33 #define TRANSEXT_PRIVATES 37 #include "factory/factory.h" 61 #define ADD_COMPLEXITY 1 62 #define MULT_COMPLEXITY 2 63 #define DIFF_COMPLEXITY 2 64 #define BOUND_COMPLEXITY 10 67 #define NUMIS1(f) (p_IsOne(NUM(f), cf->extRing)) 69 #define COM(f) (f)->complexity 76 #define ntTest(a) n_Test(a, cf) 80 #define ntRing cf->extRing 86 #define ntCoeffs cf->extRing->cf 94 BOOLEAN simpleTestsHaveAlreadyBeenPerformed);
144 if (IS0(a))
return TRUE;
146 const fraction t = (fraction)a;
149 const poly
num = NUM(t);
158 Print(
"ERROR in %s:%d: non-integer Q coeff in num. poly\n",f,l);
163 const poly
den = DEN(t);
173 Print(
"ERROR in %s:%d: non-integer Q coeff in den. poly\n",f,l);
182 Print(
"ERROR in %s:%d: constant den. poly / Zp\n",f,l);
190 Print(
"ERROR in %s:%d: non-monic den. poly / Zp\n",f,l);
204 Print(
"ERROR in %s:%d: 1 != GCD between num. & den. poly\n",f,l);
217 Print(
"?/1 in %s:%d\n",f,l);
222 Print(
"negative sign of DEN. of a fraction in %s:%d\n",f,l);
252 if (!(
SR_HDL(n) & SR_INT))
255 Print(
"rational coeff in num: %s:%d\n",f,l);
266 Print(
"rational coeff in den.:%s:%d\n",f,l);
300 cf = cf->extRing->cf;
318 fraction
f = (fraction)(*a);
334 if (a == b)
return TRUE;
335 if ((IS0(a)) && (!IS0(b)))
return FALSE;
336 if ((IS0(b)) && (!IS0(a)))
return FALSE;
339 fraction
fa = (fraction)a;
340 fraction
fb = (fraction)b;
341 if ((
COM(fa) == 1) && (
COM(fb) == 1))
347 if (DENIS1(fa) && DENIS1(fb))
return TRUE;
348 if (DENIS1(fa) && !DENIS1(fb))
return FALSE;
349 if (!DENIS1(fa) && DENIS1(fb))
return FALSE;
376 if (IS0(a))
return NULL;
377 fraction
f = (fraction)a;
382 NUM(result) =
p_Copy(g,cf->extRing);
383 DEN(result) =
p_Copy(h,cf->extRing);
421 number c; number tmp;
430 lcmOfDenominators = tmp;
439 lcmOfDenominators = tmp;
460 gcdOfCoefficients = tmp;
469 gcdOfCoefficients = tmp;
474 number inverseOfGcdOfCoefficients =
n_Invers(gcdOfCoefficients,
488 if ((DEN(f) !=
NULL) &&
510 if (IS0(a))
return NULL;
514 fraction
f = (fraction)a;
517 const BOOLEAN denis1= DENIS1 (f);
584 fraction
f = (fraction)a;
588 const BOOLEAN denis1 = DENIS1 (f);
606 if( DEN (f) !=
NULL )
674 fraction
f = (fraction)a;
683 fraction
f = (fraction)a;
684 if ((f==
NULL) || (!DENIS1(f)))
return FALSE;
697 fraction
f = (fraction)a;
777 if (IS0(a))
return 0;
779 fraction
f = (fraction)a;
780 if (!DENIS1(f))
return 0;
782 const poly aAsPoly = NUM(f);
800 if (IS0(a))
return FALSE;
801 fraction
f = (fraction)a;
814 if (IS0(b))
return FALSE;
815 fraction
fb = (fraction)b;
820 fraction
fa = (fraction)a;
824 fraction
fa = (fraction)a;
827 number aDenCoeff =
NULL;
int aDenDeg = 0;
833 fraction
fb = (fraction)b;
836 number bDenCoeff =
NULL;
int bDenDeg = 0;
842 if (aNumDeg-aDenDeg > bNumDeg-bDenDeg)
return TRUE;
843 if (aNumDeg-aDenDeg < bNumDeg-bDenDeg)
