11 #include <factory/factory.h> 23 #if defined(DO_LINLINE) && defined(P_NUMBERS_H) && !defined(LDEBUG) 24 #define LINLINE static FORCE_INLINE 90 #define nlTest(a, r) nlDBTest(a,__FILE__,__LINE__, r) 93 #define nlTest(a, r) do {} while (0) 100 #define MAX_NUM_SIZE 60 101 #define POW_2_28 (1L<<60) 102 #define POW_2_28_32 (1L<<28) 105 #define MAX_NUM_SIZE 28 106 #define POW_2_28 (1L<<28) 107 #define POW_2_28_32 (1L<<28) 115 if (mpz_cmp_ui(x->z,0L)==0)
123 LONG ui=mpz_get_si(x->z);
124 if ((((ui<<3)>>3)==ui)
125 && (mpz_cmp_si(x->z,(
long)ui)==0))
148 #ifndef BYTES_PER_MP_LIMB 149 #define BYTES_PER_MP_LIMB sizeof(mp_limb_t) 159 #define mpz_isNeg(A) ((A)->_mp_size<0) 160 #define mpz_limb_size(A) ((A)->_mp_size) 161 #define mpz_limb_d(A) ((A)->_mp_d) 178 #if (__GNU_MP_VERSION*10+__GNU_MP_VERSION_MINOR < 31) 214 mpz_init_set(z->z,(mpz_ptr) from);
239 mpz_init_set_ui(z->z,(
unsigned long) from);
252 Print(
"!!longrat: NULL in %s:%d\n",f,l);
256 if ((((
long)a)&3L)==3L)
258 Print(
" !!longrat:ptr(3) in %s:%d\n",f,l);
261 if ((((
long)a)&3L)==1L)
263 if (((((
LONG)(
long)a)<<1)>>1)!=((
LONG)(
long)a))
265 Print(
" !!longrat:arith:%lx in %s:%d\n",(
long)a, f,l);
275 if (a->debug!=123456)
277 Print(
"!!longrat:debug:%d in %s:%d\n",a->debug,f,l);
281 if ((a->s<0)||(a->s>4))
283 Print(
"!!longrat:s=%d in %s:%d\n",a->s,f,l);
291 if (a->z[0]._mp_alloc==0)
292 Print(
"!!longrat:z->alloc=0 in %s:%d\n",f,l);
296 if ((a->n[0]._mp_d[0]==0)&&(a->n[0]._mp_alloc<=1))
298 Print(
"!!longrat: n==0 in %s:%d\n",f,l);
306 if (a->z[0]._mp_alloc==0)
307 Print(
"!!longrat:n->alloc=0 in %s:%d\n",f,l);
308 if ((
mpz_size1(a->n) ==1) && (mpz_cmp_si(a->n,1L)==0))
310 Print(
"!!longrat:integer as rational in %s:%d\n",f,l);
311 mpz_clear(a->n); a->s=3;
316 Print(
"!!longrat:div. by negative in %s:%d\n",f,l);
330 if ((((ui<<3)>>3)==ui)
331 && (mpz_cmp_si(a->z,(
long)ui)==0))
333 Print(
"!!longrat:im int %d in %s:%d\n",ui,f,l);
355 long lz=mpz_get_si(n->z);
356 if (mpz_cmp_si(n->z,lz)==0) term=lz;
359 mpz_init_set( dummy,n->z );
368 mpz_init_set( num, n->z );
369 mpz_init_set( den, n->n );
370 term =
make_cf( num, den, ( n->s != 1 ));
419 mpz_init_set_ui(h1,1);
420 while((FLT_RADIX*f) < DBL_MAX && i<DBL_MANT_DIG)
423 mpz_mul_ui(h1,h1,FLT_RADIX);
428 memcpy(&(re->n),&h1,
sizeof(h1));
430 if(f_sign==-1) re=
nlNeg(re,dst);
447 size = (*f)[0]._mp_size;
465 e=(*f)[0]._mp_exp-
size;
474 al = dest->_mp_size =
size;
476 dd = (mp_ptr)
omAlloc(
sizeof(mp_limb_t)*al);
477 for (i=0;i<
size;i++) dd[i] = qp[i];
479 nn = (mp_ptr)
omAlloc0(
sizeof(mp_limb_t)*bl);
483 ndest->_mp_alloc = ndest->_mp_size = bl;
488 al = dest->_mp_size = size+e;
490 dd = (mp_ptr)
omAlloc(
sizeof(mp_limb_t)*al);
491 for (i=0;i<
size;i++) dd[i+e] = qp[i];
492 for (i=0;i<e;i++) dd[i] = 0;
497 dest->_mp_alloc = al;
498 if (negative) mpz_neg(dest,dest);
582 int s=a->z[0]._mp_alloc;
591 int d=a->n[0]._mp_alloc;
616 long ul=mpz_get_si(i->z);
