33 #define TRANSEXT_PRIVATES 38 #include <factory/factory.h> 62 #define ADD_COMPLEXITY 1 63 #define MULT_COMPLEXITY 2 64 #define DIFF_COMPLEXITY 2 65 #define BOUND_COMPLEXITY 10 68 #define NUMIS1(f) (p_IsOne(NUM(f), cf->extRing)) 70 #define COM(f) f->complexity 77 #define ntTest(a) n_Test(a, cf) 81 #define ntRing cf->extRing 87 #define ntCoeffs cf->extRing->cf 125 BOOLEAN simpleTestsHaveAlreadyBeenPerformed);
176 if (IS0(a))
return TRUE;
178 const fraction t = (fraction)a;
190 Print(
"ERROR in %s:%d: non-integer Q coeff in num. poly\n",f,l);
205 Print(
"ERROR in %s:%d: non-integer Q coeff in den. poly\n",f,l);
214 Print(
"ERROR in %s:%d: constant den. poly / Zp\n",f,l);
222 Print(
"ERROR in %s:%d: non-monic den. poly / Zp\n",f,l);
236 Print(
"ERROR in %s:%d: 1 != GCD between num. & den. poly\n",f,l);
249 Print(
"?/1 in %s:%d\n",f,l);
254 Print(
"negative sign of DEN. of a fraction in %s:%d\n",f,l);
284 if (!(
SR_HDL(n) & SR_INT))
287 Print(
"rational coeff in num: %s:%d\n",f,l);
298 Print(
"rational coeff in den.:%s:%d\n",f,l);
319 cf = cf->extRing->cf;
337 fraction
f = (fraction)(*a);
353 if (a == b)
return TRUE;
354 if ((IS0(a)) && (!IS0(b)))
return FALSE;
355 if ((IS0(b)) && (!IS0(a)))
return FALSE;
358 fraction fa = (fraction)a;
359 fraction fb = (fraction)b;
360 if ((
COM(fa) == 1) && (
COM(fb) == 1))
366 if (DENIS1(fa) && DENIS1(fb))
return TRUE;
367 if (DENIS1(fa) && !DENIS1(fb))
return FALSE;
368 if (!DENIS1(fa) && DENIS1(fb))
return FALSE;
395 if (IS0(a))
return NULL;
396 fraction
f = (fraction)a;
401 NUM(result) =
p_Copy(g,cf->extRing);
402 DEN(result) =
p_Copy(h,cf->extRing);
413 if (IS0(a))
return NULL;
417 fraction
f = (fraction)a;
420 const BOOLEAN denis1= DENIS1 (f);
487 fraction
f = (fraction)a;
491 const BOOLEAN denis1 = DENIS1 (f);
509 if( DEN (f) !=
NULL )
577 fraction
f = (fraction)a;
586 fraction
f = (fraction)a;
587 if ((f==
NULL) || (!DENIS1(f)))
return FALSE;
600 fraction
f = (fraction)a;
686 if (IS0(a))
return 0;
688 fraction
f = (fraction)a;
689 if (!DENIS1(f))
return 0;
691 const poly aAsPoly = NUM(f);
716 number aNumCoeff =
NULL;
int aNumDeg = 0;
717 number aDenCoeff =
NULL;
int aDenDeg = 0;
718 number bNumCoeff =
NULL;
int bNumDeg = 0;
719 number bDenCoeff =
NULL;
int bDenDeg = 0;
722 fraction fa = (fraction)a;
734 fraction fb = (fraction)b;
744 if (aNumDeg-aDenDeg > bNumDeg-bDenDeg)
return TRUE;
745 if (aNumDeg-aDenDeg < bNumDeg-bDenDeg)
return FALSE;
767 if (IS0(a))
return FALSE;
768 fraction
f = (fraction)a;
777 const ring
A = cf->extRing;
786 const int P =
rVar(A);
789 Print(
"// %d parameter : ", P);
791 for (
int nop=0; nop <
P; nop ++)
796 PrintS(
"\n// minpoly : 0\n");
