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);
222 Print(
"negative sign of DEN. of a fraction in %s:%d\n",
f,
l);
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;
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;
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;
584 fraction
f = (fraction)a;
606 if( DEN (
f) !=
NULL )
674 fraction
f = (fraction)a;
683 fraction
f = (fraction)a;
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;
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");
924 fraction
fa = (fraction)a;
963 fraction
fa = (fraction)a;
964 fraction
fb = (fraction)
b;
1004 fraction
fa = (fraction)a;
1005 fraction
fb = (fraction)
b;
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);
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);
1252 int expAbs =
exp;
if (expAbs < 0) expAbs = -expAbs;
1255 number
pow; number t;
1259 for (
int i = 2;
i <= expAbs;
i++)
1280 expAbs = expAbs / 2;
1310 fraction
f = (fraction)a;
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;
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);
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);
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 )
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);
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();
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);
2540 cf->factoryVarOffset =
R->cf->factoryVarOffset +
rVar(
R);
2593 cf->iNumberOfParameters =
rVar(
R);
2594 cf->pParameterNames = (
const char**)
R->names;
2596 cf->has_simple_Inverse=
FALSE;
Rational pow(const Rational &a, int e)
Concrete implementation of enumerators over polynomials.
char * naCoeffString(const coeffs r)
char * naCoeffName(const coeffs r)
const CanonicalForm CFMap CFMap & N
const CanonicalForm const CanonicalForm const CanonicalForm const CanonicalForm & cand
CanonicalForm convSingPFactoryP(poly p, const ring r)
poly convFactoryPSingP(const CanonicalForm &f, const ring r)
poly singclap_pdivide(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)
poly singclap_gcd_r(poly f, poly g, const ring r)
This is a polynomial enumerator for simple iteration over coefficients of polynomials.
go into polynomials over an alg. extension recursively
virtual reference Current()=0
Gets the current element in the collection (read and write).
virtual void Reset()=0
Sets the enumerator to its initial position: -1, which is before the first element in the collection.
virtual bool MoveNext()=0
Advances the enumerator to the next element of the collection. returns true if the enumerator was suc...
Templated enumerator interface for simple iteration over a generic collection of T's.
Coefficient rings, fields and other domains suitable for Singular polynomials.
static FORCE_INLINE number n_Mult(number a, number b, const coeffs r)
return the product of 'a' and 'b', i.e., a*b
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 number n_Copy(number n, const coeffs r)
return a copy of 'n'
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 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 FORCE_INLINE void n_CoeffWrite(const coeffs r, BOOLEAN details=TRUE)
output the coeff description
static FORCE_INLINE BOOLEAN nCoeff_is_Extension(const coeffs r)
#define n_Test(a, r)
BOOLEAN n_Test(number a, const coeffs r)
@ n_Q
rational (GMP) numbers
@ n_transExt
used for all transcendental extensions, i.e., the top-most extension in an extension tower is transce...
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,...
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 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 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 nMapFunc n_SetMap(const coeffs src, const coeffs dst)
set the mapping function pointers for translating numbers from src to 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 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.
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 BOOLEAN nCoeff_is_Q(const coeffs r)
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_IsZero(number n, const coeffs r)
TRUE iff 'n' represents the zero element.
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 FORCE_INLINE BOOLEAN nCoeff_is_Q_or_BI(const coeffs r)
static FORCE_INLINE n_coeffType getCoeffType(const coeffs r)
Returns the type of coeffs domain.
static FORCE_INLINE void n_Delete(number *p, const coeffs r)
delete 'p'
static FORCE_INLINE BOOLEAN nCoeff_is_Zn(const coeffs r)
static FORCE_INLINE BOOLEAN nCoeff_is_Zp(const coeffs r)
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 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_GetNumerator(number &n, const coeffs r)
return the numerator of n (if elements of r are by nature not fractional, result is n)
@ n_rep_gap_rat
(number), see longrat.h
@ n_rep_gap_gmp
(), see rinteger.h, new impl.
@ n_rep_rat_fct
(fraction), see transext.h
static FORCE_INLINE number n_SubringGcd(number a, number b, const coeffs r)
number(* nMapFunc)(number a, const coeffs src, const coeffs dst)
maps "a", which lives in src, into dst
static FORCE_INLINE void n_Normalize(number &n, const coeffs r)
inplace-normalization of n; produces some canonical representation of n;
static FORCE_INLINE BOOLEAN n_IsOne(number n, const coeffs r)
TRUE iff 'n' represents the one element.
