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28 if (((
long)a<0L) || ((
long)a>(
long)r->mod2mMask))
30 Print(
"wrong mod 2^n number %ld at %s,%d\n",(
long)a,
f,
l);
41 ((((
unsigned long) a) * ((
unsigned long)
b)) & r->mod2mMask);
47 ((((
unsigned long) a) + ((
unsigned long)
b)) & r->mod2mMask);
52 return (number)((
unsigned long)a < (
unsigned long)
b ?
53 r->mod2mMask+1 - (
unsigned long)
b + (
unsigned long)a:
54 (
unsigned long)a - (
unsigned long)
b);
57 #define nr2mNegM(A,r) (number)((r->mod2mMask+1 - (unsigned long)(A)) & r->mod2mMask)
58 #define nr2mEqualM(A,B) ((A)==(B))
65 if (
cf->modExponent>32)
66 snprintf(n2mCoeffName_buf,21,
"ZZ/(bigint(2)^%lu)",
cf->modExponent);
68 snprintf(n2mCoeffName_buf,21,
"ZZ/(2^%lu)",
cf->modExponent);
69 return n2mCoeffName_buf;
82 unsigned long mm=r->mod2mMask;
83 if (((mm+1)>>
m)==1L)
return TRUE;
96 long ch = r->cfInt(c, r);
98 mpz_init_set(a, r->modNumber);
99 mpz_init_set_ui(
b, ch);
104 if(mpz_cmp_ui(
gcd, 1) == 0)
106 WerrorS(
"constant in q-ideal is coprime to modulus in ground ring");
107 WerrorS(
"Unable to create qring!");
110 if(mpz_cmp_ui(
gcd, 2) == 0)
118 mpz_init(baseTokNew);
119 mpz_set(baseTokNew, r->modBase);
120 while(mpz_cmp(
gcd, baseTokNew) > 0)
123 mpz_mul(baseTokNew, baseTokNew, r->modBase);
125 mpz_clear(baseTokNew);
134 if ((
unsigned long)
k == 0)
return FALSE;
135 if ((
unsigned long)
k > ((r->mod2mMask >> 1) + 1))
return FALSE;
145 if (((
unsigned long)a == 0) || ((
unsigned long)
b == 0))
159 unsigned long res = 0;
160 if ((
unsigned long)a == 0) a = (number) 1;
161 if ((
unsigned long)
b == 0)
b = (number) 1;
162 while ((
unsigned long)a % 2 == 0)
164 a = (number)((
unsigned long)a / 2);
165 if ((
unsigned long)
b % 2 == 0)
b = (number)((
unsigned long)
b / 2);
168 while ((
unsigned long)
b % 2 == 0)
170 b = (number)((
unsigned long)
b / 2);
173 return (number)(1L <<
res);
182 unsigned long res = 0;
183 if ((
unsigned long)a == 0 && (
unsigned long)
b == 0)
return (number)1;
184 while ((
unsigned long)a % 2 == 0 && (
unsigned long)
b % 2 == 0)
186 a = (number)((
unsigned long)a / 2);
187 b = (number)((
unsigned long)
b / 2);
196 return (number)((1L <<
res));
206 mpz_ptr u = (mpz_ptr)
omAlloc(
sizeof(mpz_t));
207 mpz_init_set_ui(u, a);
208 mpz_ptr u0 = (mpz_ptr)
omAlloc(
sizeof(mpz_t));
210 mpz_ptr u1 = (mpz_ptr)
omAlloc(
sizeof(mpz_t));
211 mpz_init_set_ui(u1, 1);
212 mpz_ptr u2 = (mpz_ptr)
omAlloc(
sizeof(mpz_t));
214 mpz_ptr
v = (mpz_ptr)
omAlloc(
sizeof(mpz_t));
215 mpz_init_set_ui(
v, r->mod2mMask);
217 mpz_ptr v0 = (mpz_ptr)
omAlloc(
sizeof(mpz_t));
219 mpz_ptr v1 = (mpz_ptr)
omAlloc(
sizeof(mpz_t));
221 mpz_ptr v2 = (mpz_ptr)
omAlloc(
