46 #include "factory/factory.h" 52 #define TRANSEXT_PRIVATES 1 56 #define naTest(a) naDBTest(a,__FILE__,__LINE__,cf) 59 #define naTest(a) do {} while (0) 63 #define naRing cf->extRing 69 #define naCoeffs cf->extRing->cf 72 #define naMinpoly naRing->qideal->m[0] 124 if (
p ==
NULL)
return;
125 number n =
n_Init(1, r->cf);
167 static inline poly
p_Gcd(
const poly
p,
const poly q,
const ring r)
171 poly a =
p; poly
b = q;
199 poly ppFactor =
NULL; poly qqFactor =
NULL;
218 poly
p_ExtGcd(poly
p, poly &pFactor, poly q, poly &qFactor, ring r)
223 { a = q;
b =
p; aCorrespondsToP =
FALSE; }
225 poly aFactor =
NULL; poly bFactor =
NULL;
227 if (aCorrespondsToP) { pFactor = aFactor; qFactor = bFactor; }
228 else { pFactor = bFactor; qFactor = aFactor; }
268 cf =
cf->extRing->cf;
282 if (*a ==
NULL)
return;
284 poly aAsPoly = (poly)(*a);
320 poly aAsPoly = (poly)a;
328 poly aAsPoly = (poly)a;
343 if (
i == 0)
return NULL;
350 poly aAsPoly = (poly)a;
374 if (aDeg>bDeg)
return TRUE;
375 if (aDeg<bDeg)
return FALSE;
393 const ring
A =
cf->extRing;
402 const int P =
rVar(
A);
407 for (
int nop=0; nop < P; nop ++)
410 if (nop!=P-1)
PrintS(
", ");
415 const ideal I =
A->qideal;
447 return (number)aPlusB;
455 if (a ==
NULL)
return (number)minusB;
458 return (number)aMinusB;
468 return (number)aTimesB;
482 return (number)aDivB;
510 int expAbs =
exp;
if (expAbs < 0) expAbs = -expAbs;
513 poly
pow; poly aAsPoly = (poly)a;
517 for (
int i = 2;
i <= expAbs;
i++)
547 number n = (number)
pow;
579 poly aAsPoly = (poly)a;
597 poly aAsPoly = (poly)a;
613 *a = (number)aAsPoly;
619 number naLcm(number a, number
b,
const coeffs cf)
628 return naDiv(theProduct, theGcd,
cf);
697 const ideal mi =
naRing->qideal;
699 const ideal ii = e->
r->qideal;
716 if (a ==
NULL)
return 0;
717 poly aAsPoly = (poly)a;
719 while (aAsPoly !=
NULL)
825 poly aFactor =
NULL; poly mFactor =
NULL; poly theGcd =
NULL;
841 WerrorS(
"zero divisor found - your minpoly is not irreducible");
846 return (number)(aFactor);
853 assume(src->rep == dst->extRing->cf->rep);
876 int n =
n_Int(a, src);
877 number q =
n_Init(n, dst->extRing->cf);
886 number naCopyMap(number a,
const coeffs src,
const coeffs dst)
896 fraction
fa=(fraction)a;
929 number t=
naDiv ((number)
p,(number)q, dst);
934 WerrorS (
"mapping denominator to zero");
945 number q =
nlModP(a, src, dst->extRing->cf);
956 assume(src == dst->extRing->cf);
967 int n =
n_Int(a, src);
968 number q =
n_Init(n, dst->extRing->cf);
978 const ring rSrc =
cf->extRing;
979 const ring rDst = dst->extRing;
983 poly
g =
prMapR(
f, nMap, rSrc, rDst);
993 const ring rSrc =
cf->extRing;
994 const ring rDst = dst->extRing;
997 fraction
f = (fraction)a;
1004 h =
prMapR(DEN(
f), nMap, rSrc, rDst);
1045 if (src->ch == dst->ch)
return naMapPP;
1049 if (
h != 1)
return NULL;
1061 else if ((nMap!=
NULL) && (strcmp(
rRingVar(0,src->extRing),
rRingVar(0,dst->extRing))==0) && (
rVar (src->extRing) ==
rVar (dst->extRing)))
1074 if (a ==
NULL)
return -1;
1076 return cf->extRing->pFDeg(aa,
cf->extRing);
1084 const ring
R =
cf->extRing;
1086 assume( 0 < iParameter && iParameter <=
rVar(
R) );
1099 const ring
R =
cf->extRing;
1112 const ring
R =
cf->extRing;
1118 numberCollectionEnumerator.
