rmodulon.cc File Reference

#include "misc/auxiliary.h"
#include "misc/mylimits.h"
#include "misc/prime.h"
#include "reporter/reporter.h"
#include "coeffs/si_gmp.h"
#include "coeffs/coeffs.h"
#include "coeffs/modulop.h"
#include "coeffs/rintegers.h"
#include "coeffs/numbers.h"
#include "coeffs/mpr_complex.h"
#include "coeffs/longrat.h"
#include "coeffs/rmodulon.h"
#include <string.h>

Go to the source code of this file.

Macros
#define	nrnDelete   nrzDelete
#define	nrnSize   nrzSize

Functions
void	nrnWrite (number a, const coeffs)
static BOOLEAN	nrnDBTest (number a, const char *f, const int l, const coeffs r)
coeffs	nrnInitCfByName (char *s, n_coeffType)
static char *	nrnCoeffName (const coeffs r)
static BOOLEAN	nrnCoeffIsEqual (const coeffs r, n_coeffType n, void *parameter)
static void	nrnKillChar (coeffs r)
static coeffs	nrnQuot1 (number c, const coeffs r)
static number	nrnCopy (number a, const coeffs)
static number	nrnInit (long i, const coeffs r)
static long	nrnInt (number &n, const coeffs)
static number	nrnMult (number a, number b, const coeffs r)
static void	nrnInpMult (number &a, number b, const coeffs r)
static void	nrnPower (number a, int i, number *result, const coeffs r)
static number	nrnAdd (number a, number b, const coeffs r)
static void	nrnInpAdd (number &a, number b, const coeffs r)
static number	nrnSub (number a, number b, const coeffs r)
static BOOLEAN	nrnIsZero (number a, const coeffs)
static number	nrnNeg (number c, const coeffs r)
static number	nrnInvers (number c, const coeffs r)
static number	nrnGcd (number a, number b, const coeffs r)
static number	nrnLcm (number a, number b, const coeffs r)
static number	nrnExtGcd (number a, number b, number *s, number *t, const coeffs r)
static BOOLEAN	nrnIsOne (number a, const coeffs)
static BOOLEAN	nrnEqual (number a, number b, const coeffs)
static number	nrnGetUnit (number k, const coeffs r)
static number	nrnXExtGcd (number a, number b, number *s, number *t, number *u, number *v, const coeffs r)
static BOOLEAN	nrnIsMOne (number a, const coeffs r)
static BOOLEAN	nrnGreater (number a, number b, const coeffs)
static BOOLEAN	nrnGreaterZero (number k, const coeffs cf)
static BOOLEAN	nrnIsUnit (number a, const coeffs r)
static number	nrnAnn (number k, const coeffs r)
static BOOLEAN	nrnDivBy (number a, number b, const coeffs r)
static int	nrnDivComp (number a, number b, const coeffs r)
static number	nrnDiv (number a, number b, const coeffs r)
static number	nrnMod (number a, number b, const coeffs r)
static number	nrnQuotRem (number a, number b, number *rem, const coeffs r)
static number	nrnMapModN (number from, const coeffs, const coeffs dst)
static number	nrnMap2toM (number from, const coeffs, const coeffs dst)
static number	nrnMapZp (number from, const coeffs, const coeffs dst)
number	nrnMapGMP (number from, const coeffs, const coeffs dst)
static number	nrnMapQ (number from, const coeffs src, const coeffs dst)
static number	nrnMapZ (number from, const coeffs src, const coeffs dst)
nMapFunc	nrnSetMap (const coeffs src, const coeffs dst)
static number	nrnInitMPZ (mpz_t m, const coeffs r)
static void	nrnMPZ (mpz_t m, number &n, const coeffs)
static void	nrnSetExp (unsigned long m, coeffs r)
static void	nrnInitExp (unsigned long m, coeffs r)
static const char *	nlCPEatLongC (char *s, mpz_ptr i)
static const char *	nrnRead (const char *s, number *a, const coeffs r)
static number	nrnConvFactoryNSingN (const CanonicalForm n, const coeffs r)
static CanonicalForm	nrnConvSingNFactoryN (number n, BOOLEAN setChar, const coeffs r)
BOOLEAN	nrnInitChar (coeffs r, void *p)

Variables
EXTERN_VAR omBin	gmp_nrz_bin
STATIC_VAR char *	nrnCoeffName_buff =NULL
STATIC_VAR mpz_ptr	nrnMapCoef = NULL

Macro Definition Documentation

nrnDelete

#define nrnDelete   nrzDelete

Definition at line 175 of file rmodulon.cc.

nrnSize

#define nrnSize   nrzSize

Definition at line 176 of file rmodulon.cc.

Function Documentation

nlCPEatLongC()

const char * nlCPEatLongC ( char * s, mpz_ptr i )

static

Definition at line 937 of file rmodulon.cc.

{
  const char * start=s;
  if (!(*s >= '0' && *s <= '9'))
  {
    mpz_init_set_ui(i, 1);
    return s;
  }
  mpz_init(i);
  while (*s >= '0' && *s <= '9') s++;
  if (*s=='\0')
  {
    mpz_set_str(i,start,10);
  }
  else
  {
    char c=*s;
    *s='\0';
    mpz_set_str(i,start,10);
    *s=c;
  }
  return s;
}

nrnAdd()

number nrnAdd ( number a, number b, const coeffs r )

static

Definition at line 218 of file rmodulon.cc.

