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11 #include "factory/factory.h"
29 #if defined(DO_LINLINE) && defined(P_NUMBERS_H) && !defined(LDEBUG)
30 #define LINLINE static FORCE_INLINE
77 const char *
nlRead (
const char *
s, number *a,
const coeffs r);
93 #define nlTest(a, r) nlDBTest(a,__FILE__,__LINE__, r)
96 #define nlTest(a, r) do {} while (0)
103 #define MAX_NUM_SIZE 60
104 #define POW_2_28 (1L<<60)
105 #define POW_2_28_32 (1L<<28)
108 #define MAX_NUM_SIZE 28
109 #define POW_2_28 (1L<<28)
110 #define POW_2_28_32 (1L<<28)
126 LONG ui=mpz_get_si(
x->z);
127 if ((((ui<<3)>>3)==ui)
128 && (mpz_cmp_si(
x->z,(
long)ui)==0))
141 #ifndef BYTES_PER_MP_LIMB
142 #define BYTES_PER_MP_LIMB sizeof(mp_limb_t)
152 #define mpz_isNeg(A) ((A)->_mp_size<0)
153 #define mpz_limb_size(A) ((A)->_mp_size)
154 #define mpz_limb_d(A) ((A)->_mp_d)
171 #if (__GNU_MP_VERSION*10+__GNU_MP_VERSION_MINOR < 31)
172 void mpz_mul_si (mpz_ptr r, mpz_srcptr
s,
long int si)
207 mpz_init_set(
z->z,(mpz_ptr) from);
231 mpz_init_set_ui(
z->z,(
unsigned long) from);
244 Print(
"!!longrat: NULL in %s:%d\n",
f,
l);
248 if ((((
long)a)&3L)==3L)
250 Print(
" !!longrat:ptr(3) in %s:%d\n",
f,
l);
253 if ((((
long)a)&3L)==1L)
255 if (((((
LONG)(
long)a)<<1)>>1)!=((
LONG)(
long)a))
257 Print(
" !!longrat:arith:%lx in %s:%d\n",(
long)a,
f,
l);
267 if (a->debug!=123456)
269 Print(
"!!longrat:debug:%d in %s:%d\n",a->debug,
f,
l);
273 if ((a->s<0)||(a->s>4))
275 Print(
"!!longrat:s=%d in %s:%d\n",a->s,
f,
l);
283 if (a->z[0]._mp_alloc==0)
284 Print(
"!!longrat:z->alloc=0 in %s:%d\n",
f,
l);
288 if ((a->n[0]._mp_d[0]==0)&&(a->n[0]._mp_alloc<=1))
290 Print(
"!!longrat: n==0 in %s:%d\n",
f,
l);
298 if (a->z[0]._mp_alloc==0)
299 Print(
"!!longrat:n->alloc=0 in %s:%d\n",
f,
l);
300 if ((
mpz_size1(a->n) ==1) && (mpz_cmp_si(a->n,1L)==0))
302 Print(
"!!longrat:integer as rational in %s:%d\n",
f,
l);
303 mpz_clear(a->n); a->s=3;
308 Print(
"!!longrat:div. by negative in %s:%d\n",
f,
l);
322 if ((((ui<<3)>>3)==ui)
323 && (mpz_cmp_si(a->z,(
long)ui)==0))
325 Print(
"!!longrat:im int %d in %s:%d\n",ui,
f,
l);
347 long lz=mpz_get_si(
n->z);
348 if (mpz_cmp_si(
n->z,lz)==0)
term=lz;
351 mpz_init_set( dummy,
n->z );
360 mpz_init_set(
num,
n->z );
361 mpz_init_set(
den,
n->n );
383 if (
f.den().isOne() )
411 mpz_init_set_ui(h1,1);
412 while((FLT_RADIX*
f) < DBL_MAX &&
i<DBL_MANT_DIG)
415 mpz_mul_ui(h1,h1,FLT_RADIX);
420 memcpy(&(re->n),&h1,
sizeof(h1));
422 if(f_sign==-1) re=
nlNeg(re,dst);
439 size = (*f)[0]._mp_size;
457 e=(*f)[0]._mp_exp-
size;
464 void* (*allocfunc) (size_t);
