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 177 of file rmodulon.cc.

nrnSize

#define nrnSize   nrzSize

Definition at line 178 of file rmodulon.cc.

Function Documentation

nlCPEatLongC()

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

static

Definition at line 931 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()

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

static

Definition at line 220 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()

static number nrnAnn ( number  k, const coeffs  r  )

static

Definition at line 551 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()

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

static

Definition at line 89 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()

static char * nrnCoeffName ( const coeffs  r )

static

Definition at line 66 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;
  if (nCoeff_is_Zn(r))
  {
    if (strlen(s)<10)
      ll=snprintf(nrnCoeffName_buff,l,"ZZ/(%s)",s);
    else
      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()

static number nrnConvFactoryNSingN ( const CanonicalForm  n, const coeffs  r  )

static

Definition at line 981 of file rmodulon.cc.

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

nrnConvSingNFactoryN()

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

static

Definition at line 986 of file rmodulon.cc.

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

nrnCopy()

static number nrnCopy ( number  a, const  coeffs  )

static

Definition at line 150 of file rmodulon.cc.

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

nrnDBTest()

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

static

Definition at line 917 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()

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

static

Definition at line 583 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()

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

static

Definition at line 565 of file rmodulon.cc.

{
  /* 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()

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

static

Definition at line 575 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()

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

static

Definition at line 350 of file rmodulon.cc.

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

nrnExtGcd()

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

static

Definition at line 329 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()

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

static

Definition at line 277 of file rmodulon.cc.

{
  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()

static number nrnGetUnit ( number  k, const coeffs  r  )

static

Definition at line 355 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()

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

static

Definition at line 502 of file rmodulon.cc.

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

nrnGreaterZero()

static BOOLEAN nrnGreaterZero ( number  k, const coeffs  cf  )

static

Definition at line 507 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()

static number nrnInit ( long  i, const coeffs  r  )

static

Definition at line 160 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 35 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 993 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.
 
  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;
  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->cfReadFd      = nrzReadFd;
#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()

static void nrnInitExp ( unsigned long  m, coeffs  r  )

static

Definition at line 906 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()

static number nrnInitMPZ ( mpz_t  m, const coeffs  r  )

static

Definition at line 877 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()

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

static

Definition at line 229 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()

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

static

Definition at line 206 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()

static long nrnInt ( number &  n, const  coeffs  )

static

Definition at line 171 of file rmodulon.cc.

{
  return mpz_get_si((mpz_ptr) n);
}

nrnInvers()

static number nrnInvers ( number  c, const coeffs  r  )

static

Definition at line 257 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()

static BOOLEAN nrnIsMOne ( number  a, const coeffs  r  )

static

Definition at line 492 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()

static BOOLEAN nrnIsOne ( number  a, const  coeffs  )

static

Definition at line 345 of file rmodulon.cc.

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

nrnIsUnit()

static BOOLEAN nrnIsUnit ( number  a, const coeffs  r  )

static

Definition at line 543 of file rmodulon.cc.

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

nrnIsZero()

static BOOLEAN nrnIsZero ( number  a, const  coeffs  )

static

Definition at line 244 of file rmodulon.cc.

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

nrnKillChar()

static void nrnKillChar ( coeffs  r )

static

Definition at line 97 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()

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

static

Definition at line 296 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()

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

static

Definition at line 716 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 735 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()

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

static

Definition at line 711 of file rmodulon.cc.

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

nrnMapQ()

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

static

Definition at line 743 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()

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

static

Definition at line 764 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()

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

static

Definition at line 725 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()

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

static

Definition at line 626 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()

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

static

Definition at line 885 of file rmodulon.cc.

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

nrnMult()

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

static

Definition at line 197 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()

static number nrnNeg ( number  c, const coeffs  r  )

static

Definition at line 249 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()

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

static

Definition at line 212 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()

static coeffs nrnQuot1 ( number  c, const coeffs  r  )

static

Definition at line 105 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);
      rr = nInitChar(n_Znm, (void*)&info);
    }
    mpz_clear(gcd);
    return(rr);
}

nrnQuotRem()

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

static

Definition at line 673 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()

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

static

Definition at line 955 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()

static void nrnSetExp ( unsigned long  m, coeffs  r  )

static

Definition at line 894 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 796 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()

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

static

Definition at line 235 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 779 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()

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

static

Definition at line 401 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 33 of file rmodulon.cc.

nrnCoeffName_buff

STATIC_VAR char* nrnCoeffName_buff =NULL

Definition at line 65 of file rmodulon.cc.

nrnMapCoef

STATIC_VAR mpz_ptr nrnMapCoef = NULL

Definition at line 709 of file rmodulon.cc.