nCoeff_is_Ring_PtoM (const coeffs r)
 
static FORCE_INLINE BOOLEAN nCoeff_is_Ring_Z (const coeffs r)
 
static FORCE_INLINE BOOLEAN nCoeff_is_Ring (const coeffs r)
 
static FORCE_INLINE BOOLEAN nCoeff_is_Domain (const coeffs r)
 returns TRUE, if r is a field or r has no zero divisors (i.e is a domain) More...
 
static FORCE_INLINE BOOLEAN n_DivBy (number a, number b, const coeffs r)
 test whether 'a' is divisible 'b'; for r encoding a field: TRUE iff 'b' does not represent zero in Z: TRUE iff 'b' divides 'a' (with remainder = zero) in Z/nZ: TRUE iff (a = 0 and b divides n in Z) or (a != 0 and b/gcd(a, b) is co-prime with n, i.e. a unit in Z/nZ) in Z/2^kZ: TRUE iff ((a = 0 mod 2^k) and (b = 0 or b is a power of 2)) or ((a, b <> 0) and (b/gcd(a, b) is odd)) More...
 
static FORCE_INLINE number n_ChineseRemainderSym (number *a, number *b, int rl, BOOLEAN sym, CFArray &inv_cache, const coeffs r)
 
static FORCE_INLINE number n_Farey (number a, number b, const coeffs r)
 
static FORCE_INLINE int n_ParDeg (number n, const coeffs r)
 
static FORCE_INLINE int n_NumberOfParameters (const coeffs r)
 Returns the number of parameters. More...
 
static FORCE_INLINE char const ** n_ParameterNames (const coeffs r)
 Returns a (const!) pointer to (const char*) names of parameters. More...
 
static FORCE_INLINE number n_Param (const int iParameter, const coeffs r)
 return the (iParameter^th) parameter as a NEW number NOTE: parameter numbering: 1..n_NumberOfParameters(...) More...
 
static FORCE_INLINE number n_RePart (number i, const coeffs cf)
 
static FORCE_INLINE number n_ImPart (number i, const coeffs cf)
 
static FORCE_INLINE BOOLEAN nCoeff_has_Units (const coeffs r)
 returns TRUE, if r is not a field and r has non-trivial units More...
 
static FORCE_INLINE BOOLEAN nCoeff_is_Zp (const coeffs r)
 
static FORCE_INLINE BOOLEAN nCoeff_is_Zp (const coeffs r, int p)
 
static FORCE_INLINE BOOLEAN nCoeff_is_Q (const coeffs r)
 
static FORCE_INLINE BOOLEAN nCoeff_is_Q_or_BI (const coeffs r)
 
static FORCE_INLINE BOOLEAN nCoeff_is_numeric (const coeffs r)
 
static FORCE_INLINE BOOLEAN nCoeff_is_R (const coeffs r)
 
static FORCE_INLINE BOOLEAN nCoeff_is_GF (const coeffs r)
 
static FORCE_INLINE BOOLEAN nCoeff_is_GF (const coeffs r, int q)
 
static FORCE_INLINE BOOLEAN nCoeff_is_Extension (const coeffs r)
 
static FORCE_INLINE BOOLEAN nCoeff_is_Zp_a (const coeffs r)
 
static FORCE_INLINE BOOLEAN nCoeff_is_Zp_a (const coeffs r, int p)
 
static FORCE_INLINE BOOLEAN nCoeff_is_Q_a (const coeffs r)
 
static FORCE_INLINE BOOLEAN nCoeff_is_long_R (const coeffs r)
 
static FORCE_INLINE BOOLEAN nCoeff_is_long_C (const coeffs r)
 
static FORCE_INLINE BOOLEAN nCoeff_is_CF (const coeffs r)
 
static FORCE_INLINE BOOLEAN nCoeff_has_simple_inverse (const coeffs r)
 TRUE, if the computation of the inverse is fast, i.e. prefer leading coeff. 1 over content. More...
 
static FORCE_INLINE BOOLEAN nCoeff_has_simple_Alloc (const coeffs r)
 TRUE if n_Delete/n_New are empty operations. More...
 
static FORCE_INLINE BOOLEAN nCoeff_is_algExt (const coeffs r)
 TRUE iff r represents an algebraic extension field. More...
 
static FORCE_INLINE BOOLEAN nCoeff_is_Q_algext (const coeffs r)
 is it an alg. ext. of Q? More...
 
static FORCE_INLINE BOOLEAN nCoeff_is_transExt (const coeffs r)
 TRUE iff r represents a transcendental extension field. More...
 
static FORCE_INLINE void n_ClearContent (ICoeffsEnumerator &numberCollectionEnumerator, number &c, const coeffs r)
 Computes the content and (inplace) divides it out on a collection of numbers number c is the content (i.e. the GCD of all the coeffs, which we divide out inplace) NOTE: it assumes all coefficient numbers to be integer!!! NOTE/TODO: see also the description by Hans TODO: rename into n_ClearIntegerContent. More...
 
static FORCE_INLINE void n_ClearDenominators (ICoeffsEnumerator &numberCollectionEnumerator, number &d, const coeffs r)
 (inplace) Clears denominators on a collection of numbers number d is the LCM of all the coefficient denominators (i.e. the number with which all the number coeffs. were multiplied) NOTE/TODO: see also the description by Hans More...
 
static FORCE_INLINE void n_ClearContent (ICoeffsEnumerator &numberCollectionEnumerator, const coeffs r)
 
static FORCE_INLINE void n_ClearDenominators (ICoeffsEnumerator &numberCollectionEnumerator, const coeffs r)
 
void n_Print (number &a, const coeffs r)
 print a number (BEWARE of string buffers!) mostly for debugging More...
 
static FORCE_INLINE char * nCoeffString (const coeffs cf)
 TODO: make it a virtual method of coeffs, together with: Decompose & Compose, rParameter & rPar. More...
 
static FORCE_INLINE char * nCoeffName (const coeffs cf)
 
static FORCE_INLINE number n_Random (siRandProc p, number p1, number p2, const coeffs cf)
 
static FORCE_INLINE void n_WriteFd (number a, FILE *f, const coeffs r)
 io via ssi: More...
 
static FORCE_INLINE number n_ReadFd (s_buff f, const coeffs r)
 io via ssi: More...
 
number n_convFactoryNSingN (const CanonicalForm n, const coeffs r)
 
CanonicalForm n_convSingNFactoryN (number n, BOOLEAN setChar, const coeffs r)
 
static FORCE_INLINE void number2mpz (number n, coeffs c, mpz_t m)
 
static FORCE_INLINE number mpz2number (mpz_t m, coeffs c)
 

Variables

const unsigned short fftable []
 
omBin rnumber_bin
 

Detailed Description

Coefficient rings, fields and other domains suitable for Singular polynomials.

The main interface for Singular coefficients: coeffs is the main handler for Singular numbers

Definition in file coeffs.h.


Data Structure Documentation

§ GFInfo

struct GFInfo

Creation data needed for finite fields.

Definition at line 92 of file coeffs.h.

Data Fields
int GFChar
int GFDegree
const char * GFPar_name

§ LongComplexInfo

struct LongComplexInfo

Definition at line 99 of file coeffs.h.

Data Fields
short float_len additional char-flags, rInit
short float_len2 additional char-flags, rInit
const char * par_name parameter name

Macro Definition Documentation

§ ALLOC0_RNUMBER

#define ALLOC0_RNUMBER ( )    (number)omAlloc0Bin(rnumber_bin)

Definition at line 88 of file coeffs.h.

§ ALLOC_RNUMBER

#define ALLOC_RNUMBER ( )    (number)omAllocBin(rnumber_bin)

Definition at line 87 of file coeffs.h.

§ FREE_RNUMBER

#define FREE_RNUMBER (   x)    omFreeBin((void *)x, rnumber_bin)

Definition at line 86 of file coeffs.h.

§ n_New

#define n_New (   n,
  r 
)    nNew(n)

Definition at line 444 of file coeffs.h.

§ n_Test

#define n_Test (   a,
  r 
)    n_DBTest(a, __FILE__, __LINE__, r)

BOOLEAN n_Test(number a, const coeffs r)

Definition at line 742 of file coeffs.h.

Typedef Documentation

§ ICoeffsEnumerator

typedef IEnumerator<number> ICoeffsEnumerator

Abstract interface for an enumerator of number coefficients for an object, e.g. a polynomial.

Definition at line 78 of file coeffs.h.

§ nCoeffsEnumeratorFunc

typedef void(* nCoeffsEnumeratorFunc) (ICoeffsEnumerator &numberCollectionEnumerator, number &output, const coeffs r)

goes over coeffs given by the ICoeffsEnumerator and changes them. Additionally returns a number;

Definition at line 82 of file coeffs.h.

§ nMapFunc

typedef number(* nMapFunc) (number a, const coeffs src, const coeffs dst)

maps "a", which lives in src, into dst

Definition at line 73 of file coeffs.h.

§ numberfunc

typedef number(* numberfunc) (number a, number b, const coeffs r)

Definition at line 70 of file coeffs.h.

Enumeration Type Documentation

§ n_coeffRep

enum n_coeffRep
Enumerator
n_rep_unknown 
n_rep_int 

(int), see modulop.h

n_rep_gap_rat 

(number), see longrat.h

n_rep_gap_gmp 

(), see rinteger.h, new impl.

n_rep_poly 

(poly), see algext.h

n_rep_rat_fct 

(fraction), see transext.h

n_rep_gmp 

(mpz_ptr), see rmodulon,h

n_rep_float 

(float), see shortfl.h

n_rep_gmp_float 

(gmp_float), see

n_rep_gmp_complex 

(gmp_complex), see gnumpc.h

n_rep_gf 

(int), see ffields.h

Definition at line 107 of file coeffs.h.

108 {
109  n_rep_unknown=0,
110  n_rep_int, /**< (int), see modulop.h */
111  n_rep_gap_rat, /**< (number), see longrat.h */
112  n_rep_gap_gmp, /**< (), see rinteger.h, new impl. */
113  n_rep_poly, /**< (poly), see algext.h */
114  n_rep_rat_fct, /**< (fraction), see transext.h */
115  n_rep_gmp, /**< (mpz_ptr), see rmodulon,h */
116  n_rep_float, /**< (float), see shortfl.h */
117  n_rep_gmp_float, /**< (gmp_float), see */
118  n_rep_gmp_complex,/**< (gmp_complex), see gnumpc.h */
119  n_rep_gf /**< (int), see ffields.h */
120 };
(), see rinteger.h, new impl.
Definition: coeffs.h:112
(fraction), see transext.h
Definition: coeffs.h:114
(poly), see algext.h
Definition: coeffs.h:113
(gmp_complex), see gnumpc.h
Definition: coeffs.h:118
(mpz_ptr), see rmodulon,h
Definition: coeffs.h:115
(number), see longrat.h
Definition: coeffs.h:111
(gmp_float), see
Definition: coeffs.h:117
(int), see modulop.h
Definition: coeffs.h:110
(int), see ffields.h
Definition: coeffs.h:119
(float), see shortfl.h
Definition: coeffs.h:116

§ n_coeffType

Enumerator
n_unknown 
n_Zp 

{p < 2^31}

n_Q 

rational (GMP) numbers

n_R 

single prescision (6,6) real numbers

n_GF 

{p^n < 2^16}

n_long_R 

real floating point (GMP) numbers

n_polyExt 

used to represent polys as coeffcients

n_algExt 

used for all algebraic extensions, i.e., the top-most extension in an extension tower is algebraic

n_transExt 

used for all transcendental extensions, i.e., the top-most extension in an extension tower is transcendental

n_long_C 

complex floating point (GMP) numbers

n_Z 

only used if HAVE_RINGS is defined

n_Zn 

only used if HAVE_RINGS is defined

n_Znm 

only used if HAVE_RINGS is defined

n_Z2m 

only used if HAVE_RINGS is defined

n_CF 

?

Definition at line 27 of file coeffs.h.

28 {
29  n_unknown=0,
30  n_Zp, /**< \F{p < 2^31} */
31  n_Q, /**< rational (GMP) numbers */
32  n_R, /**< single prescision (6,6) real numbers */
33  n_GF, /**< \GF{p^n < 2^16} */
34  n_long_R, /**< real floating point (GMP) numbers */
35  n_polyExt, /**< used to represent polys as coeffcients */
36  n_algExt, /**< used for all algebraic extensions, i.e.,
37  the top-most extension in an extension tower
38  is algebraic */
39  n_transExt, /**< used for all transcendental extensions, i.e.,
40  the top-most extension in an extension tower
41  is transcendental */
42  n_long_C, /**< complex floating point (GMP) numbers */
43  n_Z, /**< only used if HAVE_RINGS is defined */
44  n_Zn, /**< only used if HAVE_RINGS is defined */
45  n_Znm, /**< only used if HAVE_RINGS is defined */
46  n_Z2m, /**< only used if HAVE_RINGS is defined */
47  n_CF /**< ? */
48 };
only used if HAVE_RINGS is defined
Definition: coeffs.h:44
?
Definition: coeffs.h:47
only used if HAVE_RINGS is defined
Definition: coeffs.h:46
used for all transcendental extensions, i.e., the top-most extension in an extension tower is transce...
Definition: coeffs.h:39
rational (GMP) numbers
Definition: coeffs.h:31
{p < 2^31}
Definition: coeffs.h:30
real floating point (GMP) numbers
Definition: coeffs.h:34
single prescision (6,6) real numbers
Definition: coeffs.h:32
only used if HAVE_RINGS is defined
Definition: coeffs.h:45
complex floating point (GMP) numbers
Definition: coeffs.h:42
only used if HAVE_RINGS is defined
Definition: coeffs.h:43
{p^n < 2^16}
Definition: coeffs.h:33
used for all algebraic extensions, i.e., the top-most extension in an extension tower is algebraic ...
Definition: coeffs.h:36
used to represent polys as coeffcients
Definition: coeffs.h:35

Function Documentation

§ getCoeffType()

static FORCE_INLINE n_coeffType getCoeffType ( const coeffs  r)
static

Returns the type of coeffs domain.