465 mp_get_memory_functions (&allocfunc,
NULL,
NULL);
468 al = dest->_mp_size =
size;
470 dd = (mp_ptr)allocfunc(
sizeof(mp_limb_t)*al);
473 nn = (mp_ptr)allocfunc(
sizeof(mp_limb_t)*bl);
477 ndest->_mp_alloc = ndest->_mp_size = bl;
482 al = dest->_mp_size =
size+e;
484 dd = (mp_ptr)allocfunc(
sizeof(mp_limb_t)*al);
486 for (
i=0;
i<e;
i++) dd[
i] = 0;
491 dest->_mp_alloc = al;
576 int s=a->z[0]._mp_alloc;
585 int d=a->n[0]._mp_alloc;
610 long ul=mpz_get_si(
i->z);
611 if (mpz_cmp_si(
i->z,ul)!=0)
return 0;
617 mpz_tdiv_q(tmp,
i->z,
i->n);
622 if (mpz_cmp_si(tmp,ul)!=0) ul=0;
641 mpz_tdiv_q(tmp->z,
i->z,
i->n);
671 mpz_init_set_ui(
n->z,1L);
676 mpz_init_set_si(
n->z,-1L);
687 mpz_init_set(
n->n,a->z);
693 mpz_init_set(
n->z,a->n);
699 if (mpz_cmp_ui(
n->n,1L)==0)
712 mpz_init_set_si(
n->z,-1L);
716 mpz_init_set_ui(
n->z,1L);
771 mpz_divexact(u->z,a->z,
b->z);
816 if (rr<0) rr+=
ABS(bb);
846 mpz_init_set(u->z,a->z);
851 else mpz_sub(u->z,u->z,rr->z);
852 mpz_divexact(u->z,u->z,
b->z);
899 mpz_init_set_si(aa, ai);
906 mpz_mod(u->z, aa,
b->z);
924 mpz_mod(u->z, a->z,
b->z);
946 return (mpz_divisible_ui_p(a->z,
SR_TO_INT(
b))!=0);
949 return mpz_divisible_p(a->z,
b->z) != 0;
971 long ch = r->cfInt(c, r);
982 mpz_init_set_ui(dummy, ch);
985 info.exp = (
unsigned long) 1;
1016 if (
j==1L)
return a;
1031 mpz_init_set_si(u->z,(
long)
i);
1032 mpz_init_set_si(u->n,(
long)
j);
1055 if (mpz_cmp(u->z,
b->z)==0)
1061 mpz_init_set(u->n,
b->z);
1070 mpz_init_set(u->n,a->n);
1090 mpz_init_set(u->n,
b->z);
1091 if (a->s<2) mpz_mul(u->n,u->n,a->n);
1092 if (
b->s<2) mpz_mul(u->z,u->z,
b->n);
1100 if (mpz_cmp_si(u->n,1L)==0)
1134 mpz_pow_ui((*u)->z,
x->z,(
unsigned long)
exp);
1137 if (mpz_cmp_si(
x->n,1L)==0)
1145 mpz_pow_ui((*u)->n,
x->n,(
unsigned long)
exp);
1221 if((
i==0L)||(
j==0L))
1244 unsigned long t=mpz_gcd_ui(
NULL,
b->z,(
long)aa);
1254 unsigned long t=mpz_gcd_ui(
NULL,a->z,(
long)bb);
1274 static int int_extgcd(
int a,
int b,
int * u,
int*
x,
int *
v,
int*
y)
1334 if (mpz_cmp(
x->z,
x->n)==0)
1357 if (mpz_cmp_si(
x->n,1L)==0)
1367 mpz_gcd(
gcd,
x->z,
x->n);
1369 if (mpz_cmp_si(
gcd,1L)!=0)
1371 mpz_divexact(
x->z,
x->z,
gcd);
1372 mpz_divexact(
x->n,
x->n,
gcd);
1373 if (mpz_cmp_si(
x->n,1L)==0)
1411 mpz_gcd(
gcd,a->z,
b->n);
1412 if (mpz_cmp_si(
gcd,1L)!=0)
1416 mpz_divexact(bt,
b->n,
gcd);
1420 mpz_mul(
result->z,bt,a->z);
1452 const unsigned long PP =
p;
1455 number
z =
n_Init( static_cast<long>(mpz_fdiv_ui(q->z, PP)), Zp );
1461 number
n =
n_Init( static_cast<long>(mpz_fdiv_ui(q->n, PP)), Zp );
1490 WarnS(
"Omitted denominator during coefficient mapping !");