return FALSE;
860 const ring
A = cf->extRing;
869 const int P =
rVar(A);
874 for (
int nop=0; nop < P; nop ++)
877 if (nop!=P-1)
PrintS(
", ");
909 fraction t = (fraction) d;
912 WerrorS(
"expected differentiation by a variable");
918 WerrorS(
"expected differentiation by a variable");
922 if (IS0(a))
return ntCopy(a, cf);
924 fraction
fa = (fraction)a;
930 if (NUM(result)==
NULL)
944 if (NUM(result)==
NULL)
return(
NULL);
960 if (IS0(a))
return ntCopy(b, cf);
961 if (IS0(b))
return ntCopy(a, cf);
963 fraction
fa = (fraction)a;
964 fraction
fb = (fraction)b;
975 if (DENIS1(fa) && DENIS1(fb)) f =
NULL;
976 else if (!DENIS1(fa) && DENIS1(fb)) f =
p_Copy(DEN(fa),
ntRing);
977 else if (DENIS1(fa) && !DENIS1(fb)) f =
p_Copy(DEN(fb),
ntRing);
1002 if (IS0(b))
return ntCopy(a, cf);
1004 fraction
fa = (fraction)a;
1005 fraction
fb = (fraction)b;
1016 if (DENIS1(fa) && DENIS1(fb)) f =
NULL;
1017 else if (!DENIS1(fa) && DENIS1(fb)) f =
p_Copy(DEN(fa),
ntRing);
1018 else if (DENIS1(fa) && !DENIS1(fb)) f =
p_Copy(DEN(fb),
ntRing);
1041 if (IS0(a) || IS0(b))
return NULL;
1043 fraction
fa = (fraction)a;
1044 fraction
fb = (fraction)b;
1054 const poly da = DEN(fa);
1055 const poly db = DEN(fb);
1106 && (DEN(result)!=
NULL))
1132 if (IS0(a))
return NULL;
1135 fraction
fa = (fraction)a;
1136 fraction
fb = (fraction)b;
1181 fraction
f = (fraction)a;
1187 const poly
den = DEN(f);
1207 DEN(result) = num_f;
1245 if (exp >= 0) *b =
NULL;
1248 else if (exp == 0) { *b =
ntInit(1, cf);
return;}
1249 else if (exp == 1) { *b =
ntCopy(a, cf);
return;}
1250 else if (exp == -1) { *b =
ntInvers(a, cf);
return;}
1252 int expAbs =
exp;
if (expAbs < 0) expAbs = -expAbs;
1255 number
pow; number t;
1259 for (
int i = 2;
i <= expAbs;
i++)
1275 t =
ntMult(pow, factor, cf);
1280 expAbs = expAbs / 2;
1283 t =
ntMult(factor, factor, cf);
1310 fraction
f = (fraction)a;
1312 if (DENIS1(f) ||
NUMIS1(f)) {
COM(f) = 0;
return; }
1330 if( DEN(f) !=
NULL )
1374 }
while(i<ntRing->
N);
1392 BOOLEAN simpleTestsHaveAlreadyBeenPerformed)
1396 fraction
f = (fraction)a;
1399 if (
COM(f)==0)
return;
1401 if (!simpleTestsHaveAlreadyBeenPerformed)
1531 if( DEN(f) !=
NULL )
1556 fraction
f = (fraction)a;
1581 fraction
f = (fraction)a;
1616 if ((DEN((fraction)a)!=
NULL)
1654 fraction
fb = (fraction)b;
1656 fraction
fa = (fraction)a;
1670 number contentpa, contentpb, tmp;
1737 fraction
fa = (fraction)a;
1738 fraction
fb = (fraction)b;
1753 number contentpa, contentpb, tmp;
1807 if (IS0(a))
return 0;
1808 fraction
f = (fraction)a;
1810 unsigned long noOfTerms = 0;
1811 unsigned long numDegree = 0;
1817 unsigned long denDegree = 0;
1825 unsigned long t= ((numDegree + denDegree)*(numDegree + denDegree) + 1) * noOfTerms;
1826 if (t>INT_MAX)
return INT_MAX;