{
  mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin);
  mpz_init(erg);
  mpz_add(erg, (mpz_ptr)a, (mpz_ptr) b);
  mpz_mod(erg, erg, r->modNumber);
  return (number) erg;
}

nrnAnn()

number nrnAnn ( number k, const coeffs r )

static

Definition at line 553 of file rmodulon.cc.

{
  mpz_ptr tmp = (mpz_ptr) omAllocBin(gmp_nrz_bin);
  mpz_init(tmp);
  mpz_gcd(tmp, (mpz_ptr) k, r->modNumber);
  if (mpz_cmp_si(tmp, 1)==0)
  {
    mpz_set_ui(tmp, 0);
    return (number) tmp;
  }
  mpz_divexact(tmp, r->modNumber, tmp);
  return (number) tmp;
}

nrnCoeffIsEqual()

BOOLEAN nrnCoeffIsEqual ( const coeffs r, n_coeffType n, void * parameter )

static

Definition at line 84 of file rmodulon.cc.

{
  /* test, if r is an instance of nInitCoeffs(n,parameter) */
  ZnmInfo *info=(ZnmInfo*)parameter;
  return (n==r->type) && (r->modExponent==info->exp)
  && (mpz_cmp(r->modBase,info->base)==0);
}

nrnCoeffName()

char * nrnCoeffName ( const coeffs r )

static

Definition at line 64 of file rmodulon.cc.

{
  if(nrnCoeffName_buff!=NULL) omFree(nrnCoeffName_buff);
  size_t l = (size_t)mpz_sizeinbase(r->modBase, 10) + 2;
  char* s = (char*) omAlloc(l);
  l+=24;
  nrnCoeffName_buff=(char*)omAlloc(l);
  s= mpz_get_str (s, 10, r->modBase);
  int ll=0;
  if (nCoeff_is_Zn(r)||nCoeff_is_Zp_long(r))
  {
      ll=snprintf(nrnCoeffName_buff,l,"ZZ/bigint(%s)",s);
  }
  else if (nCoeff_is_Ring_PtoM(r))
    ll=snprintf(nrnCoeffName_buff,l,"ZZ/(bigint(%s)^%lu)",s,r->modExponent);
  assume(ll<(int)l); // otherwise nrnCoeffName_buff too small
  omFreeSize((ADDRESS)s, l-22);
  return nrnCoeffName_buff;
}

nrnConvFactoryNSingN()

number nrnConvFactoryNSingN ( const CanonicalForm n, const coeffs r )

static

Definition at line 987 of file rmodulon.cc.

{
  return nrnInit(n.intval(),r);
}

nrnConvSingNFactoryN()

CanonicalForm nrnConvSingNFactoryN ( number n, BOOLEAN setChar, const coeffs r )

static

Definition at line 992 of file rmodulon.cc.

{
  if (setChar) setCharacteristic( r->ch );
   return CanonicalForm(nrnInt( n,r ));
}

nrnCopy()

number nrnCopy ( number a, const coeffs  )

static

Definition at line 148 of file rmodulon.cc.

{
  mpz_ptr erg = (mpz_ptr) omAllocBin(gmp_nrz_bin);
  mpz_init_set(erg, (mpz_ptr) a);
  return (number) erg;
}

nrnDBTest()

BOOLEAN nrnDBTest ( number a, const char * f, const int l, const coeffs r )

static

Definition at line 923 of file rmodulon.cc.

{
  if ( (mpz_sgn1((mpz_ptr) a) < 0) || (mpz_cmp((mpz_ptr) a, r->modNumber) > 0) )
  {
    Warn("mod-n: out of range at %s:%d\n",f,l);
    return FALSE;
  }
  return TRUE;
}

nrnDiv()

number nrnDiv ( number a, number b, const coeffs r )

static

Definition at line 589 of file rmodulon.cc.

{
  if (nrnIsZero(b,r))
  {
    WerrorS(nDivBy0);
    return nrnInit(0,r);
  }
  else if (r->is_field)
  {
    number inv=nrnInvers(b,r);
    number erg=nrnMult(a,inv,r);
    nrnDelete(&inv,r);
    return erg;
  }
  mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin);
  mpz_init(erg);
  if (mpz_divisible_p((mpz_ptr)a, (mpz_ptr)b))
  {
    mpz_divexact(erg, (mpz_ptr)a, (mpz_ptr)b);
    return (number)erg;
  }
  else
  {
    mpz_ptr gcd = (mpz_ptr)nrnGcd(a, b, r);
    mpz_divexact(erg, (mpz_ptr)b, gcd);
    if (!nrnIsUnit((number)erg, r))
    {
      WerrorS("Division not possible, even by cancelling zero divisors.");
      nrnDelete((number*) &gcd, r);
      nrnDelete((number*) &erg, r);
      return (number)NULL;
    }
    // a / gcd(a,b) * [b / gcd (a,b)]^(-1)
    mpz_ptr tmp = (mpz_ptr)nrnInvers((number) erg,r);
    mpz_divexact(erg, (mpz_ptr)a, gcd);
    mpz_mul(erg, erg, tmp);
    nrnDelete((number*) &gcd, r);
    nrnDelete((number*) &tmp, r);
    mpz_mod(erg, erg, r->modNumber);
    return (number)erg;
  }
}

nrnDivBy()

BOOLEAN nrnDivBy ( number a, number b, const coeffs r )

static

Definition at line 567 of file rmodulon.cc.