617 if (mpz_cmp_si(i->z,ul)!=0)
return 0;
623 mpz_tdiv_q(tmp,i->z,i->n);
628 if (mpz_cmp_si(tmp,ul)!=0) ul=0;
647 mpz_tdiv_q(tmp->z,i->z,i->n);
677 mpz_init_set_si(n->z,1L);
678 mpz_init_set_si(n->n,(
long)
SR_TO_INT(a));
682 mpz_init_set_si(n->z,-1L);
683 mpz_init_set_si(n->n,(
long)-
SR_TO_INT(a));
693 mpz_init_set(n->n,a->z);
699 mpz_init_set(n->z,a->n);
705 if (mpz_cmp_ui(n->n,1L)==0)
718 mpz_init_set_si(n->z,-1L);
722 mpz_init_set_si(n->z,1L);
769 mpz_divexact(u->z,a->z,b->z);
806 if (rr<0) rr+=
ABS(bb);
836 mpz_init_set(u->z,a->z);
841 else mpz_sub(u->z,u->z,rr->z);
842 mpz_divexact(u->z,u->z,b->z);
889 mpz_init_set_si(aa, ai);
896 mpz_mod(u->z, aa, b->z);
914 mpz_mod(u->z, a->z, b->z);
936 return (mpz_divisible_ui_p(a->z,
SR_TO_INT(b))!=0);
939 return mpz_divisible_p(a->z, b->z) != 0;
946 if (
nlDivBy(b, a, r))
return 2;
949 if (
nlDivBy(b, a, r))
return 1;
960 long ch = r->cfInt(c, r);
971 dummy = (mpz_ptr)
omAlloc(
sizeof(mpz_t));
972 mpz_init_set_ui(dummy, ch);
975 info.
exp = (
unsigned long) 1;
1005 if (j==1L)
return a;
1020 mpz_init_set_si(u->z,(
long)i);
1021 mpz_init_set_si(u->n,(
long)j);
1044 if (mpz_cmp(u->z,b->z)==0)
1050 mpz_init_set(u->n,b->z);
1053 else if (
SR_HDL(b) & SR_INT)
1059 mpz_init_set(u->n,a->n);
1079 mpz_init_set(u->n,b->z);
1080 if (a->s<2) mpz_mul(u->n,u->n,a->n);
1081 if (b->s<2) mpz_mul(u->z,u->z,b->n);
1089 if (mpz_cmp_si(u->n,1L)==0)
1123 mpz_pow_ui((*u)->z,x->z,(
unsigned long)exp);
1126 if (mpz_cmp_si(x->n,1L)==0)
1134 mpz_pow_ui((*u)->n,x->n,(
unsigned long)exp);
1146 if (exp<0)
Print(
"nlPower: neg. exp. %d\n",exp);
1210 if((i==0L)||(j==0L))
1228 if (((!(
SR_HDL(a) & SR_INT))&&(a->s<2))
1233 unsigned long t=mpz_gcd_ui(
NULL,b->z,(
long)aa);
1243 unsigned long t=mpz_gcd_ui(
NULL,a->z,(
long)bb);
1254 result->debug=123456;
1256 mpz_init(result->z);
1257 mpz_gcd(result->z,a->z,b->z);
1316 if (mpz_cmp_ui(x->z,0L)==0)
1323 if (mpz_cmp(x->z,x->n)==0)
1346 if (mpz_cmp_si(x->n,1L)==0)
1356 mpz_gcd(gcd,x->z,x->n);
1358 if (mpz_cmp_si(gcd,1L)!=0)
1360 mpz_divexact(x->z,x->z,gcd);
1361 mpz_divexact(x->n,x->n,gcd);
1362 if (mpz_cmp_si(x->n,1L)==0)
1391 result->debug=123456;
1396 mpz_init(result->z);
1400 mpz_gcd(gcd,a->z,b->n);
1401 if (mpz_cmp_si(gcd,1L)!=0)
1404 mpz_init_set(bt,b->n);
1405 mpz_divexact(bt,bt,gcd);
1409 mpz_mul(result->z,bt,a->z);
1416 mpz_mul(result->z,b->n,a->z);
1441 const unsigned long PP =
p;
1444 number
z =
n_Init( static_cast<long>(mpz_fdiv_ui(q->z, PP)), Zp );
1450 number
n =
n_Init( static_cast<long>(mpz_fdiv_ui(q->n, PP)), Zp );
1479 WarnS(
"Omitted denominator during coefficient mapping !");
1481 mpz_set((mpz_ptr) n, i->z);
1496 if (!(
SR_HDL(n) & SR_INT))
1505 mpz_init_set(u->z,n->n);
1525 if (!(
SR_HDL(n) & SR_INT))
1532 mpz_init_set(u->z,n->z);
1555 if (a->s!=0)
return FALSE;
1556 number
n=
b; b=
a; a=
n;
1563 if ((((
long)a) > 0L) && (
mpz_isNeg(b->z)))
1565 if ((((
long)a) < 0L) && (!