Definition at line 425 of file coeffs.h.

426 { assume(r != NULL); return r->type; }
#define assume(x)
Definition: mod2.h:403
#define NULL
Definition: omList.c:10

§ mpz2number()

static FORCE_INLINE number mpz2number ( mpz_t  m,
coeffs  c 
)
static

Definition at line 1002 of file coeffs.h.

1002 { return n_InitMPZ(m, c); }
static FORCE_INLINE number n_InitMPZ(mpz_t n, const coeffs r)
conversion of a GMP integer to number
Definition: coeffs.h:546
int m
Definition: cfEzgcd.cc:119

§ n_Add()

static FORCE_INLINE number n_Add ( number  a,
number  b,
const coeffs  r 
)
static

return the sum of 'a' and 'b', i.e., a+b

Definition at line 660 of file coeffs.h.

661 { STATISTIC(n_Add); assume(r != NULL); assume(r->cfAdd!=NULL); const number sum = r->cfAdd(a, b, r);
662 
663 #ifdef HAVE_NUMSTATS
664  // avoid double counting
665  if( r->cfIsZero(sum,r) ) STATISTIC(n_CancelOut);
666 #endif
667 
668  return sum;
669 }
#define STATISTIC(f)
Definition: numstats.h:16
const poly a
Definition: syzextra.cc:212
#define assume(x)
Definition: mod2.h:403
static FORCE_INLINE number n_Add(number a, number b, const coeffs r)
return the sum of &#39;a&#39; and &#39;b&#39;, i.e., a+b
Definition: coeffs.h:660
#define NULL
Definition: omList.c:10
const poly b
Definition: syzextra.cc:213

§ n_Ann()

static FORCE_INLINE number n_Ann ( number  a,
const coeffs  r 
)
static

if r is a ring with zero divisors, return an annihilator!=0 of b otherwise return NULL

Definition at line 705 of file coeffs.h.

706 { STATISTIC(n_Ann); assume(r != NULL); return r->cfAnn (a,r); }
#define STATISTIC(f)
Definition: numstats.h:16
const poly a
Definition: syzextra.cc:212
static FORCE_INLINE number n_Ann(number a, const coeffs r)
if r is a ring with zero divisors, return an annihilator!=0 of b otherwise return NULL ...
Definition: coeffs.h:705
#define assume(x)
Definition: mod2.h:403
#define NULL
Definition: omList.c:10

§ n_ChineseRemainderSym()

static FORCE_INLINE number n_ChineseRemainderSym ( number *  a,
number *  b,
int  rl,
BOOLEAN  sym,
CFArray inv_cache,
const coeffs  r 
)
static

Definition at line 798 of file coeffs.h.

799 { STATISTIC(n_ChineseRemainderSym); assume(r != NULL); assume(r->cfChineseRemainder != NULL); return r->cfChineseRemainder(a,b,rl,sym,inv_cache,r); }
#define STATISTIC(f)
Definition: numstats.h:16
const poly a
Definition: syzextra.cc:212
#define assume(x)
Definition: mod2.h:403
static FORCE_INLINE number n_ChineseRemainderSym(number *a, number *b, int rl, BOOLEAN sym, CFArray &inv_cache, const coeffs r)
Definition: coeffs.h:798
#define NULL
Definition: omList.c:10
const poly b
Definition: syzextra.cc:213

§ n_ClearContent() [1/2]

static FORCE_INLINE void n_ClearContent ( ICoeffsEnumerator numberCollectionEnumerator,
number &  c,
const coeffs  r 
)
static

Computes the content and (inplace) divides it out on a collection of numbers number c is the content (i.e. the GCD of all the coeffs, which we divide out inplace) NOTE: it assumes all coefficient numbers to be integer!!! NOTE/TODO: see also the description by Hans TODO: rename into n_ClearIntegerContent.

Definition at line 942 of file coeffs.h.

943 { STATISTIC(n_ClearContent); assume(r != NULL); r->cfClearContent(numberCollectionEnumerator, c, r); }
#define STATISTIC(f)
Definition: numstats.h:16
static FORCE_INLINE void n_ClearContent(ICoeffsEnumerator &numberCollectionEnumerator, number &c, const coeffs r)
Computes the content and (inplace) divides it out on a collection of numbers number c is the content ...
Definition: coeffs.h:942
#define assume(x)
Definition: mod2.h:403
#define NULL
Definition: omList.c:10

§ n_ClearContent() [2/2]

static FORCE_INLINE void n_ClearContent ( ICoeffsEnumerator numberCollectionEnumerator,
const coeffs  r 
)
static

Definition at line 958 of file coeffs.h.

959 { STATISTIC(n_ClearContent); number c; n_ClearContent(numberCollectionEnumerator, c, r); n_Delete(&c, r); }
#define STATISTIC(f)
Definition: numstats.h:16
static FORCE_INLINE void n_ClearContent(ICoeffsEnumerator &numberCollectionEnumerator, number &c, const coeffs r)
Computes the content and (inplace) divides it out on a collection of numbers number c is the content ...
Definition: coeffs.h:942
static FORCE_INLINE void n_Delete(number *p, const coeffs r)
delete &#39;p&#39;
Definition: coeffs.h:459

§ n_ClearDenominators() [1/2]

static FORCE_INLINE void n_ClearDenominators ( ICoeffsEnumerator numberCollectionEnumerator,
number &  d,
const coeffs  r 
)
static

(inplace) Clears denominators on a collection of numbers number d is the LCM of all the coefficient denominators (i.e. the number with which all the number coeffs. were multiplied) NOTE/TODO: see also the description by Hans

Definition at line 949 of file coeffs.h.

950 { STATISTIC(n_ClearDenominators); assume(r != NULL); r->cfClearDenominators(numberCollectionEnumerator, d, r); }
#define STATISTIC(f)
Definition: numstats.h:16
#define assume(x)
Definition: mod2.h:403
#define NULL
Definition: omList.c:10
static FORCE_INLINE void n_ClearDenominators(ICoeffsEnumerator &numberCollectionEnumerator, number &d, const coeffs r)
(inplace) Clears denominators on a collection of numbers number d is the LCM of all the coefficient d...
Definition: coeffs.h:949

§ n_ClearDenominators() [2/2]

static FORCE_INLINE void n_ClearDenominators ( ICoeffsEnumerator numberCollectionEnumerator,
const coeffs  r 
)
static

Definition at line 961 of file coeffs.h.

962 { STATISTIC(n_ClearDenominators); assume(r != NULL); number d; n_ClearDenominators(numberCollectionEnumerator, d, r); n_Delete(&d, r); }
#define STATISTIC(f)
Definition: numstats.h:16
#define assume(x)
Definition: mod2.h:403
#define NULL
Definition: omList.c:10
static FORCE_INLINE void n_Delete(number *p, const coeffs r)
delete &#39;p&#39;
Definition: coeffs.h:459
static FORCE_INLINE void n_ClearDenominators(ICoeffsEnumerator &numberCollectionEnumerator, number &d, const coeffs r)
(inplace) Clears denominators on a collection of numbers number d is the LCM of all the coefficient d...
Definition: coeffs.h:949

§ n_CoeffRingQuot1()

static FORCE_INLINE coeffs n_CoeffRingQuot1 ( number  c,
const coeffs  r 
)
static

Definition at line 522 of file coeffs.h.

523 { STATISTIC(n_CoeffRingQuot1); assume(r != NULL); assume(r->cfQuot1 != NULL); return r->cfQuot1(c, r); }
#define STATISTIC(f)
Definition: numstats.h:16
#define assume(x)
Definition: mod2.h:403
#define NULL
Definition: omList.c:10
static FORCE_INLINE coeffs n_CoeffRingQuot1(number c, const coeffs r)
Definition: coeffs.h:522

§ n_CoeffWrite()

static FORCE_INLINE void n_CoeffWrite ( const coeffs  r,
BOOLEAN  details = TRUE 
)
static

output the coeff description

Definition at line 745 of file coeffs.h.

746 { STATISTIC(n_CoeffWrite); assume(r != NULL); assume(r->cfCoeffWrite != NULL); r->cfCoeffWrite(r, details); }
#define STATISTIC(f)
Definition: numstats.h:16
#define assume(x)
Definition: mod2.h:403
static FORCE_INLINE void n_CoeffWrite(const coeffs r, BOOLEAN details=TRUE)
output the coeff description
Definition: coeffs.h:745
#define NULL
Definition: omList.c:10

§ n_convFactoryNSingN()

number n_convFactoryNSingN ( const CanonicalForm  n,
const coeffs  r 
)

Definition at line 573 of file numbers.cc.

575 { STATISTIC(n_convFactoryNSingN); assume(r != NULL); assume(r->convFactoryNSingN != NULL); return r->convFactoryNSingN(n, r); }
#define STATISTIC(f)
Definition: numstats.h:16
number n_convFactoryNSingN(const CanonicalForm n, const coeffs r)
Definition: numbers.cc:573
#define assume(x)
Definition: mod2.h:403
#define NULL
Definition: omList.c:10

§ n_convSingNFactoryN()

CanonicalForm n_convSingNFactoryN ( number  n,
BOOLEAN  setChar,
const coeffs  r 
)

Definition at line 578 of file numbers.cc.

580 { STATISTIC(n_convSingNFactoryN); assume(r != NULL); assume(r->convSingNFactoryN != NULL); return r->convSingNFactoryN(n, setChar, r); }
#define STATISTIC(f)
Definition: numstats.h:16
#define assume(x)
Definition: mod2.h:403
#define NULL
Definition: omList.c:10
CanonicalForm n_convSingNFactoryN(number n, BOOLEAN setChar, const coeffs r)
Definition: numbers.cc:578

§ n_Copy()

static FORCE_INLINE number n_Copy ( number  n,
const coeffs  r 
)
static

return a copy of 'n'

Definition at line 455 of file coeffs.h.

456 { STATISTIC(n_Copy); assume(r != NULL); assume(r->cfCopy!=NULL); return r->cfCopy(n, r); }
#define STATISTIC(f)
Definition: numstats.h:16
#define assume(x)
Definition: mod2.h:403
#define NULL
Definition: omList.c:10
static FORCE_INLINE number n_Copy(number n, const coeffs r)
return a copy of &#39;n&#39;
Definition: coeffs.h:455

§ n_DBTest()

static FORCE_INLINE BOOLEAN n_DBTest ( number  n,
const char *  filename,
const int  linenumber,
const coeffs  r 
)
static

test whether n is a correct number; only used if LDEBUG is defined

Definition at line 731 of file coeffs.h.

732 { STATISTIC(n_Test); assume(r != NULL); assume(r->cfDBTest != NULL); return r->cfDBTest(n, filename, linenumber, r); }
#define STATISTIC(f)
Definition: numstats.h:16
#define assume(x)
Definition: mod2.h:403
#define n_Test(a, r)
BOOLEAN n_Test(number a, const coeffs r)
Definition: coeffs.h:742
#define NULL
Definition: omList.c:10

§ n_Delete()

static FORCE_INLINE void n_Delete ( number *  p,
const coeffs  r 
)
static

delete 'p'

Definition at line 459 of file coeffs.h.

460 { STATISTIC(n_Delete); assume(r != NULL); assume(r->cfDelete!= NULL); r->cfDelete(p, r); }
#define STATISTIC(f)
Definition: numstats.h:16
return P p
Definition: myNF.cc:203
#define assume(x)
Definition: mod2.h:403
#define NULL
Definition: omList.c:10
static FORCE_INLINE void n_Delete(number *p, const coeffs r)
delete &#39;p&#39;
Definition: coeffs.h:459

§ n_Div()

static FORCE_INLINE number n_Div ( number  a,
number  b,
const coeffs  r 
)
static

return the quotient of 'a' and 'b', i.e., a/b; raises an error if 'b' is not invertible in r exception in Z: raises an error if 'a' is not divisible by 'b' always: n_Div(a,b,r)*b+n_IntMod(a,b,r)==a

Definition at line 619 of file coeffs.h.

620 { STATISTIC(n_Div); assume(r != NULL); assume(r->cfDiv!=NULL); return r->cfDiv(a,b,r); }
#define STATISTIC(f)
Definition: numstats.h:16
const poly a
Definition: syzextra.cc:212
#define assume(x)
Definition: mod2.h:403
#define NULL
Definition: omList.c:10
static FORCE_INLINE number n_Div(number a, number b, const coeffs r)
return the quotient of &#39;a&#39; and &#39;b&#39;, i.e., a/b; raises an error if &#39;b&#39; is not invertible in r exceptio...
Definition: coeffs.h:619
const poly b
Definition: syzextra.cc:213

§ n_DivBy()

static FORCE_INLINE BOOLEAN n_DivBy ( number  a,
number  b,
const coeffs  r 
)
static

test whether 'a' is divisible 'b'; for r encoding a field: TRUE iff 'b' does not represent zero in Z: TRUE iff 'b' divides 'a' (with remainder = zero) in Z/nZ: TRUE iff (a = 0 and b divides n in Z) or (a != 0 and b/gcd(a, b) is co-prime with n, i.e. a unit in Z/nZ) in Z/2^kZ: TRUE iff ((a = 0 mod 2^k) and (b = 0 or b is a power of 2)) or ((a, b <> 0) and (b/gcd(a, b) is odd))

Definition at line 787 of file coeffs.h.