1836 assume(src->rep == dst->extRing->cf->rep);
1846 fraction ff=(fraction)res;
1848 else DEN(ff)=
p_NSet(nn,dst->extRing);
1860 poly
p=
p_NSet(nMap(a, src,dst->extRing->cf), dst->extRing);
1874 int n =
n_Int(a, src);
1875 number q =
n_Init(n, dst->extRing->cf);
1888 if (IS0(a))
return NULL;
1890 const ring rSrc = cf->extRing;
1891 const ring rDst = dst->extRing;
1896 fraction
f = (fraction)a;
1897 poly
g =
prCopyR(NUM(f), rSrc, rDst);
1902 h =
prCopyR(DEN(f), rSrc, rDst);
1910 n_Test((number)result, dst);
1917 if (IS0(a))
return NULL;
1919 const ring rSrc = cf->extRing;
1920 const ring rDst = dst->extRing;
1923 fraction
f = (fraction)a;
1924 poly
g =
prMapR(NUM(f), nMap, rSrc, rDst);
1955 h =
prMapR(DEN(f), nMap, rSrc, rDst);
1989 n_Test((number)result, dst);
1997 return ntInit(
prCopyR((poly)a, cf->extRing, dst->extRing),dst);
2006 return ntInit(
prMapR((poly)a, nMap, cf->extRing, dst->extRing),dst);
2016 number q =
nlModP(a, src, dst->extRing->cf);
2024 poly
g =
p_NSet(q, dst->extRing);
2038 assume(src == dst->extRing->cf);
2039 poly
p =
p_One(dst->extRing);
2054 int n =
n_Int(a, src);
2055 number q =
n_Init(n, dst->extRing->cf);
2062 p =
p_One(dst->extRing);
2096 if (src->ch == dst->ch)
return ntMapPP;
2101 if (mpz_cmp(src->modNumber,bDst->modNumber)==0)
return ntMapPP;
2104 if (h != 1)
return NULL;
2112 if (
rVar(src->extRing) >
rVar(dst->extRing))
2115 for (
int i = 0;
i <
rVar(src->extRing);
i++)
2121 if (src->extRing->cf==dst->extRing->cf)
2128 if (src->extRing->cf==dst->extRing->cf)
2140 if (n==
ntCopyAlg) printf(
"n=ntCopyAlg\n");
2141 else if (n==
ntCopyMap) printf(
"n=ntCopyMap\n");
2142 else if (n==
ntMapUP) printf(
"n=ntMapUP\n");
2143 else if (n==
ntMap0P) printf(
"n=ntMap0P\n");
2144 else if (n==
ntMapP0) printf(
"n=ntMapP0\n");
2145 else if (n==
ntMap00) printf(
"n=ntMap00\n");
2146 else if (n==
NULL) printf(
"n=NULL\n");
2147 else printf(
"n=?\n");
2154 if ((--cf->extRing->ref) == 0)
2174 fraction
f = (fraction)n;
2181 if (IS0(a))
return -1;
2182 fraction
fa = (fraction)a;
2183 return cf->extRing->pFDeg(NUM(fa),cf->extRing);
2191 const ring
R = cf->extRing;
2193 assume( 0 < iParameter && iParameter <=
rVar(R) );
2214 const ring
R = cf->extRing;
2217 fraction
f = (fraction)m;
2219 if( DEN(f) !=
NULL )
2222 return p_Var( NUM(f), R );
2230 return NUM((fraction)n);
2242 const ring
R = cf->extRing;
2249 numberCollectionEnumerator.
Reset();
2251 if( !numberCollectionEnumerator.
MoveNext() )
2264 number &n = numberCollectionEnumerator.
Current();
2268 fraction
f = (fraction)n;
2272 const poly
den = DEN(f);
2276 const poly
num = NUM(f);
2290 while( numberCollectionEnumerator.
MoveNext() ) ;
2299 numberCollectionEnumerator.
Reset();
2300 while (numberCollectionEnumerator.
MoveNext() )
2302 number &n = numberCollectionEnumerator.