mpz_isNeg(b->z)))
1568 mpz_init_set(bb,b->n);
1570 bo=(mpz_cmp(bb,b->z)==0);
1575 if (((a->s==1) && (b->s==3))
1576 || ((b->s==1) && (a->s==3)))
1584 mpz_init_set(aa,a->z);
1585 mpz_init_set(bb,b->z);
1586 if (a->s<2) mpz_mul(bb,bb,a->n);
1587 if (b->s<2) mpz_mul(aa,aa,b->n);
1588 bo=(mpz_cmp(aa,bb)==0);
1607 mpz_init_set(b->n,a->n);
1609 mpz_init_set(b->z,a->z);
1647 #define GCD_NORM_COND(OLD,NEW) (mpz_size1(NEW->z)>mpz_size1(OLD->z)) 1653 mpz_gcd(gcd,x->z,x->n);
1655 if (mpz_cmp_si(gcd,1L)!=0)
1657 mpz_divexact(x->z,x->z,gcd);
1658 mpz_divexact(x->n,x->n,gcd);
1659 if (mpz_cmp_si(x->n,1L)==0)
1692 mpz_add(u->z,b->z,x);
1694 if (mpz_cmp_ui(u->z,0L)==0)
1700 if (mpz_cmp(u->z,b->n)==0)
1706 mpz_init_set(u->n,b->n);
1738 mpz_mul(x,b->z,a->n);
1739 mpz_mul(u->z,a->z,b->n);
1740 mpz_add(u->z,u->z,x);
1743 if (mpz_cmp_ui(u->z,0L)==0)
1750 mpz_mul(u->n,a->n,b->n);
1751 if (mpz_cmp(u->z,u->n)==0)
1764 mpz_mul(u->z,b->z,a->n);
1765 mpz_add(u->z,u->z,a->z);
1766 if (mpz_cmp_ui(u->z,0L)==0)
1772 if (mpz_cmp(u->z,a->n)==0)
1778 mpz_init_set(u->n,a->n);
1793 mpz_mul(u->z,a->z,b->n);
1794 mpz_add(u->z,u->z,b->z);
1795 if (mpz_cmp_ui(u->z,0L)==0)
1801 if (mpz_cmp(u->z,b->n)==0)
1807 mpz_init_set(u->n,b->n);
1814 mpz_add(u->z,a->z,b->z);
1839 mpz_add(a->z,a->z,x);
1857 else if (
SR_HDL(a) & SR_INT)
1873 mpz_add(u->z,b->z,x);
1876 mpz_init_set(u->n,b->n);
1911 mpz_mul(x,b->z,a->n);
1912 mpz_mul(y,a->z,b->n);
1916 mpz_mul(a->n,a->n,b->n);
1925 mpz_mul(x,b->z,a->n);
1926 mpz_add(a->z,a->z,x);
1944 mpz_mul(x,a->z,b->n);
1945 mpz_add(a->z,b->z,x);
1947 mpz_init_set(a->n,b->n);
1954 mpz_add(a->z,a->z,b->z);
1983 mpz_sub(u->z,x,b->z);
1985 if (mpz_cmp_ui(u->z,0L)==0)
1991 if (mpz_cmp(u->z,b->n)==0)
1997 mpz_init_set(u->n,b->n);
2020 else if (
SR_HDL(b) & SR_INT)
2030 mpz_sub(u->z,a->z,x);
2032 if (mpz_cmp_ui(u->z,0L)==0)
2038 if (mpz_cmp(u->z,a->n)==0)
2044 mpz_init_set(u->n,a->n);
2081 mpz_mul(x,b->z,a->n);
2082 mpz_mul(y,a->z,b->n);
2086 if (mpz_cmp_ui(u->z,0L)==0)
2093 mpz_mul(u->n,a->n,b->n);
2094 if (mpz_cmp(u->z,u->n)==0)
2109 mpz_mul(x,b->z,a->n);
2110 mpz_sub(u->z,a->z,x);
2112 if (mpz_cmp_ui(u->z,0L)==0)
2118 if (mpz_cmp(u->z,a->n)==0)
2124 mpz_init_set(u->n,a->n);
2141 mpz_mul(x,a->z,b->n);
2142 mpz_sub(u->z,x,b->z);
2144 if (mpz_cmp_ui(u->z,0L)==0)
2150 if (mpz_cmp(u->z,b->n)==0)
2156 mpz_init_set(u->n,b->n);
2163 mpz_sub(u->z,a->z,b->z);
2207 if (u->s==1) u->s=0;
2210 mpz_mul_ui(u->z,b->z,(
unsigned long)
SR_TO_INT(a));
2222 mpz_mul_ui(u->z,b->z,(
unsigned long)-
SR_TO_INT(a));
2228 if (mpz_cmp(u->z,b->n)==0)