788 { STATISTIC(n_DivBy); assume(r != NULL);
789 #ifdef HAVE_RINGS
790  if( nCoeff_is_Ring(r) )
791  {
792  assume(r->cfDivBy!=NULL); return r->cfDivBy(a,b,r);
793  }
794 #endif
795  return !n_IsZero(b, r);
796 }
#define STATISTIC(f)
Definition: numstats.h:16
const poly a
Definition: syzextra.cc:212
static FORCE_INLINE BOOLEAN nCoeff_is_Ring(const coeffs r)
Definition: coeffs.h:762
#define assume(x)
Definition: mod2.h:403
static FORCE_INLINE BOOLEAN n_DivBy(number a, number b, const coeffs r)
test whether &#39;a&#39; is divisible &#39;b&#39;; for r encoding a field: TRUE iff &#39;b&#39; does not represent zero in Z:...
Definition: coeffs.h:787
static FORCE_INLINE BOOLEAN n_IsZero(number n, const coeffs r)
TRUE iff &#39;n&#39; represents the zero element.
Definition: coeffs.h:468
#define NULL
Definition: omList.c:10
const poly b
Definition: syzextra.cc:213

§ n_DivComp()

static FORCE_INLINE int n_DivComp ( number  a,
number  b,
const coeffs  r 
)
static

Definition at line 526 of file coeffs.h.

527 { STATISTIC(n_DivComp); assume(r != NULL); assume(r->cfDivComp!=NULL); return r->cfDivComp (a,b,r); }
#define STATISTIC(f)
Definition: numstats.h:16
const poly a
Definition: syzextra.cc:212
#define assume(x)
Definition: mod2.h:403
static FORCE_INLINE int n_DivComp(number a, number b, const coeffs r)
Definition: coeffs.h:526
#define NULL
Definition: omList.c:10
const poly b
Definition: syzextra.cc:213

§ n_Equal()

static FORCE_INLINE BOOLEAN n_Equal ( number  a,
number  b,
const coeffs  r 
)
static

TRUE iff 'a' and 'b' represent the same number; they may have different representations.

Definition at line 464 of file coeffs.h.

465 { STATISTIC(n_Equal); assume(r != NULL); assume(r->cfEqual!=NULL); return r->cfEqual(a, b, r); }
#define STATISTIC(f)
Definition: numstats.h:16
const poly a
Definition: syzextra.cc:212
#define assume(x)
Definition: mod2.h:403
#define NULL
Definition: omList.c:10
static FORCE_INLINE BOOLEAN n_Equal(number a, number b, const coeffs r)
TRUE iff &#39;a&#39; and &#39;b&#39; represent the same number; they may have different representations.
Definition: coeffs.h:464
const poly b
Definition: syzextra.cc:213

§ n_EucNorm()

static FORCE_INLINE number n_EucNorm ( number  a,
const coeffs  r 
)
static

Definition at line 701 of file coeffs.h.

702 { STATISTIC(n_EucNorm); assume(r != NULL); assume(r->cfEucNorm!=NULL); return r->cfEucNorm (a,r); }
#define STATISTIC(f)
Definition: numstats.h:16
static FORCE_INLINE number n_EucNorm(number a, const coeffs r)
Definition: coeffs.h:701
const poly a
Definition: syzextra.cc:212
#define assume(x)
Definition: mod2.h:403
#define NULL
Definition: omList.c:10

§ n_ExactDiv()

static FORCE_INLINE number n_ExactDiv ( number  a,
number  b,
const coeffs  r 
)
static

assume that there is a canonical subring in cf and we know that division is possible for these a and b in the subring, n_ExactDiv performs it, may skip additional tests. Can always be substituted by n_Div at the cost of larger computing time.

Definition at line 626 of file coeffs.h.

627 { STATISTIC(n_ExactDiv); assume(r != NULL); assume(r->cfExactDiv!=NULL); return r->cfExactDiv(a,b,r); }
#define STATISTIC(f)
Definition: numstats.h:16
const poly a
Definition: syzextra.cc:212
#define assume(x)
Definition: mod2.h:403
#define NULL
Definition: omList.c:10
static FORCE_INLINE number n_ExactDiv(number a, number b, const coeffs r)
assume that there is a canonical subring in cf and we know that division is possible for these a and ...
Definition: coeffs.h:626
const poly b
Definition: syzextra.cc:213

§ n_ExtGcd()

static FORCE_INLINE number n_ExtGcd ( number  a,
number  b,
number *  s,
number *  t,
const coeffs  r 
)
static

beware that ExtGCD is only relevant for a few chosen coeff. domains and may perform something unexpected in some cases...

Definition at line 697 of file coeffs.h.

698 { STATISTIC(n_ExtGcd); assume(r != NULL); assume(r->cfExtGcd!=NULL); return r->cfExtGcd (a,b,s,t,r); }
#define STATISTIC(f)
Definition: numstats.h:16
const CanonicalForm int s
Definition: facAbsFact.cc:55
const poly a
Definition: syzextra.cc:212
#define assume(x)
Definition: mod2.h:403
static FORCE_INLINE number n_ExtGcd(number a, number b, number *s, number *t, const coeffs r)
beware that ExtGCD is only relevant for a few chosen coeff. domains and may perform something unexpec...
Definition: coeffs.h:697
#define NULL
Definition: omList.c:10
const poly b
Definition: syzextra.cc:213

§ n_Farey()

static FORCE_INLINE number n_Farey ( number  a,
number  b,
const coeffs  r 
)
static

Definition at line 801 of file coeffs.h.

802 { STATISTIC(n_Farey); assume(r != NULL); assume(r->cfFarey != NULL); return r->cfFarey(a,b,r); }
#define STATISTIC(f)
Definition: numstats.h:16
const poly a
Definition: syzextra.cc:212
#define assume(x)
Definition: mod2.h:403
static FORCE_INLINE number n_Farey(number a, number b, const coeffs r)
Definition: coeffs.h:801
#define NULL
Definition: omList.c:10
const poly b
Definition: syzextra.cc:213

§ n_Gcd()

static FORCE_INLINE number n_Gcd ( number  a,
number  b,
const coeffs  r 
)
static

in Z: return the gcd of 'a' and 'b' in Z/nZ, Z/2^kZ: computed as in the case Z in Z/pZ, C, R: not implemented in Q: return the gcd of the numerators of 'a' and 'b' in K(a)/<p(a)>: not implemented in K(t_1, ..., t_n): not implemented

Definition at line 690 of file coeffs.h.

691 { STATISTIC(n_Gcd); assume(r != NULL); assume(r->cfGcd!=NULL); return r->cfGcd(a,b,r); }
#define STATISTIC(f)
Definition: numstats.h:16
static FORCE_INLINE number n_Gcd(number a, number b, const coeffs r)
in Z: return the gcd of &#39;a&#39; and &#39;b&#39; in Z/nZ, Z/2^kZ: computed as in the case Z in Z/pZ...
Definition: coeffs.h:690
const poly a
Definition: syzextra.cc:212
#define assume(x)
Definition: mod2.h:403
#define NULL
Definition: omList.c:10
const poly b
Definition: syzextra.cc:213

§ n_GetChar()

static FORCE_INLINE int n_GetChar ( const coeffs  r)
static

Return the characteristic of the coeff. domain.

Definition at line 448 of file coeffs.h.

449 { STATISTIC(n_GetChar); assume(r != NULL); return r->ch; }
#define STATISTIC(f)
Definition: numstats.h:16
static FORCE_INLINE int n_GetChar(const coeffs r)
Return the characteristic of the coeff. domain.
Definition: coeffs.h:448
#define assume(x)
Definition: mod2.h:403
#define NULL
Definition: omList.c:10

§ n_GetDenom()

static FORCE_INLINE number n_GetDenom ( number &  n,
const coeffs  r 
)
static

return the denominator of n (if elements of r are by nature not fractional, result is 1)

Definition at line 607 of file coeffs.h.

608 { STATISTIC(n_GetDenom); assume(r != NULL); assume(r->cfGetDenom!=NULL); return r->cfGetDenom(n, r); }
#define STATISTIC(f)
Definition: numstats.h:16
#define assume(x)
Definition: mod2.h:403
#define NULL
Definition: omList.c:10
static FORCE_INLINE number n_GetDenom(number &n, const coeffs r)
return the denominator of n (if elements of r are by nature not fractional, result is 1) ...
Definition: coeffs.h:607

§ n_GetNumerator()

static FORCE_INLINE number n_GetNumerator ( number &  n,
const coeffs  r 
)
static

return the numerator of n (if elements of r are by nature not fractional, result is n)

Definition at line 612 of file coeffs.h.

613 { STATISTIC(n_GetNumerator); assume(r != NULL); assume(r->cfGetNumerator!=NULL); return r->cfGetNumerator(n, r); }
#define STATISTIC(f)
Definition: numstats.h:16
static FORCE_INLINE number n_GetNumerator(number &n, const coeffs r)
return the numerator of n (if elements of r are by nature not fractional, result is n) ...
Definition: coeffs.h:612
#define assume(x)
Definition: mod2.h:403
#define NULL
Definition: omList.c:10

§ n_GetUnit()

static FORCE_INLINE number n_GetUnit ( number  n,
const coeffs  r 
)
static

in Z: 1 in Z/kZ (where k is not a prime): largest divisor of n (taken in Z) that is co-prime with k in Z/2^kZ: largest odd divisor of n (taken in Z) other cases: not implemented

Definition at line 536 of file coeffs.h.

537 { STATISTIC(n_GetUnit); assume(r != NULL); assume(r->cfGetUnit!=NULL); return r->cfGetUnit(n,r); }
#define STATISTIC(f)
Definition: numstats.h:16
static FORCE_INLINE number n_GetUnit(number n, const coeffs r)
in Z: 1 in Z/kZ (where k is not a prime): largest divisor of n (taken in Z) that is co-prime with k i...
Definition: coeffs.h:536
#define assume(x)
Definition: mod2.h:403
#define NULL
Definition: omList.c:10

§ n_Greater()

static FORCE_INLINE BOOLEAN n_Greater ( number  a,
number  b,
const coeffs  r 
)
static

ordered fields: TRUE iff 'a' is larger than 'b'; in Z/pZ: TRUE iff la > lb, where la and lb are the long's representing

in C: TRUE iff (Im(a) > Im(b)) in K(a)/<p(a)>: TRUE iff (a != 0 and (b == 0 or deg(a) > deg(b)) in K(t_1, ..., t_n): TRUE only if one or both numerator polynomials are zero or if their degrees are equal. In this case, TRUE if LC(numerator(a)) > LC(numerator(b)) in Z/2^kZ: TRUE if n_DivBy(a, b) in Z/mZ: TRUE iff the internal mpz's fulfill the relation '>' in Z: TRUE iff a > b

!!! Recommendation: remove implementations for unordered fields !!! and raise errors instead, in these cases

Definition at line 515 of file coeffs.h.

516 { STATISTIC(n_Greater); assume(r != NULL); assume(r->cfGreater!=NULL); return r->cfGreater(a,b,r); }
static FORCE_INLINE BOOLEAN n_Greater(number a, number b, const coeffs r)
ordered fields: TRUE iff &#39;a&#39; is larger than &#39;b&#39;; in Z/pZ: TRUE iff la > lb, where la and lb are the l...
Definition: coeffs.h:515
#define STATISTIC(f)
Definition: numstats.h:16
const poly a
Definition: syzextra.cc:212
#define assume(x)
Definition: mod2.h:403
#define NULL
Definition: omList.c:10
const poly b
Definition: syzextra.cc:213

§ n_GreaterZero()

static FORCE_INLINE BOOLEAN n_GreaterZero ( number  n,
const coeffs  r 
)
static

ordered fields: TRUE iff 'n' is positive; in Z/pZ: TRUE iff 0 < m <= roundedBelow(p/2), where m is the long representing n in C: TRUE iff (Im(n) != 0 and Im(n) >= 0) or (Im(n) == 0 and Re(n) >= 0) in K(a)/<p(a)>: TRUE iff (n != 0 and (LC(n) > 0 or deg(n) > 0)) in K(t_1, ..., t_n): TRUE iff (LC(numerator(n) is a constant and > 0) or (LC(numerator(n) is not a constant) in Z/2^kZ: TRUE iff 0 < n <= 2^(k-1) in Z/mZ: TRUE iff the internal mpz is greater than zero in Z: TRUE iff n > 0

!!! Recommendation: remove implementations for unordered fields !!! and raise errors instead, in these cases !!! Do not follow this recommendation: while writing polys, !!! between 2 monomials will be an additional + iff !n_GreaterZero(next coeff) Then change definition to include n_GreaterZero => printing does NOT start with -

Definition at line 498 of file coeffs.h.

499 { STATISTIC(n_GreaterZero); assume(r != NULL); assume(r->cfGreaterZero!=NULL); return r->cfGreaterZero(n,r); }
#define STATISTIC(f)
Definition: numstats.h:16
#define assume(x)
Definition: mod2.h:403
#define NULL
Definition: omList.c:10
static FORCE_INLINE BOOLEAN n_GreaterZero(number n, const coeffs r)
ordered fields: TRUE iff &#39;n&#39; is positive; in Z/pZ: TRUE iff 0 < m <= roundedBelow(p/2), where m is the long representing n in C: TRUE iff (Im(n) != 0 and Im(n) >= 0) or (Im(n) == 0 and Re(n) >= 0) in K(a)/<p(a)>: TRUE iff (n != 0 and (LC(n) > 0 or deg(n) > 0)) in K(t_1, ..., t_n): TRUE iff (LC(numerator(n) is a constant and > 0) or (LC(numerator(n) is not a constant) in Z/2^kZ: TRUE iff 0 < n <= 2^(k-1) in Z/mZ: TRUE iff the internal mpz is greater than zero in Z: TRUE iff n > 0
Definition: coeffs.h:498

§ n_ImPart()

static FORCE_INLINE number n_ImPart ( number  i,
const coeffs  cf 
)
static

Definition at line 827 of file coeffs.h.

