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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);
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;
480 return (number)aDivB;
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)
626 return naDiv(theProduct, theGcd,
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)
823 poly aFactor =
NULL; poly mFactor =
NULL; poly theGcd =
NULL;
839 WerrorS(
"zero divisor found - your minpoly is not irreducible");
844 return (number)(aFactor);
851 assume(src->rep == dst->extRing->cf->rep);
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;
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);
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;
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();
1150 }
while (numberCollectionEnumerator.
MoveNext() );
1157 numberCollectionEnumerator.
Reset();
1160 while (numberCollectionEnumerator.
MoveNext() )
1162 number& n = numberCollectionEnumerator.
Current();
1165 if( (--normalcount) <= 0)
1215 numberCollectionEnumerator.
Reset();
1218 while (numberCollectionEnumerator.
MoveNext() )
1220 number& n = numberCollectionEnumerator.
Current();
1231 n = (number)
p_Mult_q(cInverse, (poly)n,
R);
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));
1409 (e->
r->qideal->m[0] !=
NULL) );
1415 const ring
R = e->
r;
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;
1752 cf->iNumberOfParameters =
rVar(
R);
1753 cf->pParameterNames = (
const char**)
R->names;
static FORCE_INLINE n_coeffType getCoeffType(const coeffs r)
Returns the type of coeffs domain.
int dReportError(const char *fmt,...)
char * n2pCoeffString(const coeffs cf)
static FORCE_INLINE BOOLEAN nCoeff_is_Zp(const coeffs r)
void StringAppendS(const char *st)
static long p_GetExp(const poly p, const unsigned long iBitmask, const int VarOffset)
get a single variable exponent @Note: the integer VarOffset encodes:
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 ...
#define p_SetCoeff0(p, n, r)
void p_Normalize(poly p, const ring r)
virtual reference Current()=0
Gets the current element in the collection (read and write).
void p_Write0(poly p, ring lmRing, ring tailRing)
nMapFunc naSetMap(const coeffs src, const coeffs dst)
Get a mapping function from src into the domain of this type (n_algExt)
void naCoeffWrite(const coeffs cf, BOOLEAN details)
static BOOLEAN rCanShortOut(const ring r)
number napNormalizeHelper(number b, const coeffs cf)
const CanonicalForm int const CFList const Variable & y
BOOLEAN naIsOne(number a, const coeffs cf)
char * naCoeffName(const coeffs r)
void n2pCoeffWrite(const coeffs cf, BOOLEAN details)
int naIsParam(number m, const coeffs cf)
if m == var(i)/1 => return i,
const char * n2pRead(const char *s, number *a, const coeffs cf)
void n2pPower(number a, int exp, number *b, const coeffs cf)
number naDiv(number a, number b, const coeffs cf)
static poly p_Gcd(const poly p, const poly q, const ring r)
number naGenMap(number a, const coeffs cf, const coeffs dst)
BOOLEAN naInitChar(coeffs cf, void *infoStruct)
Initialize the coeffs object.
number naGcd(number a, number b, const coeffs cf)
int p_Var(poly m, const ring r)
static FORCE_INLINE char * nCoeffString(const coeffs cf)
TODO: make it a virtual method of coeffs, together with: Decompose & Compose, rParameter & rPar.
number n2pInvers(number a, const coeffs cf)
number naChineseRemainder(number *x, number *q, int rl, BOOLEAN, CFArray &inv_cache, const coeffs cf)
static poly p_Neg(poly p, const ring r)
int naParDeg(number a, const coeffs cf)
number naInvers(number a, const coeffs cf)
number naFarey(number p, number n, const coeffs cf)
static BOOLEAN length(leftv result, leftv arg)
number naMap00(number a, const coeffs src, const coeffs dst)
poly p_ChineseRemainder(poly *xx, number *x, number *q, int rl, CFArray &inv_cache, const ring R)
poly singclap_pdivide(poly f, poly g, const ring r)
void naWriteLong(number a, const coeffs cf)
static FORCE_INLINE BOOLEAN nCoeff_is_Q_or_BI(const coeffs r)
static coeffs nCoeff_bottom(const coeffs r, int &height)
number ndCopyMap(number a, const coeffs aRing, const coeffs r)
poly prMapR(poly src, nMapFunc nMap, ring src_r, ring dest_r)
static FORCE_INLINE void n_Delete(number *p, const coeffs r)
delete 'p'
BOOLEAN naDBTest(number a, const char *f, const int l, const coeffs r)
number naMapPP(number a, const coeffs src, const coeffs dst)
number naAdd(number a, number b, const coeffs cf)
static FORCE_INLINE BOOLEAN n_IsZero(number n, const coeffs r)
TRUE iff 'n' represents the zero element.
static FORCE_INLINE int n_NumberOfParameters(const coeffs r)
Returns the number of parameters.