2234 mpz_init_set(u->n,b->n);
2244 mpz_mul(u->z,a->z,b->z);
2254 if (mpz_cmp(u->z,b->n)==0)
2260 mpz_init_set(u->n,b->n);
2268 if (mpz_cmp(u->z,a->n)==0)
2274 mpz_init_set(u->n,a->n);
2280 mpz_mul(u->n,a->n,b->n);
2281 if (mpz_cmp(u->z,u->n)==0)
2350 mpz_init_set_si(z->z,i);
2364 mpz_init_set_si(z->z,(
long)i);
2365 mpz_init_set_si(z->n,(
long)j);
2377 mpz_init_set(z->z,i);
2378 mpz_init_set(z->n,j);
2404 #if defined(DO_LINLINE) || !defined(P_NUMBERS_H) 2423 #if MAX_NUM_SIZE == 60 2424 if (((i << 3) >> 3) == i) n=
INT_TO_SR(i);
2428 if ( ((((
long)ii)==i) && ((ii << 3) >> 3) == ii )) n=
INT_TO_SR(ii);
2452 if (mpz_cmp_si(a->z,0L)==0)
2454 printf(
"gmp-0 in nlIsZero\n");
2520 if ( ((r << 1) >> 1) == r )
2521 return (number)(long)r;
2539 if ( ((r << 1) >> 1) == r )
2562 number u=((number) ((r>>1)+
SR_INT));
2563 if (((((LONG)
SR_HDL(u))<<1)>>1)==
SR_HDL(u))
return (u);
2586 if ( ((r << 1) >> 1) == r )
2588 return (number)(long)r;
2610 mpz_mul(aa->z,a->z,b->z);
2615 mpz_init_set(a->n,b->n);
2623 mpz_mul(a->n,a->n,b->n);
2629 #endif // DO_LINLINE 2638 else mpz_init_set(m, (mpz_ptr)n->z);
2649 mpz_init_set(z->z, m);
2675 mpz_init_set(aa, a->z);
2683 mpz_init_set(bb, b->z);
2685 mpz_t erg; mpz_t bs; mpz_t bt;
2690 mpz_gcdext(erg, bs, bt, aa, bb);
2692 mpz_div(aa, aa, erg);
2715 else if (
SR_HDL(a) & SR_INT)
2728 else if (
SR_HDL(b) & SR_INT)
2735 rr = mpz_divmod_ui(qq, rrr, a->z, (
unsigned long)
ABS(
SR_TO_INT(b)));
2749 mpz_divmod(qq, rr, a->z, b->z);
2769 mpz_gcd(a->z,a->z,b->z);
2786 else mpz_sub(a->z,a->z,rr->z);
2787 mpz_divexact(a->z,a->z,b->z);
2794 mpz_t tmp; mpz_init(tmp);
2797 else mpz_init_set(N,nN->z);
2799 else mpz_init_set(P,nP->z);
2802 mpz_init_set_si(A,0L);
2803 mpz_init_set_ui(B,(
unsigned long)1);
2804 mpz_init_set_si(C,0L);
2808 while(mpz_cmp_si(N,0L)!=0)
2811 mpz_add(tmp,tmp,tmp);
2812 if (mpz_cmp(tmp,P)<0)
2821 if (mpz_cmp_ui(tmp,1)==0)
2828 mpz_init_set(z->z,N);
2829 mpz_init_set(z->n,B);
2842 mpz_divmod(tmp,D,E,N);
2865 mpz_init((*s)->z); (*s)->s=3;
2867 mpz_init((*t)->z); (*t)->s=3;
2869 mpz_init(g->z); g->s=3;
2877 aa=(mpz_ptr)
omAlloc(
sizeof(mpz_t));
2886 bb=(mpz_ptr)
omAlloc(
sizeof(mpz_t));
2893 mpz_gcdext(g->z,(*s)->z,(*t)->z,aa,bb);
2913 PrintS(
"// characteristic : 0\n");
2915 PrintS(
"// coeff. ring is : Integers\n");
2926 for(i=rl-1;i>=0;i--)
2928 X[
i]=CF->convSingNFactoryN(x[i],
FALSE,CF);
2929 Q[
i]=CF->convSingNFactoryN(q[i],
FALSE,CF);
2936 number
n=CF->convFactoryNSingN(xnew,CF);
2939 number
p=CF->convFactoryNSingN(qnew,CF);
2943 number n2=
nlSub(n,p,CF);
2963 numberCollectionEnumerator.
Reset();