{
  if(r->is_field)
  {
    return !nrnIsZero(b,r);
  }
  /* b divides a iff b/gcd(a, b) is a unit in the given ring: */
  number n = nrnGcd(a, b, r);
  mpz_tdiv_q((mpz_ptr)n, (mpz_ptr)b, (mpz_ptr)n);
  bool result = nrnIsUnit(n, r);
  nrnDelete(&n, NULL);
  return result;
}

nrnDivComp()

int nrnDivComp ( number a, number b, const coeffs r )

static

Definition at line 581 of file rmodulon.cc.

{
  if (nrnEqual(a, b,r)) return 2;
  if (mpz_divisible_p((mpz_ptr) a, (mpz_ptr) b)) return -1;
  if (mpz_divisible_p((mpz_ptr) b, (mpz_ptr) a)) return 1;
  return 0;
}

nrnEqual()

BOOLEAN nrnEqual ( number a, number b, const coeffs  )

static

Definition at line 352 of file rmodulon.cc.

{
  return 0 == mpz_cmp((mpz_ptr)a, (mpz_ptr)b);
}

nrnExtGcd()

number nrnExtGcd ( number a, number b, number * s, number * t, const coeffs r )

static

Definition at line 331 of file rmodulon.cc.

{
  mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin);
  mpz_ptr bs  = (mpz_ptr)omAllocBin(gmp_nrz_bin);
  mpz_ptr bt  = (mpz_ptr)omAllocBin(gmp_nrz_bin);
  mpz_init(erg);
  mpz_init(bs);
  mpz_init(bt);
  mpz_gcdext(erg, bs, bt, (mpz_ptr)a, (mpz_ptr)b);
  mpz_mod(bs, bs, r->modNumber);
  mpz_mod(bt, bt, r->modNumber);
  *s = (number)bs;
  *t = (number)bt;
  return (number)erg;
}

nrnGcd()

number nrnGcd ( number a, number b, const coeffs r )

static

Definition at line 275 of file rmodulon.cc.

{
  if(!(nrnIsZero(a,r) && nrnIsZero(b,r)) && r->is_field )
  {
    return nrnInit(1,r);
  }
  mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin);
  mpz_init_set(erg, r->modNumber);
  if (a != NULL) mpz_gcd(erg, erg, (mpz_ptr)a);
  mpz_gcd(erg, erg, (mpz_ptr)b);
  if(mpz_cmp(erg,r->modNumber)==0)
  {
    mpz_clear(erg);
    omFreeBin((ADDRESS)erg,gmp_nrz_bin);
    return nrnInit(0,r);
  }
  return (number)erg;
}

nrnGetUnit()

number nrnGetUnit ( number k, const coeffs r )

static

Definition at line 357 of file rmodulon.cc.

{
  if (mpz_divisible_p(r->modNumber, (mpz_ptr)k)) return nrnInit(1,r);
 
  mpz_ptr unit = (mpz_ptr)nrnGcd(NULL, k, r);
  mpz_tdiv_q(unit, (mpz_ptr)k, unit);
  mpz_ptr gcd = (mpz_ptr)nrnGcd(NULL, (number)unit, r);
  if (!nrnIsOne((number)gcd,r))
  {
    mpz_ptr ctmp;
    // tmp := unit^2
    mpz_ptr tmp = (mpz_ptr) nrnMult((number) unit,(number) unit,r);
    // gcd_new := gcd(tmp, 0)
    mpz_ptr gcd_new = (mpz_ptr) nrnGcd(NULL, (number) tmp, r);
    while (!nrnEqual((number) gcd_new,(number) gcd,r))
    {
      // gcd := gcd_new
      ctmp = gcd;
      gcd = gcd_new;
      gcd_new = ctmp;
      // tmp := tmp * unit
      mpz_mul(tmp, tmp, unit);
      mpz_mod(tmp, tmp, r->modNumber);
      // gcd_new := gcd(tmp, 0)
      mpz_gcd(gcd_new, tmp, r->modNumber);
    }
    // unit := unit + modNumber / gcd_new
    mpz_tdiv_q(tmp, r->modNumber, gcd_new);
    mpz_add(unit, unit, tmp);
    mpz_mod(unit, unit, r->modNumber);
    nrnDelete((number*) &gcd_new, r);
    nrnDelete((number*) &tmp, r);
  }
  nrnDelete((number*) &gcd, r);
  return (number)unit;
}

nrnGreater()

BOOLEAN nrnGreater ( number a, number b, const coeffs  )

static

Definition at line 504 of file rmodulon.cc.

{
  return 0 < mpz_cmp((mpz_ptr)a, (mpz_ptr)b);
}

nrnGreaterZero()

BOOLEAN nrnGreaterZero ( number k, const coeffs cf )

static

Definition at line 509 of file rmodulon.cc.

{
  if (cf->is_field)
  {
    if (mpz_cmp_ui(cf->modBase,2)==0)
    {
      return TRUE;
    }
    #if 0
    mpz_t ch2; mpz_init_set(ch2, cf->modBase);
    mpz_sub_ui(ch2,ch2,1); //cf->modBase is odd
    mpz_divexact_ui(ch2,ch2,2);
    if (mpz_cmp(ch2,(mpz_ptr)k)<0)
    {
      mpz_clear(ch2);
      return FALSE;
    }
    mpz_clear(ch2);
    #endif
  }
  #if 0
  else
  {
    mpz_t ch2; mpz_init_set(ch2, cf->modBase);
    mpz_tdiv_q_ui(ch2,ch2,2);
    if (mpz_cmp(ch2,(mpz_ptr)k)<0)
    {
      mpz_clear(ch2);
      return FALSE;
    }
    mpz_clear(ch2);
  }
  #endif
  return 0 < mpz_sgn1((mpz_ptr)k);
}

nrnInit()

number nrnInit ( long i, const coeffs r )

static

Definition at line 158 of file rmodulon.cc.