828 { STATISTIC(n_ImPart); assume(cf != NULL); assume(cf->cfImPart!=NULL); return cf->cfImPart(i,cf); }
#define STATISTIC(f)
Definition: numstats.h:16
#define assume(x)
Definition: mod2.h:403
int i
Definition: cfEzgcd.cc:123
static FORCE_INLINE number n_ImPart(number i, const coeffs cf)
Definition: coeffs.h:827
#define NULL
Definition: omList.c:10

§ n_Init()

static FORCE_INLINE number n_Init ( long  i,
const coeffs  r 
)
static

a number representing i in the given coeff field/ring r

Definition at line 542 of file coeffs.h.

543 { STATISTIC(n_Init); assume(r != NULL); assume(r->cfInit!=NULL); return r->cfInit(i,r); }
#define STATISTIC(f)
Definition: numstats.h:16
static FORCE_INLINE number n_Init(long i, const coeffs r)
a number representing i in the given coeff field/ring r
Definition: coeffs.h:542
#define assume(x)
Definition: mod2.h:403
int i
Definition: cfEzgcd.cc:123
#define NULL
Definition: omList.c:10

§ n_InitMPZ()

static FORCE_INLINE number n_InitMPZ ( mpz_t  n,
const coeffs  r 
)
static

conversion of a GMP integer to number

Definition at line 546 of file coeffs.h.

547 { STATISTIC(n_InitMPZ); assume(r != NULL); assume(r->cfInitMPZ != NULL); return r->cfInitMPZ(n,r); }
#define STATISTIC(f)
Definition: numstats.h:16
#define assume(x)
Definition: mod2.h:403
static FORCE_INLINE number n_InitMPZ(mpz_t n, const coeffs r)
conversion of a GMP integer to number
Definition: coeffs.h:546
#define NULL
Definition: omList.c:10

§ n_InpAdd()

static FORCE_INLINE void n_InpAdd ( number &  a,
number  b,
const coeffs  r 
)
static

addition of 'a' and 'b'; replacement of 'a' by the sum a+b

Definition at line 650 of file coeffs.h.

651 { STATISTIC(n_InpAdd); assume(r != NULL); assume(r->cfInpAdd!=NULL); r->cfInpAdd(a,b,r);
652 
653 #ifdef HAVE_NUMSTATS
654  // avoid double counting
655  if( r->cfIsZero(a,r) ) STATISTIC(n_CancelOut);
656 #endif
657 }
#define STATISTIC(f)
Definition: numstats.h:16
const poly a
Definition: syzextra.cc:212
static FORCE_INLINE void n_InpAdd(number &a, number b, const coeffs r)
addition of &#39;a&#39; and &#39;b&#39;; replacement of &#39;a&#39; by the sum a+b
Definition: coeffs.h:650
#define assume(x)
Definition: mod2.h:403
#define NULL
Definition: omList.c:10
const poly b
Definition: syzextra.cc:213

§ n_InpMult()

static FORCE_INLINE void n_InpMult ( number &  a,
number  b,
const coeffs  r 
)
static

multiplication of 'a' and 'b'; replacement of 'a' by the product a*b

Definition at line 645 of file coeffs.h.

646 { STATISTIC(n_InpMult); assume(r != NULL); assume(r->cfInpMult!=NULL); r->cfInpMult(a,b,r); }
#define STATISTIC(f)
Definition: numstats.h:16
const poly a
Definition: syzextra.cc:212
static FORCE_INLINE void n_InpMult(number &a, number b, const coeffs r)
multiplication of &#39;a&#39; and &#39;b&#39;; replacement of &#39;a&#39; by the product a*b
Definition: coeffs.h:645
#define assume(x)
Definition: mod2.h:403
#define NULL
Definition: omList.c:10
const poly b
Definition: syzextra.cc:213

§ n_InpNeg()

static FORCE_INLINE number n_InpNeg ( number  n,
const coeffs  r 
)
static

in-place negation of n MUST BE USED: n = n_InpNeg(n) (no copy is returned)

Definition at line 561 of file coeffs.h.

562 { STATISTIC(n_InpNeg); assume(r != NULL); assume(r->cfInpNeg!=NULL); return r->cfInpNeg(n,r); }
#define STATISTIC(f)
Definition: numstats.h:16
#define assume(x)
Definition: mod2.h:403
static FORCE_INLINE number n_InpNeg(number n, const coeffs r)
in-place negation of n MUST BE USED: n = n_InpNeg(n) (no copy is returned)
Definition: coeffs.h:561
#define NULL
Definition: omList.c:10

§ n_Int()

static FORCE_INLINE long n_Int ( number &  n,
const coeffs  r 
)
static

conversion of n to an int; 0 if not possible in Z/pZ: the representing int lying in (-p/2 .. p/2]

Definition at line 551 of file coeffs.h.

552 { STATISTIC(n_Int); assume(r != NULL); assume(r->cfInt!=NULL); return r->cfInt(n,r); }
#define STATISTIC(f)
Definition: numstats.h:16
static FORCE_INLINE long n_Int(number &n, const coeffs r)
conversion of n to an int; 0 if not possible in Z/pZ: the representing int lying in (-p/2 ...
Definition: coeffs.h:551
#define assume(x)
Definition: mod2.h:403
#define NULL
Definition: omList.c:10

§ n_IntMod()

static FORCE_INLINE number n_IntMod ( number  a,
number  b,
const coeffs  r 
)
static

for r a field, return n_Init(0,r) always: n_Div(a,b,r)*b+n_IntMod(a,b,r)==a n_IntMod(a,b,r) >=0

Definition at line 632 of file coeffs.h.

633 { STATISTIC(n_IntMod); assume(r != NULL); return r->cfIntMod(a,b,r); }
#define STATISTIC(f)
Definition: numstats.h:16
static FORCE_INLINE number n_IntMod(number a, number b, const coeffs r)
for r a field, return n_Init(0,r) always: n_Div(a,b,r)*b+n_IntMod(a,b,r)==a n_IntMod(a,b,r) >=0
Definition: coeffs.h:632
const poly a
Definition: syzextra.cc:212
#define assume(x)
Definition: mod2.h:403
#define NULL
Definition: omList.c:10
const poly b
Definition: syzextra.cc:213

§ n_Invers()

static FORCE_INLINE number n_Invers ( number  a,
const coeffs  r 
)
static

return the multiplicative inverse of 'a'; raise an error if 'a' is not invertible

!!! Recommendation: rename to 'n_Inverse'

Definition at line 568 of file coeffs.h.

569 { STATISTIC(n_Invers); assume(r != NULL); assume(r->cfInvers!=NULL); return r->cfInvers(a,r); }
#define STATISTIC(f)
Definition: numstats.h:16
const poly a
Definition: syzextra.cc:212
#define assume(x)
Definition: mod2.h:403
static FORCE_INLINE number n_Invers(number a, const coeffs r)
return the multiplicative inverse of &#39;a&#39;; raise an error if &#39;a&#39; is not invertible ...
Definition: coeffs.h:568
#define NULL
Definition: omList.c:10

§ n_IsMOne()

static FORCE_INLINE BOOLEAN n_IsMOne ( number  n,
const coeffs  r 
)
static

TRUE iff 'n' represents the additive inverse of the one element, i.e. -1.

Definition at line 476 of file coeffs.h.

477 { STATISTIC(n_IsMOne); assume(r != NULL); assume(r->cfIsMOne!=NULL); return r->cfIsMOne(n,r); }
#define STATISTIC(f)
Definition: numstats.h:16
#define assume(x)
Definition: mod2.h:403
#define NULL
Definition: omList.c:10
static FORCE_INLINE BOOLEAN n_IsMOne(number n, const coeffs r)
TRUE iff &#39;n&#39; represents the additive inverse of the one element, i.e. -1.
Definition: coeffs.h:476

§ n_IsOne()

static FORCE_INLINE BOOLEAN n_IsOne ( number  n,
const coeffs  r 
)
static

TRUE iff 'n' represents the one element.

Definition at line 472 of file coeffs.h.

473 { STATISTIC(n_IsOne); assume(r != NULL); assume(r->cfIsOne!=NULL); return r->cfIsOne(n,r); }
#define STATISTIC(f)
Definition: numstats.h:16
static FORCE_INLINE BOOLEAN n_IsOne(number n, const coeffs r)
TRUE iff &#39;n&#39; represents the one element.
Definition: coeffs.h:472
#define assume(x)
Definition: mod2.h:403
#define NULL
Definition: omList.c:10

§ n_IsUnit()

static FORCE_INLINE BOOLEAN n_IsUnit ( number  n,
const coeffs  r 
)
static

TRUE iff n has a multiplicative inverse in the given coeff field/ring r.

Definition at line 519 of file coeffs.h.

520 { STATISTIC(n_IsUnit); assume(r != NULL); assume(r->cfIsUnit!=NULL); return r->cfIsUnit(n,r); }
#define STATISTIC(f)
Definition: numstats.h:16
static FORCE_INLINE BOOLEAN n_IsUnit(number n, const coeffs r)
TRUE iff n has a multiplicative inverse in the given coeff field/ring r.
Definition: coeffs.h:519
#define assume(x)
Definition: mod2.h:403
#define NULL
Definition: omList.c:10

§ n_IsZero()

static FORCE_INLINE BOOLEAN n_IsZero ( number  n,
const coeffs  r 
)
static

TRUE iff 'n' represents the zero element.

Definition at line 468 of file coeffs.h.

469 { STATISTIC(n_IsZero); assume(r != NULL); assume(r->cfIsZero!=NULL); return r->cfIsZero(n,r); }
#define STATISTIC(f)
Definition: numstats.h:16
#define assume(x)
Definition: mod2.h:403
static FORCE_INLINE BOOLEAN n_IsZero(number n, const coeffs r)
TRUE iff &#39;n&#39; represents the zero element.
Definition: coeffs.h:468
#define NULL
Definition: omList.c:10

§ n_Lcm()

static FORCE_INLINE number n_Lcm ( number  a,
number  b,
const coeffs  r 
)
static

in Z: return the lcm of 'a' and 'b' in Z/nZ, Z/2^kZ: computed as in the case Z in Z/pZ, C, R: not implemented in K(a)/<p(a)>: not implemented in K(t_1, ..., t_n): not implemented

Definition at line 716 of file coeffs.h.

717 { STATISTIC(n_Lcm); assume(r != NULL); assume(r->cfLcm!=NULL); return r->cfLcm(a,b,r); }
#define STATISTIC(f)
Definition: numstats.h:16
const poly a
Definition: syzextra.cc:212
#define assume(x)
Definition: mod2.h:403
static FORCE_INLINE number n_Lcm(number a, number b, const coeffs r)
in Z: return the lcm of &#39;a&#39; and &#39;b&#39; in Z/nZ, Z/2^kZ: computed as in the case Z in Z/pZ...
Definition: coeffs.h:716
#define NULL
Definition: omList.c:10
const poly b
Definition: syzextra.cc:213

§ n_MPZ()

static FORCE_INLINE void n_MPZ ( mpz_t  result,
number &  n,
const coeffs  r 
)
static

conversion of n to a GMP integer; 0 if not possible

Definition at line 555 of file coeffs.h.

556 { STATISTIC(n_MPZ); assume(r != NULL); assume(r->cfMPZ!=NULL); r->cfMPZ(result, n, r); }
#define STATISTIC(f)
Definition: numstats.h:16
#define assume(x)
Definition: mod2.h:403
#define NULL
Definition: omList.c:10
static FORCE_INLINE void n_MPZ(mpz_t result, number &n, const coeffs r)
conversion of n to a GMP integer; 0 if not possible
Definition: coeffs.h:555
return result
Definition: facAbsBiFact.cc:76

§ n_Mult()

static FORCE_INLINE number n_Mult ( number  a,
number  b,
const coeffs  r 
)
static

return the product of 'a' and 'b', i.e., a*b

Definition at line 640 of file coeffs.h.

641 { STATISTIC(n_Mult); assume(r != NULL); assume(r->cfMult!=NULL); return r->cfMult(a, b, r); }
#define STATISTIC(f)
Definition: numstats.h:16
const poly a
Definition: syzextra.cc:212
static FORCE_INLINE number n_Mult(number a, number b, const coeffs r)
return the product of &#39;a&#39; and &#39;b&#39;, i.e., a*b
Definition: coeffs.h:640
#define assume(x)
Definition: mod2.h:403
#define NULL
Definition: omList.c:10
const poly b
Definition: syzextra.cc:213

§ n_Normalize()

static FORCE_INLINE void n_Normalize ( number &  n,
const coeffs  r 
)
static

inplace-normalization of n; produces some canonical representation of n;

!!! Recommendation: remove this method from the user-interface, i.e., !!! this should be hidden

Definition at line 582 of file coeffs.h.