Reset();
1120 if( !numberCollectionEnumerator.
MoveNext() )
1129 int s1;
int s=2147483647;
1133 int normalcount = 0;
1139 number& n = numberCollectionEnumerator.
Current();
1152 }
while (numberCollectionEnumerator.
MoveNext() );
1159 numberCollectionEnumerator.
Reset();
1162 while (numberCollectionEnumerator.
MoveNext() )
1164 number& n = numberCollectionEnumerator.
Current();
1167 if( (--normalcount) <= 0)
1217 numberCollectionEnumerator.
Reset();
1220 while (numberCollectionEnumerator.
MoveNext() )
1222 number& n = numberCollectionEnumerator.
Current();
1233 n = (number)
p_Mult_q(cInverse, (poly)n,
R);
1324 c = (number)
p_NSet(n,
cf->extRing);
1329 if ((--
cf->extRing->ref) == 0)
1340 l+=(strlen(
p[
i])+1);
1344 snprintf(
s,10+1,
"%d",r->ch);
1363 l+=(strlen(
p[
i])+1);
1367 snprintf(
s,10+1,
"%d",r->ch);
1381 poly *P=(poly*)
omAlloc(rl*
sizeof(poly*));
1382 number *X=(number *)
omAlloc(rl*
sizeof(number));
1411 (e->
r->qideal->m[0] !=
NULL) );
1417 const ring
R = e->
r;
1482 cf->iNumberOfParameters =
rVar(
R);
1483 cf->pParameterNames = (
const char**)
R->names;
1485 cf->has_simple_Inverse=
R->cf->has_simple_Inverse;
1516 #define n2pTest(a) n2pDBTest(a,__FILE__,__LINE__,cf) 1519 #define n2pTest(a) do {} while (0) 1523 #define n2pRing cf->extRing 1529 #define n2pCoeffs cf->extRing->cf 1551 return (number)aTimesB;
1574 *a = (number)aAsPoly;
1606 l+=(strlen(
p[
i])+1);
1609 char *
s=(
char *)
omAlloc(
l+5+strlen(cf_s));
1611 snprintf(
s,strlen(cf_s)+2,
"%s",cf_s);
1622 else { tt[0]=
']'; strcat(
s,tt); }
1634 l+=(strlen(
p[
i])+1);
1639 snprintf(
s,strlen(cf_s)+2,
"%s",cf_s);
1650 else { tt[0]=
']'; strcat(
s,tt); }
1659 const ring
A =
cf->extRing;
1662 PrintS(
"// polynomial ring as coefficient ring :\n");
1696 const ring
R = e->
r;
1754 cf->iNumberOfParameters =
rVar(
R);
1755 cf->pParameterNames = (
const char**)
R->names;
void n2pNormalize(number &a, const coeffs cf)
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 l...
static FORCE_INLINE char const ** n_ParameterNames(const coeffs r)
Returns a (const!) pointer to (const char*) names of parameters.
const CanonicalForm int s
const CanonicalForm int const CFList const Variable & y
poly singclap_gcd_r(poly f, poly g, const ring r)
void naDelete(number *a, const coeffs cf)
static void p_Monic(poly p, const ring r)
returns NULL if p == NULL, otherwise makes p monic by dividing by its leading coefficient (only done ...
static FORCE_INLINE BOOLEAN nCoeff_is_Zp(const coeffs r)
number ndGcd(number, number, const coeffs r)
BOOLEAN naIsZero(number a, const coeffs cf)
gmp_float exp(const gmp_float &a)
char * naCoeffName(const coeffs r)
BOOLEAN naInitChar(coeffs cf, void *infoStruct)
Initialize the coeffs object.