sizeof(mpz_t));
222 mpz_init_set_ui(v2, 1);
223 mpz_ptr q = (mpz_ptr)
omAlloc(
sizeof(mpz_t));
225 mpz_ptr rr = (mpz_ptr)
omAlloc(
sizeof(mpz_t));
236 mpz_mul(u2, u2, q); mpz_sub(u2, u1, u2);
237 mpz_mul(v2, v2, q); mpz_sub(v2, v1, v2);
245 mpz_add_ui(u1, u1, r->mod2mMask);
246 mpz_add_ui(u1, u1, 1);
262 static unsigned long InvMod(
unsigned long a,
const coeffs r)
264 assume((
unsigned long)a % 2 != 0);
272 assume((
unsigned long)c % 2 != 0);
275 inv =
InvMod((
unsigned long)c,r);
281 if ((
unsigned long)c % 2 == 0)
283 WerrorS(
"division by zero divisor");
295 unsigned long res = 0;
296 if ((
unsigned long)a == 0 && (
unsigned long)
b == 0)
return (number)1;
297 while ((
unsigned long)a % 2 == 0 && (
unsigned long)
b % 2 == 0)
299 a = (number)((
unsigned long)a / 2);
300 b = (number)((
unsigned long)
b / 2);
303 if ((
unsigned long)
b % 2 == 0)
307 return (number)((1L <<
res));
313 return (number)((1L <<
res));
321 *(
unsigned long *)
result = 1;
339 if (
i == 0)
return (number)(
unsigned long)
i;
342 unsigned long j = (
unsigned long)1;
343 if (ii < 0) {
j = r->mod2mMask; ii = -ii; }
344 unsigned long k = (
unsigned long)ii;
345 k =
k & r->mod2mMask;
347 return (number)
nr2mMult((number)
j, (number)
k, r);
356 unsigned long nn = (
unsigned long)
n;
357 unsigned long l = r->mod2mMask >> 1;
l++;
358 if ((
unsigned long)nn >
l)
359 return (
long)((
unsigned long)nn - r->mod2mMask - 1);
361 return (
long)((
unsigned long)nn);
380 return ((
unsigned long)a % 2 == 1);
385 if (
k ==
NULL)
return (number)1;
386 unsigned long erg = (
unsigned long)
k;
387 while (erg % 2 == 0) erg = erg / 2;
393 return 0 == (
unsigned long)a;
398 return 1 == (
unsigned long)a;
403 return ((r->mod2mMask == (
unsigned long)a) &&(1L!=(
long)a));
413 if ((
unsigned long)a == 0)
return (number)0;
414 else if ((
unsigned long)
b % 2 == 0)
416 if ((
unsigned long)
b != 0)
418 while (((
unsigned long)
b % 2 == 0) && ((
unsigned long)a % 2 == 0))
420 a = (number)((
unsigned long)a / 2);
421 b = (number)((
unsigned long)
b / 2);
424 if ((
unsigned long)
b % 2 == 0)
426 WerrorS(
"Division not possible, even by cancelling zero divisors.");
427 WerrorS(
"Result is integer division without remainder.");
428 return (number) ((
unsigned long) a / (
unsigned long)
b);
443 unsigned long c = r->mod2mMask + 1;
445 return (c % (
unsigned long)
b) == 0;
450 c = (
unsigned long)
b;
453 if ((c % 2) != 0)
return FALSE;
474 unsigned long a = (
unsigned long)as;
475 unsigned long b = (
unsigned long)bs;
477 while (a % 2 == 0 &&
b % 2 == 0)
522 assume((
unsigned long)
b != 0);
524 unsigned long b_div = (
unsigned long)
b;
532 unsigned long rr = 0;
533 while ((g < r->mod2mMask ) && (b_div > 0) && (b_div % 2 == 0))
