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Macros | Functions
algext.cc File Reference
#include "misc/auxiliary.h"
#include "reporter/reporter.h"
#include "coeffs/coeffs.h"
#include "coeffs/numbers.h"
#include "coeffs/longrat.h"
#include "polys/monomials/ring.h"
#include "polys/monomials/p_polys.h"
#include "polys/simpleideals.h"
#include "polys/PolyEnumerator.h"
#include "factory/factory.h"
#include "polys/clapconv.h"
#include "polys/clapsing.h"
#include "polys/prCopy.h"
#include "polys/ext_fields/algext.h"
#include "polys/ext_fields/transext.h"

Go to the source code of this file.

Macros

#define TRANSEXT_PRIVATES   1
 ABSTRACT: numbers in an algebraic extension field K[a] / < f(a) > Assuming that we have a coeffs object cf, then these numbers are polynomials in the polynomial ring K[a] represented by cf->extRing. More...
 
#define naTest(a)   naDBTest(a,__FILE__,__LINE__,cf)
 
#define naRing   cf->extRing
 
#define naCoeffs   cf->extRing->cf
 
#define naMinpoly   naRing->qideal->m[0]
 
#define n2pTest(a)   n2pDBTest(a,__FILE__,__LINE__,cf)
 ABSTRACT: numbers as polys in the ring K[a] Assuming that we have a coeffs object cf, then these numbers are polynomials in the polynomial ring K[a] represented by cf->extRing. More...
 
#define n2pRing   cf->extRing
 
#define n2pCoeffs   cf->extRing->cf
 

Functions

BOOLEAN naDBTest (number a, const char *f, const int l, const coeffs r)
 
BOOLEAN naGreaterZero (number a, const coeffs cf)
 forward declarations More...
 
BOOLEAN naGreater (number a, number b, const coeffs cf)
 
BOOLEAN naEqual (number a, number b, const coeffs cf)
 
BOOLEAN naIsOne (number a, const coeffs cf)
 
BOOLEAN naIsMOne (number a, const coeffs cf)
 
number naInit (long i, const coeffs cf)
 
number naNeg (number a, const coeffs cf)
 this is in-place, modifies a More...
 
number naInvers (number a, const coeffs cf)
 
number naAdd (number a, number b, const coeffs cf)
 
number naSub (number a, number b, const coeffs cf)
 
number naMult (number a, number b, const coeffs cf)
 
number naDiv (number a, number b, const coeffs cf)
 
void naPower (number a, int exp, number *b, const coeffs cf)
 
number naCopy (number a, const coeffs cf)
 
void naWriteLong (number a, const coeffs cf)
 
void naWriteShort (number a, const coeffs cf)
 
number naGetDenom (number &a, const coeffs cf)
 
number naGetNumerator (number &a, const coeffs cf)
 
number naGcd (number a, number b, const coeffs cf)
 
void naDelete (number *a, const coeffs cf)
 
void naCoeffWrite (const coeffs cf, BOOLEAN details)
 
const char * naRead (const char *s, number *a, const coeffs cf)
 
static BOOLEAN naCoeffIsEqual (const coeffs cf, n_coeffType n, void *param)
 
static void p_Monic (poly p, const ring r)
 returns NULL if p == NULL, otherwise makes p monic by dividing by its leading coefficient (only done if this is not already 1); this assumes that we are over a ground field so that division is well-defined; modifies p More...
 
static poly p_GcdHelper (poly &p, poly &q, const ring r)
 see p_Gcd; additional assumption: deg(p) >= deg(q); must destroy p and q (unless one of them is returned) More...
 
static poly p_Gcd (const poly p, const poly q, const ring r)
 
static poly p_ExtGcdHelper (poly &p, poly &pFactor, poly &q, poly &qFactor, ring r)
 
poly p_ExtGcd (poly p, poly &pFactor, poly q, poly &qFactor, ring r)
 assumes that p and q are univariate polynomials in r, mentioning the same variable; assumes a global monomial ordering in r; assumes that not both p and q are NULL; returns the gcd of p and q; moreover, afterwards pFactor and qFactor contain appropriate factors such that gcd(p, q) = p * pFactor + q * qFactor; leaves p and q unmodified More...
 