BOOLEAN pa(leftv res, leftv args)
BOOLEAN pb(leftv res, leftv args)
BOOLEAN fa(leftv res, leftv args)
BOOLEAN fb(leftv res, leftv args)
const CanonicalForm int s
void WerrorS(const char *s)
number nlModP(number q, const coeffs, const coeffs Zp)
static FORCE_INLINE BOOLEAN nlIsInteger(number 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
gmp_float exp(const gmp_float &a)
The main handler for Singular numbers which are suitable for Singular polynomials.
number ndCopyMap(number a, const coeffs aRing, const coeffs r)
const char *const nDivBy0
#define omFreeSize(addr, size)
#define omFreeBin(addr, bin)
#define omGetSpecBin(size)
poly p_Diff(poly a, int k, const ring r)
poly p_Farey(poly p, number N, const ring r)
poly p_ISet(long i, const ring r)
returns the poly representing the integer i
poly p_Div_nn(poly p, const number n, const ring r)
void p_Normalize(poly p, const ring r)
void p_Norm(poly p1, const ring r)
const char * p_Read(const char *st, poly &rc, const ring r)
poly p_Cleardenom(poly p, const ring r)
int p_Var(poly m, const ring r)
poly p_Sub(poly p1, poly p2, const ring r)
poly p_NSet(number n, const ring r)
returns the poly representing the number n, destroys n
poly p_ChineseRemainder(poly *xx, number *x, number *q, int rl, CFArray &inv_cache, const ring R)
BOOLEAN p_EqualPolys(poly p1, poly p2, const ring r)
static poly p_Neg(poly p, const ring r)
static poly p_Add_q(poly p, poly q, const ring r)
static poly p_Mult_q(poly p, poly q, const ring r)
void p_Write(poly p, ring lmRing, ring tailRing)
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
static void p_ExpVectorDiff(poly pr, poly p1, poly p2, const ring r)
void p_String0Long(const poly p, ring lmRing, ring tailRing)
print p in a long way
void p_String0Short(const poly p, ring lmRing, ring tailRing)
print p in a short way, if possible
static void p_Setm(poly p, const ring r)
static number p_SetCoeff(poly p, number n, ring r)
static BOOLEAN p_LmIsConstantComp(const poly p, const ring r)
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 BOOLEAN p_LmIsConstant(const poly p, const ring r)
static BOOLEAN p_IsOne(const poly p, const ring R)
either poly(1) or gen(k)?!
static BOOLEAN p_IsConstant(const poly p, const ring r)
static void p_Delete(poly *p, const ring r)
static unsigned pLength(poly a)
static poly pp_Mult_qq(poly p, poly q, const ring r)
static poly p_LmFreeAndNext(poly p, ring)
static poly p_Copy(poly p, const ring r)
returns a copy of p
static long p_Totaldegree(poly p, const ring r)
#define __p_Mult_nn(p, n, r)
void p_wrp(poly p, ring lmRing, ring tailRing)
poly prMapR(poly src, nMapFunc nMap, ring src_r, ring dest_r)
poly prCopyR(poly p, ring src_r, ring dest_r)
void StringAppendS(const char *st)
void PrintS(const char *s)
void rDelete(ring r)
unconditionally deletes fields in r
BOOLEAN rEqual(ring r1, ring r2, BOOLEAN qr)
returns TRUE, if r1 equals r2 FALSE, otherwise Equality is determined componentwise,...
static char * rRingVar(short i, const ring r)
static BOOLEAN rCanShortOut(const ring r)
static short rVar(const ring r)
#define rVar(r) (r->N)
static poly convert(const number &n)
static int ntSize(number a, const coeffs cf)
static BOOLEAN ntDBTest(number a, const char *f, const int l, const coeffs r)
static number ntParameter(const int iParameter, const coeffs cf)
return the specified parameter as a number in the given trans.ext.