{
  mpz_ptr erg = (mpz_ptr) omAllocBin(gmp_nrz_bin);
  mpz_init_set_si(erg, i);
  mpz_mod(erg, erg, r->modNumber);
  return (number) erg;
}

nrnInitCfByName()

coeffs nrnInitCfByName	(	char *	s,
		n_coeffType	n )

Definition at line 33 of file rmodulon.cc.

{
  const char start[]="ZZ/bigint(";
  const int start_len=strlen(start);
  if (strncmp(s,start,start_len)==0)
  {
    s+=start_len;
    mpz_t z;
    mpz_init(z);
    s=nEatLong(s,z);
    ZnmInfo info;
    info.base=z;
    info.exp= 1;
    while ((*s!='\0') && (*s!=')')) s++;
    // expect ")" or ")^exp"
    if (*s=='\0') { mpz_clear(z); return NULL; }
    if (((*s)==')') && (*(s+1)=='^'))
    {
      s=s+2;
      int i;
      s=nEati(s,&i,0);
      info.exp=(unsigned long)i;
      return nInitChar(n_Znm,(void*) &info);
    }
    else
      return nInitChar(n_Zn,(void*) &info);
  }
  else return NULL;
}

nrnInitChar()

BOOLEAN nrnInitChar	(	coeffs	r,
		void *	p )

Definition at line 999 of file rmodulon.cc.

{
  assume( (getCoeffType(r) == n_Zn) || (getCoeffType (r) == n_Znm) );
  ZnmInfo * info= (ZnmInfo *) p;
  r->modBase= (mpz_ptr)nrnCopy((number)info->base, r); //this circumvents the problem
  //in bigintmat.cc where we cannot create a "legal" nrn that can be freed.
  //If we take a copy, we can do whatever we want.
 
  if (info->exp==1) r->type=n_Zn;
 
  nrnInitExp (info->exp, r);
 
  /* next computation may yield wrong characteristic as r->modNumber
     is a GMP number */
  r->ch = mpz_get_ui(r->modNumber);
 
  r->is_field=FALSE;
  r->is_domain=FALSE;
  if(r->modExponent==1)
  {
    if (mpz_probab_prime_p(r->modNumber,15)>0)
    {
      r->is_field=TRUE;
      r->is_domain=TRUE;
    }
  }
  r->rep=n_rep_gmp;
 
  r->cfInit        = nrnInit;
  r->cfDelete      = nrnDelete;
  r->cfCopy        = nrnCopy;
  r->cfSize        = nrnSize;
  r->cfInt         = nrnInt;
  r->cfAdd         = nrnAdd;
  r->cfInpAdd      = nrnInpAdd;
  r->cfSub         = nrnSub;
  r->cfMult        = nrnMult;
  r->cfInpMult     = nrnInpMult;
  r->cfDiv         = nrnDiv;
  r->cfAnn         = nrnAnn;
  r->cfIntMod      = nrnMod;
  r->cfExactDiv    = nrnDiv;
  r->cfInpNeg      = nrnNeg;
  r->cfInvers      = nrnInvers;
  r->cfDivBy       = nrnDivBy;
  r->cfDivComp     = nrnDivComp;
  r->cfGreater     = nrnGreater;
  r->cfEqual       = nrnEqual;
  r->cfIsZero      = nrnIsZero;
  r->cfIsOne       = nrnIsOne;
  r->cfIsMOne      = nrnIsMOne;
  r->cfGreaterZero = nrnGreaterZero;
  r->cfWriteLong   = nrnWrite;
  r->cfRead        = nrnRead;
  r->cfPower       = nrnPower;
  r->cfSetMap      = nrnSetMap;
  //r->cfNormalize   = ndNormalize;
  r->cfLcm         = nrnLcm;
  r->cfGcd         = nrnGcd;
  r->cfIsUnit      = nrnIsUnit;
  r->cfGetUnit     = nrnGetUnit;
  r->cfExtGcd      = nrnExtGcd;
  r->cfXExtGcd     = nrnXExtGcd;
  r->cfQuotRem     = nrnQuotRem;
  r->cfCoeffName   = nrnCoeffName;
  r->nCoeffIsEqual = nrnCoeffIsEqual;
  r->cfKillChar    = nrnKillChar;
  r->cfQuot1       = nrnQuot1;
  r->cfInitMPZ     = nrnInitMPZ;
  r->cfMPZ         = nrnMPZ;
#if SI_INTEGER_VARIANT==2
  r->cfWriteFd     = nrzWriteFd;
  r->cfWriteFd_S   = nrzWriteFd_S;
  r->cfReadFd      = nrzReadFd;
  r->cfReadFd_S    = nrzReadFd_S;
#endif
 
#ifdef LDEBUG
  r->cfDBTest      = nrnDBTest;
#endif
  if ((r->modExponent==1)&&(mpz_size1(r->modBase)==1))
  {
    long p=mpz_get_si(r->modBase);
    if ((p<=FACTORY_MAX_PRIME)&&(p==IsPrime(p))) /*factory limit: <2^29*/
    {
      r->convFactoryNSingN=nrnConvFactoryNSingN;
      r->convSingNFactoryN=nrnConvSingNFactoryN;
    }
  }
  return FALSE;
}

nrnInitExp()

void nrnInitExp ( unsigned long m, coeffs r )

static

Definition at line 912 of file rmodulon.cc.