1516 mpz_init_set(u->z,
n->n);
1543 mpz_init_set(u->z,
n->z);
1566 if (a->s!=0)
return FALSE;
1567 number
n=
b;
b=a; a=
n;
1581 bo=(mpz_cmp(bb,
b->z)==0);
1586 if (((a->s==1) && (
b->s==3))
1587 || ((
b->s==1) && (a->s==3)))
1595 mpz_init_set(aa,a->z);
1596 mpz_init_set(bb,
b->z);
1597 if (a->s<2) mpz_mul(bb,bb,a->n);
1598 if (
b->s<2) mpz_mul(aa,aa,
b->n);
1599 bo=(mpz_cmp(aa,bb)==0);
1618 mpz_init_set(
b->n,a->n);
1620 mpz_init_set(
b->z,a->z);
1658 #define GCD_NORM_COND(OLD,NEW) (mpz_size1(NEW->z)>mpz_size1(OLD->z))
1664 mpz_gcd(
gcd,
x->z,
x->n);
1666 if (mpz_cmp_si(
gcd,1L)!=0)
1668 mpz_divexact(
x->z,
x->z,
gcd);
1669 mpz_divexact(
x->n,
x->n,
gcd);
1670 if (mpz_cmp_si(
x->n,1L)==0)
1703 mpz_add(u->z,
b->z,
x);
1711 if (mpz_cmp(u->z,
b->n)==0)
1717 mpz_init_set(u->n,
b->n);
1749 mpz_mul(
x,
b->z,a->n);
1750 mpz_mul(u->z,a->z,
b->n);
1751 mpz_add(u->z,u->z,
x);
1761 mpz_mul(u->n,a->n,
b->n);
1762 if (mpz_cmp(u->z,u->n)==0)
1775 mpz_mul(u->z,
b->z,a->n);
1776 mpz_add(u->z,u->z,a->z);
1783 if (mpz_cmp(u->z,a->n)==0)
1789 mpz_init_set(u->n,a->n);
1804 mpz_mul(u->z,a->z,
b->n);
1805 mpz_add(u->z,u->z,
b->z);
1812 if (mpz_cmp(u->z,
b->n)==0)
1818 mpz_init_set(u->n,
b->n);
1825 mpz_add(u->z,a->z,
b->z);
1850 mpz_add(a->z,a->z,
x);
1884 mpz_add(u->z,
b->z,
x);
1887 mpz_init_set(u->n,
b->n);
1923 mpz_mul(
x,
b->z,a->n);
1924 mpz_mul(
y,a->z,
b->n);
1928 mpz_mul(a->n,a->n,
b->n);
1938 mpz_mul(
x,
b->z,a->n);
1939 mpz_add(a->z,a->z,
x);
1958 mpz_mul(
x,a->z,
b->n);
1959 mpz_add(a->z,
b->z,
x);
1961 mpz_init_set(a->n,
b->n);
1969 mpz_add(a->z,a->z,
b->z);
1998 mpz_sub(u->z,
x,
b->z);
2006 if (mpz_cmp(u->z,
b->n)==0)
2012 mpz_init_set(u->n,
b->n);
2045 mpz_sub(u->z,a->z,
x);
2053 if (mpz_cmp(u->z,a->n)==0)
2059 mpz_init_set(u->n,a->n);
2096 mpz_mul(
x,
b->z,a->n);
2097 mpz_mul(
y,a->z,
b->n);
2108 mpz_mul(u->n,a->n,
b->n);
2109 if (mpz_cmp(u->z,u->n)==0)
2124 mpz_mul(
x,
b->z,a->n);
2125 mpz_sub(u->z,a->z,
x);
2133 if (mpz_cmp(u->z,a->n)==0)
2139 mpz_init_set(u->n,a->n);
2156 mpz_mul(
x,a->z,
b->n);
2157 mpz_sub(u->z,
x,
b->z);
2165 if (mpz_cmp(u->z,
b->n)==0)
2171 mpz_init_set(u->n,
b->n);
2178 mpz_sub(u->z,a->z,
b->z);
2222 if (u->s==1) u->s=0;
2225 mpz_mul_ui(u->z,
b->z,(
unsigned long)
SR_TO_INT(a));
2237 mpz_mul_ui(u->z,
b->z,(
unsigned long)-
SR_TO_INT(a));
2243 if (mpz_cmp(u->z,
b->n)==0)
2249 mpz_init_set(u->n,
b->n);
2259 mpz_mul(u->z,a->z,
b->z);
2269 if (mpz_cmp(u->z,
b->n)==0)
2275 mpz_init_set(u->n,
b->n);
2283 if (mpz_cmp(u->z,a->n)==0)
2289 mpz_init_set(u->n,a->n);
2295 mpz_mul(u->n,a->n,
b->n);
2296 if (mpz_cmp(u->z,u->n)==0)
