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)
84 #define ntRing cf->extRing
90 #define ntCoeffs cf->extRing->cf
128 BOOLEAN simpleTestsHaveAlreadyBeenPerformed);
179 if (IS0(a))
return TRUE;
181 const fraction t = (fraction)a;
193 Print(
"ERROR in %s:%d: non-integer Q coeff in num. poly\n",f,l);
208 Print(
"ERROR in %s:%d: non-integer Q coeff in den. poly\n",f,l);
217 Print(
"ERROR in %s:%d: constant den. poly / Zp\n",f,l);
225 Print(
"ERROR in %s:%d: non-monic den. poly / Zp\n",f,l);
237 Print(
"ERROR in %s:%d: 1 != GCD between num. & den. poly\n",f,l);
251 Print(
"?/1 in %s:%d\n",f,l);
256 Print(
"negative sign of DEN. of a fraction in %s:%d\n",f,l);
286 if (!(
SR_HDL(n) & SR_INT))
289 Print(
"rational coeff in num: %s:%d\n",f,l);
300 Print(
"rational coeff in den.:%s:%d\n",f,l);
321 cf = cf->extRing->cf;
339 fraction
f = (fraction)(*a);
355 if (a == b)
return TRUE;
356 if ((IS0(a)) && (!IS0(b)))
return FALSE;
357 if ((IS0(b)) && (!IS0(a)))
return FALSE;
360 fraction fa = (fraction)a;
361 fraction fb = (fraction)b;
362 if ((
COM(fa) == 1) && (
COM(fb) == 1))
368 if (DENIS1(fa) && DENIS1(fb))
return TRUE;
369 if (DENIS1(fa) && !DENIS1(fb))
return FALSE;
370 if (!DENIS1(fa) && DENIS1(fb))
return FALSE;
397 if (IS0(a))
return NULL;
398 fraction
f = (fraction)a;
403 NUM(result) =
p_Copy(g,cf->extRing);
404 DEN(result) =
p_Copy(h,cf->extRing);
415 if (IS0(a))
return NULL;
419 fraction
f = (fraction)a;
422 const BOOLEAN denis1= DENIS1 (f);
489 fraction
f = (fraction)a;
493 const BOOLEAN denis1 = DENIS1 (f);
511 if( DEN (f) !=
NULL )
579 fraction
f = (fraction)a;
588 fraction
f = (fraction)a;
589 if ((f==
NULL) || (!DENIS1(f)))
return FALSE;
602 fraction
f = (fraction)a;
688 if (IS0(a))
return 0;
690 fraction
f = (fraction)a;
691 if (!DENIS1(f))
return 0;
693 const poly aAsPoly = NUM(f);
718 number aNumCoeff =
NULL;
int aNumDeg = 0;
719 number aDenCoeff =
NULL;
int aDenDeg = 0;
720 number bNumCoeff =
NULL;
int bNumDeg = 0;
721 number bDenCoeff =
NULL;
int bDenDeg = 0;
724 fraction fa = (fraction)a;
736 fraction fb = (fraction)b;
746 if (aNumDeg-aDenDeg > bNumDeg-bDenDeg)
return TRUE;
747 if (aNumDeg-aDenDeg < bNumDeg-bDenDeg)
return FALSE;
769 if (IS0(a))
return FALSE;
770 fraction
f = (fraction)a;
779 const ring
A = cf->extRing;
788 const int P =
rVar(A);
791 Print(
"// %d parameter : ", P);
793 for (
int nop=0; nop <
P; nop ++)
798 PrintS(
"\n// minpoly : 0\n");
825 fraction t = (fraction) d;
828 WerrorS(
"expected differentiation by a variable");
834 WerrorS(
"expected differentiation by a variable");
838 if (IS0(a))
return ntCopy(a, cf);
840 fraction fa = (fraction)a;
846 if (NUM(result)==
NULL)
860 if (NUM(result)==
NULL)
return(
NULL);
877 if (IS0(a))
return ntCopy(b, cf);
878 if (IS0(b))
return ntCopy(a, cf);
880 fraction fa = (fraction)a;
881 fraction fb = (fraction)b;
892 if (DENIS1(fa) && DENIS1(fb)) f =
NULL;
893 else if (!DENIS1(fa) && DENIS1(fb)) f =
p_Copy(DEN(fa),
ntRing);
894 else if (DENIS1(fa) && !DENIS1(fb)) f =
p_Copy(DEN(fb),
ntRing);
919 if (IS0(b))
return ntCopy(a, cf);
921 fraction fa = (fraction)a;
922 fraction fb = (fraction)b;