823 fraction t = (fraction) d;
826 WerrorS(
"expected differentiation by a variable");
832 WerrorS(
"expected differentiation by a variable");
836 if (IS0(a))
return ntCopy(a, cf);
838 fraction fa = (fraction)a;
844 if (NUM(result)==
NULL)
858 if (NUM(result)==
NULL)
return(
NULL);
875 if (IS0(a))
return ntCopy(b, cf);
876 if (IS0(b))
return ntCopy(a, cf);
878 fraction fa = (fraction)a;
879 fraction fb = (fraction)b;
890 if (DENIS1(fa) && DENIS1(fb)) f =
NULL;
891 else if (!DENIS1(fa) && DENIS1(fb)) f =
p_Copy(DEN(fa),
ntRing);
892 else if (DENIS1(fa) && !DENIS1(fb)) f =
p_Copy(DEN(fb),
ntRing);
917 if (IS0(b))
return ntCopy(a, cf);
919 fraction fa = (fraction)a;
920 fraction fb = (fraction)b;
931 if (DENIS1(fa) && DENIS1(fb)) f =
NULL;
932 else if (!DENIS1(fa) && DENIS1(fb)) f =
p_Copy(DEN(fa),
ntRing);
933 else if (DENIS1(fa) && !DENIS1(fb)) f =
p_Copy(DEN(fb),
ntRing);
956 if (IS0(a) || IS0(b))
return NULL;
958 fraction fa = (fraction)a;
959 fraction fb = (fraction)b;
969 const poly da = DEN(fa);
970 const poly db = DEN(fb);
1024 && (DEN(result)!=
NULL))
1031 NUM(result)=
p_Mult_nn(NUM(result),inv,R);
1050 if (IS0(a))
return NULL;
1053 fraction fa = (fraction)a;
1054 fraction fb = (fraction)b;
1101 if (exp >= 0) *b =
NULL;
1104 else if (exp == 0) { *b =
ntInit(1, cf);
return;}
1105 else if (exp == 1) { *b =
ntCopy(a, cf);
return;}
1106 else if (exp == -1) { *b =
ntInvers(a, cf);
return;}
1108 int expAbs =
exp;
if (expAbs < 0) expAbs = -expAbs;
1111 number
pow; number t;
1115 for (
int i = 2;
i <= expAbs;
i++)
1131 t =
ntMult(pow, factor, cf);
1136 expAbs = expAbs / 2;
1139 t =
ntMult(factor, factor, cf);
1192 number c; number tmp;
1201 lcmOfDenominators = tmp;
1210 lcmOfDenominators = tmp;
1231 gcdOfCoefficients = tmp;
1240 gcdOfCoefficients = tmp;
1245 number inverseOfGcdOfCoefficients =
n_Invers(gcdOfCoefficients,
1259 if ((DEN(f) !=
NULL) &&
1266 if( DEN(f) !=
NULL )
1282 fraction
f = (fraction)a;
1284 if (DENIS1(f) ||
NUMIS1(f)) {
COM(f) = 0;
return; }
1302 if( DEN(f) !=
NULL )
1346 }
while(i<ntRing->
N);
1364 BOOLEAN simpleTestsHaveAlreadyBeenPerformed)
1368 fraction
f = (fraction)a;
1372 if (!simpleTestsHaveAlreadyBeenPerformed)
1494 if( DEN(f) !=
NULL )
1519 fraction
f = (fraction)a;
1544 fraction
f = (fraction)a;
1579 if ((DEN((fraction)a)!=
NULL)
1617 fraction fb = (fraction)b;
1619 fraction fa = (fraction)a;
1634 number contentpa, contentpb, tmp;
1707 fraction fa = (fraction)a;
1708 fraction fb = (fraction)b;
1723 number contentpa, contentpb, tmp;
1780 if (IS0(a))
return -1;
1785 fraction
f = (fraction)a;
1801 return numDegree + denDegree + noOfTerms;
1813 fraction