Current();
2303 const number t =
ntDiv(n, c, cf);
2320 number gg =
ntMult(g, c, cf);
2334 numberCollectionEnumerator.
Reset();
2336 if( !numberCollectionEnumerator.
MoveNext() )
2347 const ring
R = cf->extRing;
2356 number &n = numberCollectionEnumerator.
Current();
2364 const poly
den = NUM(f);
2391 while( numberCollectionEnumerator.
MoveNext() );
2401 numberCollectionEnumerator.
Reset();
2405 while (numberCollectionEnumerator.
MoveNext() )
2407 number &n = numberCollectionEnumerator.
Current();
2408 number t =
ntMult(n, c, cf);
2414 fraction
f = (fraction)t;
2417 const poly
den = DEN(f);
2436 numberCollectionEnumerator.
Reset();
2437 while (numberCollectionEnumerator.
MoveNext() )
2439 number &n = numberCollectionEnumerator.
Current();
2440 fraction
f = (fraction)n;
2444 const poly
den = DEN(f);
2464 NUM((fraction)c) =
__p_Mult_nn(NUM((fraction)c), d, R);
2476 poly *P=(poly*)
omAlloc(rl*
sizeof(poly*));
2477 number *X=(number *)
omAlloc(rl*
sizeof(number));
2481 for(i=0;i<rl;i++) P[i]=
p_Copy(NUM((fraction)(x[
i])),cf->extRing);
2486 P[
i]=
p_Copy(DEN((fraction)(x[i])),cf->extRing);
2499 return ((number)result);
2506 NUM(result)=
p_Farey(
p_Copy(NUM((fraction)p),cf->extRing),n,cf->extRing);
2507 DEN(result)=
p_Farey(
p_Copy(DEN((fraction)p),cf->extRing),n,cf->extRing);
2509 return ((number)result);
2540 cf->factoryVarOffset = R->cf->factoryVarOffset +
rVar(R);
2556 cf->cfInpNeg =
ntNeg;
2560 cf->cfExactDiv =
ntDiv;
2577 cf->cfSubringGcd =
ntGcd;
2593 cf->iNumberOfParameters =
rVar(R);
2594 cf->pParameterNames = (
const char**)R->names;
2596 cf->has_simple_Inverse=
FALSE;
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 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) ...
BOOLEAN fb(leftv res, leftv args)
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
poly p_Diff(poly a, int k, const ring r)
#define BOUND_COMPLEXITY
maximum complexity of a number
poly singclap_gcd_r(poly f, poly g, const ring r)
poly singclap_gcd_and_divide(poly &f, poly &g, const ring r)
clears denominators of f and g, divides by gcd(f,g)
static BOOLEAN ntIsMOne(number a, const coeffs cf)
static void ntNormalizeDen(fraction result, const ring R)
static BOOLEAN ntDBTest(number a, const char *f, const int l, const coeffs r)
static BOOLEAN p_LmIsConstantComp(const poly p, const ring r)
number ntDiff(number a, number d, const coeffs cf)
static FORCE_INLINE BOOLEAN nCoeff_is_Zp(const coeffs r)
poly prCopyR(poly p, ring src_r, ring dest_r)
gmp_float exp(const gmp_float &a)
char * naCoeffName(const coeffs r)
static poly convert(const number &n)
used for all transcendental extensions, i.e., the top-most extension in an extension tower is transce...
number nlModP(number q, const coeffs, const coeffs Zp)
#define DIFF_COMPLEXITY
complexity increase due to diff
static BOOLEAN ntIsOne(number a, const coeffs cf)
void p_String0Long(const poly p, ring lmRing, ring tailRing)
print p in a long way
static FORCE_INLINE BOOLEAN nlIsInteger(number q, const coeffs r)
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)
static void ntPower(number a, int exp, number *b, const coeffs cf)
static void definiteGcdCancellation(number a, const coeffs cf, BOOLEAN simpleTestsHaveAlreadyBeenPerformed)
modifies a
poly gcd_over_Q(poly f, poly g, const ring r)
helper routine for calling singclap_gcd_r
static BOOLEAN ntIsZero(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
static FORCE_INLINE BOOLEAN nCoeff_is_Q_or_BI(const coeffs r)
#define omFreeSize(addr, size)
static short rVar(const ring r)
#define rVar(r) (r->N)
(), see rinteger.h, new impl.