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 BOOLEAN n_IsOne(number n, const coeffs r)
TRUE iff 'n' represents the one element.
CanonicalForm naConvSingNFactoryN(number n, BOOLEAN, const coeffs cf)
#define __p_Mult_nn(p, n, r)
static FORCE_INLINE void n_Normalize(number &n, const coeffs r)
inplace-normalization of n; produces some canonical representation of n;
void p_String0Short(const poly p, ring lmRing, ring tailRing)
print p in a short way, if possible
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,...
number n2pMult(number a, number b, const coeffs cf)
poly gcd_over_Q(poly f, poly g, const ring r)
helper routine for calling singclap_gcd_r
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
virtual void Reset()=0
Sets the enumerator to its initial position: -1, which is before the first element in the collection.
number naLcmContent(number a, number b, const coeffs cf)
static FORCE_INLINE BOOLEAN nCoeff_is_Q(const coeffs r)
BOOLEAN rEqual(ring r1, ring r2, BOOLEAN qr)
returns TRUE, if r1 equals r2 FALSE, otherwise Equality is determined componentwise,...
static FORCE_INLINE void n_CoeffWrite(const coeffs r, BOOLEAN details=TRUE)
output the coeff description
static poly p_Copy(poly p, const ring r)
returns a copy of p
poly p_Power(poly p, int i, const ring r)
number naCopy(number a, const coeffs cf)
void definiteReduce(poly &p, poly reducer, const coeffs cf)
static short rVar(const ring r)
#define rVar(r) (r->N)
used to represent polys as coeffcients
#define n2pTest(a)
ABSTRACT: numbers as polys in the ring K[a] Assuming that we have a coeffs object cf,...
struct for passing initialization parameters to naInitChar
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)
number(* nMapFunc)(number a, const coeffs src, const coeffs dst)
maps "a", which lives in src, into dst
const char *const nDivBy0
void PrintS(const char *s)
#define omFreeSize(addr, size)
static FORCE_INLINE BOOLEAN nCoeff_is_algExt(const coeffs r)
TRUE iff r represents an algebraic extension field.
static char * rRingVar(short i, const ring r)
void naClearDenominators(ICoeffsEnumerator &numberCollectionEnumerator, number &c, const coeffs cf)
BOOLEAN naGreaterZero(number a, const coeffs cf)
forward declarations
BOOLEAN naGreater(number a, number b, const coeffs cf)
int naSize(number a, const coeffs cf)
char * n2pCoeffName(const coeffs cf)
static void naClearContent(ICoeffsEnumerator &numberCollectionEnumerator, number &c, const coeffs cf)
number naParameter(const int iParameter, const coeffs cf)
return the specified parameter as a number in the given alg. field
number naGetDenom(number &a, const coeffs cf)
number ndGcd(number, number, const coeffs r)
void p_String0Long(const poly p, ring lmRing, ring tailRing)
print p in a long way
poly p_Farey(poly p, number N, const ring r)
number naGetNumerator(number &a, const coeffs cf)
long naInt(number &a, const coeffs cf)
static poly pp_Mult_qq(poly p, poly q, const ring r)
number naMult(number a, number b, const coeffs cf)
BOOLEAN fa(leftv res, leftv args)
number naMapUP(number a, const coeffs src, const coeffs dst)
char * naCoeffString(const coeffs r)
static FORCE_INLINE number n_Mult(number a, number b, const coeffs r)
return the product of 'a' and 'b', i.e., a*b
number naConvFactoryNSingN(const CanonicalForm n, 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)
const char * p_Read(const char *st, poly &rc, const ring r)
number nlModP(number q, const coeffs, const coeffs Zp)
static poly p_Init(const ring r, omBin bin)
void naWriteShort(number a, const coeffs cf)
number n2pDiv(number a, number b, 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 naKillChar(coeffs cf)
static FORCE_INLINE BOOLEAN nCoeff_is_Extension(const coeffs r)
static FORCE_INLINE BOOLEAN nCoeff_is_transExt(const coeffs r)
TRUE iff r represents a transcendental extension field.