f = (fraction)a;
1839 DEN(result) = num_f;
1868 assume(src->rep == dst->extRing->cf->rep);
1878 fraction ff=(fraction)res;
1880 else DEN(ff)=
p_NSet(nn,dst->extRing);
1892 poly p=
p_NSet(nMap(a, src,dst->extRing->cf), dst->extRing);
1906 int n =
n_Int(a, src);
1907 number q =
n_Init(n, dst->extRing->cf);
1920 if (IS0(a))
return NULL;
1922 const ring rSrc = cf->extRing;
1923 const ring rDst = dst->extRing;
1928 fraction
f = (fraction)a;
1934 h =
prCopyR(DEN(f), rSrc, rDst);
1942 n_Test((number)result, dst);
1949 if (IS0(a))
return NULL;
1951 const ring rSrc = cf->extRing;
1952 const ring rDst = dst->extRing;
1955 fraction
f = (fraction)a;
1987 h =
prMapR(DEN(f), nMap, rSrc, rDst);
2021 n_Test((number)result, dst);
2048 number q =
nlModP(a, src, dst->extRing->cf);
2070 assume(src == dst->extRing->cf);
2086 int n =
n_Int(a, src);
2087 number q =
n_Init(n, dst->extRing->cf);
2094 p =
p_One(dst->extRing);
2128 if (src->ch == dst->ch)
return ntMapPP;
2132 if (h != 1)
return NULL;
2140 if (
rVar(src->extRing) >
rVar(dst->extRing))
2143 for (
int i = 0;
i <
rVar(src->extRing);
i++)
2149 if (src->extRing->cf==dst->extRing->cf)
2156 if (src->extRing->cf==dst->extRing->cf)
2168 if (n==
ntCopyAlg) printf(
"n=ntCopyAlg\n");
2169 else if (n==
ntCopyMap) printf(
"n=ntCopyMap\n");
2170 else if (n==
ntMapUP) printf(
"n=ntMapUP\n");
2171 else if (n==
ntMap0P) printf(
"n=ntMap0P\n");
2172 else if (n==
ntMapP0) printf(
"n=ntMapP0\n");
2173 else if (n==
ntMap00) printf(
"n=ntMap00\n");
2174 else if (n==
NULL) printf(
"n=NULL\n");
2175 else printf(
"n=?\n");
2182 if ((--cf->extRing->ref) == 0)
2202 fraction
f = (fraction)n;
2209 if (IS0(a))
return -1;
2210 fraction fa = (fraction)a;
2211 return cf->extRing->pFDeg(NUM(fa),cf->extRing);
2219 const ring
R = cf->extRing;
2221 assume( 0 < iParameter && iParameter <=
rVar(R) );
2242 const ring
R = cf->extRing;
2245 fraction
f = (fraction)m;
2247 if( DEN(f) !=
NULL )
2250 return p_Var( NUM(f), R );
2258 return NUM((fraction)n);
2270 const ring
R = cf->extRing;
2277 numberCollectionEnumerator.
Reset();
2279 if( !numberCollectionEnumerator.
MoveNext() )
2292 number &n = numberCollectionEnumerator.
Current();
2296 fraction
f = (fraction)n;
2314 while( numberCollectionEnumerator.
MoveNext() ) ;
2323 numberCollectionEnumerator.
Reset();
2324 while (numberCollectionEnumerator.
MoveNext() )
2326 number &n = numberCollectionEnumerator.
Current();
2327 const number t =
ntDiv(n, c, cf);
2344 number gg =
ntMult(g, c, cf);
2358 numberCollectionEnumerator.
Reset();
2360 if( !numberCollectionEnumerator.
MoveNext() )
2371 const ring
R = cf->extRing;
2380 number &n = numberCollectionEnumerator.
