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30 if (((
long)a<0L) || ((
long)a>(
long)r->mod2mMask))
32 Print(
"wrong mod 2^n number %ld at %s,%d\n",(
long)a,
f,
l);
43 ((((
unsigned long) a) * ((
unsigned long)
b)) & r->mod2mMask);
49 ((((
unsigned long) a) + ((
unsigned long)
b)) & r->mod2mMask);
54 return (number)((
unsigned long)a < (
unsigned long)
b ?
55 r->mod2mMask+1 - (
unsigned long)
b + (
unsigned long)a:
56 (
unsigned long)a - (
unsigned long)
b);
59 #define nr2mNegM(A,r) (number)((r->mod2mMask+1 - (unsigned long)(A)) & r->mod2mMask)
60 #define nr2mEqualM(A,B) ((A)==(B))
66 static char n2mCoeffName_buf[22];
67 snprintf(n2mCoeffName_buf,21,
"ZZ/(2^%lu)",
cf->modExponent);
68 return n2mCoeffName_buf;
73 Print(
"ZZ/(2^%lu)", r->modExponent);
81 unsigned long mm=r->mod2mMask;
82 if (((mm+1)>>
m)==1L)
return TRUE;
91 sprintf(
s,
"ZZ/(2^%lu)",r->modExponent);
98 long ch = r->cfInt(c, r);
100 mpz_init_set(a, r->modNumber);
101 mpz_init_set_ui(
b, ch);
106 if(mpz_cmp_ui(
gcd, 1) == 0)
108 WerrorS(
"constant in q-ideal is coprime to modulus in ground ring");
109 WerrorS(
"Unable to create qring!");
112 if(mpz_cmp_ui(
gcd, 2) == 0)
120 mpz_init(baseTokNew);
121 mpz_set(baseTokNew, r->modBase);
122 while(mpz_cmp(
gcd, baseTokNew) > 0)
125 mpz_mul(baseTokNew, baseTokNew, r->modBase);
127 mpz_clear(baseTokNew);
136 if ((
unsigned long)
k == 0)
return FALSE;
137 if ((
unsigned long)
k > ((r->mod2mMask >> 1) + 1))
return FALSE;
147 if (((
unsigned long)a == 0) || ((
unsigned long)
b == 0))
161 unsigned long res = 0;
162 if ((
unsigned long)a == 0) a = (number) 1;
163 if ((
unsigned long)
b == 0)
b = (number) 1;
164 while ((
unsigned long)a % 2 == 0)
166 a = (number)((
unsigned long)a / 2);
167 if ((
unsigned long)
b % 2 == 0)
b = (number)((
unsigned long)
b / 2);
170 while ((
unsigned long)
b % 2 == 0)
172 b = (number)((
unsigned long)
b / 2);
175 return (number)(1L <<
res);
184 unsigned long res = 0;
185 if ((
unsigned long)a == 0 && (
unsigned long)
b == 0)
return (number)1;
186 while ((
unsigned long)a % 2 == 0 && (
unsigned long)
b % 2 == 0)
188 a = (number)((
unsigned long)a / 2);
189 b = (number)((
unsigned long)
b / 2);
198 return (number)((1L <<
res));
208 mpz_ptr u = (mpz_ptr)
omAlloc(
sizeof(mpz_t));
209 mpz_init_set_ui(u, a);
210 mpz_ptr u0 = (mpz_ptr)
omAlloc(
sizeof(mpz_t));
212 mpz_ptr u1 = (mpz_ptr)
omAlloc(
sizeof(mpz_t));
213 mpz_init_set_ui(u1, 1);
214 mpz_ptr u2 = (mpz_ptr)
omAlloc(
sizeof(mpz_t));
216 mpz_ptr
v = (mpz_ptr)
omAlloc(
sizeof(mpz_t));
217 mpz_init_set_ui(
v, r->mod2mMask);
219 mpz_ptr v0 = (mpz_ptr)
omAlloc(
sizeof(mpz_t));
221 mpz_ptr v1 = (mpz_ptr)
omAlloc(
sizeof(mpz_t));
223 mpz_ptr v2 = (mpz_ptr)
omAlloc(
sizeof(mpz_t));
224 mpz_init_set_ui(v2, 1);
225 mpz_ptr q = (mpz_ptr)
omAlloc(
sizeof(mpz_t));
227 mpz_ptr rr = (mpz_ptr)
omAlloc(