void heuristicReduce (poly &p, poly reducer, const coeffs cf)
 
void definiteReduce (poly &p, poly reducer, const coeffs cf)
 
static coeffs nCoeff_bottom (const coeffs r, int &height)
 
BOOLEAN naIsZero (number a, const coeffs cf)
 
long naInt (number &a, const coeffs cf)
 
number napNormalizeHelper (number b, const coeffs cf)
 
number naLcmContent (number a, number b, const coeffs cf)
 
int naSize (number a, const coeffs cf)
 
void naNormalize (number &a, const coeffs cf)
 
number naConvFactoryNSingN (const CanonicalForm n, const coeffs cf)
 
CanonicalForm naConvSingNFactoryN (number n, BOOLEAN, const coeffs cf)
 
number naMap00 (number a, const coeffs src, const coeffs dst)
 
number naMapZ0 (number a, const coeffs src, const coeffs dst)
 
number naMapP0 (number a, const coeffs src, const coeffs dst)
 
number naCopyTrans2AlgExt (number a, const coeffs src, const coeffs dst)
 
number naMap0P (number a, const coeffs src, const coeffs dst)
 
number naMapPP (number a, const coeffs src, const coeffs dst)
 
number naMapUP (number a, const coeffs src, const coeffs dst)
 
number naGenMap (number a, const coeffs cf, const coeffs dst)
 
number naGenTrans2AlgExt (number a, const coeffs cf, const coeffs dst)
 
nMapFunc naSetMap (const coeffs src, const coeffs dst)
 Get a mapping function from src into the domain of this type (n_algExt) More...
 
int naParDeg (number a, const coeffs cf)
 
number naParameter (const int iParameter, const coeffs cf)
 return the specified parameter as a number in the given alg. field More...
 
int naIsParam (number m, const coeffs cf)
 if m == var(i)/1 => return i, More...
 
static void naClearContent (ICoeffsEnumerator &numberCollectionEnumerator, number &c, const coeffs cf)
 
void naClearDenominators (ICoeffsEnumerator &numberCollectionEnumerator, number &c, const coeffs cf)
 
void naKillChar (coeffs cf)
 
char * naCoeffName (const coeffs r)
 
number naChineseRemainder (number *x, number *q, int rl, BOOLEAN, CFArray &inv_cache, const coeffs cf)
 
number naFarey (number p, number n, const coeffs cf)
 
BOOLEAN naInitChar (coeffs cf, void *infoStruct)
 Initialize the coeffs object. More...
 
BOOLEAN n2pDBTest (number a, const char *f, const int l, const coeffs r)
 
void n2pNormalize (number &a, const coeffs cf)
 
number n2pMult (number a, number b, const coeffs cf)
 
number n2pDiv (number a, number b, const coeffs cf)
 
void n2pPower (number a, int exp, number *b, const coeffs cf)
 
const char * n2pRead (const char *s, number *a, const coeffs cf)
 
static BOOLEAN n2pCoeffIsEqual (const coeffs cf, n_coeffType n, void *param)
 
char * n2pCoeffName (const coeffs cf)
 
void n2pCoeffWrite (const coeffs cf, BOOLEAN details)
 
number n2pInvers (number a, const coeffs cf)
 
BOOLEAN n2pInitChar (coeffs cf, void *infoStruct)
 

Macro Definition Documentation

◆ n2pCoeffs

#define n2pCoeffs   cf->extRing->cf

Definition at line 1502 of file algext.cc.

◆ n2pRing

#define n2pRing   cf->extRing

Definition at line 1496 of file algext.cc.

◆ n2pTest

#define n2pTest (   a)    n2pDBTest(a,__FILE__,__LINE__,cf)

ABSTRACT: numbers as polys in the ring K[a] Assuming that we have a coeffs object cf, then these numbers are polynomials in the polynomial ring K[a] represented by cf->extRing.

IMPORTANT ASSUMPTIONS: 1.) So far we assume that cf->extRing is a valid polynomial ring

Definition at line 1489 of file algext.cc.

◆ naCoeffs

#define naCoeffs   cf->extRing->cf

Definition at line 67 of file algext.cc.

◆ naMinpoly

#define naMinpoly   naRing->qideal->m[0]

Definition at line 70 of file algext.cc.

◆ naRing

#define naRing   cf->extRing

Definition at line 61 of file algext.cc.