static void ntWriteLong(number a, const coeffs cf)
static BOOLEAN ntCoeffIsEqual(const coeffs cf, n_coeffType n, void *param)
static void heuristicGcdCancellation(number a, const coeffs cf)
forward declarations
number ntDiff(number a, number d, const coeffs cf)
nMapFunc ntSetMap(const coeffs src, const coeffs dst)
Get a mapping function from src into the domain of this type (n_transExt)
static number ntSub(number a, number b, const coeffs cf)
static number ntCopyAlg(number a, const coeffs cf, const coeffs dst)
static long ntInt(number &a, const coeffs cf)
static number ntMapPP(number a, const coeffs src, const coeffs dst)
static void ntDelete(number *a, const coeffs cf)
static BOOLEAN ntIsOne(number a, const coeffs cf)
static void ntNormalizeDen(fraction result, const ring R)
poly gcd_over_Q(poly f, poly g, const ring r)
helper routine for calling singclap_gcd_r
BOOLEAN ntInitChar(coeffs cf, void *infoStruct)
Initialize the coeffs object.
static BOOLEAN ntIsZero(number a, const coeffs cf)
static number ntGetNumerator(number &a, const coeffs cf)
TODO: normalization of a!?
static CanonicalForm ntConvSingNFactoryN(number n, BOOLEAN, const coeffs cf)
static void ntClearDenominators(ICoeffsEnumerator &numberCollectionEnumerator, number &c, const coeffs cf)
static BOOLEAN ntIsMOne(number a, const coeffs cf)
static number ntMapZ0(number a, const coeffs src, const coeffs dst)
static void ntCoeffWrite(const coeffs cf, BOOLEAN details)
static number ntMap0P(number a, const coeffs src, const coeffs dst)
#define NUMIS1(f)
TRUE iff num. represents 1.
static number ntGcd(number a, number b, const coeffs cf)
static number ntConvFactoryNSingN(const CanonicalForm n, const coeffs cf)
static void ntClearContent(ICoeffsEnumerator &numberCollectionEnumerator, number &c, const coeffs cf)
static number ntInvers(number a, const coeffs cf)
static number ntNormalizeHelper(number a, number b, const coeffs cf)
static void ntPower(number a, int exp, number *b, const coeffs cf)
number ntInit(long i, const coeffs cf)
static number ntMapP0(number a, const coeffs src, const coeffs dst)
static number ntGetDenom(number &a, const coeffs cf)
TODO: normalization of a!?
static const char * ntRead(const char *s, number *a, const coeffs cf)
static number ntMapUP(number a, const coeffs src, const coeffs dst)
#define MULT_COMPLEXITY
complexity increase due to * and /
static void ntKillChar(coeffs cf)
static void ntWriteShort(number a, const coeffs cf)
static number ntDiv(number a, number b, const coeffs cf)
static number ntCopy(number a, const coeffs cf)
static int ntParDeg(number a, const coeffs cf)
static BOOLEAN ntGreaterZero(number a, const coeffs cf)
static number ntChineseRemainder(number *x, number *q, int rl, BOOLEAN, CFArray &inv_cache, const coeffs cf)
static number ntGenMap(number a, const coeffs cf, const coeffs dst)
int ntIsParam(number m, const coeffs cf)
if m == var(i)/1 => return i,
static number ntMap00(number a, const coeffs src, const coeffs dst)
static number ntMult(number a, number b, const coeffs cf)
#define ADD_COMPLEXITY
complexity increase due to + and -
static number ntGenAlg(number a, const coeffs cf, const coeffs dst)
static number ntNeg(number a, const coeffs cf)
this is in-place, modifies a
static void definiteGcdCancellation(number a, const coeffs cf, BOOLEAN simpleTestsHaveAlreadyBeenPerformed)
modifies a
static number ntAdd(number a, number b, const coeffs cf)
static number ntFarey(number p, number n, const coeffs cf)
static number ntCopyMap(number a, const coeffs cf, const coeffs dst)
static void ntNormalize(number &a, const coeffs cf)
static BOOLEAN ntEqual(number a, number b, const coeffs cf)
VAR omBin fractionObjectBin
static coeffs nCoeff_bottom(const coeffs r, int &height)
#define DIFF_COMPLEXITY
complexity increase due to diff
static BOOLEAN ntGreater(number a, number b, const coeffs cf)
static void handleNestedFractionsOverQ(fraction f, const coeffs cf)
#define BOUND_COMPLEXITY
maximum complexity of a number
struct for passing initialization parameters to naInitChar