44 #include "factory/factory.h" 50 #define TRANSEXT_PRIVATES 1 54 #define naTest(a) naDBTest(a,__FILE__,__LINE__,cf) 57 #define naTest(a) do {} while (0) 61 #define naRing cf->extRing 67 #define naCoeffs cf->extRing->cf 70 #define naMinpoly naRing->qideal->m[0] 122 if (p ==
NULL)
return;
123 number n =
n_Init(1, r->cf);
127 if (
n_IsOne(lc, r->cf))
return;
128 number lcInverse =
n_Invers(lc, r->cf);
165 static inline poly
p_Gcd(
const poly
p,
const poly q,
const ring r)
169 poly a =
p; poly
b = q;
197 poly ppFactor =
NULL; poly qqFactor =
NULL;
216 poly
p_ExtGcd(poly
p, poly &pFactor, poly q, poly &qFactor, ring r)
221 { a = q; b =
p; aCorrespondsToP =
FALSE; }
223 poly aFactor =
NULL; poly bFactor =
NULL;
225 if (aCorrespondsToP) { pFactor = aFactor; qFactor = bFactor; }
226 else { pFactor = bFactor; qFactor = aFactor; }
266 cf = cf->extRing->cf;
280 if (*a ==
NULL)
return;
282 poly aAsPoly = (poly)(*a);
318 poly aAsPoly = (poly)a;
326 poly aAsPoly = (poly)a;
341 if (i == 0)
return NULL;
348 poly aAsPoly = (poly)a;
372 if (aDeg>bDeg)
return TRUE;
373 if (aDeg<bDeg)
return FALSE;
391 const ring
A = cf->extRing;
400 const int P =
rVar(A);
405 for (
int nop=0; nop < P; nop ++)
408 if (nop!=P-1)
PrintS(
", ");
413 const ideal I = A->qideal;
445 return (number)aPlusB;
453 if (a ==
NULL)
return (number)minusB;
456 return (number)aMinusB;
466 return (number)aTimesB;
474 poly bInverse = (poly)
naInvers(b, cf);
480 return (number)aDivB;
500 if (exp >= 0) *b =
NULL;
504 else if (exp == 0) { *b =
naInit(1, cf);
return; }
505 else if (exp == 1) { *b =
naCopy(a, cf);
return; }
506 else if (exp == -1) { *b =
naInvers(a, cf);
return; }
508 int expAbs =
exp;
if (expAbs < 0) expAbs = -expAbs;
511 poly
pow; poly aAsPoly = (poly)a;
515 for (
int i = 2;
i <= expAbs;
i++)
545 number n = (number)pow;
577 poly aAsPoly = (poly)a;
595 poly aAsPoly = (poly)a;
611 *a = (number)aAsPoly;
617 number naLcm(number a, number
b,
const coeffs cf)
625 number theGcd =
naGcd(a,
b, cf);
626 return naDiv(theProduct, theGcd, cf);
648 number
g =
ndGcd(a, b, cf);
695 const ideal mi =
naRing->qideal;
697 const ideal ii = e->
r->qideal;
714 if (a ==
NULL)
return 0;
715 poly aAsPoly = (poly)a;
717 while (aAsPoly !=
NULL)
721 if (d > theDegree) theDegree = d;
724 return (theDegree +1) * noOfTerms;
823 poly aFactor =
NULL; poly mFactor =
NULL; poly theGcd =
NULL;
837 if( !
naIsOne((number)theGcd, cf) )
839 WerrorS(
"zero divisor found - your minpoly is not irreducible");
844 return (number)(aFactor);
851 assume(src->rep == dst->extRing->cf->rep);
863 p_SetCoeff(result, nMap(a, src, dst->extRing->cf), dst->extRing);
874 int n =
n_Int(a, src);
875 number q =
n_Init(n, dst->extRing->cf);
884 number naCopyMap(number a,
const coeffs src,
const coeffs dst)
894 fraction
fa=(fraction)a;
898 p =
p_Copy(NUM(fa),src->extRing);
901 q =
p_Copy(DEN(fa),src->extRing);
927 number t=
naDiv ((number)p,(number)q, dst);
932 WerrorS (
"mapping denominator to zero");
943 number q =
nlModP(a, src, dst->extRing->cf);
954 assume(src == dst->extRing->cf);
965 int n =
n_Int(a, src);
966 number q =
n_Init(n, dst->extRing->cf);
976 const ring rSrc = cf->extRing;
977 const ring rDst = dst->extRing;
981 poly
g =
prMapR(f, nMap, rSrc, rDst);
991 const ring rSrc = cf->extRing;
992 const ring rDst = dst->extRing;
995 fraction
f = (fraction)a;
996 poly
g =
prMapR(NUM(f), nMap, rSrc, rDst);
1002 h =
prMapR(DEN(f), nMap, rSrc, rDst);
1006 result=
naDiv((number)g,(number)h,dst);
1013 n_Test((number)result, dst);
1043 if (src->ch == dst->ch)
return naMapPP;
1047 if (h != 1)
return NULL;
1059 else if ((nMap!=
NULL) && (strcmp(
rRingVar(0,src->extRing),
rRingVar(0,dst->extRing))==0) && (
rVar (src->extRing) ==
rVar (dst->extRing)))
1072 if (a ==
NULL)
return -1;
1074 return cf->extRing->pFDeg(aa,cf->extRing);
1082 const ring
R = cf->extRing;
1084 assume( 0 < iParameter && iParameter <=
rVar(R) );
1097 const ring
R = cf->extRing;
1100 return p_Var( (poly)m, R );
1110 const ring
R = cf->extRing;
1116 numberCollectionEnumerator.