◆ naTest

#define naTest (   a)    naDBTest(a,__FILE__,__LINE__,cf)

Definition at line 54 of file algext.cc.

◆ TRANSEXT_PRIVATES

#define TRANSEXT_PRIVATES   1

ABSTRACT: numbers in an algebraic extension field K[a] / < f(a) > Assuming that we have a coeffs object cf, then these numbers are polynomials in the polynomial ring K[a] represented by cf->extRing.

IMPORTANT ASSUMPTIONS: 1.) So far we assume that cf->extRing is a valid polynomial ring in exactly one variable, i.e., K[a], where K is allowed to be any field (representable in SINGULAR and which may itself be some extension field, thus allowing for extension towers). 2.) Moreover, this implementation assumes that cf->extRing->qideal is not NULL but an ideal with at least one non-zero generator which may be accessed by cf->extRing->qideal->m[0] and which represents the minimal polynomial f(a) of the extension variable 'a' in K[a]. 3.) As soon as an std method for polynomial rings becomes availabe, all reduction steps modulo f(a) should be replaced by a call to std. Moreover, in this situation one can finally move from K[a] / < f(a) > to K[a_1, ..., a_s] / I, with I some zero-dimensional ideal in K[a_1, ..., a_s] given by a lex Gröbner basis. The code in algext.h and algext.cc is then capable of computing in K[a_1, ..., a_s] / I.

Definition at line 50 of file algext.cc.

Function Documentation

◆ definiteReduce()

void definiteReduce ( poly &  p,
poly  reducer,
const coeffs  cf 
)

Definition at line 730 of file algext.cc.

731 {
732  #ifdef LDEBUG
733  p_Test((poly)p, naRing);
734  p_Test((poly)reducer, naRing);
735  #endif
736  if ((p!=NULL) && (p_GetExp(p,1,naRing)>=p_GetExp(reducer,1,naRing)))
737  {
738  p_PolyDiv(p, reducer, FALSE, naRing);
739  }
740 }
#define naRing
Definition: algext.cc:61
#define FALSE
Definition: auxiliary.h:96
int p
Definition: cfModGcd.cc:4080
#define NULL
Definition: omList.c:12
poly p_PolyDiv(poly &p, const poly divisor, const BOOLEAN needResult, const ring r)
assumes that p and divisor are univariate polynomials in r, mentioning the same variable; assumes div...
Definition: p_polys.cc:1857
static long p_GetExp(const poly p, const unsigned long iBitmask, const int VarOffset)
get a single variable exponent @Note: the integer VarOffset encodes:
Definition: p_polys.h:469
#define p_Test(p, r)
Definition: p_polys.h:162

◆ heuristicReduce()

void heuristicReduce ( poly &  p,
poly  reducer,
const coeffs  cf 
)

Definition at line 560 of file algext.cc.

561 {
562  #ifdef LDEBUG
563  p_Test((poly)p, naRing);
564  p_Test((poly)reducer, naRing);
565  #endif
566  if (p_Totaldegree(p, naRing) > 10 * p_Totaldegree(reducer, naRing))
567  definiteReduce(p, reducer, cf);
568 }
void definiteReduce(poly &p, poly reducer, const coeffs cf)
Definition: algext.cc:730
CanonicalForm cf
Definition: cfModGcd.cc:4085
static long p_Totaldegree(poly p, const ring r)
Definition: p_polys.h:1467

◆ n2pCoeffIsEqual()

static BOOLEAN n2pCoeffIsEqual ( const coeffs  cf,
n_coeffType  n,
void *  param 
)
static

Definition at line 1552 of file algext.cc.