Current();
2415 while( numberCollectionEnumerator.
MoveNext() );
2425 numberCollectionEnumerator.
Reset();
2429 while (numberCollectionEnumerator.
MoveNext() )
2431 number &n = numberCollectionEnumerator.
Current();
2432 number t =
ntMult(n, c, cf);
2438 fraction
f = (fraction)t;
2460 numberCollectionEnumerator.
Reset();
2461 while (numberCollectionEnumerator.
MoveNext() )
2463 number &n = numberCollectionEnumerator.
Current();
2464 fraction
f = (fraction)n;
2488 NUM((fraction)c) =
p_Mult_nn(NUM((fraction)c), d, R);
2501 number *X=(number *)
omAlloc(rl*
sizeof(number));
2505 for(i=0;i<rl;i++) P[i]=
p_Copy(NUM((fraction)(x[
i])),cf->extRing);
2510 P[
i]=
p_Copy(DEN((fraction)(x[i])),cf->extRing);
2523 return ((number)result);
2530 NUM(result)=
p_Farey(
p_Copy(NUM((fraction)p),cf->extRing),n,cf->extRing);
2531 DEN(result)=
p_Farey(
p_Copy(DEN((fraction)p),cf->extRing),n,cf->extRing);
2533 return ((number)result);
2564 cf->factoryVarOffset = R->cf->factoryVarOffset +
rVar(R);
2578 cf->cfInpNeg =
ntNeg;
2583 cf->cfExactDiv =
ntDiv;
2600 cf->cfSubringGcd =
ntGcd;
2616 cf->iNumberOfParameters =
rVar(R);
2617 cf->pParameterNames = (
const char**)R->names;
2619 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) ...
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...
long ntInt(number &a, const coeffs cf)
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)
number ntNormalizeHelper(number a, number b, const coeffs cf)
static void ntNormalizeDen(fraction result, const ring 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)
number ntMap00(number a, const coeffs src, const coeffs dst)
number ntMapUP(number a, const coeffs src, const coeffs dst)
poly prCopyR(poly p, ring src_r, ring dest_r)
number ntGenMap(number a, const coeffs cf, const coeffs dst)
number ntImPart(number a, const coeffs cf)
void ntWriteLong(number a, const coeffs cf)
void ntDelete(number *a, const coeffs cf)
static poly convert(const number &n)
used for all transcendental extensions, i.e., the top-most extension in an extension tower is transce...
#define DIFF_COMPLEXITY
complexity increase due to * and /
void p_String0Long(const poly p, ring lmRing, ring tailRing)
print p in a long way
number ntDiv(number a, number b, const coeffs cf)
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)
BOOLEAN ntIsMOne(number a, const coeffs cf)
number ntMult(number a, number b, 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)
number ntSub(number a, number b, const coeffs cf)
static short rVar(const ring r)
#define rVar(r) (r->N)
poly singclap_gcd(poly f, poly g, const ring r)
destroys f and g
(), 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)
int ntSize(number a, const coeffs cf)
void handleNestedFractionsOverQ(fraction f, const coeffs cf)
static long p_Totaldegree(poly p, const ring r)
BOOLEAN ntIsZero(number a, const coeffs cf)
static FORCE_INLINE void n_Normalize(number &n, const coeffs r)
inplace-normalization of n; produces some canonical representation of n;
void ntWriteShort(number a, const coeffs cf)
BOOLEAN ntDBTest(number a, const char *f, const int l, const coeffs r)
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 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 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 int pLength(poly a)
BOOLEAN ntIsOne(number a, const coeffs cf)
static poly p_Copy(poly p, const ring r)
returns a copy of p
void ntNormalize(number &a, const coeffs cf)
poly prMapR(poly src, nMapFunc nMap, ring src_r, ring dest_r)
number ntInvers(number a, const coeffs cf)
static BOOLEAN p_LmIsConstant(const poly p, const ring r)
BOOLEAN ntGreater(number a, number b, const coeffs cf)
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)
number ntCopyMap(number a, const coeffs cf, const coeffs dst)
const char * ntRead(const char *s, number *a, 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 void ntClearDenominators(ICoeffsEnumerator &numberCollectionEnumerator, number &c, const coeffs cf)
number ntMapPP(number a, const coeffs src, const coeffs dst)
Coefficient rings, fields and other domains suitable for Singular polynomials.