{
  nrnSetExp(m, r);
  assume (r->modNumber != NULL);
//CF: in general, the modulus is computed somewhere. I don't want to
//  check it's size before I construct the best ring.
//  if (mpz_cmp_ui(r->modNumber,2) <= 0)
//    WarnS("nrnInitExp failed (m in Z/m too small)");
}

nrnInitMPZ()

number nrnInitMPZ ( mpz_t m, const coeffs r )

static

Definition at line 883 of file rmodulon.cc.

{
  mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin);
  mpz_init_set(erg,m);
  mpz_mod(erg, erg, r->modNumber);
  return (number) erg;
}

nrnInpAdd()

void nrnInpAdd ( number & a, number b, const coeffs r )

static

Definition at line 227 of file rmodulon.cc.

{
  mpz_add((mpz_ptr)a, (mpz_ptr)a, (mpz_ptr) b);
  mpz_mod((mpz_ptr)a, (mpz_ptr)a, r->modNumber);
}

nrnInpMult()

void nrnInpMult ( number & a, number b, const coeffs r )

static

Definition at line 204 of file rmodulon.cc.

{
  mpz_mul((mpz_ptr)a, (mpz_ptr)a, (mpz_ptr) b);
  mpz_mod((mpz_ptr)a, (mpz_ptr)a, r->modNumber);
}

nrnInt()

long nrnInt ( number & n, const coeffs  )

static

Definition at line 169 of file rmodulon.cc.

{
  return mpz_get_si((mpz_ptr) n);
}

nrnInvers()

number nrnInvers ( number c, const coeffs r )

static

Definition at line 255 of file rmodulon.cc.

{
  mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin);
  mpz_init(erg);
  if (nrnIsZero(c,r))
  {
    WerrorS(nDivBy0);
  }
  else
  {
    mpz_invert(erg, (mpz_ptr)c, r->modNumber);
  }
  return (number) erg;
}

nrnIsMOne()

BOOLEAN nrnIsMOne ( number a, const coeffs r )

static

Definition at line 494 of file rmodulon.cc.

{
  if((r->ch==2) && (nrnIsOne(a,r))) return FALSE;
  mpz_t t; mpz_init_set(t, (mpz_ptr)a);
  mpz_add_ui(t, t, 1);
  bool erg = (0 == mpz_cmp(t, r->modNumber));
  mpz_clear(t);
  return erg;
}

nrnIsOne()

BOOLEAN nrnIsOne ( number a, const coeffs  )

static

Definition at line 347 of file rmodulon.cc.

{
  return 0 == mpz_cmp_si((mpz_ptr)a, 1);
}

nrnIsUnit()

BOOLEAN nrnIsUnit ( number a, const coeffs r )

static

Definition at line 545 of file rmodulon.cc.

{
  number tmp = nrnGcd(a, (number)r->modNumber, r);
  bool res = nrnIsOne(tmp, r);
  nrnDelete(&tmp, r);
  return res;
}

nrnIsZero()

BOOLEAN nrnIsZero ( number a, const coeffs  )

static

Definition at line 242 of file rmodulon.cc.

{
  return 0 == mpz_sgn1((mpz_ptr)a);
}

nrnKillChar()

void nrnKillChar ( coeffs r )

static

Definition at line 92 of file rmodulon.cc.

{
  mpz_clear(r->modNumber);
  mpz_clear(r->modBase);
  omFreeBin((void *) r->modBase, gmp_nrz_bin);
  omFreeBin((void *) r->modNumber, gmp_nrz_bin);
}

nrnLcm()

number nrnLcm ( number a, number b, const coeffs r )

static

Definition at line 298 of file rmodulon.cc.

{
  number erg = nrnGcd(NULL, a, r);
  number tmp = nrnGcd(NULL, b, r);
  mpz_lcm((mpz_ptr)erg, (mpz_ptr)erg, (mpz_ptr)tmp);
  nrnDelete(&tmp, r);
  return (number)erg;
}

nrnMap2toM()

number nrnMap2toM ( number from, const coeffs , const coeffs dst )

static

Definition at line 722 of file rmodulon.cc.

{
  mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin);
  mpz_init(erg);
  mpz_mul_ui(erg, nrnMapCoef, (unsigned long)from);
  mpz_mod(erg, erg, dst->modNumber);
  return (number)erg;
}

nrnMapGMP()

number nrnMapGMP	(	number	from,
		const coeffs	,
		const coeffs	dst )

Definition at line 741 of file rmodulon.cc.

{
  mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin);
  mpz_init(erg);
  mpz_mod(erg, (mpz_ptr)from, dst->modNumber);
  return (number)erg;
}

nrnMapModN()

number nrnMapModN ( number from, const coeffs , const coeffs dst )

static

Definition at line 717 of file rmodulon.cc.

{
  return nrnMult(from, (number) nrnMapCoef, dst);
}

nrnMapQ()

number nrnMapQ ( number from, const coeffs src, const coeffs dst )

static

Definition at line 749 of file rmodulon.cc.