583 { STATISTIC(n_Normalize); assume(r != NULL); assume(r->cfNormalize!=NULL); r->cfNormalize(n,r); }
#define STATISTIC(f)
Definition: numstats.h:16
static FORCE_INLINE void n_Normalize(number &n, const coeffs r)
inplace-normalization of n; produces some canonical representation of n;
Definition: coeffs.h:582
#define assume(x)
Definition: mod2.h:403
#define NULL
Definition: omList.c:10

§ n_NormalizeHelper()

static FORCE_INLINE number n_NormalizeHelper ( number  a,
number  b,
const coeffs  r 
)
static

assume that r is a quotient field (otherwise, return 1) for arguments (a1/a2,b1/b2) return (lcm(a1,b2)/1)

Definition at line 721 of file coeffs.h.

722 { STATISTIC(n_NormalizeHelper); assume(r != NULL); assume(r->cfNormalizeHelper!=NULL); return r->cfNormalizeHelper(a,b,r); }
#define STATISTIC(f)
Definition: numstats.h:16
const poly a
Definition: syzextra.cc:212
static FORCE_INLINE number n_NormalizeHelper(number a, number b, const coeffs r)
assume that r is a quotient field (otherwise, return 1) for arguments (a1/a2,b1/b2) return (lcm(a1...
Definition: coeffs.h:721
#define assume(x)
Definition: mod2.h:403
#define NULL
Definition: omList.c:10
const poly b
Definition: syzextra.cc:213

§ n_NumberOfParameters()

static FORCE_INLINE int n_NumberOfParameters ( const coeffs  r)
static

Returns the number of parameters.

Definition at line 808 of file coeffs.h.

809 { STATISTIC(n_NumberOfParameters); assume(r != NULL); return r->iNumberOfParameters; }
#define STATISTIC(f)
Definition: numstats.h:16
static FORCE_INLINE int n_NumberOfParameters(const coeffs r)
Returns the number of parameters.
Definition: coeffs.h:808
#define assume(x)
Definition: mod2.h:403
#define NULL
Definition: omList.c:10

§ n_Param()

static FORCE_INLINE number n_Param ( const int  iParameter,
const coeffs  r 
)
static

return the (iParameter^th) parameter as a NEW number NOTE: parameter numbering: 1..n_NumberOfParameters(...)

Definition at line 817 of file coeffs.h.

818 { assume(r != NULL);
819  assume((iParameter >= 1) || (iParameter <= n_NumberOfParameters(r)));
820  assume(r->cfParameter != NULL);
821  STATISTIC(n_Param); return r->cfParameter(iParameter, r);
822 }
#define STATISTIC(f)
Definition: numstats.h:16
static FORCE_INLINE int n_NumberOfParameters(const coeffs r)
Returns the number of parameters.
Definition: coeffs.h:808
static FORCE_INLINE number n_Param(const int iParameter, const coeffs r)
return the (iParameter^th) parameter as a NEW number NOTE: parameter numbering: 1..n_NumberOfParameters(...)
Definition: coeffs.h:817
#define assume(x)
Definition: mod2.h:403
#define NULL
Definition: omList.c:10

§ n_ParameterNames()

static FORCE_INLINE char const* * n_ParameterNames ( const coeffs  r)
static

Returns a (const!) pointer to (const char*) names of parameters.

Definition at line 812 of file coeffs.h.

813 { STATISTIC(n_ParameterNames); assume(r != NULL); return r->pParameterNames; }
#define STATISTIC(f)
Definition: numstats.h:16
static FORCE_INLINE char const ** n_ParameterNames(const coeffs r)
Returns a (const!) pointer to (const char*) names of parameters.
Definition: coeffs.h:812
#define assume(x)
Definition: mod2.h:403
#define NULL
Definition: omList.c:10

§ n_ParDeg()

static FORCE_INLINE int n_ParDeg ( number  n,
const coeffs  r 
)
static

Definition at line 804 of file coeffs.h.

805 { STATISTIC(n_ParDeg); assume(r != NULL); assume(r->cfParDeg != NULL); return r->cfParDeg(n,r); }
#define STATISTIC(f)
Definition: numstats.h:16
static FORCE_INLINE int n_ParDeg(number n, const coeffs r)
Definition: coeffs.h:804
#define assume(x)
Definition: mod2.h:403
#define NULL
Definition: omList.c:10

§ n_Power()

static FORCE_INLINE void n_Power ( number  a,
int  b,
number *  res,
const coeffs  r 
)
static

fill res with the power a^b

Definition at line 636 of file coeffs.h.

637 { STATISTIC(n_Power); assume(r != NULL); assume(r->cfPower!=NULL); r->cfPower(a,b,res,r); }
#define STATISTIC(f)
Definition: numstats.h:16
const poly a
Definition: syzextra.cc:212
poly res
Definition: myNF.cc:322
#define assume(x)
Definition: mod2.h:403
static FORCE_INLINE void n_Power(number a, int b, number *res, const coeffs r)
fill res with the power a^b
Definition: coeffs.h:636
#define NULL
Definition: omList.c:10
const poly b
Definition: syzextra.cc:213

§ n_Print()

void n_Print ( number &  a,
const coeffs  r 
)

print a number (BEWARE of string buffers!) mostly for debugging

Definition at line 562 of file numbers.cc.

564 {
565  assume(r != NULL);
566  n_Test(a,r);
567 
568  StringSetS("");
569  n_Write(a, r);
570  { char* s = StringEndS(); Print("%s", s); omFree(s); }
const CanonicalForm int s
Definition: facAbsFact.cc:55
const poly a
Definition: syzextra.cc:212
#define Print
Definition: emacs.cc:83
char * StringEndS()
Definition: reporter.cc:151
#define omFree(addr)
Definition: omAllocDecl.h:261
#define assume(x)
Definition: mod2.h:403
void StringSetS(const char *st)
Definition: reporter.cc:128
static FORCE_INLINE void n_Write(number &n, const coeffs r, const BOOLEAN bShortOut=TRUE)
Definition: coeffs.h:595
#define n_Test(a, r)
BOOLEAN n_Test(number a, const coeffs r)
Definition: coeffs.h:742
#define NULL
Definition: omList.c:10

§ n_QuotRem()

static FORCE_INLINE number n_QuotRem ( number  a,
number  b,
number *  q,
const coeffs  r 
)
static

Definition at line 707 of file coeffs.h.

708 { STATISTIC(n_QuotRem); assume(r != NULL); assume(r->cfQuotRem!=NULL); return r->cfQuotRem (a,b,q,r); }
#define STATISTIC(f)
Definition: numstats.h:16
const poly a
Definition: syzextra.cc:212
#define assume(x)
Definition: mod2.h:403
static FORCE_INLINE number n_QuotRem(number a, number b, number *q, const coeffs r)
Definition: coeffs.h:707
#define NULL
Definition: omList.c:10
const poly b
Definition: syzextra.cc:213

§ n_Random()

static FORCE_INLINE number n_Random ( siRandProc  p,
number  p1,
number  p2,
const coeffs  cf 
)
static

Definition at line 980 of file coeffs.h.

981 { STATISTIC(n_Random); assume( cf != NULL ); assume( cf->cfRandom != NULL ); return cf->cfRandom(p, p1, p2, cf); }
#define STATISTIC(f)
Definition: numstats.h:16
return P p
Definition: myNF.cc:203
static FORCE_INLINE number n_Random(siRandProc p, number p1, number p2, const coeffs cf)
Definition: coeffs.h:980
#define assume(x)
Definition: mod2.h:403
#define NULL
Definition: omList.c:10
END_NAMESPACE const void * p2
Definition: syzextra.cc:202

§ n_Read()

static FORCE_INLINE const char* n_Read ( const char *  s,
number *  a,
const coeffs  r 
)
static

!!! Recommendation: This method is too cryptic to be part of the user- !!! interface. As defined here, it is merely a helper !!! method for parsing number input strings.

Definition at line 602 of file coeffs.h.

603 { STATISTIC(n_Read); assume(r != NULL); assume(r->cfRead!=NULL); return r->cfRead(s, a, r); }
#define STATISTIC(f)
Definition: numstats.h:16
const CanonicalForm int s
Definition: facAbsFact.cc:55
const poly a
Definition: syzextra.cc:212
static FORCE_INLINE const char * n_Read(const char *s, number *a, const coeffs r)
!!! Recommendation: This method is too cryptic to be part of the user- !!! interface. As defined here, it is merely a helper !!! method for parsing number input strings.
Definition: coeffs.h:602
#define assume(x)
Definition: mod2.h:403
#define NULL
Definition: omList.c:10

§ n_ReadFd()

static FORCE_INLINE number n_ReadFd ( s_buff  f,
const coeffs  r 
)
static

io via ssi:

Definition at line 988 of file coeffs.h.

989 { STATISTIC(n_ReadFd); assume(r != NULL); assume(r->cfReadFd != NULL); return r->cfReadFd(f, r); }
#define STATISTIC(f)
Definition: numstats.h:16
static FORCE_INLINE number n_ReadFd(s_buff f, const coeffs r)
io via ssi:
Definition: coeffs.h:988
#define assume(x)
Definition: mod2.h:403
FILE * f
Definition: checklibs.c:7
#define NULL
Definition: omList.c:10

§ n_RePart()

static FORCE_INLINE number n_RePart ( number  i,
const coeffs  cf 
)
static

Definition at line 824 of file coeffs.h.

825 { STATISTIC(n_RePart); assume(cf != NULL); assume(cf->cfRePart!=NULL); return cf->cfRePart(i,cf); }
#define STATISTIC(f)
Definition: numstats.h:16
#define assume(x)
Definition: mod2.h:403
int i
Definition: cfEzgcd.cc:123
#define NULL
Definition: omList.c:10
static FORCE_INLINE number n_RePart(number i, const coeffs cf)
Definition: coeffs.h:824

§ n_SetMap()

static FORCE_INLINE nMapFunc n_SetMap ( const coeffs  src,
const coeffs  dst 
)
static

set the mapping function pointers for translating numbers from src to dst

Definition at line 725 of file coeffs.h.

726 { STATISTIC(n_SetMap); assume(src != NULL && dst != NULL); assume(dst->cfSetMap!=NULL); return dst->cfSetMap(src,dst); }
#define STATISTIC(f)
Definition: numstats.h:16
#define assume(x)
Definition: mod2.h:403
static FORCE_INLINE nMapFunc n_SetMap(const coeffs src, const coeffs dst)
set the mapping function pointers for translating numbers from src to dst
Definition: coeffs.h:725
#define NULL
Definition: omList.c:10

§ n_Size()

static FORCE_INLINE int n_Size ( number  n,
const coeffs  r 
)
static

return a non-negative measure for the complexity of n; return 0 only when n represents zero; (used for pivot strategies in matrix computations with entries from r)

Definition at line 574 of file coeffs.h.

575 { STATISTIC(n_Size); assume(r != NULL); assume(r->cfSize!=NULL); return r->cfSize(n,r); }
#define STATISTIC(f)
Definition: numstats.h:16
#define assume(x)
Definition: mod2.h:403
#define NULL
Definition: omList.c:10
static FORCE_INLINE int n_Size(number n, const coeffs r)
return a non-negative measure for the complexity of n; return 0 only when n represents zero; (used fo...
Definition: coeffs.h:574

§ n_Sub()

static FORCE_INLINE number n_Sub ( number  a,
number  b,
const coeffs  r 
)
static

return the difference of 'a' and 'b', i.e., a-b

Definition at line 673 of file coeffs.h.

674 { STATISTIC(n_Sub); assume(r != NULL); assume(r->cfSub!=NULL); const number d = r->cfSub(a, b, r);
675 
676 #ifdef HAVE_NUMSTATS
677  // avoid double counting
678  if( r->cfIsZero(d,r) ) STATISTIC(n_CancelOut);
679 #endif
680 
681  return d;
682 }
static FORCE_INLINE number n_Sub(number a, number b, const coeffs r)
return the difference of &#39;a&#39; and &#39;b&#39;, i.e., a-b
Definition: coeffs.h:673
#define STATISTIC(f)
Definition: numstats.h:16
const poly a
Definition: syzextra.cc:212
#define assume(x)
Definition: mod2.h:403
#define NULL
Definition: omList.c:10
const poly b
Definition: syzextra.cc:213

§ n_SubringGcd()

static FORCE_INLINE number n_SubringGcd ( number  a,
number  b,
const coeffs  r 
)
static

Definition at line 692 of file coeffs.h.

693 { STATISTIC(n_SubringGcd); assume(r != NULL); assume(r->cfSubringGcd!=NULL); return r->cfSubringGcd(a,b,r); }
#define STATISTIC(f)
Definition: numstats.h:16
const poly a
Definition: syzextra.cc:212
#define assume(x)
Definition: mod2.h:403
#define NULL
Definition: omList.c:10
static FORCE_INLINE number n_SubringGcd(number a, number b, const coeffs r)
Definition: coeffs.h:692
const poly b
Definition: syzextra.cc:213

§ n_Write()

static FORCE_INLINE void n_Write ( number &  n,
const coeffs  r,
const BOOLEAN  bShortOut = TRUE 
)
static

Definition at line 595 of file coeffs.h.

596 { STATISTIC(n_Write); if (bShortOut) n_WriteShort(n, r); else n_WriteLong(n, r); }
#define STATISTIC(f)
Definition: numstats.h:16
static FORCE_INLINE void n_Write(number &n, const coeffs r, const BOOLEAN bShortOut=TRUE)
Definition: coeffs.h:595
static FORCE_INLINE void n_WriteShort(number &n, const coeffs r)
write to the output buffer of the currently used reporter in a shortest possible way, e.g. in K(a): a2 instead of a^2
Definition: coeffs.h:592
static FORCE_INLINE void n_WriteLong(number &n, const coeffs r)
write to the output buffer of the currently used reporter
Definition: coeffs.h:587

§ n_WriteFd()

static FORCE_INLINE void n_WriteFd ( number  a,
FILE *  f,
const coeffs  r 
)
static

io via ssi:

Definition at line 984 of file coeffs.h.