2365 mpz_init_set_si(
z->z,
i);
2379 mpz_init_set_si(
z->z,(
long)
i);
2380 mpz_init_set_si(
z->n,(
long)
j);
2392 mpz_init_set(
z->z,
i);
2393 mpz_init_set(
z->n,
j);
2419 #if defined(DO_LINLINE) || !defined(P_NUMBERS_H)
2438 #if MAX_NUM_SIZE == 60
2443 if ( ((((
long)ii)==
i) && ((ii << 3) >> 3) == ii ))
n=
INT_TO_SR(ii);
2467 if (mpz_cmp_si(a->z,0L)==0)
2469 printf(
"gmp-0 in nlIsZero\n");
2535 if ( ((r << 1) >> 1) == r )
2536 return (number)(long)r;
2554 if ( ((r << 1) >> 1) == r )
2577 number u=((number) ((r>>1)+
SR_INT));
2601 if ( ((r << 1) >> 1) == r )
2603 return (number)(long)r;
2625 mpz_mul(aa->z,a->z,
b->z);
2630 mpz_init_set(a->n,
b->n);
2638 mpz_mul(a->n,a->n,
b->n);
2644 #endif // DO_LINLINE
2653 else mpz_init_set(
m, (mpz_ptr)
n->z);
2664 mpz_init_set(
z->z,
m);
2669 number
nlXExtGcd (number a, number
b, number *
s, number *t, number *u, number *
v,
const coeffs r)
2690 mpz_init_set(aa, a->z);
2698 mpz_init_set(bb,
b->z);
2700 mpz_t erg; mpz_t bs; mpz_t bt;
2705 mpz_gcdext(erg, bs, bt, aa, bb);
2707 mpz_div(aa, aa, erg);
2750 rr = mpz_divmod_ui(qq, rrr, a->z, (
unsigned long)
ABS(
SR_TO_INT(
b)));
2764 mpz_divmod(qq, rr, a->z,
b->z);
2784 mpz_gcd(a->z,a->z,
b->z);
2801 else mpz_sub(a->z,a->z,rr->z);
2802 mpz_divexact(a->z,a->z,
b->z);
2809 mpz_t
A,
B,C,
D,
E,
N,P,tmp;
2811 else mpz_init_set(P,nP->z);
2812 const mp_bitcnt_t bits=2*(
mpz_size1(P)+1)*GMP_LIMB_BITS;
2815 else mpz_set(
N,nN->z);
2818 mpz_init2(
A,bits); mpz_set_ui(
A,0L);
2819 mpz_init2(
B,bits); mpz_set_ui(
B,1L);
2820 mpz_init2(C,bits); mpz_set_ui(C,0L);
2822 mpz_init2(
E,bits); mpz_set(
E,P);
2823 mpz_init2(tmp,bits);
2828 mpz_add(tmp,tmp,tmp);
2829 if (mpz_cmp(tmp,P)<0)
2838 if (mpz_cmp_ui(tmp,1)==0)
2845 mpz_init_set(
z->z,
N);
2846 mpz_init_set(
z->n,
B);
2859 mpz_divmod(tmp,
D,
E,
N);
2882 mpz_init((*s)->z); (*s)->s=3;
2884 mpz_init((*t)->z); (*t)->s=3;
2886 mpz_init(
g->z);
g->s=3;
2894 aa=(mpz_ptr)
omAlloc(
sizeof(mpz_t));
2903 bb=(mpz_ptr)
omAlloc(
sizeof(mpz_t));
2910 mpz_gcdext(
g->z,(*s)->z,(*t)->z,aa,bb);
2943 for(
i=rl-1;
i>=0;
i--)
2945 X[
i]=CF->convSingNFactoryN(
x[
i],
FALSE,CF);
2946 Q[
i]=CF->convSingNFactoryN(q[
i],
FALSE,CF);
2953 number
n=CF->convFactoryNSingN(xnew,CF);
2956 number
p=CF->convFactoryNSingN(qnew,CF);
2959 else p2=CF->cfDiv(
p,CF->cfInit(2, CF),CF);
2960 if (CF->cfGreater(
n,p2,CF))
2962 number n2=CF->cfSub(
n,
p,CF);
2963 CF->cfDelete(&
n,CF);
2966 CF->cfDelete(&p2,CF);
2967 CF->cfDelete(&
p,CF);
2969 CF->cfNormalize(
n,CF);
2973 number nlChineseRemainder(number *
x, number *q,
int rl,
const coeffs C)
2984 numberCollectionEnumerator.