number nlModP(number q, const coeffs, const coeffs Zp)
void p_String0Long(const poly p, ring lmRing, ring tailRing)
print p in a long way
number n2pInvers(number a, const coeffs cf)
static FORCE_INLINE BOOLEAN n_IsOne(number n, const coeffs r)
TRUE iff 'n' represents the one element.
poly p_NSet(number n, const ring r)
returns the poly representing the number n, destroys n
number ndCopyMap(number a, const coeffs aRing, const coeffs r)
poly gcd_over_Q(poly f, poly g, const ring r)
helper routine for calling singclap_gcd_r
number naChineseRemainder(number *x, number *q, int rl, BOOLEAN, CFArray &inv_cache, const coeffs cf)
number naMapZ0(number a, const coeffs src, const coeffs dst)
void naKillChar(coeffs cf)
const char * n2pRead(const char *s, number *a, const coeffs cf)
static FORCE_INLINE number n_Init(long i, const coeffs r)
a number representing i in the given coeff field/ring r
void naPower(number a, int exp, number *b, const coeffs cf)
static FORCE_INLINE BOOLEAN nCoeff_is_Q_or_BI(const coeffs r)
#define omFreeSize(addr, size)
number naSub(number a, number b, const coeffs cf)
static short rVar(const ring r)
#define rVar(r) (r->N)
(), see rinteger.h, new impl.
const char * naRead(const char *s, number *a, const coeffs cf)
nMapFunc naSetMap(const coeffs src, const coeffs dst)
Get a mapping function from src into the domain of this type (n_algExt)
number naInit(long i, const coeffs cf)
number naParameter(const int iParameter, const coeffs cf)
return the specified parameter as a number in the given alg. field
static long p_Totaldegree(poly p, const ring r)
static FORCE_INLINE void n_Normalize(number &n, const coeffs r)
inplace-normalization of n; produces some canonical representation of n;
number naMap00(number a, const coeffs src, const coeffs dst)
void WerrorS(const char *s)
long naInt(number &a, const coeffs cf)
BOOLEAN naGreater(number a, number b, const coeffs cf)
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,...
static poly p_GcdHelper(poly &p, poly &q, const ring r)
see p_Gcd; additional assumption: deg(p) >= deg(q); must destroy p and q (unless one of them is retur...
Templated accessor interface for accessing individual data (for instance, of an enumerator).
static FORCE_INLINE BOOLEAN nCoeff_is_Q(const coeffs r)
static number & pGetCoeff(poly p)
return an alias to the leading coefficient of p assumes that p != NULL NOTE: not copy
char * naCoeffString(const coeffs r)
poly singclap_pdivide(poly f, poly g, const ring r)
#define n2pTest(a)
ABSTRACT: numbers as polys in the ring K[a] Assuming that we have a coeffs object cf,...
static BOOLEAN naCoeffIsEqual(const coeffs cf, n_coeffType n, void *param)
static number p_SetCoeff(poly p, number n, ring r)
static BOOLEAN rCanShortOut(const ring r)
static poly p_Gcd(const poly p, const poly q, const ring r)
BOOLEAN n2pInitChar(coeffs cf, void *infoStruct)
static poly p_Copy(poly p, const ring r)
returns a copy of p
void n2pCoeffWrite(const coeffs cf, BOOLEAN details)
int naParDeg(number a, const coeffs cf)
number naMapP0(number a, const coeffs src, const coeffs dst)
static FORCE_INLINE int n_NumberOfParameters(const coeffs r)
Returns the number of parameters.
poly prMapR(poly src, nMapFunc nMap, ring src_r, ring dest_r)
BOOLEAN naGreaterZero(number a, const coeffs cf)
forward declarations
static FORCE_INLINE number n_Mult(number a, number b, const coeffs r)
return the product of 'a' and 'b', i.e., a*b
virtual void Reset()=0
Sets the enumerator to its initial position: -1, which is before the first element in the collection.
char * n2pCoeffName(const coeffs cf)
number naFarey(number p, number n, const coeffs cf)
const char * p_Read(const char *st, poly &rc, const ring r)
static poly p_ExtGcdHelper(poly &p, poly &pFactor, poly &q, poly &qFactor, ring r)
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 ...
