14 #include <factory/factory.h> 34 #ifdef HAVE_POLYEXTENSIONS 41 struct SNumberStatistic number_stats;
56 char *
s=(
char *)
omAlloc(11);snprintf(s,11,
"Coeffs(%d)",r->type);
62 snprintf(s,11,
"Coeffs(%d)",r->type);
67 number n=r->cfMult(a,b,r);
73 number n=r->cfAdd(a,b,r);
82 *res = r->cfInit(1, r);
86 *res = r->cfCopy(a, r);
90 *res = r->cfMult(a, a, r);
94 number
b = r->cfInvers(a, r);
101 r->cfInpMult(*res, *res, r);
104 r->cfInpMult(*res, a, r);
122 Werror(
"ChineseRemainder not implemented for %s (c=%d)",r->cfCoeffString(r),
getCoeffType(r));
123 return r->cfInit(0,r);
128 return (-r->cfIsZero(n,r));
133 Werror(
"ndParameter: n_Parameter is not implemented/relevant for (coeff_type = %d)",
getCoeffType(r));
141 if( (c != 0) && !ret )
143 number ch =
n_Init( c, r );
144 number
g =
n_Gcd( ch, a, r );
154 static number
ndGcd(number, number,
const coeffs r) {
return r->cfInit(1,r); }
168 numberCollectionEnumerator.
Reset();
170 if( !numberCollectionEnumerator.
MoveNext() )
176 number &curr = numberCollectionEnumerator.
Current();
192 while( numberCollectionEnumerator.
MoveNext() )
194 number &n = numberCollectionEnumerator.
Current();
220 while( numberCollectionEnumerator.
MoveNext() )
222 number &n = numberCollectionEnumerator.
Current();
247 assume(aRing->rep==r->rep);
251 return r->cfCopy(a, r);
262 static number
ndExtGcd (number, number, number *, number *,
const coeffs r) {
return r->cfInit(1,r); }
268 WerrorS(
"no conversion to factory");
274 WerrorS(
"no conversion from factory");
283 mpz_init_set_si( result, r->cfInt(n, r) );
288 return r->cfInit( mpz_get_si(m), r);
307 #ifdef HAVE_POLYEXTENSIONS 404 Werror(
"Sorry: the coeff type [%d] was not registered: it is missing in nInitCharTable", (
int)t);
512 if (cf_root==r) cf_root=n->
next;
514 assume (r->cfKillChar!=
NULL); r->cfKillChar(r);
520 WarnS(
"cf_root list destroyed");
562 && (strcmp(cf_name,n->
cfCoeffName(n))==0))
return n;
number nd_Copy(number a, const coeffs r)
static BOOLEAN ndIsUnit(number a, const coeffs r)
void n_Print(number &a, const coeffs r)
print a number (BEWARE of string buffers!) mostly for debugging
BOOLEAN(* cfDivBy)(number a, number b, const coeffs r)
BOOLEAN nrInitChar(coeffs n, void *p)
Initialize 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 i...
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...
const CanonicalForm int s
number(* cfCopy)(number a, const coeffs r)
return a copy of a
static FORCE_INLINE BOOLEAN nCoeff_is_numeric(const coeffs r)
number(* cfExtGcd)(number a, number b, number *s, number *t, const coeffs r)
int(* cfDivComp)(number a, number b, const coeffs r)
coeffs nFindCoeffByName(const char *cf_name)
find an existing coeff by its "CoeffName"
static FORCE_INLINE BOOLEAN nCoeff_is_Zp(const coeffs r)
static void ndPower(number a, int i, number *res, const coeffs r)
static number ndParameter(const int, const coeffs r)
number nNULL
the 0 as constant, NULL by default
static void ndKillChar(coeffs)
static FORCE_INLINE BOOLEAN nCoeff_is_Zp_a(const coeffs r)
static BOOLEAN ndDBTest(number, const char *, const int, const coeffs)
BOOLEAN(* cfDBTest)(number a, const char *f, const int l, const coeffs r)
Test: is "a" a correct number?
void(* cfMPZ)(mpz_t result, number &n, const coeffs r)
Converts a non-negative number n into a GMP number, 0 if impossible.
void(* cfSetChar)(const coeffs r)
BOOLEAN naInitChar(coeffs cf, void *infoStruct)
Initialize the coeffs object.
static BOOLEAN ndDivBy(number, number, const coeffs)
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
static FORCE_INLINE BOOLEAN n_IsOne(number n, const coeffs r)
TRUE iff 'n' represents the one element.