985 { STATISTIC(n_WriteFd); assume(r != NULL); assume(r->cfWriteFd != NULL); return r->cfWriteFd(a, f, r); }
#define STATISTIC(f)
Definition: numstats.h:16
const poly a
Definition: syzextra.cc:212
#define assume(x)
Definition: mod2.h:403
FILE * f
Definition: checklibs.c:7
static FORCE_INLINE void n_WriteFd(number a, FILE *f, const coeffs r)
io via ssi:
Definition: coeffs.h:984
#define NULL
Definition: omList.c:10

§ n_WriteLong()

static FORCE_INLINE void n_WriteLong ( number &  n,
const coeffs  r 
)
static

write to the output buffer of the currently used reporter

Definition at line 587 of file coeffs.h.

588 { STATISTIC(n_WriteLong); assume(r != NULL); assume(r->cfWriteLong!=NULL); r->cfWriteLong(n,r); }
#define STATISTIC(f)
Definition: numstats.h:16
#define assume(x)
Definition: mod2.h:403
#define NULL
Definition: omList.c:10
static FORCE_INLINE void n_WriteLong(number &n, const coeffs r)
write to the output buffer of the currently used reporter
Definition: coeffs.h:587

§ n_WriteShort()

static FORCE_INLINE void n_WriteShort ( number &  n,
const coeffs  r 
)
static

write to the output buffer of the currently used reporter in a shortest possible way, e.g. in K(a): a2 instead of a^2

Definition at line 592 of file coeffs.h.

593 { STATISTIC(n_WriteShort); assume(r != NULL); assume(r->cfWriteShort!=NULL); r->cfWriteShort(n,r); }
#define STATISTIC(f)
Definition: numstats.h:16
#define assume(x)
Definition: mod2.h:403
#define NULL
Definition: omList.c:10
static FORCE_INLINE void n_WriteShort(number &n, const coeffs r)
write to the output buffer of the currently used reporter in a shortest possible way, e.g. in K(a): a2 instead of a^2
Definition: coeffs.h:592

§ n_XExtGcd()

static FORCE_INLINE number n_XExtGcd ( number  a,
number  b,
number *  s,
number *  t,
number *  u,
number *  v,
const coeffs  r 
)
static

Definition at line 699 of file coeffs.h.

700 { STATISTIC(n_XExtGcd); assume(r != NULL); assume(r->cfXExtGcd!=NULL); return r->cfXExtGcd (a,b,s,t,u,v,r); }
#define STATISTIC(f)
Definition: numstats.h:16
const CanonicalForm int s
Definition: facAbsFact.cc:55
const poly a
Definition: syzextra.cc:212
static FORCE_INLINE number n_XExtGcd(number a, number b, number *s, number *t, number *u, number *v, const coeffs r)
Definition: coeffs.h:699
#define assume(x)
Definition: mod2.h:403
const Variable & v
< [in] a sqrfree bivariate poly
Definition: facBivar.h:37
#define NULL
Definition: omList.c:10
const poly b
Definition: syzextra.cc:213

§ nCoeff_has_simple_Alloc()

static FORCE_INLINE BOOLEAN nCoeff_has_simple_Alloc ( const coeffs  r)
static

TRUE if n_Delete/n_New are empty operations.

Definition at line 920 of file coeffs.h.

921 { assume(r != NULL); return r->has_simple_Alloc; }
#define assume(x)
Definition: mod2.h:403
#define NULL
Definition: omList.c:10

§ nCoeff_has_simple_inverse()

static FORCE_INLINE BOOLEAN nCoeff_has_simple_inverse ( const coeffs  r)
static

TRUE, if the computation of the inverse is fast, i.e. prefer leading coeff. 1 over content.

Definition at line 916 of file coeffs.h.

917 { assume(r != NULL); return r->has_simple_Inverse; }
#define assume(x)
Definition: mod2.h:403
#define NULL
Definition: omList.c:10

§ nCoeff_has_Units()

static FORCE_INLINE BOOLEAN nCoeff_has_Units ( const coeffs  r)
static

returns TRUE, if r is not a field and r has non-trivial units

Definition at line 831 of file coeffs.h.

832 { assume(r != NULL); return ((getCoeffType(r)==n_Zn) || (getCoeffType(r)==n_Z2m) || (getCoeffType(r)==n_Znm)); }
only used if HAVE_RINGS is defined
Definition: coeffs.h:44
only used if HAVE_RINGS is defined
Definition: coeffs.h:46
only used if HAVE_RINGS is defined
Definition: coeffs.h:45
#define assume(x)
Definition: mod2.h:403
static FORCE_INLINE n_coeffType getCoeffType(const coeffs r)
Returns the type of coeffs domain.
Definition: coeffs.h:425
#define NULL
Definition: omList.c:10

§ nCoeff_is_algExt()

static FORCE_INLINE BOOLEAN nCoeff_is_algExt ( const coeffs  r)
static

TRUE iff r represents an algebraic extension field.

Definition at line 924 of file coeffs.h.

925 { assume(r != NULL); return (getCoeffType(r)==n_algExt); }
#define assume(x)
Definition: mod2.h:403
static FORCE_INLINE n_coeffType getCoeffType(const coeffs r)
Returns the type of coeffs domain.
Definition: coeffs.h:425
#define NULL
Definition: omList.c:10
used for all algebraic extensions, i.e., the top-most extension in an extension tower is algebraic ...
Definition: coeffs.h:36

§ nCoeff_is_CF()

static FORCE_INLINE BOOLEAN nCoeff_is_CF ( const coeffs  r)
static

Definition at line 911 of file coeffs.h.

912 { assume(r != NULL); return getCoeffType(r)==n_CF; }
?
Definition: coeffs.h:47
#define assume(x)
Definition: mod2.h:403
static FORCE_INLINE n_coeffType getCoeffType(const coeffs r)
Returns the type of coeffs domain.
Definition: coeffs.h:425
#define NULL
Definition: omList.c:10

§ nCoeff_is_Domain()

static FORCE_INLINE BOOLEAN nCoeff_is_Domain ( const coeffs  r)
static

returns TRUE, if r is a field or r has no zero divisors (i.e is a domain)

Definition at line 773 of file coeffs.h.

774 {
775  assume(r != NULL);
776  return (r->is_domain);
777 }
#define assume(x)
Definition: mod2.h:403
#define NULL
Definition: omList.c:10

§ nCoeff_is_Extension()

static FORCE_INLINE BOOLEAN nCoeff_is_Extension ( const coeffs  r)
static

Definition at line 860 of file coeffs.h.

861 {
862  assume(r != NULL);
863  return (getCoeffType(r)==n_algExt) || (getCoeffType(r)==n_transExt);
864 }
used for all transcendental extensions, i.e., the top-most extension in an extension tower is transce...
Definition: coeffs.h:39
#define assume(x)
Definition: mod2.h:403
static FORCE_INLINE n_coeffType getCoeffType(const coeffs r)
Returns the type of coeffs domain.
Definition: coeffs.h:425
#define NULL
Definition: omList.c:10
used for all algebraic extensions, i.e., the top-most extension in an extension tower is algebraic ...
Definition: coeffs.h:36

§ nCoeff_is_GF() [1/2]

static FORCE_INLINE BOOLEAN nCoeff_is_GF ( const coeffs  r)
static

Definition at line 853 of file coeffs.h.

854 { assume(r != NULL); return getCoeffType(r)==n_GF; }
#define assume(x)
Definition: mod2.h:403
static FORCE_INLINE n_coeffType getCoeffType(const coeffs r)
Returns the type of coeffs domain.
Definition: coeffs.h:425
#define NULL
Definition: omList.c:10
{p^n < 2^16}
Definition: coeffs.h:33

§ nCoeff_is_GF() [2/2]

static FORCE_INLINE BOOLEAN nCoeff_is_GF ( const coeffs  r,
int  q 
)
static

Definition at line 856 of file coeffs.h.

857 { assume(r != NULL); return (getCoeffType(r)==n_GF) && (r->ch == q); }
#define assume(x)
Definition: mod2.h:403
static FORCE_INLINE n_coeffType getCoeffType(const coeffs r)
Returns the type of coeffs domain.
Definition: coeffs.h:425
#define NULL
Definition: omList.c:10
{p^n < 2^16}
Definition: coeffs.h:33

§ nCoeff_is_long_C()

static FORCE_INLINE BOOLEAN nCoeff_is_long_C ( const coeffs  r)
static

Definition at line 908 of file coeffs.h.

909 { assume(r != NULL); return getCoeffType(r)==n_long_C; }
#define assume(x)
Definition: mod2.h:403
complex floating point (GMP) numbers
Definition: coeffs.h:42
static FORCE_INLINE n_coeffType getCoeffType(const coeffs r)
Returns the type of coeffs domain.
Definition: coeffs.h:425
#define NULL
Definition: omList.c:10

§ nCoeff_is_long_R()

static FORCE_INLINE BOOLEAN nCoeff_is_long_R ( const coeffs  r)
static

Definition at line 905 of file coeffs.h.

906 { assume(r != NULL); return getCoeffType(r)==n_long_R; }
real floating point (GMP) numbers
Definition: coeffs.h:34
#define assume(x)
Definition: mod2.h:403
static FORCE_INLINE n_coeffType getCoeffType(const coeffs r)
Returns the type of coeffs domain.
Definition: coeffs.h:425
#define NULL
Definition: omList.c:10

§ nCoeff_is_numeric()

static FORCE_INLINE BOOLEAN nCoeff_is_numeric ( const coeffs  r)
static

Definition at line 846 of file coeffs.h.

847 { assume(r != NULL); return (getCoeffType(r)==n_R) || (getCoeffType(r)==n_long_R) || (getCoeffType(r)==n_long_C); }
real floating point (GMP) numbers
Definition: coeffs.h:34
single prescision (6,6) real numbers
Definition: coeffs.h:32
#define assume(x)
Definition: mod2.h:403
complex floating point (GMP) numbers
Definition: coeffs.h:42
static FORCE_INLINE n_coeffType getCoeffType(const coeffs r)
Returns the type of coeffs domain.
Definition: coeffs.h:425
#define NULL
Definition: omList.c:10

§ nCoeff_is_Q()

static FORCE_INLINE BOOLEAN nCoeff_is_Q ( const coeffs  r)
static

Definition at line 840 of file coeffs.h.

841 { assume(r != NULL); return getCoeffType(r)==n_Q && (r->is_field); }
rational (GMP) numbers
Definition: coeffs.h:31
#define assume(x)
Definition: mod2.h:403
static FORCE_INLINE n_coeffType getCoeffType(const coeffs r)
Returns the type of coeffs domain.
Definition: coeffs.h:425
#define NULL
Definition: omList.c:10

§ nCoeff_is_Q_a()

static FORCE_INLINE BOOLEAN nCoeff_is_Q_a ( const coeffs  r)
static

Definition at line 899 of file coeffs.h.

900 {
901  assume(r != NULL);
902  return ((n_GetChar(r) == 0) && nCoeff_is_Extension(r));
903 }
static FORCE_INLINE int n_GetChar(const coeffs r)
Return the characteristic of the coeff. domain.
Definition: coeffs.h:448
#define assume(x)
Definition: mod2.h:403
#define NULL
Definition: omList.c:10
static FORCE_INLINE BOOLEAN nCoeff_is_Extension(const coeffs r)
Definition: coeffs.h:860

§ nCoeff_is_Q_algext()

static FORCE_INLINE BOOLEAN nCoeff_is_Q_algext ( const coeffs  r)
static

is it an alg. ext. of Q?

Definition at line 928 of file coeffs.h.

929 { assume(r != NULL); return ((n_GetChar(r) == 0) && nCoeff_is_algExt(r)); }
static FORCE_INLINE int n_GetChar(const coeffs r)
Return the characteristic of the coeff. domain.
Definition: coeffs.h:448
static FORCE_INLINE BOOLEAN nCoeff_is_algExt(const coeffs r)
TRUE iff r represents an algebraic extension field.
Definition: coeffs.h:924
#define assume(x)
Definition: mod2.h:403
#define NULL
Definition: omList.c:10

§ nCoeff_is_Q_or_BI()

static FORCE_INLINE BOOLEAN nCoeff_is_Q_or_BI ( const coeffs  r)
static

Definition at line 843 of file coeffs.h.

844 { assume(r != NULL); return getCoeffType(r)==n_Q; }
rational (GMP) numbers
Definition: coeffs.h:31
#define assume(x)
Definition: mod2.h:403
static FORCE_INLINE n_coeffType getCoeffType(const coeffs r)
Returns the type of coeffs domain.
Definition: coeffs.h:425
#define NULL
Definition: omList.c:10

§ nCoeff_is_R()

static FORCE_INLINE BOOLEAN nCoeff_is_R ( const coeffs  r)
static

Definition at line 850 of file coeffs.h.

851 { assume(r != NULL); return getCoeffType(r)==n_R; }
single prescision (6,6) real numbers
Definition: coeffs.h:32
#define assume(x)
Definition: mod2.h:403
static FORCE_INLINE n_coeffType getCoeffType(const coeffs r)
Returns the type of coeffs domain.
Definition: coeffs.h:425
#define NULL
Definition: omList.c:10

§ nCoeff_is_Ring()

static FORCE_INLINE BOOLEAN nCoeff_is_Ring ( const coeffs  r)
static

Definition at line 762 of file coeffs.h.