int naSize(number a, const coeffs cf)
long p_Deg(poly a, const ring r)
poly p_PermPoly(poly p, const int *perm, const ring oldRing, const ring dst, nMapFunc nMap, const int *par_perm, int OldPar, BOOLEAN use_mult)
Coefficient rings, fields and other domains suitable for Singular polynomials.
number naCopyTrans2AlgExt(number a, const coeffs src, const coeffs dst)
number naMapPP(number a, const coeffs src, const coeffs dst)
poly p_Farey(poly p, number N, const ring r)
static FORCE_INLINE BOOLEAN nCoeff_is_algExt(const coeffs r)
TRUE iff r represents an algebraic extension field.
int naIsParam(number m, const coeffs cf)
if m == var(i)/1 => return i,
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 ....
BOOLEAN naEqual(number a, number b, const coeffs cf)
number naConvFactoryNSingN(const CanonicalForm n, const coeffs cf)
Concrete implementation of enumerators over polynomials.
static long p_GetExp(const poly p, const unsigned long iBitmask, const int VarOffset)
get a single variable exponent @Note: the integer VarOffset encodes:
number naDiv(number a, number b, const coeffs cf)
BOOLEAN fa(leftv res, leftv args)
number naGetDenom(number &a, const coeffs cf)
BOOLEAN naDBTest(number a, const char *f, const int l, const coeffs r)
static BOOLEAN p_IsConstant(const poly p, const ring r)
The main handler for Singular numbers which are suitable for Singular polynomials.
static void naClearContent(ICoeffsEnumerator &numberCollectionEnumerator, number &c, const coeffs cf)
Templated enumerator interface for simple iteration over a generic collection of T's.
number n2pMult(number a, number b, const coeffs cf)
static poly pp_Mult_qq(poly p, poly q, const ring r)
void StringAppendS(const char *st)
char * n2pCoeffString(const coeffs cf)
poly convFactoryPSingP(const CanonicalForm &f, const ring r)
number(* nMapFunc)(number a, const coeffs src, const coeffs dst)
maps "a", which lives in src, into dst
number naGenMap(number a, const coeffs cf, const coeffs dst)
number naMult(number a, number b, const coeffs cf)
virtual reference Current()=0
Gets the current element in the collection (read and write).
number naGenTrans2AlgExt(number a, const coeffs cf, const coeffs dst)
#define n_Test(a, r)
BOOLEAN n_Test(number a, const coeffs r)
number n2pDiv(number a, number b, const coeffs cf)
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
BOOLEAN rSamePolyRep(ring r1, ring r2)
returns TRUE, if r1 and r2 represents the monomials in the same way FALSE, otherwise this is an analo...
const char *const nDivBy0
poly p_ExtGcd(poly p, poly &pFactor, poly q, poly &qFactor, ring r)
assumes that p and q are univariate polynomials in r, mentioning the same variable; assumes a global ...
static FORCE_INLINE BOOLEAN nCoeff_is_transExt(const coeffs r)
TRUE iff r represents a transcendental extension field.
void heuristicReduce(poly &p, poly reducer, const coeffs cf)
void PrintS(const char *s)
static char * rRingVar(short i, const ring r)
void naWriteLong(number a, const coeffs cf)
void rWrite(ring r, BOOLEAN details)
static FORCE_INLINE BOOLEAN n_IsZero(number n, const coeffs r)
TRUE iff 'n' represents the zero element.
BOOLEAN rEqual(ring r1, ring r2, BOOLEAN qr)
returns TRUE, if r1 equals r2 FALSE, otherwise Equality is determined componentwise,...
static FORCE_INLINE nMapFunc n_SetMap(const coeffs src, const coeffs dst)
set the mapping function pointers for translating numbers from src to dst
number naInvers(number a, const coeffs cf)
poly p_PolyDiv(poly &p, const poly divisor, const BOOLEAN needResult, const ring r)
assumes that p and divisor are univariate polynomials in r, mentioning the same variable; assumes div...
void naCoeffWrite(const coeffs cf, BOOLEAN details)
go into polynomials over an alg. extension recursively
static FORCE_INLINE n_coeffType getCoeffType(const coeffs r)
Returns the type of coeffs domain.