char const ** pParameterNames
array containing the names of Parameters (default NULL)
number ndCopyMap(number a, const coeffs aRing, const coeffs r)
static number ndCopy(number a, const coeffs)
static n_coeffType nLastCoeffs
static number ndChineseRemainder(number *, number *, int, BOOLEAN, CFArray &, const coeffs r)
void(* cfDelete)(number *a, const coeffs r)
static void ndNormalize(number &, const coeffs)
BOOLEAN(*)(*)(*)(*) cfIsOne(number a, const coeffs r)
static FORCE_INLINE number n_Init(long i, const coeffs r)
a number representing i in the given coeff field/ring r
#define omFreeSize(addr, size)
number(* cfSubringGcd)(number a, number b, const coeffs r)
BOOLEAN n_IsZeroDivisor(number a, const coeffs r)
Test whether a is a zero divisor in r i.e. not coprime with char. of r very inefficient implementatio...
static number ndConvFactoryNSingN(const CanonicalForm, const coeffs)
[in, out] a bigint number >= 0
number n_convFactoryNSingN(const CanonicalForm n, const coeffs r)
BOOLEAN(* cfGreater)(number a, number b, const coeffs r)
void(* cfNormalize)(number &a, const coeffs r)
static char * ndCoeffString(const coeffs r)
number(* cfRePart)(number a, const coeffs r)
static FORCE_INLINE int n_GetChar(const coeffs r)
Return the characteristic of the coeff. domain.
static void ndDelete(number *d, const coeffs)
static int ndDivComp(number, number, const coeffs)
static FORCE_INLINE void n_Normalize(number &n, const coeffs r)
inplace-normalization of n; produces some canonical representation of n;
coeffs nInitChar(n_coeffType t, void *parameter)
one-time initialisations for new coeffs in case of an error return NULL
void(* cfCoeffWrite)(const coeffs r, BOOLEAN details)
output of coeff description via Print
void WerrorS(const char *s)
BOOLEAN nr2mInitChar(coeffs r, void *p)
static char * ndCoeffName(const coeffs r)
BOOLEAN(* cfIsUnit)(number a, const coeffs r)
number(* cfGetUnit)(number a, const coeffs r)
static FORCE_INLINE BOOLEAN nCoeff_is_Q(const coeffs r)
number(* cfFarey)(number p, number n, const coeffs)
rational reconstruction: "best" rational a/b with a/b = p mod n
BOOLEAN npInitChar(coeffs r, void *p)
BOOLEAN nlInitChar(coeffs r, void *p)
number(* cfInitMPZ)(mpz_t i, const coeffs r)
init with a GMP integer
char *(* cfCoeffString)(const coeffs r)
string output of coeff description
static FORCE_INLINE BOOLEAN nCoeff_is_Ring(const coeffs r)
BOOLEAN n2pInitChar(coeffs cf, void *infoStruct)
BOOLEAN(* nCoeffIsEqual)(const coeffs r, n_coeffType n, void *parameter)
static number ndReturn0(number, const coeffs r)
static void ndInpMult(number &a, number b, const coeffs r)
virtual void Reset()=0
Sets the enumerator to its initial position: -1, which is before the first element in the collection...
#define omReallocSize(addr, o_size, size)
number(* cfInit)(long i, const coeffs r)
init with an integer
number(* cfNormalizeHelper)(number a, number b, const coeffs r)
BOOLEAN(* cfInitCharProc)(coeffs, void *)
initialize an object of type coeff, return FALSE in case of success
static number ndInitMPZ(mpz_t m, const coeffs r)
BOOLEAN ngcInitChar(coeffs n, void *parameter)
Initialize r (n_long_C)
static int ndParDeg(number n, const coeffs r)
Coefficient rings, fields and other domains suitable for Singular polynomials.
BOOLEAN(*)(*)(*)(*)(*)(*) cfGreaterZero(number a, const coeffs r)
static FORCE_INLINE BOOLEAN nCoeff_is_algExt(const coeffs r)
TRUE iff r represents an algebraic extension field.
long(* cfInt)(number &n, const coeffs r)
convertion to long, 0 if impossible
void(* cfInpMult)(number &a, number b, const coeffs r)
Inplace: a *= b.
n_coeffType nRegister(n_coeffType n, cfInitCharProc p)
void nKillChar(coeffs r)
undo all initialisations
static void ndClearContent(ICoeffsEnumerator &numberCollectionEnumerator, number &c, const coeffs r)
BOOLEAN nrnInitChar(coeffs r, void *p)
static number ndGetDenom(number &, const coeffs r)
number(* cfImPart)(number a, const coeffs r)
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...
The main handler for Singular numbers which are suitable for Singular polynomials.