1553 {
1554  if (n_polyExt != n) return FALSE;
1555  AlgExtInfo *e = (AlgExtInfo *)param;
1556  /* for extension coefficient fields we expect the underlying
1557  polynomial rings to be IDENTICAL, i.e. the SAME OBJECT;
1558  this expectation is based on the assumption that we have properly
1559  registered cf and perform reference counting rather than creating
1560  multiple copies of the same coefficient field/domain/ring */
1561  if (n2pRing == e->r)
1562  return TRUE;
1563  // NOTE: Q(a)[x] && Q(a)[y] should better share the _same_ Q(a)...
1564  if( rEqual(n2pRing, e->r, TRUE) ) // also checks the equality of qideals
1565  {
1566  rDelete(e->r);
1567  return TRUE;
1568  }
1569  return FALSE;
1570 }
#define n2pRing
Definition: algext.cc:1496
ring r
Definition: algext.h:37
struct for passing initialization parameters to naInitChar
Definition: algext.h:37
#define TRUE
Definition: auxiliary.h:100
@ n_polyExt
used to represent polys as coeffcients
Definition: coeffs.h:35
void rDelete(ring r)
unconditionally deletes fields in r
Definition: ring.cc:449
BOOLEAN rEqual(ring r1, ring r2, BOOLEAN qr)
returns TRUE, if r1 equals r2 FALSE, otherwise Equality is determined componentwise,...
Definition: ring.cc:1660

◆ n2pCoeffName()

char* n2pCoeffName ( const coeffs  cf)

Definition at line 1572 of file algext.cc.

1573 {
1574  const char* const* p=n_ParameterNames(cf);
1575  int l=0;
1576  int i;
1577  for(i=0; i<rVar(n2pRing);i++)
1578  {
1579  l+=(strlen(p[i])+1);
1580  }
1581  char *cf_s=nCoeffName(n2pRing->cf);
1582  STATIC_VAR char s[200];
1583  s[0]='\0';
1584  snprintf(s,strlen(cf_s)+2,"%s",cf_s);
1585  char tt[2];
1586  tt[0]='[';
1587  tt[1]='\0';
1588  strcat(s,tt);
1589  tt[0]=',';
1590  for(i=0; i<rVar(n2pRing);i++)
1591  {
1592  strcat(s,p[i]);
1593  if (i+1!=rVar(n2pRing)) strcat(s,tt);
1594  else { tt[0]=']'; strcat(s,tt); }
1595  }
1596  return s;
1597 }
int l
Definition: cfEzgcd.cc:100
int i
Definition: cfEzgcd.cc:132
static FORCE_INLINE char * nCoeffName(const coeffs cf)
Definition: coeffs.h:987
static FORCE_INLINE char const ** n_ParameterNames(const coeffs r)
Returns a (const!) pointer to (const char*) names of parameters.
Definition: coeffs.h:802
const CanonicalForm int s
Definition: facAbsFact.cc:51
#define STATIC_VAR
Definition: globaldefs.h:7
static short rVar(const ring r)
#define rVar(r) (r->N)
Definition: ring.h:594

◆ n2pCoeffWrite()

void n2pCoeffWrite ( const coeffs  cf,
BOOLEAN  details 
)

Definition at line 1599 of file algext.cc.

1600 {
1601  assume( cf != NULL );
1602 
1603  const ring A = cf->extRing;
1604 
1605  assume( A != NULL );
1606  PrintS("// polynomial ring as coefficient ring :\n");
1607  rWrite(A);
1608  PrintLn();
1609 }
#define assume(x)
Definition: mod2.h:387
void PrintS(const char *s)
Definition: reporter.cc:284
void PrintLn()
Definition: reporter.cc:310
void rWrite(ring r, BOOLEAN details)
Definition: ring.cc:226
#define A
Definition: sirandom.c:24

◆ n2pDBTest()

BOOLEAN n2pDBTest ( number  a,
const char *  f,
const int  l,
const coeffs  r 
)

Definition at line 1505 of file algext.cc.

1506 {
1507  if (a == NULL) return TRUE;
1508  return p_Test((poly)a, n2pRing);
1509 }

◆ n2pDiv()

number n2pDiv ( number  a,
number  b,
const coeffs  cf 
)

Definition at line 1527 of file algext.cc.

1528 {
1529  n2pTest(a); n2pTest(b);
1530  if (b == NULL) WerrorS(nDivBy0);
1531  if (a == NULL) return NULL;
1532  poly p=singclap_pdivide((poly)a,(poly)b,n2pRing);
1533  return (number)p;
1534 }
#define n2pTest(a)
ABSTRACT: numbers as polys in the ring K[a] Assuming that we have a coeffs object cf,...
Definition: algext.cc:1489
CanonicalForm b
Definition: cfModGcd.cc:4105
poly singclap_pdivide(poly f, poly g, const ring r)
Definition: clapsing.cc:590
void WerrorS(const char *s)
Definition: feFopen.cc:24
const char *const nDivBy0
Definition: numbers.h:87

◆ n2pInitChar()

BOOLEAN n2pInitChar ( coeffs  cf,
void *  infoStruct 
)

first check whether cf->extRing != NULL and delete old ring???