poly p_Farey(poly p, number N, const ring r)
CanonicalForm ntConvSingNFactoryN(number n, BOOLEAN, const coeffs cf)
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 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.
number ntInit(long i, const coeffs cf)
static BOOLEAN p_IsConstant(const poly p, const ring r)
The main handler for Singular numbers which are suitable for Singular polynomials.
Templated enumerator interface for simple iteration over a generic collection of T's.
number ntFarey(number p, number n, const coeffs cf)
number ntGetDenom(number &a, const coeffs cf)
TODO: normalization of a!?
number ntGenAlg(number a, const coeffs cf, const coeffs dst)
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
number ntMapP0(number a, const coeffs src, const coeffs dst)
number nlModP(number q, const coeffs Q, const coeffs Zp)
virtual reference Current()=0
Gets the current element in the collection (read and write).
number ntNeg(number a, const coeffs cf)
this is in-place, modifies a
#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 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 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 poly p_Mult_nn(poly p, number n, const ring r)
BOOLEAN ntGreaterZero(number a, const coeffs cf)
forward declarations
number ntRePart(number a, const coeffs cf)
static poly p_LmFreeAndNext(poly p, ring)
void definiteGcdCancellation(number a, const coeffs cf, BOOLEAN simpleTestsHaveAlreadyBeenPerformed)
modifies 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.
BOOLEAN p_EqualPolys(poly p1, poly p2, const ring r)
number ntCopy(number a, const coeffs cf)
static void ntClearContent(ICoeffsEnumerator &numberCollectionEnumerator, number &c, 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
void heuristicGcdCancellation(number a, const coeffs cf)
static FORCE_INLINE void n_CoeffWrite(const coeffs r, BOOLEAN details=TRUE)
output the coeff description
CanonicalForm convSingPFactoryP(poly p, const ring r)
number ntAdd(number a, number b, 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
BOOLEAN ntEqual(number a, number b, const coeffs cf)
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 ntMapZ0(number a, const coeffs src, const coeffs dst)
void ntPower(number a, int exp, number *b, const coeffs cf)
poly p_ChineseRemainder(poly *xx, number *x, number *q, int rl, CFArray &inv_cache, const ring R)
void ntKillChar(coeffs cf)
number ntConvFactoryNSingN(const CanonicalForm n, const coeffs cf)
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 FORCE_INLINE number n_SubringGcd(number a, number b, const coeffs r)
number ntGetNumerator(number &a, const coeffs cf)
TODO: normalization of a!?
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 poly p_Neg(poly p, const ring r)
number ntMap0P(number a, const coeffs src, const coeffs dst)
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.
void p_Write(poly p, ring lmRing, ring tailRing)
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
number ntChineseRemainder(number *x, number *q, int rl, BOOLEAN, CFArray &inv_cache, const coeffs cf)
#define ADD_COMPLEXITY
complexity increase due to + and -
static poly p_Add_q(poly p, poly q, const ring r)
#define omFreeBin(addr, bin)
Rational pow(const Rational &a, int e)
number ntCopyAlg(number a, const coeffs cf, const coeffs dst)
number ntGcd(number a, number b, const coeffs cf)
int p_Var(poly m, const ring r)
#define MULT_COMPLEXITY
complexity increase due to * and /
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 ntCoeffWrite(const coeffs cf, BOOLEAN details)
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...
BOOLEAN ntInitChar(coeffs cf, void *infoStruct)
Initialize the coeffs object.