763 { assume(r != NULL); return (r->is_field==0); }
#define assume(x)
Definition: mod2.h:403
#define NULL
Definition: omList.c:10

§ nCoeff_is_Ring_2toM()

static FORCE_INLINE BOOLEAN nCoeff_is_Ring_2toM ( const coeffs  r)
static

Definition at line 750 of file coeffs.h.

751 { assume(r != NULL); return (getCoeffType(r)==n_Z2m); }
only used if HAVE_RINGS is defined
Definition: coeffs.h:46
#define assume(x)
Definition: mod2.h:403
static FORCE_INLINE n_coeffType getCoeffType(const coeffs r)
Returns the type of coeffs domain.
Definition: coeffs.h:425
#define NULL
Definition: omList.c:10

§ nCoeff_is_Ring_ModN()

static FORCE_INLINE BOOLEAN nCoeff_is_Ring_ModN ( const coeffs  r)
static

Definition at line 753 of file coeffs.h.

754 { assume(r != NULL); return (getCoeffType(r)==n_Zn); }
only used if HAVE_RINGS is defined
Definition: coeffs.h:44
#define assume(x)
Definition: mod2.h:403
static FORCE_INLINE n_coeffType getCoeffType(const coeffs r)
Returns the type of coeffs domain.
Definition: coeffs.h:425
#define NULL
Definition: omList.c:10

§ nCoeff_is_Ring_PtoM()

static FORCE_INLINE BOOLEAN nCoeff_is_Ring_PtoM ( const coeffs  r)
static

Definition at line 756 of file coeffs.h.

757 { assume(r != NULL); return (getCoeffType(r)==n_Znm); }
only used if HAVE_RINGS is defined
Definition: coeffs.h:45
#define assume(x)
Definition: mod2.h:403
static FORCE_INLINE n_coeffType getCoeffType(const coeffs r)
Returns the type of coeffs domain.
Definition: coeffs.h:425
#define NULL
Definition: omList.c:10

§ nCoeff_is_Ring_Z()

static FORCE_INLINE BOOLEAN nCoeff_is_Ring_Z ( const coeffs  r)
static

Definition at line 759 of file coeffs.h.

760 { assume(r != NULL); return (getCoeffType(r)==n_Z); }
#define assume(x)
Definition: mod2.h:403
only used if HAVE_RINGS is defined
Definition: coeffs.h:43
static FORCE_INLINE n_coeffType getCoeffType(const coeffs r)
Returns the type of coeffs domain.
Definition: coeffs.h:425
#define NULL
Definition: omList.c:10

§ nCoeff_is_transExt()

static FORCE_INLINE BOOLEAN nCoeff_is_transExt ( const coeffs  r)
static

TRUE iff r represents a transcendental extension field.

Definition at line 932 of file coeffs.h.

933 { assume(r != NULL); return (getCoeffType(r)==n_transExt); }
used for all transcendental extensions, i.e., the top-most extension in an extension tower is transce...
Definition: coeffs.h:39
#define assume(x)
Definition: mod2.h:403
static FORCE_INLINE n_coeffType getCoeffType(const coeffs r)
Returns the type of coeffs domain.
Definition: coeffs.h:425
#define NULL
Definition: omList.c:10

§ nCoeff_is_Zp() [1/2]

static FORCE_INLINE BOOLEAN nCoeff_is_Zp ( const coeffs  r)
static

Definition at line 834 of file coeffs.h.

835 { assume(r != NULL); return getCoeffType(r)==n_Zp; }
{p < 2^31}
Definition: coeffs.h:30
#define assume(x)
Definition: mod2.h:403
static FORCE_INLINE n_coeffType getCoeffType(const coeffs r)
Returns the type of coeffs domain.
Definition: coeffs.h:425
#define NULL
Definition: omList.c:10

§ nCoeff_is_Zp() [2/2]

static FORCE_INLINE BOOLEAN nCoeff_is_Zp ( const coeffs  r,
int  p 
)
static

Definition at line 837 of file coeffs.h.

838 { assume(r != NULL); return ((getCoeffType(r)==n_Zp) && (r->ch == p)); }
return P p
Definition: myNF.cc:203
{p < 2^31}
Definition: coeffs.h:30
#define assume(x)
Definition: mod2.h:403
static FORCE_INLINE n_coeffType getCoeffType(const coeffs r)
Returns the type of coeffs domain.
Definition: coeffs.h:425
#define NULL
Definition: omList.c:10

§ nCoeff_is_Zp_a() [1/2]

static FORCE_INLINE BOOLEAN nCoeff_is_Zp_a ( const coeffs  r)
static

Definition at line 873 of file coeffs.h.

874 {
875  assume(r != NULL);
876  return ((!nCoeff_is_Ring(r)) && (n_GetChar(r) != 0) && nCoeff_is_Extension(r));
877 }
static FORCE_INLINE int n_GetChar(const coeffs r)
Return the characteristic of the coeff. domain.
Definition: coeffs.h:448
static FORCE_INLINE BOOLEAN nCoeff_is_Ring(const coeffs r)
Definition: coeffs.h:762
#define assume(x)
Definition: mod2.h:403
#define NULL
Definition: omList.c:10
static FORCE_INLINE BOOLEAN nCoeff_is_Extension(const coeffs r)
Definition: coeffs.h:860

§ nCoeff_is_Zp_a() [2/2]

static FORCE_INLINE BOOLEAN nCoeff_is_Zp_a ( const coeffs  r,
int  p 
)
static

Definition at line 886 of file coeffs.h.

887 {
888  assume(r != NULL);
889  assume(p != 0);
890  return ((!nCoeff_is_Ring(r)) && (n_GetChar(r) == p) && nCoeff_is_Extension(r));
891 }
return P p
Definition: myNF.cc:203
static FORCE_INLINE int n_GetChar(const coeffs r)
Return the characteristic of the coeff. domain.
Definition: coeffs.h:448
static FORCE_INLINE BOOLEAN nCoeff_is_Ring(const coeffs r)
Definition: coeffs.h:762
#define assume(x)
Definition: mod2.h:403
#define NULL
Definition: omList.c:10
static FORCE_INLINE BOOLEAN nCoeff_is_Extension(const coeffs r)
Definition: coeffs.h:860

§ nCoeffName()

static FORCE_INLINE char* nCoeffName ( const coeffs  cf)
static

Definition at line 977 of file coeffs.h.

978 { STATISTIC(nCoeffName); assume( cf != NULL ); return cf->cfCoeffName(cf); }
#define STATISTIC(f)
Definition: numstats.h:16
#define assume(x)
Definition: mod2.h:403
static FORCE_INLINE char * nCoeffName(const coeffs cf)
Definition: coeffs.h:977
#define NULL
Definition: omList.c:10

§ nCoeffString()

static FORCE_INLINE char* nCoeffString ( const coeffs  cf)
static

TODO: make it a virtual method of coeffs, together with: Decompose & Compose, rParameter & rPar.

Definition at line 973 of file coeffs.h.

974 { STATISTIC(nCoeffString); assume( cf != NULL ); return cf->cfCoeffString(cf); }
#define STATISTIC(f)
Definition: numstats.h:16
#define assume(x)
Definition: mod2.h:403
#define NULL
Definition: omList.c:10
static FORCE_INLINE char * nCoeffString(const coeffs cf)
TODO: make it a virtual method of coeffs, together with: Decompose & Compose, rParameter & rPar...
Definition: coeffs.h:973

§ nCopyCoeff()

static FORCE_INLINE coeffs nCopyCoeff ( const coeffs  r)
static

"copy" coeffs, i.e. increment ref

Definition at line 433 of file coeffs.h.

434 { assume(r!=NULL); r->ref++; return r;}
const ring r
Definition: syzextra.cc:208
#define assume(x)
Definition: mod2.h:403
#define NULL
Definition: omList.c:10

§ nInitChar()

coeffs nInitChar ( n_coeffType  t,
void *  parameter 
)

one-time initialisations for new coeffs in case of an error return NULL

Definition at line 329 of file numbers.cc.