Definition at line 1627 of file algext.cc.

1628 {
1629  assume( infoStruct != NULL );
1630 
1631  AlgExtInfo *e = (AlgExtInfo *)infoStruct;
1632  /// first check whether cf->extRing != NULL and delete old ring???
1633 
1634  assume(e->r != NULL); // extRing;
1635  assume(e->r->cf != NULL); // extRing->cf;
1636 
1637  assume( cf != NULL );
1638 
1639  rIncRefCnt(e->r); // increase the ref.counter for the ground poly. ring!
1640  const ring R = e->r; // no copy!
1641  cf->extRing = R;
1642 
1643  /* propagate characteristic up so that it becomes
1644  directly accessible in cf: */
1645  cf->ch = R->cf->ch;
1646  cf->is_field=FALSE;
1647  cf->is_domain=TRUE;
1648 
1649  cf->cfCoeffName = n2pCoeffName;
1650 
1651  cf->cfGreaterZero = naGreaterZero;
1652  cf->cfGreater = naGreater;
1653  cf->cfEqual = naEqual;
1654  cf->cfIsZero = naIsZero;
1655  cf->cfIsOne = naIsOne;
1656  cf->cfIsMOne = naIsMOne;
1657  cf->cfInit = naInit;
1658  cf->cfFarey = naFarey;
1659  cf->cfChineseRemainder= naChineseRemainder;
1660  cf->cfInt = naInt;
1661  cf->cfInpNeg = naNeg;
1662  cf->cfAdd = naAdd;
1663  cf->cfSub = naSub;
1664  cf->cfMult = n2pMult;
1665  cf->cfDiv = n2pDiv;
1666  cf->cfPower = n2pPower;
1667  cf->cfCopy = naCopy;
1668 
1669  cf->cfWriteLong = naWriteLong;
1670 
1671  if( rCanShortOut(n2pRing) )
1672  cf->cfWriteShort = naWriteShort;
1673  else
1674  cf->cfWriteShort = naWriteLong;
1675 
1676  cf->cfRead = n2pRead;
1677  cf->cfDelete = naDelete;
1678  cf->cfSetMap = naSetMap;
1679  cf->cfGetDenom = naGetDenom;
1680  cf->cfGetNumerator = naGetNumerator;
1681  cf->cfRePart = naCopy;
1682  cf->cfCoeffWrite = n2pCoeffWrite;
1683  cf->cfNormalize = n2pNormalize;
1684  cf->cfKillChar = naKillChar;
1685 #ifdef LDEBUG
1686  cf->cfDBTest = naDBTest;
1687 #endif
1688  cf->cfGcd = naGcd;
1689  cf->cfNormalizeHelper = naLcmContent;
1690  cf->cfSize = naSize;
1691  cf->nCoeffIsEqual = n2pCoeffIsEqual;
1692  cf->cfInvers = n2pInvers;
1693  cf->convFactoryNSingN=naConvFactoryNSingN;
1694  cf->convSingNFactoryN=naConvSingNFactoryN;
1695  cf->cfParDeg = naParDeg;
1696 
1697  cf->iNumberOfParameters = rVar(R);
1698  cf->pParameterNames = (const char**)R->names;
1699  cf->cfParameter = naParameter;
1700  cf->has_simple_Inverse=FALSE;
1701  /* cf->has_simple_Alloc= FALSE; */
1702 
1703  if( nCoeff_is_Q(R->cf) )
1704  {
1705  cf->cfClearContent = naClearContent;
1706  cf->cfClearDenominators = naClearDenominators;
1707  }
1708 
1709  return FALSE;
1710 }
number n2pDiv(number a, number b, const coeffs cf)
Definition: algext.cc:1527
BOOLEAN naGreater(number a, number b, const coeffs cf)
Definition: algext.cc:358
number naNeg(number a, const coeffs cf)
this is in-place, modifies a
Definition: algext.cc:332
number n2pMult(number a, number b, const coeffs cf)
Definition: algext.cc:1519
long naInt(number &a, const coeffs cf)
Definition: algext.cc:345
number naCopy(number a, const coeffs cf)
Definition: algext.cc:296
BOOLEAN naIsOne(number a, const coeffs cf)
Definition: algext.cc:315
CanonicalForm naConvSingNFactoryN(number n, BOOLEAN, const coeffs cf)