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...
poly p_Div_nn(poly p, const number n, const ring r)
static number ntFarey(number p, number n, const coeffs cf)
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;
static number ntCopyMap(number a, const coeffs cf, const coeffs dst)
void WerrorS(const char *s)
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...
(fraction), see transext.h
nMapFunc ntSetMap(const coeffs src, const coeffs dst)
Get a mapping function from src into the domain of this type (n_transExt)
void p_Norm(poly p1, const ring r)
static number ntCopy(number a, const coeffs cf)
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)
static BOOLEAN ntGreaterZero(number a, const coeffs cf)
static number p_SetCoeff(poly p, number n, ring r)
poly p_Sub(poly p1, poly p2, const ring r)
static coeffs nCoeff_bottom(const coeffs r, int &height)
static BOOLEAN rCanShortOut(const ring r)
static number ntConvFactoryNSingN(const CanonicalForm n, const coeffs cf)
BOOLEAN pb(leftv res, leftv args)
static void ntWriteShort(number a, const coeffs cf)
static poly p_Copy(poly p, const ring r)
returns a copy of p
static number ntGcd(number a, number b, const coeffs cf)
poly prMapR(poly src, nMapFunc nMap, ring src_r, ring dest_r)
static BOOLEAN p_LmIsConstant(const poly p, const ring r)
static int ntParDeg(number a, const coeffs cf)
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...
const char * p_Read(const char *st, poly &rc, const ring r)
static number ntMap00(number a, const coeffs src, const coeffs dst)
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 void ntClearDenominators(ICoeffsEnumerator &numberCollectionEnumerator, number &c, const coeffs cf)
Coefficient rings, fields and other domains suitable for Singular polynomials.
static void ntNormalize(number &a, const coeffs cf)
poly p_Farey(poly p, number N, const ring 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 ...
const CanonicalForm CFMap CFMap & N
Concrete implementation of enumerators over polynomials.
static number ntAdd(number a, number b, const coeffs cf)
static void ntWriteLong(number a, const coeffs cf)
static long p_GetExp(const poly p, const unsigned long iBitmask, const int VarOffset)
get a single variable exponent : the integer VarOffset encodes:
This is a polynomial enumerator for simple iteration over coefficients of polynomials.
BOOLEAN fa(leftv res, leftv args)
static long ntInt(number &a, const coeffs cf)
number ntInit(long i, const coeffs cf)
static BOOLEAN p_IsConstant(const poly p, const ring r)
static void ntKillChar(coeffs cf)
The main handler for Singular numbers which are suitable for Singular polynomials.
static number ntMapZ0(number a, const coeffs src, const coeffs dst)
Templated enumerator interface for simple iteration over a generic collection of T's.
static poly pp_Mult_qq(poly p, poly q, const ring r)
void StringAppendS(const char *st)
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
static BOOLEAN ntEqual(number a, number b, const coeffs cf)
virtual reference Current()=0
Gets the current element in the collection (read and write).
#define n_Test(a, r)
BOOLEAN n_Test(number a, const coeffs r)
static void ntDelete(number *a, 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 ...
static number ntMapUP(number a, const coeffs src, const coeffs dst)
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)
static BOOLEAN ntCoeffIsEqual(const coeffs cf, n_coeffType n, void *param)
#define NUMIS1(f)
TRUE iff num. represents 1.
struct for passing initialization parameters to naInitChar
const char *const nDivBy0
static void ntCoeffWrite(const coeffs cf, BOOLEAN details)
static BOOLEAN p_IsOne(const poly p, const ring R)
either poly(1) or gen(k)?!
void PrintS(const char *s)
static char * rRingVar(short i, const ring r)
static const char * ntRead(const char *s, number *a, const coeffs cf)
static poly p_LmFreeAndNext(poly p, ring)
static unsigned pLength(poly a)
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
go into polynomials over an alg. extension recursively
static FORCE_INLINE n_coeffType getCoeffType(const coeffs r)
Returns the type of coeffs domain.