BOOLEAN p_EqualPolys(poly p1, poly p2, const ring r)
static coeffs nCoeff_bottom(const coeffs r, int &height)
void p_Normalize(poly p, const ring r)
void p_Write0(poly p, ring lmRing, ring tailRing)
static void p_Delete(poly *p, const ring r)
number napNormalizeHelper(number b, const coeffs cf)
static BOOLEAN n2pCoeffIsEqual(const coeffs cf, n_coeffType n, void *param)
static unsigned long p_SetExp(poly p, const unsigned long e, const unsigned long iBitmask, const int VarOffset)
set a single variable exponent @Note: VarOffset encodes the position in p->exp
void n2pPower(number a, int exp, number *b, const coeffs cf)
number naLcmContent(number a, number b, const coeffs cf)
#define __p_Mult_nn(p, n, r)
static FORCE_INLINE void n_CoeffWrite(const coeffs r, BOOLEAN details=TRUE)
output the coeff description
CanonicalForm convSingPFactoryP(poly p, const ring r)
number naAdd(number a, number b, const coeffs cf)
static FORCE_INLINE number n_Copy(number n, const coeffs r)
return a copy of 'n'
struct for passing initialization parameters to naInitChar
void rDelete(ring r)
unconditionally deletes fields in r
CanonicalForm naConvSingNFactoryN(number n, BOOLEAN, const coeffs cf)
used for all algebraic extensions, i.e., the top-most extension in an extension tower is algebraic
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 exceptio...
virtual bool MoveNext()=0
Advances the enumerator to the next element of the collection. returns true if the enumerator was suc...
number naCopy(number a, const coeffs cf)
number naGcd(number a, number b, const coeffs cf)
static BOOLEAN length(leftv result, leftv arg)
number naMap0P(number a, const coeffs src, const coeffs dst)
static FORCE_INLINE BOOLEAN nCoeff_is_Q_algext(const coeffs r)
is it an alg. ext. of Q?
poly p_ChineseRemainder(poly *xx, number *x, number *q, int rl, CFArray &inv_cache, const ring R)
BOOLEAN singclap_extgcd(poly f, poly g, poly &res, poly &pa, poly &pb, const ring r)
static void p_Setm(poly p, const ring r)
void naClearDenominators(ICoeffsEnumerator &numberCollectionEnumerator, number &c, const coeffs cf)
static FORCE_INLINE number n_SubringGcd(number a, number b, const coeffs r)
int dReportError(const char *fmt,...)
number naNeg(number a, const coeffs cf)
this is in-place, modifies a
static FORCE_INLINE BOOLEAN nCoeff_is_Extension(const coeffs r)
static poly p_Neg(poly p, const ring r)
#define p_SetCoeff0(p, n, r)
static FORCE_INLINE void n_Delete(number *p, const coeffs r)
delete 'p'
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.
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),...
void definiteReduce(poly &p, poly reducer, const coeffs cf)
static FORCE_INLINE char * nCoeffString(const coeffs cf)
TODO: make it a virtual method of coeffs, together with: Decompose & Compose, rParameter & rPar.
number naMapUP(number a, const coeffs src, const coeffs dst)
static poly p_Add_q(poly p, poly q, const ring r)
BOOLEAN naIsOne(number a, const coeffs cf)
Rational pow(const Rational &a, int e)
static poly p_Init(const ring r, omBin bin)
int p_Var(poly m, const ring r)
poly p_ISet(long i, const ring r)
returns the poly representing the integer i
static poly p_Mult_q(poly p, poly q, const ring r)
poly p_Power(poly p, int i, const ring r)
BOOLEAN naIsMOne(number a, const coeffs cf)
void p_String0Short(const poly p, ring lmRing, ring tailRing)
print p in a short way, if possible
void naWriteShort(number a, const coeffs cf)
BOOLEAN n2pDBTest(number a, const char *f, const int l, const coeffs r)
void naNormalize(number &a, const coeffs cf)
const CanonicalForm const CanonicalForm const CanonicalForm const CanonicalForm & cand
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...
used to represent polys as coeffcients
number naGetNumerator(number &a, const coeffs cf)