Reset();
1118 if( !numberCollectionEnumerator.
MoveNext() )
1127 int s1;
int s=2147483647;
1131 int normalcount = 0;
1137 number& n = numberCollectionEnumerator.
Current();
1144 s1 =
p_Deg(cand1, R);
1150 }
while (numberCollectionEnumerator.
MoveNext() );
1157 numberCollectionEnumerator.
Reset();
1160 while (numberCollectionEnumerator.
MoveNext() )
1162 number& n = numberCollectionEnumerator.
Current();
1165 if( (--normalcount) <= 0)
1207 cand =
p_Neg(cand, R);
1209 c = (number)cand;
naTest(c);
1211 poly cInverse = (poly)
naInvers(c, cf);
1215 numberCollectionEnumerator.
Reset();
1218 while (numberCollectionEnumerator.
MoveNext() )
1220 number& n = numberCollectionEnumerator.
Current();
1231 n = (number)
p_Mult_q(cInverse, (poly)n,
R);
1316 const coeffs Q = cf->extRing->cf;
1322 c = (number)
p_NSet(n, cf->extRing);
1327 if ((--cf->extRing->ref) == 0)
1338 l+=(strlen(p[i])+1);
1342 snprintf(s,10+1,
"%d",r->ch);
1361 l+=(strlen(p[i])+1);
1365 snprintf(s,10+1,
"%d",r->ch);
1379 poly *P=(poly*)
omAlloc(rl*
sizeof(poly*));
1380 number *X=(number *)
omAlloc(rl*
sizeof(number));
1382 for(i=0;i<rl;i++) P[i]=
p_Copy((poly)(x[
i]),cf->extRing);
1386 return ((number)result);
1393 return ((number)result);
1409 (e->
r->qideal->m[0] !=
NULL) );
1415 const ring
R = e->
r;
1443 cf->cfInpNeg =
naNeg;
1448 cf->cfExactDiv =
naDiv;
1480 cf->iNumberOfParameters =
rVar(R);
1481 cf->pParameterNames = (
const char**)R->names;
1483 cf->has_simple_Inverse= R->cf->has_simple_Inverse;
1514 #define n2pTest(a) n2pDBTest(a,__FILE__,__LINE__,cf) 1517 #define n2pTest(a) do {} while (0) 1521 #define n2pRing cf->extRing 1527 #define n2pCoeffs cf->extRing->cf 1549 return (number)aTimesB;
1572 *a = (number)aAsPoly;
1604 l+=(strlen(p[i])+1);
1607 char *
s=(
char *)
omAlloc(l+5+strlen(cf_s));
1609 snprintf(s,strlen(cf_s)+2,
"%s",cf_s);
1620 else { tt[0]=
']'; strcat(s,tt); }
1632 l+=(strlen(p[i])+1);
1637 snprintf(s,strlen(cf_s)+2,
"%s",cf_s);
1648 else { tt[0]=
']'; strcat(s,tt); }
1657 const ring
A = cf->extRing;
1660 PrintS(
"// polynomial ring as coefficient ring :\n");
1694 const ring
R = e->
r;
1716 cf->cfInpNeg =
naNeg;
1752 cf->iNumberOfParameters =
rVar(R);
1753 cf->pParameterNames = (
const char**)R->names;
1755 cf->has_simple_Inverse=
FALSE;
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 : 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, if qr == 1, then qrideal equality is tested, as well
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 : 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), 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
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)