Reset();
2986 if( !numberCollectionEnumerator.
MoveNext() )
3001 int normalcount = 0;
3004 number&
n = numberCollectionEnumerator.
Current();
3016 }
while (numberCollectionEnumerator.
MoveNext() );
3023 numberCollectionEnumerator.
Reset();
3025 while (numberCollectionEnumerator.
MoveNext() )
3027 number&
n = numberCollectionEnumerator.
Current();
3029 if( (--normalcount) <= 0)
3043 numberCollectionEnumerator.
Reset();
3045 while (numberCollectionEnumerator.
MoveNext() )
3047 number& nn = numberCollectionEnumerator.
Current();
3060 numberCollectionEnumerator.
Reset();
3062 while (numberCollectionEnumerator.
MoveNext() )
3064 number&
n = numberCollectionEnumerator.
Current();
3075 numberCollectionEnumerator.
Reset();
3077 if( !numberCollectionEnumerator.
MoveNext() )
3100 number& cand1 = numberCollectionEnumerator.
Current();
3110 mpz_init_set(
cand->z, cand1->n);
3115 mpz_lcm(
cand->z,
cand->z, cand1->n);
3120 while (numberCollectionEnumerator.
MoveNext() );
3135 numberCollectionEnumerator.
Reset();
3136 while (numberCollectionEnumerator.
MoveNext() )
3138 number&
n = numberCollectionEnumerator.
Current();
3150 numberCollectionEnumerator.
Reset();
3157 while (numberCollectionEnumerator.
MoveNext() )
3159 number &
n = numberCollectionEnumerator.
Current();
3167 if (r->cfDiv==
nlDiv)
return (
char*)
"QQ";
3168 else return (
char*)
"ZZ";
3182 #if SIZEOF_LONG == 4
3189 fprintf(
f,
"4 %d ",nnn);
3194 mpz_init_set_si(tmp,nn);
3205 fprintf(
f,
"%d ",
n->s+5);
3246 #if SIZEOF_LONG == 8
3275 #if SIZEOF_LONG == 8
3281 default:
Werror(
"error in reading number: invalid subtype %d",sub_type);
3344 r->cfSubringGcd =
nlGcd;
3367 r->cfInpNeg =
nlNeg;
3411 r->has_simple_Alloc=
FALSE;
3412 r->has_simple_Inverse=
FALSE;
3419 number nlMod(number a, number
b)
3441 mpz_mod(r->z,al->z,bl->z);
3446 LONG ui=(int)mpz_get_si(&r->z);
3447 if ((((ui<<3)>>3)==ui)
3448 && (mpz_cmp_si(
x->z,(
long)ui)==0))
3458 #endif // not P_NUMBERS_H
3459 #endif // LONGRAT_CC
static FORCE_INLINE n_coeffType getCoeffType(const coeffs r)
Returns the type of coeffs domain.
static number nlLcm(number a, number b, const coeffs r)
(mpz_ptr), see rmodulon,h
#define omCheckAddrSize(addr, size)
only used if HAVE_RINGS is defined
BOOLEAN nlIsUnit(number a, const coeffs)
LINLINE BOOLEAN nlIsZero(number za, const coeffs r)
static const int SW_RATIONAL
set to 1 for computations over Q
static FORCE_INLINE BOOLEAN nCoeff_is_Zp(const coeffs r)
coeffs nlQuot1(number c, const coeffs r)
LINLINE number nl_Copy(number a, const coeffs r)
static FORCE_INLINE BOOLEAN nCoeff_is_R(const coeffs r)
virtual reference Current()=0
Gets the current element in the collection (read and write).