2965 if( !numberCollectionEnumerator.
MoveNext() )
2980 int normalcount = 0;
2983 number&
n = numberCollectionEnumerator.
Current();
2995 }
while (numberCollectionEnumerator.
MoveNext() );
3002 numberCollectionEnumerator.
Reset();
3004 while (numberCollectionEnumerator.
MoveNext() )
3006 number&
n = numberCollectionEnumerator.
Current();
3008 if( (--normalcount) <= 0)
3022 numberCollectionEnumerator.
Reset();
3024 while (numberCollectionEnumerator.
MoveNext() )
3026 number& nn = numberCollectionEnumerator.
Current();
3036 cand =
nlNeg(cand,cf);
3039 numberCollectionEnumerator.
Reset();
3041 while (numberCollectionEnumerator.
MoveNext() )
3043 number&
n = numberCollectionEnumerator.
Current();
3054 numberCollectionEnumerator.
Reset();
3056 if( !numberCollectionEnumerator.
MoveNext() )
3079 number& cand1 = numberCollectionEnumerator.
Current();
3084 if ((!(
SR_HDL(cand1)&SR_INT))
3089 mpz_init_set(cand->z, cand1->n);
3094 mpz_lcm(cand->z, cand->z, cand1->n);
3099 while (numberCollectionEnumerator.
MoveNext() );
3114 numberCollectionEnumerator.
Reset();
3115 while (numberCollectionEnumerator.
MoveNext() )
3117 number&
n = numberCollectionEnumerator.
Current();
3129 numberCollectionEnumerator.
Reset();
3132 cand =
nlNeg(cand, cf);
3136 while (numberCollectionEnumerator.
MoveNext() )
3138 number &
n = numberCollectionEnumerator.
Current();
3146 if (r->cfDiv==
nlDiv)
return (
char*)
"QQ";
3147 else return (
char*)
"ZZ";
3161 #if SIZEOF_LONG == 4 3168 fprintf(f,
"4 %d ",nnn);
3173 mpz_init_set_si(tmp,nn);
3184 fprintf(f,
"%d ",n->s+5);
3225 #if SIZEOF_LONG == 8 3254 #if SIZEOF_LONG == 8 3260 default:
Werror(
"error in reading number: invalid subtype %d",sub_type);
3293 number c=
nlDiv(a,b,cf);
3324 r->cfSubringGcd =
nlGcd;
3348 r->cfInpNeg =
nlNeg;
3394 r->has_simple_Alloc=
FALSE;
3395 r->has_simple_Inverse=
FALSE;
3402 number nlMod(number
a, number
b)
3424 mpz_mod(r->z,al->z,bl->z);
3429 LONG ui=(int)mpz_get_si(&r->z);
3430 if ((((ui<<3)>>3)==ui)
3431 && (mpz_cmp_si(
x->z,(
long)ui)==0))
3441 #endif // not P_NUMBERS_H 3442 #endif // LONGRAT_CC
number nlGetUnit(number n, const coeffs r)
LINLINE number nlSub(number la, number li, const coeffs r)
static void nlClearDenominators(ICoeffsEnumerator &numberCollectionEnumerator, number &c, const coeffs cf)
const CanonicalForm int s
const CanonicalForm int const CFList const Variable & y
void mpz_mul_si(mpz_ptr r, mpz_srcptr s, long int si)
#define omCheckAddrSize(addr, size)
BOOLEAN nlCoeffIsEqual(const coeffs r, n_coeffType n, void *p)
only used if HAVE_RINGS is defined: ?