static poly p_ExtGcdHelper(poly &p, poly &pFactor, poly &q, poly &qFactor, ring r)
static FORCE_INLINE const char ** n_ParameterNames(const coeffs r)
Returns a (const!) pointer to (const char*) names of parameters.
CanonicalForm convSingPFactoryP(poly p, const ring r)
gmp_float exp(const gmp_float &a)
number naInit(long i, const coeffs cf)
const char * naRead(const char *s, number *a, const coeffs cf)
void rDelete(ring r)
unconditionally deletes fields in r
const CanonicalForm const CanonicalForm const CanonicalForm const CanonicalForm & cand
long p_Deg(poly a, const ring r)
static void p_Delete(poly *p, const ring r)
static poly p_Add_q(poly p, poly q, const ring r)
BOOLEAN singclap_extgcd(poly f, poly g, poly &res, poly &pa, poly &pb, const ring r)
virtual bool MoveNext()=0
Advances the enumerator to the next element of the collection. returns true if the enumerator was suc...
number naSub(number a, number b, const coeffs cf)
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 ...
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 p_EqualPolys(poly p1, poly p2, const ring r)
void rWrite(ring r, BOOLEAN details)
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...
void naNormalize(number &a, const coeffs cf)
number naGenTrans2AlgExt(number a, const coeffs cf, const coeffs dst)
void heuristicReduce(poly &p, poly reducer, const coeffs cf)
poly p_NSet(number n, const ring r)
returns the poly representing the number n, destroys n
static BOOLEAN naCoeffIsEqual(const coeffs cf, n_coeffType n, void *param)
static BOOLEAN n2pCoeffIsEqual(const coeffs cf, n_coeffType n, void *param)
poly singclap_gcd_r(poly f, poly g, const ring r)
BOOLEAN naIsZero(number a, const coeffs cf)
static number p_SetCoeff(poly p, number n, ring r)
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),...
static FORCE_INLINE number n_Copy(number n, const coeffs r)
return a copy of 'n'
Rational pow(const Rational &a, int e)
void WerrorS(const char *s)
number naMapP0(number a, const coeffs src, const coeffs dst)
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 number n_SubringGcd(number a, number b, const coeffs r)
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 ....
static FORCE_INLINE BOOLEAN nCoeff_is_Q_algext(const coeffs r)
is it an alg. ext. of Q?
number naNeg(number a, const coeffs cf)
this is in-place, modifies a
static void p_Setm(poly p, const ring r)
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...
static long p_Totaldegree(poly p, const ring r)
static BOOLEAN p_IsConstant(const poly p, const ring r)
void naDelete(number *a, const coeffs cf)
number naCopyTrans2AlgExt(number a, const coeffs src, const coeffs dst)
const CanonicalForm int s
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...
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...
static FORCE_INLINE nMapFunc n_SetMap(const coeffs src, const coeffs dst)
set the mapping function pointers for translating numbers from src to dst
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)
BOOLEAN naIsMOne(number a, const coeffs cf)
static number & pGetCoeff(poly p)
return an alias to the leading coefficient of p assumes that p != NULL NOTE: not copy
BOOLEAN naEqual(number a, number b, const coeffs cf)
#define n_Test(a, r)
BOOLEAN n_Test(number a, const coeffs r)
BOOLEAN n2pInitChar(coeffs cf, void *infoStruct)
poly convFactoryPSingP(const CanonicalForm &f, const ring r)
BOOLEAN n2pDBTest(number a, const char *f, const int l, const coeffs r)
go into polynomials over an alg. extension recursively
number naMapZ0(number a, const coeffs src, const coeffs dst)
void n2pNormalize(number &a, const coeffs cf)
used for all algebraic extensions, i.e., the top-most extension in an extension tower is algebraic
number naMap0P(number a, const coeffs src, const coeffs dst)
(), see rinteger.h, new impl.