BOOLEAN nrzInitChar(coeffs r, void *)
Templated enumerator interface for simple iteration over a generic collection of T's.
static int ndSize(number a, const coeffs r)
void StringSetS(const char *st)
static FORCE_INLINE BOOLEAN nCoeff_has_Units(const coeffs r)
returns TRUE, if r is not a field and r has non-trivial units
void(* cfPower)(number a, int i, number *result, const coeffs r)
static FORCE_INLINE BOOLEAN nCoeff_has_simple_Alloc(const coeffs r)
TRUE if n_Delete/n_New are empty operations.
static FORCE_INLINE void n_Write(number n, const coeffs r, const BOOLEAN bShortOut=TRUE)
virtual reference Current()=0
Gets the current element in the collection (read and write).
nCoeffsEnumeratorFunc cfClearContent
function pointer behind n_ClearContent
#define n_Test(a, r)
BOOLEAN n_Test(number a, const coeffs r)
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 ...
static FORCE_INLINE BOOLEAN nCoeff_is_transExt(const coeffs r)
TRUE iff r represents a transcendental extension field.
static BOOLEAN ndCoeffIsEqual(const coeffs r, n_coeffType n, void *)
static CanonicalForm ndConvSingNFactoryN(number, BOOLEAN, const coeffs)
static FORCE_INLINE BOOLEAN n_IsZero(number n, const coeffs r)
TRUE iff 'n' represents the zero element.
static FORCE_INLINE BOOLEAN nCoeff_is_GF(const coeffs r)
const char *(* cfRead)(const char *s, number *a, const coeffs r)
static FORCE_INLINE n_coeffType getCoeffType(const coeffs r)
Returns the type of coeffs domain.
BOOLEAN nfInitChar(coeffs r, void *parameter)
cfInitCharProc nInitCharTableDefault[]
static number ndGcd(number, number, const coeffs r)
static number ndExtGcd(number, number, number *, number *, const coeffs r)
static cfInitCharProc * nInitCharTable
static FORCE_INLINE number n_Copy(number n, const coeffs r)
return a copy of 'n'
void(* cfWriteLong)(number a, const coeffs r)
print a given number (long format)
BOOLEAN ngfInitChar(coeffs n, void *parameter)
Initialize r.
virtual bool MoveNext()=0
Advances the enumerator to the next element of the collection. returns true if the enumerator was suc...
number(* cfGcd)(number a, number b, const coeffs r)
static void ndSetChar(const coeffs)
static FORCE_INLINE BOOLEAN nCoeff_is_Q_algext(const coeffs r)
is it an alg. ext. of Q?
number(* cfLcm)(number a, number b, const coeffs r)
static void ndInpAdd(number &a, number b, const coeffs r)
number(* convFactoryNSingN)(const CanonicalForm n, const coeffs r)
conversion to CanonicalForm(factory) to number
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
static number ndGetNumerator(number &a, const coeffs r)
static number ndAnn(number, const coeffs)
static number ndIntMod(number, number, const coeffs r)
CanonicalForm n_convSingNFactoryN(number n, BOOLEAN setChar, const coeffs r)
static number ndFarey(number, number, const coeffs r)
static void ndClearDenominators(ICoeffsEnumerator &, number &d, const coeffs r)
nMapFunc(* cfSetMap)(const coeffs src, const coeffs dst)
char *(* cfCoeffName)(const coeffs r)
default name of cf, should substitue cfCoeffWrite, cfCoeffString
int(* cfSize)(number n, const coeffs r)
how complicated, (0) => 0, or positive
static FORCE_INLINE void n_Delete(number *p, const coeffs r)
delete 'p'
number(* cfAnn)(number a, const coeffs r)
number(* cfParameter)(const int i, const coeffs r)
create i^th parameter or NULL if not possible
BOOLEAN(*)(*)(*)(*)(*) cfIsMOne(number a, const coeffs r)
CanonicalForm(* convSingNFactoryN)(number n, BOOLEAN setChar, const coeffs r)
void(* cfKillChar)(coeffs r)
static void ndMPZ(mpz_t result, number &n, const coeffs r)
Converts a non-negative bigint number into a GMP number.
void Werror(const char *fmt,...)
void(* cfInpAdd)(number &a, number b, const coeffs r)
Inplace: a += b.
number(* cfGetNumerator)(number &n, const coeffs r)
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 ...
int iNumberOfParameters
Number of Parameters in the coeffs (default 0)
number(* cfGetDenom)(number &n, const coeffs r)
BOOLEAN(*)(*)(*) cfIsZero(number a, const coeffs r)
BOOLEAN(*)(*) cfEqual(number a, number b, const coeffs r)
tests
BOOLEAN ntInitChar(coeffs cf, void *infoStruct)
Initialize the coeffs object.
nCoeffsEnumeratorFunc cfClearDenominators
function pointer behind n_ClearDenominators
int(* cfParDeg)(number x, const coeffs r)
degree for coeffcients: -1 for 0, 0 for "constants", ...