static FORCE_INLINE BOOLEAN nCoeff_is_Zp(const coeffs r)
static int int_extgcd(int a, int b, int *u, int *x, int *v, int *y)
char * nlCoeffName(const coeffs r)
long npInt(number &n, const coeffs r)
static number nlConvFactoryNSingN(const CanonicalForm f, const coeffs r)
BOOLEAN nlGreaterZero(number za, const coeffs r)
static void nlMPZ(mpz_t m, number &n, const coeffs r)
number _nlMult_aNoImm_OR_bNoImm(number a, number b)
number nlShort1(number x)
number nlNormalizeHelper(number a, number b, const coeffs r)
number ndCopyMap(number a, const coeffs aRing, const coeffs r)
static FORCE_INLINE BOOLEAN nCoeff_is_long_R(const coeffs r)
LINLINE void nlInpAdd(number &a, number b, const coeffs r)
number nlGetDenom(number &n, const coeffs r)
void nlWrite(number a, const coeffs r)
int nlSize(number a, const coeffs)
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_R(const coeffs r)
#define omCheckIf(cond, test)
#define omFreeSize(addr, size)
LINLINE number nlAdd(number la, number li, const coeffs r)
void nlInpGcd(number &a, number b, const coeffs r)
BOOLEAN nlIsMOne(number a, const coeffs r)
static FORCE_INLINE BOOLEAN nCoeff_is_Ring_2toM(const coeffs r)
(), see rinteger.h, new impl.
void nlCoeffWrite(const coeffs r, BOOLEAN details)
number nlIntDiv(number a, number b, const coeffs r)
static FORCE_INLINE int n_GetChar(const coeffs r)
Return the characteristic of the coeff. domain.
number nlGcd(number a, number b, const coeffs r)
coeffs nlQuot1(number c, const coeffs r)
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)
void WerrorS(const char *s)
void s_readmpz_base(s_buff F, mpz_ptr a, int base)
CanonicalForm make_cf(const mpz_ptr n)
void nlGMP(number &i, number n, const coeffs r)
number nlIntMod(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 ...
BOOLEAN nlInitChar(coeffs r, void *p)
BOOLEAN nlGreater(number a, number b, const coeffs r)
LINLINE number nl_Copy(number a, const coeffs r)
static number nlInitMPZ(mpz_t m, const coeffs)
real floating point (GMP) numbers
number nlMapZ(number from, const coeffs src, const coeffs dst)
LINLINE BOOLEAN nlIsOne(number a, const coeffs r)
virtual void Reset()=0
Sets the enumerator to its initial position: -1, which is before the first element in the collection...
single prescision (6,6) real numbers
static number nlLcm(number a, number b, const coeffs r)
static number nlMapP(number from, const coeffs src, const coeffs dst)
LINLINE number nlNeg(number za, const coeffs r)
number nlXExtGcd(number a, number b, number *s, number *t, number *u, number *v, const coeffs r)
float nrFloat(number n)
Converts a n_R number into a float. Needed by Maps.