{
  mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin);
  nlMPZ(erg, from, src);
  mpz_mod(erg, erg, dst->modNumber);
  return (number)erg;
}

nrnMapZ()

number nrnMapZ ( number from, const coeffs src, const coeffs dst )

static

Definition at line 770 of file rmodulon.cc.

{
  if (SR_HDL(from) & SR_INT)
  {
    long f_i=SR_TO_INT(from);
    return nrnInit(f_i,dst);
  }
  return nrnMapGMP(from,src,dst);
}

nrnMapZp()

number nrnMapZp ( number from, const coeffs , const coeffs dst )

static

Definition at line 731 of file rmodulon.cc.

{
  mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin);
  mpz_init(erg);
  // TODO: use npInt(...)
  mpz_mul_si(erg, nrnMapCoef, (unsigned long)from);
  mpz_mod(erg, erg, dst->modNumber);
  return (number)erg;
}

nrnMod()

number nrnMod ( number a, number b, const coeffs r )

static

Definition at line 632 of file rmodulon.cc.

{
  /*
    We need to return the number rr which is uniquely determined by the
    following two properties:
      (1) 0 <= rr < |b| (with respect to '<' and '<=' performed in Z x Z)
      (2) There exists some k in the integers Z such that a = k * b + rr.
    Consider g := gcd(n, |b|). Note that then |b|/g is a unit in Z/n.
    Now, there are three cases:
      (a) g = 1
          Then |b| is a unit in Z/n, i.e. |b| (and also b) divides a.
          Thus rr = 0.
      (b) g <> 1 and g divides a
          Then a = (a/g) * (|b|/g)^(-1) * b (up to sign), i.e. again rr = 0.
      (c) g <> 1 and g does not divide a
          Then denote the division with remainder of a by g as this:
          a = s * g + t. Then t = a - s * g = a - s * (|b|/g)^(-1) * |b|
          fulfills (1) and (2), i.e. rr := t is the correct result. Hence
          in this third case, rr is the remainder of division of a by g in Z.
     Remark: according to mpz_mod: a,b are always non-negative
  */
  mpz_ptr g = (mpz_ptr)omAllocBin(gmp_nrz_bin);
  mpz_ptr rr = (mpz_ptr)omAllocBin(gmp_nrz_bin);
  mpz_init(g);
  mpz_init_set_ui(rr, 0);
  mpz_gcd(g, (mpz_ptr)r->modNumber, (mpz_ptr)b); // g is now as above
  if (mpz_cmp_si(g, 1L) != 0) mpz_mod(rr, (mpz_ptr)a, g); // the case g <> 1
  mpz_clear(g);
  omFreeBin(g, gmp_nrz_bin);
  return (number)rr;
}

nrnMPZ()

void nrnMPZ ( mpz_t m, number & n, const coeffs  )

static

Definition at line 891 of file rmodulon.cc.

{
  mpz_init_set(m, (mpz_ptr)n);
}

nrnMult()

number nrnMult ( number a, number b, const coeffs r )

static

Definition at line 195 of file rmodulon.cc.

{
  mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin);
  mpz_init(erg);
  mpz_mul(erg, (mpz_ptr)a, (mpz_ptr) b);
  mpz_mod(erg, erg, r->modNumber);
  return (number) erg;
}

nrnNeg()

number nrnNeg ( number c, const coeffs r )

static

Definition at line 247 of file rmodulon.cc.

{
  if( !nrnIsZero(c, r) )
    // Attention: This method operates in-place.
    mpz_sub((mpz_ptr)c, r->modNumber, (mpz_ptr)c);
  return c;
}

nrnPower()

void nrnPower ( number a, int i, number * result, const coeffs r )

static

Definition at line 210 of file rmodulon.cc.

{
  mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin);
  mpz_init(erg);
  mpz_powm_ui(erg, (mpz_ptr)a, i, r->modNumber);
  *result = (number) erg;
}

nrnQuot1()

coeffs nrnQuot1 ( number c, const coeffs r )

static

Definition at line 100 of file rmodulon.cc.

{
    coeffs rr;
    long ch = r->cfInt(c, r);
    mpz_t a,b;
    mpz_init_set(a, r->modNumber);
    mpz_init_set_ui(b, ch);
    mpz_t gcd;
    mpz_init(gcd);
    mpz_gcd(gcd, a,b);
    if(mpz_cmp_ui(gcd, 1) == 0)
    {
      WerrorS("constant in q-ideal is coprime to modulus in ground ring");
      WerrorS("Unable to create qring!");
      return NULL;
    }
    if(r->modExponent == 1)
    {
      ZnmInfo info;
      info.base = gcd;
      info.exp = (unsigned long) 1;
      rr = nInitChar(n_Zn, (void*)&info);
    }
    else
    {
      ZnmInfo info;
      info.base = r->modBase;
      int kNew = 1;
      mpz_t baseTokNew;
      mpz_init(baseTokNew);
      mpz_set(baseTokNew, r->modBase);
      while(mpz_cmp(gcd, baseTokNew) > 0)
      {
        kNew++;
        mpz_mul(baseTokNew, baseTokNew, r->modBase);
      }
      //printf("\nkNew = %i\n",kNew);
      info.exp = kNew;
      mpz_clear(baseTokNew);
      if (kNew==1)
        rr = nInitChar(n_Zn, (void*)&info);
      else
        rr = nInitChar(n_Znm, (void*)&info);
    }
    mpz_clear(gcd);
    return(rr);
}

nrnQuotRem()

number nrnQuotRem ( number a, number b, number * rem, const coeffs r )

static

Definition at line 679 of file rmodulon.cc.