933 if (DENIS1(fa) && DENIS1(fb)) f =
NULL;
934 else if (!DENIS1(fa) && DENIS1(fb)) f =
p_Copy(DEN(fa),
ntRing);
935 else if (DENIS1(fa) && !DENIS1(fb)) f =
p_Copy(DEN(fb),
ntRing);
958 if (IS0(a) || IS0(b))
return NULL;
960 fraction fa = (fraction)a;
961 fraction fb = (fraction)b;
971 const poly da = DEN(fa);
972 const poly db = DEN(fb);
1028 if (IS0(a))
return NULL;
1031 fraction fa = (fraction)a;
1032 fraction fb = (fraction)b;
1078 if (exp >= 0) *b =
NULL;
1081 else if (exp == 0) { *b =
ntInit(1, cf);
return;}
1082 else if (exp == 1) { *b =
ntCopy(a, cf);
return;}
1083 else if (exp == -1) { *b =
ntInvers(a, cf);
return;}
1085 int expAbs =
exp;
if (expAbs < 0) expAbs = -expAbs;
1088 number
pow; number t;
1092 for (
int i = 2;
i <= expAbs;
i++)
1108 t =
ntMult(pow, factor, cf);
1113 expAbs = expAbs / 2;
1116 t =
ntMult(factor, factor, cf);
1169 number c; number tmp;
1178 lcmOfDenominators = tmp;
1187 lcmOfDenominators = tmp;
1208 gcdOfCoefficients = tmp;
1217 gcdOfCoefficients = tmp;
1222 number inverseOfGcdOfCoefficients =
n_Invers(gcdOfCoefficients,
1236 if ((DEN(f) !=
NULL) &&
1243 if( DEN(f) !=
NULL )
1259 fraction
f = (fraction)a;
1261 if (DENIS1(f) ||
NUMIS1(f)) {
COM(f) = 0;
return; }
1279 if( DEN(f) !=
NULL )
1323 }
while(i<ntRing->
N);
1333 BOOLEAN simpleTestsHaveAlreadyBeenPerformed)
1337 fraction
f = (fraction)a;
1341 if (!simpleTestsHaveAlreadyBeenPerformed)
1463 if( DEN(f) !=
NULL )
1488 fraction
f = (fraction)a;
1513 fraction
f = (fraction)a;
1548 if ((DEN((fraction)a)!=
NULL)
1585 fraction fb = (fraction)b;
1587 fraction fa = (fraction)a;
1602 number contentpa, contentpb, tmp;
1675 fraction fa = (fraction)a;
1676 fraction fb = (fraction)b;
1691 number contentpa, contentpb, tmp;
1748 if (IS0(a))
return -1;
1753 fraction
f = (fraction)a;
1769 return numDegree + denDegree + noOfTerms;
1781 fraction
f = (fraction)a;
1807 DEN(result) = num_f;
1835 assume(src->rep == dst->extRing->cf->rep);
1845 fraction ff=(fraction)res;
1847 else DEN(ff)=
p_NSet(nn,dst->extRing);
1859 poly p=
p_NSet(nMap(a, src,dst->extRing->cf), dst->extRing);
1874 number q =
n_Init(n, dst->extRing->cf);
1887 if (IS0(a))
return NULL;
1889 const ring rSrc = cf->extRing;
1890 const ring rDst = dst->extRing;
1895 fraction
f = (fraction)a;
1901 h =
prCopyR(DEN(f), rSrc, rDst);
1909 n_Test((number)result, dst);
1916 if (IS0(a))
return NULL;
1918 const ring rSrc = cf->extRing;
1919 const ring rDst = dst->extRing;
1922 fraction
f = (fraction)a;
1954 h =
prMapR(DEN(f), nMap, rSrc, rDst);
1988 n_Test((number)result, dst);
2015 number q =
nlModP(a, src, dst->extRing->cf);
2037 assume(src == dst->extRing->cf);
2054 number q =
n_Init(n, dst->extRing->cf);
2061 p =
p_One(dst->extRing);
2095 if (src->ch == dst->ch)
return ntMapPP;
2099 if (h != 1)
return NULL;
2107 if (
rVar(src->extRing) >
rVar(dst->extRing))
2110 for (
int i = 0;
i <
rVar(src->extRing);
i++)
2116 if (src->extRing->cf==dst->extRing->cf)
2123 if (src->extRing->cf==dst->extRing->cf)
2135 if (n==
ntCopyAlg) printf(
"n=ntCopyAlg\n");
2136 else if (n==
ntCopyMap) printf(
"n=ntCopyMap\n");
2137 else if (n==
ntMapUP) printf(
"n=ntMapUP\n");