Definition: algext.cc:756
number naGcd(number a, number b, const coeffs cf)
Definition: algext.cc:770
void naClearDenominators(ICoeffsEnumerator &numberCollectionEnumerator, number &c, const coeffs cf)
Definition: algext.cc:1307
BOOLEAN naDBTest(number a, const char *f, const int l, const coeffs r)
Definition: algext.cc:233
number naInit(long i, const coeffs cf)
Definition: algext.cc:339
BOOLEAN naIsZero(number a, const coeffs cf)
Definition: algext.cc:272
const char * n2pRead(const char *s, number *a, const coeffs cf)
Definition: algext.cc:1543
number naGetNumerator(number &a, const coeffs cf)
Definition: algext.cc:304
static void naClearContent(ICoeffsEnumerator &numberCollectionEnumerator, number &c, const coeffs cf)
Definition: algext.cc:1102
number naSub(number a, number b, const coeffs cf)
Definition: algext.cc:448
BOOLEAN naEqual(number a, number b, const coeffs cf)
Definition: algext.cc:287
void naWriteShort(number a, const coeffs cf)
Definition: algext.cc:588
number naChineseRemainder(number *x, number *q, int rl, BOOLEAN, CFArray &inv_cache, const coeffs cf)
Definition: algext.cc:1353
void naKillChar(coeffs cf)
Definition: algext.cc:1323
void naWriteLong(number a, const coeffs cf)
Definition: algext.cc:570
void naDelete(number *a, const coeffs cf)
Definition: algext.cc:278
number naLcmContent(number a, number b, const coeffs cf)
Definition: algext.cc:643
number naGetDenom(number &a, const coeffs cf)
Definition: algext.cc:309
static BOOLEAN n2pCoeffIsEqual(const coeffs cf, n_coeffType n, void *param)
Definition: algext.cc:1552
char * n2pCoeffName(const coeffs cf)
Definition: algext.cc:1572
number naConvFactoryNSingN(const CanonicalForm n, const coeffs cf)
Definition: algext.cc:750
nMapFunc naSetMap(const coeffs src, const coeffs dst)
Get a mapping function from src into the domain of this type (n_algExt)
Definition: algext.cc:1017
number n2pInvers(number a, const coeffs cf)
Definition: algext.cc:1611
int naParDeg(number a, const coeffs cf)
Definition: algext.cc:1068
number naAdd(number a, number b, const coeffs cf)
Definition: algext.cc:437
int naSize(number a, const coeffs cf)
Definition: algext.cc:712
number naParameter(const int iParameter, const coeffs cf)
return the specified parameter as a number in the given alg. field
Definition: algext.cc:1076
BOOLEAN naGreaterZero(number a, const coeffs cf)
forward declarations
Definition: algext.cc:378
void n2pCoeffWrite(const coeffs cf, BOOLEAN details)
Definition: algext.cc:1599
void n2pNormalize(number &a, const coeffs cf)
Definition: algext.cc:1512
number naFarey(number p, number n, const coeffs cf)
Definition: algext.cc:1365
BOOLEAN naIsMOne(number a, const coeffs cf)
Definition: algext.cc:323
void n2pPower(number a, int exp, number *b, const coeffs cf)
Definition: algext.cc:1536
static FORCE_INLINE BOOLEAN nCoeff_is_Q(const coeffs r)
Definition: coeffs.h:830
static ring rIncRefCnt(ring r)
Definition: ring.h:844
static BOOLEAN rCanShortOut(const ring r)
Definition: ring.h:588
#define R
Definition: sirandom.c:27