{
  mpz_t g, aa, bb;
  mpz_ptr qq = (mpz_ptr)omAllocBin(gmp_nrz_bin);
  mpz_ptr rr = (mpz_ptr)omAllocBin(gmp_nrz_bin);
  mpz_init(qq);
  mpz_init(rr);
  mpz_init(g);
  mpz_init_set(aa, (mpz_ptr)a);
  mpz_init_set(bb, (mpz_ptr)b);
 
  mpz_gcd(g, bb, r->modNumber);
  mpz_mod(rr, aa, g);
  mpz_sub(aa, aa, rr);
  mpz_gcd(g, aa, g);
  mpz_div(aa, aa, g);
  mpz_div(bb, bb, g);
  mpz_div(g, r->modNumber, g);
  mpz_invert(g, bb, g);
  mpz_mul(qq, aa, g);
  if (rem)
    *rem = (number)rr;
  else {
    mpz_clear(rr);
    omFreeBin(rr, gmp_nrz_bin);
  }
  mpz_clear(g);
  mpz_clear(aa);
  mpz_clear(bb);
  return (number) qq;
}

nrnRead()

const char * nrnRead ( const char * s, number * a, const coeffs r )

static

Definition at line 961 of file rmodulon.cc.

{
  mpz_ptr z = (mpz_ptr) omAllocBin(gmp_nrz_bin);
  {
    s = nlCPEatLongC((char *)s, z);
  }
  mpz_mod(z, z, r->modNumber);
  if ((*s)=='/')
  {
    mpz_ptr n = (mpz_ptr) omAllocBin(gmp_nrz_bin);
    s++;
    s=nlCPEatLongC((char*)s,n);
    if (!nrnIsOne((number)n,r))
    {
      *a=nrnDiv((number)z,(number)n,r);
      mpz_clear(z);
      omFreeBin((void *)z, gmp_nrz_bin);
      mpz_clear(n);
      omFreeBin((void *)n, gmp_nrz_bin);
    }
  }
  else
    *a = (number) z;
  return s;
}

nrnSetExp()

void nrnSetExp ( unsigned long m, coeffs r )

static

Definition at line 900 of file rmodulon.cc.

{
  /* clean up former stuff */
  if (r->modNumber != NULL) mpz_clear(r->modNumber);
 
  r->modExponent= m;
  r->modNumber = (mpz_ptr)omAllocBin(gmp_nrz_bin);
  mpz_init_set (r->modNumber, r->modBase);
  mpz_pow_ui (r->modNumber, r->modNumber, m);
}

nrnSetMap()

nMapFunc nrnSetMap	(	const coeffs	src,
		const coeffs	dst )

Definition at line 802 of file rmodulon.cc.

{
  /* dst = nrn */
  if ((src->rep==n_rep_gmp) && nCoeff_is_Z(src))
  {
    return nrnMapZ;
  }
  if ((src->rep==n_rep_gap_gmp) /*&& nCoeff_is_Z(src)*/)
  {
    return nrnMapZ;
  }
  if (src->rep==n_rep_gap_rat) /*&& nCoeff_is_Q(src)) or Z*/
  {
    return nrnMapQ;
  }
  // Some type of Z/n ring / field
  if (nCoeff_is_Zn(src) || nCoeff_is_Ring_PtoM(src) ||
      nCoeff_is_Ring_2toM(src) || nCoeff_is_Zp(src))
  {
    if (   (!nCoeff_is_Zp(src))
        && (mpz_cmp(src->modBase, dst->modBase) == 0)
        && (src->modExponent == dst->modExponent)) return ndCopyMap;
    else
    {
      mpz_ptr nrnMapModul = (mpz_ptr) omAllocBin(gmp_nrz_bin);
      // Computing the n of Z/n
      if (nCoeff_is_Zp(src))
      {
        mpz_init_set_si(nrnMapModul, src->ch);
      }
      else
      {
        mpz_init(nrnMapModul);
        mpz_set(nrnMapModul, src->modNumber);
      }
      // nrnMapCoef = 1 in dst       if dst is a subring of src
      // nrnMapCoef = 0 in dst / src if src is a subring of dst
      if (nrnMapCoef == NULL)
      {
        nrnMapCoef = (mpz_ptr) omAllocBin(gmp_nrz_bin);
        mpz_init(nrnMapCoef);
      }
      if (mpz_divisible_p(nrnMapModul, dst->modNumber))
      {
        mpz_set_ui(nrnMapCoef, 1);
      }
      else
      if (mpz_divisible_p(dst->modNumber,nrnMapModul))
      {
        mpz_divexact(nrnMapCoef, dst->modNumber, nrnMapModul);
        mpz_ptr tmp = dst->modNumber;
        dst->modNumber = nrnMapModul;
        if (!nrnIsUnit((number) nrnMapCoef,dst))
        {
          dst->modNumber = tmp;
          nrnDelete((number*) &nrnMapModul, dst);
          return NULL;
        }
        mpz_ptr inv = (mpz_ptr) nrnInvers((number) nrnMapCoef,dst);
        dst->modNumber = tmp;
        mpz_mul(nrnMapCoef, nrnMapCoef, inv);
        mpz_mod(nrnMapCoef, nrnMapCoef, dst->modNumber);
        nrnDelete((number*) &inv, dst);
      }
      else
      {
        nrnDelete((number*) &nrnMapModul, dst);
        return NULL;
      }
      nrnDelete((number*) &nrnMapModul, dst);
      if (nCoeff_is_Ring_2toM(src))
        return nrnMap2toM;
      else if (nCoeff_is_Zp(src))
        return nrnMapZp;
      else
        return nrnMapModN;
    }
  }
  return NULL;      // default
}

nrnSub()

number nrnSub ( number a, number b, const coeffs r )

static

Definition at line 233 of file rmodulon.cc.