2138 else if (n==
ntMap0P) printf(
"n=ntMap0P\n");
2139 else if (n==
ntMapP0) printf(
"n=ntMapP0\n");
2140 else if (n==
ntMap00) printf(
"n=ntMap00\n");
2141 else if (n==
NULL) printf(
"n=NULL\n");
2142 else printf(
"n=?\n");
2149 if ((--cf->extRing->ref) == 0)
2169 fraction
f = (fraction)n;
2176 if (IS0(a))
return -1;
2177 fraction fa = (fraction)a;
2178 return cf->extRing->pFDeg(NUM(fa),cf->extRing);
2186 const ring
R = cf->extRing;
2188 assume( 0 < iParameter && iParameter <=
rVar(R) );
2209 const ring
R = cf->extRing;
2212 fraction
f = (fraction)m;
2214 if( DEN(f) !=
NULL )
2217 return p_Var( NUM(f), R );
2225 return NUM((fraction)n);
2237 const ring
R = cf->extRing;
2244 numberCollectionEnumerator.
Reset();
2246 if( !numberCollectionEnumerator.
MoveNext() )
2259 number &n = numberCollectionEnumerator.
Current();
2263 fraction
f = (fraction)n;
2281 while( numberCollectionEnumerator.
MoveNext() ) ;
2290 numberCollectionEnumerator.
Reset();
2291 while (numberCollectionEnumerator.
MoveNext() )
2293 number &n = numberCollectionEnumerator.
Current();
2294 const number t =
ntDiv(n, c, cf);
2311 number gg =
ntMult(g, c, cf);
2325 numberCollectionEnumerator.
Reset();
2327 if( !numberCollectionEnumerator.
MoveNext() )
2338 const ring
R = cf->extRing;
2347 number &n = numberCollectionEnumerator.
Current();
2382 while( numberCollectionEnumerator.
MoveNext() );
2392 numberCollectionEnumerator.
Reset();
2396 while (numberCollectionEnumerator.
MoveNext() )
2398 number &n = numberCollectionEnumerator.
Current();
2399 number t =
ntMult(n, c, cf);
2405 fraction
f = (fraction)t;
2427 numberCollectionEnumerator.
Reset();
2428 while (numberCollectionEnumerator.
MoveNext() )
2430 number &n = numberCollectionEnumerator.
Current();
2431 fraction
f = (fraction)n;
2455 NUM((fraction)c) =
p_Mult_nn(NUM((fraction)c), d, R);
2468 number *X=(number *)
omAlloc(rl*
sizeof(number));
2472 for(i=0;i<rl;i++) P[i]=
p_Copy(NUM((fraction)(x[
i])),cf->extRing);
2477 P[
i]=
p_Copy(DEN((fraction)(x[i])),cf->extRing);
2490 return ((number)result);
2497 NUM(result)=
p_Farey(
p_Copy(NUM((fraction)p),cf->extRing),n,cf->extRing);
2498 DEN(result)=
p_Farey(
p_Copy(DEN((fraction)p),cf->extRing),n,cf->extRing);
2500 return ((number)result);
2531 cf->factoryVarOffset = R->cf->factoryVarOffset +
rVar(R);
2545 cf->cfInpNeg =
ntNeg;
2550 cf->cfExactDiv =
ntDiv;
2567 cf->cfSubringGcd =
ntGcd;
2583 cf->iNumberOfParameters =
rVar(R);
2584 cf->pParameterNames = (
const char**)R->names;
2586 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)
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)
const CanonicalForm CFMap CFMap int &both_non_zero int n
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.
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)
static const n_coeffType ID
Our own type!
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 ntChineseRemainder(number *x, number *q, int rl, BOOLEAN sym, CFArray &inv_cache, const coeffs cf)
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)/
: 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)
#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.