539 if (
g != 1) rr = (
unsigned long)a %
g;
545 static number nr2mIntDiv(number a, number
b,
const coeffs r)
547 if ((
unsigned long)a == 0)
549 if ((
unsigned long)
b == 0)
551 if ((
unsigned long)
b == 1)
553 unsigned long c = r->mod2mMask + 1;
555 return (number)(c / (
unsigned long)
b);
559 mpz_ptr cc = (mpz_ptr)
omAlloc(
sizeof(mpz_t));
560 mpz_init_set_ui(cc, r->mod2mMask); mpz_add_ui(cc, cc, 1);
561 mpz_div_ui(cc, cc, (
unsigned long)(
unsigned long)
b);
562 unsigned long s = mpz_get_ui(cc);
564 return (number)(
unsigned long)
s;
569 if ((
unsigned long)
b == 0)
571 return (number)((
unsigned long) a / (
unsigned long)
b);
578 if ((
unsigned long)
b == 0)
580 if ((
unsigned long)
b == 1)
582 unsigned long c = r->mod2mMask + 1;
584 return (number)(c / (
unsigned long)
b);
588 mpz_ptr cc = (mpz_ptr)
omAlloc(
sizeof(mpz_t));
589 mpz_init_set_ui(cc, r->mod2mMask); mpz_add_ui(cc, cc, 1);
590 mpz_div_ui(cc, cc, (
unsigned long)(
unsigned long)
b);
591 unsigned long s = mpz_get_ui(cc);
593 return (number)(
unsigned long)
s;
599 if ((
unsigned long)c == 0)
return c;
607 unsigned long i = ((
unsigned long)from) % (dst->mod2mMask + 1) ;
613 unsigned long i = ((
unsigned long)from) % (dst->mod2mMask + 1);
619 unsigned long j = (
unsigned long)1;
620 long ii = (long)from;
621 if (ii < 0) {
j = dst->mod2mMask; ii = -ii; }
622 unsigned long i = (
unsigned long)ii;
623 i =
i & dst->mod2mMask;
625 return (number)
nr2mMult((number)
i, (number)
j, dst);
632 mpz_ptr
k = (mpz_ptr)
omAlloc(
sizeof(mpz_t));
633 mpz_init_set_ui(
k, dst->mod2mMask);
635 mpz_and(erg, (mpz_ptr)from,
k);
636 number
res = (number) mpz_get_ui(erg);
648 nlGMP(from, gmp, src);
667 && (src->mod2mMask == dst->mod2mMask))
672 && (src->mod2mMask < dst->mod2mMask))
677 && (src->mod2mMask > dst->mod2mMask))
701 if (mpz_divisible_2exp_p(src->modNumber,dst->modExponent))
719 for (
int i = 1;
i <
m;
i++) r->mod2mMask = (r->mod2mMask << 1) + 1;
733 WarnS(
"nr2mInitExp unexpectedly called with m = 1 (we continue with Z/2^2");
745 if (((*
s) >=
'0') && ((*
s) <=
'9'))
752 if ((*
i) >= (
MAX_INT_VAL / 10)) (*i) = (*i) & r->mod2mMask;
754 while (((*
s) >=
'0') && ((*
s) <=
'9'));
755 (*i) = (*i) & r->mod2mMask;
761 static const char *
nr2mRead (
const char *
s, number *a,
const coeffs r)
773 *a = (number)(
long)
z;
775 *a =
nr2mDiv((number)(
long)
z,(number)(
long)
n,r);
794 mpz_init_set_si (r->modBase, 2L);
796 mpz_init (r->modNumber);
797 mpz_pow_ui (r->modNumber, r->modBase, r->modExponent);
800 r->ch = (int)r->mod2mMask + 1;
838 r->has_simple_Alloc=
TRUE;
static FORCE_INLINE n_coeffType getCoeffType(const coeffs r)
Returns the type of coeffs domain.