LINLINE void nlInpMult(number &a, number b, const coeffs r)
static FORCE_INLINE BOOLEAN nCoeff_is_Ring_2toM(const coeffs r)
static void nlWriteFd(number n, FILE *f, const coeffs)
nMapFunc nlSetMap(const coeffs src, const coeffs dst)
long nlInt(number &n, const coeffs r)
const CanonicalForm int const CFList const Variable & y
number nlMapZ(number from, const coeffs src, const coeffs dst)
number nlExtGcd(number a, number b, number *s, number *t, const coeffs)
static FORCE_INLINE int n_GetChar(const coeffs r)
Return the characteristic of the coeff. domain.
LINLINE BOOLEAN nlIsOne(number a, const coeffs r)
number nlChineseRemainderSym(number *x, number *q, int rl, BOOLEAN sym, CFArray &inv_cache, const coeffs CF)
LINLINE number nlCopy(number a, const coeffs r)
number _nlMult_aNoImm_OR_bNoImm(number a, number b)
BOOLEAN nlIsMOne(number a, const coeffs r)
char * nlCoeffName(const coeffs r)
void nlCoeffWrite(const coeffs r, BOOLEAN details)
void _nlDelete_NoImm(number *a)
static number nlMapR(number from, const coeffs src, const coeffs dst)
int nlDivComp(number a, number b, const coeffs r)
number nlCopyMap(number a, const coeffs, const coeffs)
SI_FLOAT nrFloat(number n)
Converts a n_R number into a float. Needed by Maps.
number ndCopyMap(number a, const coeffs aRing, const coeffs r)
static FORCE_INLINE void n_Delete(number *p, const coeffs r)
delete 'p'
REvaluation E(1, terms.length(), IntRandom(25))
coeffs nInitChar(n_coeffType t, void *parameter)
one-time initialisations for new coeffs in case of an error return NULL
BOOLEAN nlDivBy(number a, number b, const coeffs)
number nlMapMachineInt(number from, const coeffs, const coeffs)
CanonicalForm make_cf(const mpz_ptr n)
number nlShort1(number x)
const CanonicalForm CFMap CFMap & N
LINLINE void nlInpAdd(number &a, number b, const coeffs r)
number _nlSub_aNoImm_OR_bNoImm(number a, number b)
LINLINE number nlInit(long i, const coeffs r)
LINLINE number nlSub(number la, number li, const coeffs r)
void s_readmpz(s_buff F, mpz_t a)
BOOLEAN nlDBTest(number a, const char *f, const int l)
real floating point (GMP) numbers
virtual void Reset()=0
Sets the enumerator to its initial position: -1, which is before the first element in the collection.
int nlSize(number a, const coeffs)
LINLINE BOOLEAN nlEqual(number a, number b, const coeffs r)
static number nlRandom(siRandProc p, number v2, number, const coeffs cf)
void nlPower(number x, int exp, number *lu, const coeffs r)
static void nlClearContent(ICoeffsEnumerator &numberCollectionEnumerator, number &c, const coeffs cf)
static int int_extgcd(int a, int b, int *u, int *x, int *v, int *y)
number(* nMapFunc)(number a, const coeffs src, const coeffs dst)
maps "a", which lives in src, into dst
const char *const nDivBy0
void PrintS(const char *s)
#define omFreeSize(addr, size)
static void nlClearDenominators(ICoeffsEnumerator &numberCollectionEnumerator, number &c, const coeffs cf)
void nlWrite(number a, const coeffs r)
number nlXExtGcd(number a, number b, number *s, number *t, number *u, number *v, const coeffs r)
number nlGetUnit(number n, const coeffs cf)
number nlNormalizeHelper(number a, number b, const coeffs r)
static number nlConvFactoryNSingN(const CanonicalForm f, const coeffs r)
static void nlNormalize_Gcd(number &x)
static void nlMPZ(mpz_t m, number &n, const coeffs r)
number nlGcd(number a, number b, const coeffs r)
static CanonicalForm nlConvSingNFactoryN(number n, const BOOLEAN setChar, const coeffs)
static number nlInitMPZ(mpz_t m, const coeffs)
void nlNormalize(number &x, const coeffs r)
static FORCE_INLINE BOOLEAN nCoeff_is_long_R(const coeffs r)
void chineseRemainderCached(CFArray &a, CFArray &n, CanonicalForm &xnew, CanonicalForm &prod, CFArray &inv)
number nlGetNumerator(number &n, const coeffs r)
void chineseRemainder(const CanonicalForm &x1, const CanonicalForm &q1, const CanonicalForm &x2, const CanonicalForm &q2, CanonicalForm &xnew, CanonicalForm &qnew)
void chineseRemainder ( const CanonicalForm & x1, const CanonicalForm & q1, const CanonicalForm & x2,...