Coefficient rings, fields and other domains suitable for Singular polynomials.
void s_readmpz(s_buff F, mpz_t a)
const CanonicalForm CFMap CFMap & N
number nlDiv(number a, number b, const coeffs r)
LINLINE number nlMult(number a, number b, const coeffs r)
number nlInvers(number a, const coeffs r)
number _nlCopy_NoImm(number a)
void _nlInpAdd_aNoImm_OR_bNoImm(number &a, number b)
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.
int nlDivComp(number a, number b, const coeffs r)
LINLINE void nlInpMult(number &a, number b, const coeffs r)
static void nlWriteFd(number n, FILE *f, const coeffs)
const ExtensionInfo & info
< [in] sqrfree poly
number(* nMapFunc)(number a, const coeffs src, const coeffs dst)
maps "a", which lives in src, into dst
void _nlDelete_NoImm(number *a)
number nlModP(number q, const coeffs Q, const coeffs Zp)
virtual reference Current()=0
Gets the current element in the collection (read and write).
static number nlMapLongR(number from, const coeffs src, const coeffs dst)
number nlCopyMap(number a, const coeffs src, const coeffs dst)
static const int SW_RATIONAL
set to 1 for computations over Q
const char *const nDivBy0
LINLINE BOOLEAN nlEqual(number a, number b, const coeffs r)
void nlPower(number x, int exp, number *lu, const coeffs r)
void PrintS(const char *s)
number nlQuotRem(number a, number b, number *r, const coeffs R)
static number nlReadFd(s_buff f, const coeffs)
void nlInpIntDiv(number &a, number b, const coeffs r)
number nlExtGcd(number a, number b, number *s, number *t, const coeffs)
LINLINE BOOLEAN nlIsZero(number za, const coeffs r)
(mpz_ptr), see rmodulon,h
static void nlNormalize_Gcd(number &x)
BOOLEAN _nlEqual_aNoImm_OR_bNoImm(number a, number b)
number nlShort3_noinline(number x)
static void nlClearContent(ICoeffsEnumerator &numberCollectionEnumerator, number &c, const coeffs cf)
static CanonicalForm nlConvSingNFactoryN(number n, const BOOLEAN setChar, const coeffs)
static FORCE_INLINE n_coeffType getCoeffType(const coeffs r)
Returns the type of coeffs domain.
number nlChineseRemainder(number *x, number *q, int rl, const coeffs C)
number nlBigInt(number &n)
void chineseRemainderCached(CFArray &a, CFArray &n, CanonicalForm &xnew, CanonicalForm &prod, CFArray &inv)
void gmp_numerator(const CanonicalForm &f, mpz_ptr result)
void nlNormalize(number &x, 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 nlChineseRemainderSym(number *x, number *q, int rl, BOOLEAN sym, CFArray &inv_cache, const coeffs CF)
const Variable & v
< [in] a sqrfree bivariate poly
number _nlNeg_NoImm(number a)
static number nlShort3(number x)
static number nlRandom(siRandProc p, number v2, number, const coeffs cf)
REvaluation E(1, terms.length(), IntRandom(25))
LINLINE void nlDelete(number *a, const coeffs r)
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...
BOOLEAN nlDivBy(number a, number b, const coeffs)
virtual bool MoveNext()=0
Advances the enumerator to the next element of the collection. returns true if the enumerator was suc...
BOOLEAN nlIsUnit(number a, const coeffs)
long nlInt(number &n, const coeffs r)
number _nlMult_aImm_bImm_rNoImm(number a, number b)
nMapFunc nlSetMap(const coeffs src, const coeffs dst)
number _nlAdd_aNoImm_OR_bNoImm(number a, number b)
#define GCD_NORM_COND(OLD, NEW)
long s_readlong(s_buff F)
number nlExactDiv(number a, number b, const coeffs r)
number _nlSub_aNoImm_OR_bNoImm(number a, number b)
number nlMapGMP(number from, const coeffs src, const coeffs dst)
BOOLEAN nlDBTest(number a, const char *f, const int l)
LINLINE number nlInit(long i, const coeffs r)
static char * nlCoeffString(const coeffs r)
static FORCE_INLINE void n_Delete(number *p, const coeffs r)
delete 'p'
number nlMapMachineInt(number from, const coeffs, const coeffs)
static number nlMapR(number from, const coeffs src, const coeffs dst)
number nlGetNumerator(number &n, const coeffs r)
LINLINE number nlCopy(number a, const coeffs r)
void Werror(const char *fmt,...)
const CanonicalForm const CanonicalForm const CanonicalForm const CanonicalForm & cand
number nlFarey(number nN, number nP, const coeffs CF)
void gmp_denominator(const CanonicalForm &f, mpz_ptr result)
coeffs nInitChar(n_coeffType t, void *parameter)
one-time initialisations for new coeffs in case of an error return NULL