(mpz_ptr), see rmodulon,h
static number nr2mMapProject(number from, const coeffs, const coeffs dst)
static BOOLEAN nr2mGreaterZero(number k, const coeffs r)
static FORCE_INLINE BOOLEAN nCoeff_is_Zp(const coeffs r)
static number nr2mNeg(number c, const coeffs r)
static FORCE_INLINE BOOLEAN nCoeff_is_Z(const coeffs r)
static FORCE_INLINE BOOLEAN nCoeff_is_Ring_2toM(const coeffs r)
static number nr2mLcm(number a, number b, const coeffs)
static number nr2mSub(number a, number b, const coeffs r)
EXTERN_VAR omBin gmp_nrz_bin
static number nr2mAdd(number a, number b, const coeffs r)
static int nr2mDivComp(number as, number bs, const coeffs)
only used if HAVE_RINGS is defined
static number nr2mMult(number a, number b, const coeffs r)
static number nr2mInvers(number c, const coeffs r)
number ndCopyMap(number a, const coeffs aRing, const coeffs r)
static BOOLEAN nr2mIsUnit(number a, const coeffs)
coeffs nInitChar(n_coeffType t, void *parameter)
one-time initialisations for new coeffs in case of an error return NULL
static void nr2mInitExp(int m, coeffs r)
static number nr2mAnn(number b, const coeffs r)
static const char * nr2mRead(const char *s, number *a, const coeffs r)
static number nr2mGcd(number a, number b, const coeffs)
static number nr2mInit(long i, const coeffs r)
static void nr2mCoeffWrite(const coeffs r, BOOLEAN)
static number nr2mMapQ(number from, const coeffs src, const coeffs dst)
static FORCE_INLINE BOOLEAN nCoeff_is_Q(const coeffs r)
static void specialXGCD(unsigned long &s, unsigned long a, const coeffs r)
static BOOLEAN nr2mIsMOne(number a, const coeffs r)
static number nr2mSubM(number a, number b, const coeffs r)
static void nr2mSetExp(int m, coeffs r)
number(* nMapFunc)(number a, const coeffs src, const coeffs dst)
maps "a", which lives in src, into dst
static char * nr2mCoeffName(const coeffs cf)
static unsigned long InvMod(unsigned long a, const coeffs r)
void PrintS(const char *s)
static number nr2mDiv(number a, number b, const coeffs r)
static const char * nr2mEati(const char *s, int *i, const coeffs r)
static number nr2mMod(number a, number b, const coeffs r)
static FORCE_INLINE BOOLEAN nCoeff_is_Ring_PtoM(const coeffs r)
static number nr2mMultM(number a, number b, const coeffs r)
static number nr2mGetUnit(number k, const coeffs)
number nr2mMapZp(number from, const coeffs, const coeffs dst)
static nMapFunc nr2mSetMap(const coeffs src, const coeffs dst)
static number nr2mMapZ(number from, const coeffs src, const coeffs dst)
static number nr2mMapMachineInt(number from, const coeffs, const coeffs dst)
static coeffs nr2mQuot1(number c, const coeffs r)
static long nr2mInt(number &n, const coeffs r)
static number nr2mExtGcd(number a, number b, number *s, number *t, const coeffs r)
static number nr2mMapGMP(number from, const coeffs, const coeffs dst)
static BOOLEAN nr2mIsZero(number a, const coeffs)
void WerrorS(const char *s)
static number nr2mInversM(number c, const coeffs r)
static FORCE_INLINE BOOLEAN nCoeff_is_Zn(const coeffs r)
static BOOLEAN nr2mCoeffIsEqual(const coeffs r, n_coeffType n, void *p)
static void nr2mWrite(number a, const coeffs r)
static char * nr2mCoeffString(const coeffs r)
static BOOLEAN nr2mGreater(number a, number b, const coeffs r)
const Variable & v
< [in] a sqrfree bivariate poly
static BOOLEAN nr2mIsOne(number a, const coeffs)
static BOOLEAN nr2mDivBy(number a, number b, const coeffs r)
const CanonicalForm int s
BOOLEAN nr2mDBTest(number a, const char *f, const int l, const coeffs r)
static BOOLEAN nr2mEqual(number a, number b, const coeffs)
#define n_Test(a, r)
BOOLEAN n_Test(number a, const coeffs r)
BOOLEAN nr2mInitChar(coeffs r, void *p)
static number nr2mAddM(number a, number b, const coeffs r)
static void nr2mPower(number a, int i, number *result, const coeffs r)
void nlGMP(number &i, mpz_t n, const coeffs r)
(), see rinteger.h, new impl.