number nlGetDenom(number &n, 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
long s_readlong(s_buff F)
number nlModP(number q, const coeffs, const coeffs Zp)
number nlQuotRem(number a, number b, number *r, const coeffs R)
BOOLEAN nlGreaterZero(number za, const coeffs r)
BOOLEAN _nlEqual_aNoImm_OR_bNoImm(number a, number b)
number nlIntMod(number a, number b, const coeffs r)
number nlMapGMP(number from, const coeffs src, const coeffs dst)
number _nlMult_aImm_bImm_rNoImm(number a, number b)
single prescision (6,6) real numbers
gmp_float exp(const gmp_float &a)
long npInt(number &n, const coeffs r)
const CanonicalForm const CanonicalForm const CanonicalForm const CanonicalForm & cand
void nlInpGcd(number &a, number b, const coeffs r)
void mpz_mul_si(mpz_ptr r, mpz_srcptr s, long int si)
number nlDiv(number a, number b, const coeffs r)
virtual bool MoveNext()=0
Advances the enumerator to the next element of the collection. returns true if the enumerator was suc...
number _nlCopy_NoImm(number a)
LINLINE number nlAdd(number la, number li, const coeffs r)
void Werror(const char *fmt,...)
static number nlReadFd(s_buff f, const coeffs)
number nlInvers(number a, const coeffs r)
number nlBigInt(number &n)
void nlInpIntDiv(number &a, number b, const coeffs r)
void WerrorS(const char *s)
static number nlShort3(number x)
number nlFarey(number nN, number nP, const coeffs CF)
#define omCheckIf(cond, test)
number nlInit2(int i, int j, const coeffs r)
create a rational i/j (implicitly) over Q NOTE: make sure to use correct Q in debug mode
const char * nlRead(const char *s, number *a, const coeffs r)
static number nlMapP(number from, const coeffs src, const coeffs dst)
void _nlInpAdd_aNoImm_OR_bNoImm(number &a, number b)
number nlIntDiv(number a, number b, const coeffs r)
void gmp_denominator(const CanonicalForm &f, mpz_ptr result)
void gmp_numerator(const CanonicalForm &f, mpz_ptr result)
number nlShort3_noinline(number x)
const Variable & v
< [in] a sqrfree bivariate poly
LINLINE number nlMult(number a, number b, const coeffs r)
number nlInit2gmp(mpz_t i, mpz_t j, const coeffs r)
create a rational i/j (implicitly) over Q NOTE: make sure to use correct Q in debug mode
LINLINE number nlNeg(number za, const coeffs r)
const CanonicalForm int s
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...
void s_readmpz_base(s_buff F, mpz_ptr a, int base)
LINLINE void nlDelete(number *a, const coeffs r)
static number nlMapLongR(number from, const coeffs src, const coeffs dst)
BOOLEAN nlInitChar(coeffs r, void *p)
number _nlNeg_NoImm(number a)
const ExtensionInfo & info
< [in] sqrfree poly
number nlExactDiv(number a, number b, const coeffs r)
BOOLEAN nlCoeffIsEqual(const coeffs r, n_coeffType n, void *p)
#define GCD_NORM_COND(OLD, NEW)
BOOLEAN nlGreater(number a, number b, const coeffs r)
static char * nlCoeffString(const coeffs r)
number _nlAdd_aNoImm_OR_bNoImm(number a, number b)
void nlGMP(number &i, mpz_t n, const coeffs r)
(), see rinteger.h, new impl.