static number ntChineseRemainder(number *x, number *q, int rl, BOOLEAN, CFArray &inv_cache, const coeffs cf)
BOOLEAN p_EqualPolys(poly p1, poly p2, const ring r)
static void ntClearContent(ICoeffsEnumerator &numberCollectionEnumerator, number &c, const coeffs cf)
static number ntNormalizeHelper(number a, number b, const coeffs cf)
void p_Normalize(poly p, const ring r)
static void p_Delete(poly *p, const ring r)
#define omGetSpecBin(size)
static void p_ExpVectorDiff(poly pr, poly p1, poly p2, const ring r)
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
#define __p_Mult_nn(p, n, r)
static FORCE_INLINE void n_CoeffWrite(const coeffs r, BOOLEAN details=TRUE)
output the coeff description
static void heuristicGcdCancellation(number a, const coeffs cf)
forward declarations
static number ntMult(number a, number b, const coeffs cf)
CanonicalForm convSingPFactoryP(poly p, const ring r)
static void handleNestedFractionsOverQ(fraction f, const coeffs cf)
static FORCE_INLINE number n_Copy(number n, const coeffs r)
return a copy of 'n'
static number ntParameter(const int iParameter, const coeffs cf)
return the specified parameter as a number in the given trans.ext.
void rDelete(ring r)
unconditionally deletes fields in r
static number ntMap0P(number a, const coeffs src, const coeffs dst)
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 int ntSize(number a, const coeffs cf)
static number ntInvers(number a, const coeffs cf)
virtual bool MoveNext()=0
Advances the enumerator to the next element of the collection. returns true if the enumerator was suc...
static number ntNeg(number a, const coeffs cf)
this is in-place, modifies a
poly p_ChineseRemainder(poly *xx, number *x, number *q, int rl, CFArray &inv_cache, const ring R)
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) ...
static void p_Setm(poly p, const ring r)
static number ntMapP0(number a, const coeffs src, const coeffs dst)
static FORCE_INLINE number n_SubringGcd(number a, number b, const coeffs r)
static number ntDiv(number a, number b, const coeffs cf)
static FORCE_INLINE BOOLEAN nCoeff_is_Extension(const coeffs r)
int ntIsParam(number m, const coeffs cf)
if m == var(i)/1 => return i,
static number ntGetDenom(number &a, const coeffs cf)
TODO: normalization of a!?
static poly p_Neg(poly p, const ring r)
static number ntGenAlg(number a, const coeffs cf, const coeffs dst)
BOOLEAN pa(leftv res, leftv args)
static FORCE_INLINE void n_Delete(number *p, const coeffs r)
delete 'p'
void p_wrp(poly p, ring lmRing, ring tailRing)
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 number ntSub(number a, number b, const coeffs cf)
void p_Write(poly p, ring lmRing, ring tailRing)
static CanonicalForm ntConvSingNFactoryN(number n, BOOLEAN, const coeffs cf)
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
#define ADD_COMPLEXITY
complexity increase due to + and -
static poly p_Add_q(poly p, poly q, const ring r)
static BOOLEAN ntGreater(number a, number b, const coeffs cf)
#define omFreeBin(addr, bin)
Rational pow(const Rational &a, int e)
static number ntGenMap(number a, const coeffs cf, const coeffs dst)
poly p_Cleardenom(poly p, const ring r)
int p_Var(poly m, const ring r)
static number ntCopyAlg(number a, const coeffs cf, const coeffs dst)
static FORCE_INLINE BOOLEAN nCoeff_is_Zn(const coeffs r)
#define MULT_COMPLEXITY
complexity increase due to * and /
static number ntGetNumerator(number &a, const coeffs cf)
TODO: normalization of a!?
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)
void p_String0Short(const poly p, ring lmRing, ring tailRing)
print p in a short way, if possible
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...
static number ntMapPP(number a, const coeffs src, const coeffs dst)
BOOLEAN ntInitChar(coeffs cf, void *infoStruct)
Initialize the coeffs object.