331 {
332  n_Procs_s *n=cf_root;
333 
334  while((n!=NULL) && (n->nCoeffIsEqual!=NULL) && (!n->nCoeffIsEqual(n,t,parameter)))
335  n=n->next;
336 
337  if (n==NULL)
338  {
339  n=(n_Procs_s*)omAlloc0(sizeof(n_Procs_s));
340  n->next=cf_root;
341  n->ref=1;
342  n->type=t;
343 
344  // default entries (different from NULL) for some routines:
346  n->cfSize = ndSize;
349  n->cfImPart=ndReturn0;
350  n->cfDelete= ndDelete;
351  n->cfAnn = ndAnn;
352  n->cfCoeffString = ndCoeffString; // should alway be changed!
353  n->cfInpMult=ndInpMult;
354  n->cfInpAdd=ndInpAdd;
355  n->cfCopy = ndCopy;
356  n->cfIntMod=ndIntMod; /* dummy !! */
358  n->cfGcd = ndGcd;
359  n->cfNormalizeHelper = ndGcd; /* tricky, isn't it ?*/
360  n->cfLcm = ndGcd; /* tricky, isn't it ?*/
361  n->cfInitMPZ = ndInitMPZ;
362  n->cfMPZ = ndMPZ;
363  n->cfPower = ndPower;
365 
366  n->cfKillChar = ndKillChar; /* dummy */
367  n->cfSetChar = ndSetChar; /* dummy */
368  // temp. removed to catch all the coeffs which miss to implement this!
369 
371  n->cfFarey = ndFarey;
372  n->cfParDeg = ndParDeg;
373 
375 
378 
379  n->cfIsUnit = ndIsUnit;
380 #ifdef HAVE_RINGS
381  n->cfDivComp = ndDivComp;
382  n->cfDivBy = ndDivBy;
383  n->cfExtGcd = ndExtGcd;
384  //n->cfGetUnit = (nMapFunc)NULL;
385 #endif
386 
387 #ifdef LDEBUG
388  n->cfDBTest=ndDBTest;
389 #endif
390 
393 
394  BOOLEAN nOK=TRUE;
395  // init
396  if ((t<=nLastCoeffs) && (nInitCharTable[t]!=NULL))
397  nOK = (nInitCharTable[t])(n,parameter);
398  else
399  Werror("Sorry: the coeff type [%d] was not registered: it is missing in nInitCharTable", (int)t);
400  if (nOK)
401  {
402  omFreeSize(n,sizeof(*n));
403  return NULL;
404  }
405  cf_root=n;
406  // post init settings:
407  if (n->cfRePart==NULL) n->cfRePart=n->cfCopy;
408  if (n->cfExactDiv==NULL) n->cfExactDiv=n->cfDiv;
409  if (n->cfSubringGcd==NULL) n->cfSubringGcd=n->cfGcd;
410 
411 #ifdef HAVE_RINGS
412  if (n->cfGetUnit==NULL) n->cfGetUnit=n->cfCopy;
413 #endif
414 
415  if(n->cfWriteShort==NULL)
416  n->cfWriteShort = n->cfWriteLong;
417 
419  assume(n->cfSetChar!=NULL);
421  assume(n->cfMult!=NULL);
422  assume(n->cfSub!=NULL);
423  assume(n->cfAdd!=NULL);
424  assume(n->cfDiv!=NULL);
425  assume(n->cfIntMod!=NULL);
426  assume(n->cfExactDiv!=NULL);
427  assume(n->cfInit!=NULL);
428  assume(n->cfInitMPZ!=NULL);
429  assume(n->cfSize!=NULL);
430  assume(n->cfInt!=NULL);
431  assume(n->cfMPZ!=NULL);
432  //assume(n->n->cfDivComp!=NULL);
433  //assume(n->cfIsUnit!=NULL);
434  //assume(n->cfGetUnit!=NULL);
435  //assume(n->cfExtGcd!=NULL);
436  assume(n->cfInpNeg!=NULL);
437  assume(n->cfCopy!=NULL);
438 
439  assume(n->cfWriteLong!=NULL);
440  assume(n->cfWriteShort!=NULL);
441 
442  assume(n->iNumberOfParameters>= 0);
443 
444  assume( (n->iNumberOfParameters == 0 && n->pParameterNames == NULL) ||
445  (n->iNumberOfParameters > 0 && n->pParameterNames != NULL) );
446 
447  assume(n->cfParameter!=NULL);
448  assume(n->cfParDeg!=NULL);
449 
450  assume(n->cfRead!=NULL);
451  assume(n->cfNormalize!=NULL);
452  assume(n->cfGreater!=NULL);
453  //assume(n->cfDivBy!=NULL);
454  assume(n->cfEqual!=NULL);
455  assume(n->cfIsZero!=NULL);
456  assume(n->cfIsOne!=NULL);
457  assume(n->cfIsMOne!=NULL);
459  assume(n->cfGetDenom!=NULL);
461  assume(n->cfGcd!=NULL);
463  assume(n->cfDelete!=NULL);
464  assume(n->cfSetMap!=NULL);
465  assume(n->cfInpMult!=NULL);
466 // assume(n->cfInit_bigint!=NULL);
467  assume(n->cfCoeffWrite != NULL);
468 
469  assume(n->cfClearContent != NULL);
471 
472  assume(n->type==t);
473 
474 #ifndef SING_NDEBUG
475  if(n->cfKillChar==NULL) Warn("cfKillChar is NULL for coeff %d",t);
476  if(n->cfWriteLong==NULL) Warn("cfWrite is NULL for coeff %d",t);
477  if(n->cfWriteShort==NULL) Warn("cfWriteShort is NULL for coeff %d",t);
478  if(n->cfCoeffString==ndCoeffString) Warn("cfCoeffString is undefined for coeff %d",t);
479 #endif
480 
481  if( n->nNULL == NULL )
482  n->nNULL = n->cfInit(0, n); // may still remain NULL
483  }
484  else
485  {
486  n->ref++;
487  }
488  return n;
static BOOLEAN ndIsUnit(number a, const coeffs r)
Definition: numbers.cc:103
BOOLEAN(* cfDivBy)(number a, number b, const coeffs r)
Definition: coeffs.h:385
number(* cfCopy)(number a, const coeffs r)
return a copy of a
Definition: coeffs.h:199
number(* cfExtGcd)(number a, number b, number *s, number *t, const coeffs r)
Definition: coeffs.h:248
numberfunc cfIntMod
Definition: coeffs.h:175
int(* cfDivComp)(number a, number b, const coeffs r)
Definition: coeffs.h:381
static void ndPower(number a, int i, number *res, const coeffs r)
Definition: numbers.cc:72
static number ndParameter(const int, const coeffs r)
Definition: numbers.cc:125
number nNULL
the 0 as constant, NULL by default
Definition: coeffs.h:320
static void ndKillChar(coeffs)
Definition: numbers.cc:249
static BOOLEAN ndDBTest(number, const char *, const int, const coeffs)
Definition: numbers.cc:106
BOOLEAN(* cfDBTest)(number a, const char *f, const int l, const coeffs r)
Test: is "a" a correct number?
Definition: coeffs.h:419
void(* cfMPZ)(mpz_t result, number &n, const coeffs r)
Converts a non-negative number n into a GMP number, 0 if impossible.
Definition: coeffs.h:190
void(* cfSetChar)(const coeffs r)
Definition: coeffs.h:161
static BOOLEAN ndDivBy(number, number, const coeffs)
Definition: numbers.cc:255
char const ** pParameterNames
array containing the names of Parameters (default NULL)
Definition: coeffs.h:326
coeffs next
Definition: coeffs.h:125
static number ndCopy(number a, const coeffs)
Definition: numbers.cc:238
static n_coeffType nLastCoeffs
Definition: numbers.cc:293
static number ndChineseRemainder(number *, number *, int, BOOLEAN, CFArray &, const coeffs r)
Definition: numbers.cc:114
void(* cfDelete)(number *a, const coeffs r)
Definition: coeffs.h:272
static void ndNormalize(number &, const coeffs)
Definition: numbers.cc:146
BOOLEAN(*)(*)(*)(*) cfIsOne(number a, const coeffs r)
Definition: coeffs.h:229
#define omFreeSize(addr, size)
Definition: omAllocDecl.h:260
number(* cfSubringGcd)(number a, number b, const coeffs r)
Definition: coeffs.h:247
static number ndConvFactoryNSingN(const CanonicalForm, const coeffs)
[in, out] a bigint number >= 0
Definition: numbers.cc:267
numberfunc cfAdd
Definition: coeffs.h:175
BOOLEAN(* cfGreater)(number a, number b, const coeffs r)
Definition: coeffs.h:225
void(* cfNormalize)(number &a, const coeffs r)
Definition: coeffs.h:223
static char * ndCoeffString(const coeffs r)
Definition: numbers.cc:54
number(* cfRePart)(number a, const coeffs r)
Definition: coeffs.h:200
#define TRUE
Definition: auxiliary.h:101
static void ndDelete(number *d, const coeffs)
Definition: numbers.cc:52
static int ndDivComp(number, number, const coeffs)
Definition: numbers.cc:256
void(* cfCoeffWrite)(const coeffs r, BOOLEAN details)
output of coeff description via Print
Definition: coeffs.h:148
static char * ndCoeffName(const coeffs r)
Definition: numbers.cc:153
BOOLEAN(* cfIsUnit)(number a, const coeffs r)
Definition: coeffs.h:382
number(* cfGetUnit)(number a, const coeffs r)
Definition: coeffs.h:383
number(* cfFarey)(number p, number n, const coeffs)
rational reconstruction: "best" rational a/b with a/b = p mod n
Definition: coeffs.h:291
number(* cfInitMPZ)(mpz_t i, const coeffs r)
init with a GMP integer
Definition: coeffs.h:181
char *(* cfCoeffString)(const coeffs r)
string output of coeff description
Definition: coeffs.h:151
BOOLEAN(* nCoeffIsEqual)(const coeffs r, n_coeffType n, void *parameter)
Definition: coeffs.h:145
static number ndReturn0(number, const coeffs r)
Definition: numbers.cc:147
static void ndInpMult(number &a, number b, const coeffs r)
Definition: numbers.cc:59
number(* cfInit)(long i, const coeffs r)
init with an integer
Definition: coeffs.h:178
number(* cfNormalizeHelper)(number a, number b, const coeffs r)
Definition: coeffs.h:271
static number ndInitMPZ(mpz_t m, const coeffs r)
Definition: numbers.cc:280
static int ndParDeg(number n, const coeffs r)
Definition: numbers.cc:120
BOOLEAN(*)(*)(*)(*)(*)(*) cfGreaterZero(number a, const coeffs r)
Definition: coeffs.h:237
long(* cfInt)(number &n, const coeffs r)
convertion to long, 0 if impossible
Definition: coeffs.h:187
void(* cfInpMult)(number &a, number b, const coeffs r)
Inplace: a *= b.
Definition: coeffs.h:281
numberfunc cfSub
Definition: coeffs.h:175
static void ndClearContent(ICoeffsEnumerator &numberCollectionEnumerator, number &c, const coeffs r)
Definition: numbers.cc:155
static number ndGetDenom(number &, const coeffs r)
Definition: numbers.cc:150
number(* cfImPart)(number a, const coeffs r)
Definition: coeffs.h:201
#define assume(x)
Definition: mod2.h:403
number(* cfInpNeg)(number a, const coeffs r)
changes argument inline: a:= -a return -a! (no copy is returned) the result should be assigned to the...
Definition: coeffs.h:195
static int ndSize(number a, const coeffs r)
Definition: numbers.cc:152
int ref
Definition: coeffs.h:126
void(* cfPower)(number a, int i, number *result, const coeffs r)
Definition: coeffs.h:239
nCoeffsEnumeratorFunc cfClearContent
function pointer behind n_ClearContent
Definition: coeffs.h:309
n_Procs_s * cf_root
Definition: numbers.cc:47
numberfunc cfExactDiv
Definition: coeffs.h:175
static BOOLEAN ndCoeffIsEqual(const coeffs r, n_coeffType n, void *)
Definition: numbers.cc:286
n_coeffType type
Definition: coeffs.h:128
static CanonicalForm ndConvSingNFactoryN(number, BOOLEAN, const coeffs)
Definition: numbers.cc:260
numberfunc cfDiv
Definition: coeffs.h:175
const char *(* cfRead)(const char *s, number *a, const coeffs r)
Definition: coeffs.h:221
numberfunc cfMult
Definition: coeffs.h:175
static number ndGcd(number, number, const coeffs r)
Definition: numbers.cc:148
static number ndExtGcd(number, number, number *, number *, const coeffs r)
Definition: numbers.cc:257
static cfInitCharProc * nInitCharTable
Definition: numbers.cc:325
#define NULL
Definition: omList.c:10
void(* cfWriteLong)(number a, const coeffs r)
print a given number (long format)
Definition: coeffs.h:204
number(* cfGcd)(number a, number b, const coeffs r)
Definition: coeffs.h:246
static void ndSetChar(const coeffs)
Definition: numbers.cc:250
number(* cfLcm)(number a, number b, const coeffs r)
Definition: coeffs.h:270
static void ndInpAdd(number &a, number b, const coeffs r)
Definition: numbers.cc:65
number(* convFactoryNSingN)(const CanonicalForm n, const coeffs r)
conversion to CanonicalForm(factory) to number
Definition: coeffs.h:315
number(* cfChineseRemainder)(number *x, number *q, int rl, BOOLEAN sym, CFArray &inv_cache, const coeffs)
chinese remainder returns X with X mod q[i]=x[i], i=0..rl-1
Definition: coeffs.h:297
static number ndGetNumerator(number &a, const coeffs r)
Definition: numbers.cc:151
static number ndAnn(number, const coeffs)
Definition: numbers.cc:53
static number ndIntMod(number, number, const coeffs r)
Definition: numbers.cc:149
static number ndFarey(number, number, const coeffs r)
Definition: numbers.cc:109
static void ndClearDenominators(ICoeffsEnumerator &, number &d, const coeffs r)
Definition: numbers.cc:229
nMapFunc(* cfSetMap)(const coeffs src, const coeffs dst)
Definition: coeffs.h:275
char *(* cfCoeffName)(const coeffs r)
default name of cf, should substitue cfCoeffWrite, cfCoeffString
Definition: coeffs.h:154
int(* cfSize)(number n, const coeffs r)
how complicated, (0) => 0, or positive
Definition: coeffs.h:184
number(* cfAnn)(number a, const coeffs r)
Definition: coeffs.h:261
number(* cfParameter)(const int i, const coeffs r)
create i^th parameter or NULL if not possible
Definition: coeffs.h:303
BOOLEAN(*)(*)(*)(*)(*) cfIsMOne(number a, const coeffs r)
Definition: coeffs.h:232
CanonicalForm(* convSingNFactoryN)(number n, BOOLEAN setChar, const coeffs r)
Definition: coeffs.h:316
void(* cfKillChar)(coeffs r)
Definition: coeffs.h:159
int BOOLEAN
Definition: auxiliary.h:88
static void ndMPZ(mpz_t result, number &n, const coeffs r)
Converts a non-negative bigint number into a GMP number.
Definition: numbers.cc:275
void Werror(const char *fmt,...)
Definition: reporter.cc:189
void(* cfInpAdd)(number &a, number b, const coeffs r)
Inplace: a += b.
Definition: coeffs.h:284
number(* cfGetNumerator)(number &n, const coeffs r)
Definition: coeffs.h:241
void(* cfWriteShort)(number a, const coeffs r)
print a given number in a shorter way, if possible e.g. in K(a): a2 instead of a^2 ...
Definition: coeffs.h:208
#define omAlloc0(size)
Definition: omAllocDecl.h:211
int iNumberOfParameters
Number of Parameters in the coeffs (default 0)
Definition: coeffs.h:323
number(* cfGetDenom)(number &n, const coeffs r)
Definition: coeffs.h:240
BOOLEAN(*)(*)(*) cfIsZero(number a, const coeffs r)
Definition: coeffs.h:228
BOOLEAN(*)(*) cfEqual(number a, number b, const coeffs r)
tests
Definition: coeffs.h:227
nCoeffsEnumeratorFunc cfClearDenominators
function pointer behind n_ClearDenominators
Definition: coeffs.h:312
#define Warn
Definition: emacs.cc:80
int(* cfParDeg)(number x, const coeffs r)
degree for coeffcients: -1 for 0, 0 for "constants", ...
Definition: coeffs.h:300

§ nKillChar()

void nKillChar ( coeffs  r)

undo all initialisations

Definition at line 490 of file numbers.cc.

492 {
494  if (r!=NULL)
495  {
496  r->ref--;
497  if (r->ref<=0)
498  {
499  n_Procs_s tmp;
500  n_Procs_s* n=&tmp;
501  tmp.next=cf_root;
502  while((n->next!=NULL) && (n->next!=r)) n=n->next;
503  if (n->next==r)
504  {
505  n->next=n->next->next;
506  if (cf_root==r) cf_root=n->next;
507  n_Delete(&(r->nNULL),r);
508  assume (r->cfKillChar!=NULL); r->cfKillChar(r); // STATISTIC(nKillChar);
509  omFreeSize((void *)r, sizeof(n_Procs_s));
510  r=NULL;
511  }
512  else
513  {
514  WarnS("cf_root list destroyed");
515  }
516  }
517  }
#define STATISTIC(f)
Definition: numstats.h:16
coeffs next
Definition: coeffs.h:125
#define omFreeSize(addr, size)
Definition: omAllocDecl.h:260
#define WarnS
Definition: emacs.cc:81
void nKillChar(coeffs r)
undo all initialisations
Definition: numbers.cc:490
#define assume(x)
Definition: mod2.h:403
n_Procs_s * cf_root
Definition: numbers.cc:47
#define NULL
Definition: omList.c:10
static FORCE_INLINE void n_Delete(number *p, const coeffs r)
delete &#39;p&#39;
Definition: coeffs.h:459

§ nNew()

void nNew ( number *  a)

Definition at line 49 of file numbers.cc.

49 { *d=NULL; }
#define NULL
Definition: omList.c:10

§ nSetChar()

static FORCE_INLINE void nSetChar ( const coeffs  r)
static

initialisations after each ring change

Definition at line 440 of file coeffs.h.

441 { STATISTIC(nSetChar); assume(r!=NULL); assume(r->cfSetChar != NULL); r->cfSetChar(r); }
#define STATISTIC(f)
Definition: numstats.h:16
static FORCE_INLINE void nSetChar(const coeffs r)
initialisations after each ring change
Definition: coeffs.h:440
#define assume(x)
Definition: mod2.h:403
#define NULL
Definition: omList.c:10

§ number2mpz()

static FORCE_INLINE void number2mpz ( number  n,
coeffs  c,
mpz_t  m 
)
static

Definition at line 1001 of file coeffs.h.

1001 { n_MPZ(m, n, c); }
int m
Definition: cfEzgcd.cc:119
static FORCE_INLINE void n_MPZ(mpz_t result, number &n, const coeffs r)
conversion of n to a GMP integer; 0 if not possible
Definition: coeffs.h:555

Variable Documentation

§ fftable

const unsigned short fftable[]

Definition at line 61 of file ffields.cc.

§ rnumber_bin

omBin rnumber_bin

Definition at line 23 of file longrat0.cc.