{
  mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin);
  mpz_init(erg);
  mpz_sub(erg, (mpz_ptr)a, (mpz_ptr) b);
  mpz_mod(erg, erg, r->modNumber);
  return (number) erg;
}

nrnWrite()

void nrnWrite	(	number	a,
		const coeffs	)

Definition at line 785 of file rmodulon.cc.

{
  char *s,*z;
  if (a==NULL)
  {
    StringAppendS("o");
  }
  else
  {
    int l=mpz_sizeinbase((mpz_ptr) a, 10) + 2;
    s=(char*)omAlloc(l);
    z=mpz_get_str(s,10,(mpz_ptr) a);
    StringAppendS(z);
    omFreeSize((ADDRESS)s,l);
  }
}

nrnXExtGcd()

number nrnXExtGcd ( number a, number b, number * s, number * t, number * u, number * v, const coeffs r )

static

Definition at line 403 of file rmodulon.cc.

{
  number xx;
#ifdef CF_DEB
  StringSetS("XExtGcd of ");
  nrnWrite(a, r);
  StringAppendS("\t");
  nrnWrite(b, r);
  StringAppendS(" modulo ");
  nrnWrite(xx = (number)r->modNumber, r);
  Print("%s\n", StringEndS());
#endif
 
  mpz_ptr one = (mpz_ptr)omAllocBin(gmp_nrz_bin);
  mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin);
  mpz_ptr bs  = (mpz_ptr)omAllocBin(gmp_nrz_bin);
  mpz_ptr bt  = (mpz_ptr)omAllocBin(gmp_nrz_bin);
  mpz_ptr bu  = (mpz_ptr)omAllocBin(gmp_nrz_bin);
  mpz_ptr bv  = (mpz_ptr)omAllocBin(gmp_nrz_bin);
  mpz_init(erg);
  mpz_init(one);
  mpz_init_set(bs, (mpz_ptr) a);
  mpz_init_set(bt, (mpz_ptr) b);
  mpz_init(bu);
  mpz_init(bv);
  mpz_gcd(erg, bs, bt);
 
#ifdef CF_DEB
  StringSetS("1st gcd:");
  nrnWrite(xx= (number)erg, r);
#endif
 
  mpz_gcd(erg, erg, r->modNumber);
 
  mpz_div(bs, bs, erg);
  mpz_div(bt, bt, erg);
 
#ifdef CF_DEB
  Print("%s\n", StringEndS());
  StringSetS("xgcd: ");
#endif
 
  mpz_gcdext(one, bu, bv, bs, bt);
  number ui = nrnGetUnit(xx = (number) one, r);
#ifdef CF_DEB
  n_Write(xx, r);
  StringAppendS("\t");
  n_Write(ui, r);
  Print("%s\n", StringEndS());
#endif
  nrnDelete(&xx, r);
  if (!nrnIsOne(ui, r))
  {
#ifdef CF_DEB
    PrintS("Scaling\n");
#endif
    number uii = nrnInvers(ui, r);
    nrnDelete(&ui, r);
    ui = uii;
    mpz_ptr uu = (mpz_ptr)omAllocBin(gmp_nrz_bin);
    mpz_init_set(uu, (mpz_ptr)ui);
    mpz_mul(bu, bu, uu);
    mpz_mul(bv, bv, uu);
    mpz_clear(uu);
    omFreeBin(uu, gmp_nrz_bin);
  }
  nrnDelete(&ui, r);
#ifdef CF_DEB
  StringSetS("xgcd");
  nrnWrite(xx= (number)bs, r);
  StringAppendS("*");
  nrnWrite(xx= (number)bu, r);
  StringAppendS(" + ");
  nrnWrite(xx= (number)bt, r);
  StringAppendS("*");
  nrnWrite(xx= (number)bv, r);
  Print("%s\n", StringEndS());
#endif
 
  mpz_mod(bs, bs, r->modNumber);
  mpz_mod(bt, bt, r->modNumber);
  mpz_mod(bu, bu, r->modNumber);
  mpz_mod(bv, bv, r->modNumber);
  *s = (number)bu;
  *t = (number)bv;
  *u = (number)bt;
  *u = nrnNeg(*u, r);
  *v = (number)bs;
  return (number)erg;
}

Variable Documentation

gmp_nrz_bin

EXTERN_VAR omBin gmp_nrz_bin

Definition at line 31 of file rmodulon.cc.

nrnCoeffName_buff

STATIC_VAR char* nrnCoeffName_buff =NULL

Definition at line 63 of file rmodulon.cc.

nrnMapCoef

STATIC_VAR mpz_ptr nrnMapCoef = NULL

Definition at line 715 of file rmodulon.cc.