sizeof(mpz_t));
238 mpz_mul(u2, u2, q); mpz_sub(u2, u1, u2);
239 mpz_mul(v2, v2, q); mpz_sub(v2, v1, v2);
247 mpz_add_ui(u1, u1, r->mod2mMask);
248 mpz_add_ui(u1, u1, 1);
264 static unsigned long InvMod(
unsigned long a,
const coeffs r)
266 assume((
unsigned long)a % 2 != 0);
274 assume((
unsigned long)c % 2 != 0);
277 inv =
InvMod((
unsigned long)c,r);
283 if ((
unsigned long)c % 2 == 0)
285 WerrorS(
"division by zero divisor");
297 unsigned long res = 0;
298 if ((
unsigned long)a == 0 && (
unsigned long)
b == 0)
return (number)1;
299 while ((
unsigned long)a % 2 == 0 && (
unsigned long)
b % 2 == 0)
301 a = (number)((
unsigned long)a / 2);
302 b = (number)((
unsigned long)
b / 2);
305 if ((
unsigned long)
b % 2 == 0)
309 return (number)((1L <<
res));
315 return (number)((1L <<
res));
323 *(
unsigned long *)
result = 1;
341 if (
i == 0)
return (number)(
unsigned long)
i;
344 unsigned long j = (
unsigned long)1;
345 if (ii < 0) {
j = r->mod2mMask; ii = -ii; }
346 unsigned long k = (
unsigned long)ii;
347 k =
k & r->mod2mMask;
349 return (number)
nr2mMult((number)
j, (number)
k, r);
358 unsigned long nn = (
unsigned long)
n;
359 unsigned long l = r->mod2mMask >> 1;
l++;
360 if ((
unsigned long)nn >
l)
361 return (
long)((
unsigned long)nn - r->mod2mMask - 1);
363 return (
long)((
unsigned long)nn);
382 return ((
unsigned long)a % 2 == 1);
387 if (
k ==
NULL)
return (number)1;
388 unsigned long erg = (
unsigned long)
k;
389 while (erg % 2 == 0) erg = erg / 2;
395 return 0 == (
unsigned long)a;
400 return 1 == (
unsigned long)a;
405 return ((r->mod2mMask == (
unsigned long)a) &&(1L!=(
long)a));
415 if ((
unsigned long)a == 0)
return (number)0;
416 else if ((
unsigned long)
b % 2 == 0)
418 if ((
unsigned long)
b != 0)
420 while (((
unsigned long)
b % 2 == 0) && ((
unsigned long)a % 2 == 0))
422 a = (number)((
unsigned long)a / 2);
423 b = (number)((
unsigned long)
b / 2);
426 if ((
unsigned long)
b % 2 == 0)
428 WerrorS(
"Division not possible, even by cancelling zero divisors.");
429 WerrorS(
"Result is integer division without remainder.");
430 return (number) ((
unsigned long) a / (
unsigned long)
b);
445 unsigned long c = r->mod2mMask + 1;
447 return (c % (
unsigned long)
b) == 0;
452 c = (
unsigned long)
b;
455 if ((c % 2) != 0)
return FALSE;
476 unsigned long a = (
unsigned long)as;
477 unsigned long b = (
unsigned long)bs;
479 while (a % 2 == 0 &&
b % 2 == 0)
524 assume((
unsigned long)
b != 0);
526 unsigned long b_div = (
unsigned long)
b;
534 unsigned long rr = 0;
535 while ((g < r->mod2mMask ) && (b_div > 0) && (b_div % 2 == 0))
541 if (
g != 1) rr = (
unsigned long)a %
g;
547 static number nr2mIntDiv(number a, number
b,
const coeffs r)
549 if ((
unsigned long)a == 0)
551 if ((
unsigned long)
b == 0)
553 if ((
unsigned long)
b == 1)
555 unsigned long c = r->mod2mMask + 1;
557 return (number)(c / (
unsigned long)
b);
561 mpz_ptr cc = (mpz_ptr)
omAlloc(
sizeof(mpz_t));
562 mpz_init_set_ui(cc, r->mod2mMask); mpz_add_ui(cc, cc, 1);
563 mpz_div_ui(cc, cc, (
unsigned long)(
unsigned long)
b);
564 unsigned long s = mpz_get_ui(cc);
566 return (number)(
unsigned long)
s;
571 if ((
unsigned long)
b == 0)
573 return (number)((
unsigned long) a / (
unsigned long)
b);
580 if ((
unsigned long)
b == 0)
582 if ((
unsigned long)
b == 1)
584 unsigned long c = r->mod2mMask + 1;
586 return (number)(c / (
unsigned long)
b);
590 mpz_ptr cc = (mpz_ptr)
omAlloc(
sizeof(mpz_t));
591 mpz_init_set_ui(cc, r->mod2mMask); mpz_add_ui(cc, cc, 1);
592 mpz_div_ui(cc, cc, (
unsigned long)(
unsigned long)
b);
593 unsigned long s = mpz_get_ui(cc);
595 return (number)(
unsigned long)
s;
601 if ((
unsigned long)c == 0)
return c;
609 unsigned long i = ((
unsigned long)from) % (dst->mod2mMask + 1) ;
615 unsigned long i = ((
unsigned long)from) % (dst->mod2mMask + 1);
621 unsigned long j = (
unsigned long)1;
622 long ii = (long)from;
623 if (ii < 0) {
j = dst->mod2mMask; ii = -ii; }
624 unsigned long i = (
unsigned long)ii;
625 i =
i & dst->mod2mMask;
627 return (number)
nr2mMult((number)
i, (number)
j, dst);
634 mpz_ptr
k = (mpz_ptr)
omAlloc(
sizeof(mpz_t));
635 mpz_init_set_ui(
k, dst->mod2mMask);
637 mpz_and(erg, (mpz_ptr)from,
k);
638 number
res = (number) mpz_get_ui(erg);
650 nlGMP(from, gmp, src);
669 && (src->mod2mMask == dst->mod2mMask))
674 && (src->mod2mMask < dst->mod2mMask))
679 && (src->mod2mMask > dst->mod2mMask))
703 if (mpz_divisible_2exp_p(src->modNumber,dst->modExponent))
721 for (
int i = 1;
i <
m;
i++) r->mod2mMask = (r->mod2mMask << 1) + 1;
735 WarnS(
"nr2mInitExp unexpectedly called with m = 1 (we continue with Z/2^2");
747 if (((*
s) >=
'0') && ((*
s) <=
'9'))
754 if ((*
i) >= (
MAX_INT_VAL / 10)) (*i) = (*i) & r->mod2mMask;
756 while (((*
s) >=
'0') && ((*
s) <=
'9'));
757 (*i) = (*i) & r->mod2mMask;
763 static const char *
nr2mRead (
const char *
s, number *a,
const coeffs r)
775 *a = (number)(
long)
z;
777 *a =
nr2mDiv((number)(
long)
z,(number)(
long)
n,r);
796 mpz_init_set_si (r->modBase, 2L);
798 mpz_init (r->modNumber);
799 mpz_pow_ui (r->modNumber, r->modBase, r->modExponent);
802 r->ch = (int)r->mod2mMask + 1;
840 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_Ring_2toM(const coeffs r)
static number nr2mLcm(number a, number b, const coeffs)
static number nr2mSub(number a, number b, const coeffs r)
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 FORCE_INLINE BOOLEAN nCoeff_is_Ring_ModN(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)
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 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 FORCE_INLINE BOOLEAN nCoeff_is_Ring_Z(const coeffs r)
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.