◆ n2pInvers()

number n2pInvers ( number  a,
const coeffs  cf 
)

Definition at line 1611 of file algext.cc.

1612 {
1613  poly aa=(poly)a;
1614  if(p_IsConstant(aa, n2pRing))
1615  {
1616  poly p=p_Init(n2pRing);
1618  return (number)p;
1619  }
1620  else
1621  {
1622  WerrorS("not invertible");
1623  return NULL;
1624  }
1625 }
#define n2pCoeffs
Definition: algext.cc:1502
static FORCE_INLINE number n_Invers(number a, const coeffs r)
return the multiplicative inverse of 'a'; raise an error if 'a' is not invertible
Definition: coeffs.h:565
#define p_SetCoeff0(p, n, r)
Definition: monomials.h:60
static number & pGetCoeff(poly p)
return an alias to the leading coefficient of p assumes that p != NULL NOTE: not copy
Definition: monomials.h:44
static BOOLEAN p_IsConstant(const poly p, const ring r)
Definition: p_polys.h:1971
static poly p_Init(const ring r, omBin bin)
Definition: p_polys.h:1280

◆ n2pMult()

number n2pMult ( number  a,
number  b,
const coeffs  cf 
)

Definition at line 1519 of file algext.cc.

1520 {
1521  n2pTest(a); n2pTest(b);
1522  if ((a == NULL)||(b == NULL)) return NULL;
1523  poly aTimesB = pp_Mult_qq((poly)a, (poly)b, n2pRing);
1524  return (number)aTimesB;
1525 }
static poly pp_Mult_qq(poly p, poly q, const ring r)
Definition: p_polys.h:1111

◆ n2pNormalize()

void n2pNormalize ( number &  a,
const coeffs  cf 
)

Definition at line 1512 of file algext.cc.

1513 {
1514  poly aa=(poly)a;
1515  p_Normalize(aa,n2pRing);
1516 }
void p_Normalize(poly p, const ring r)
Definition: p_polys.cc:3842

◆ n2pPower()

void n2pPower ( number  a,
int  exp,
number *  b,
const coeffs  cf 
)

Definition at line 1536 of file algext.cc.

1537 {
1538  n2pTest(a);
1539 
1540  *b= (number)p_Power((poly)a,exp,n2pRing);
1541 }
gmp_float exp(const gmp_float &a)
Definition: mpr_complex.cc:357
poly p_Power(poly p, int i, const ring r)
Definition: p_polys.cc:2184

◆ n2pRead()

const char* n2pRead ( const char *  s,
number *  a,
const coeffs  cf 
)

Definition at line 1543 of file algext.cc.

1544 {
1545  poly aAsPoly;
1546  const char * result = p_Read(s, aAsPoly, n2pRing);
1547  *a = (number)aAsPoly;
1548  return result;
1549 }
return result
Definition: facAbsBiFact.cc:75
const char * p_Read(const char *st, poly &rc, const ring r)
Definition: p_polys.cc:1365

◆ naAdd()

number naAdd ( number  a,
number  b,
const coeffs  cf 
)

Definition at line 437 of file algext.cc.

438 {
439  naTest(a); naTest(b);
440  if (a == NULL) return naCopy(b, cf);
441  if (b == NULL) return naCopy(a, cf);
442  poly aPlusB = p_Add_q(p_Copy((poly)a, naRing),
443  p_Copy((poly)b, naRing), naRing);
444  //definiteReduce(aPlusB, naMinpoly, cf);
445  return (number)aPlusB;
446 }
#define naTest(a)
Definition: algext.cc:54
static poly p_Add_q(poly p, poly q, const ring r)
Definition: p_polys.h:896
static poly p_Copy(poly p, const ring r)
returns a copy of p
Definition: p_polys.h:812

◆ naChineseRemainder()

number naChineseRemainder ( number *  x,
number *  q,
int  rl,
BOOLEAN  ,
CFArray inv_cache,
const coeffs  cf 
)

Definition at line 1353 of file algext.cc.

1354 {
1355  poly *P=(poly*)omAlloc(rl*sizeof(poly*));
1356  number *X=(number *)omAlloc(rl*sizeof(number));
1357  int i;
1358  for(i=0;i<rl;i++) P[i]=p_Copy((poly)(x[i]),cf->extRing);
1359  poly result=p_ChineseRemainder(P,X,q,rl,inv_cache,cf->extRing);
1360  omFreeSize(X,rl*sizeof(number));
1361  omFreeSize(P,rl*sizeof(poly*));
1362  return ((number)result);
1363 }
Variable x
Definition: cfModGcd.cc:4084
poly p_ChineseRemainder(poly *xx, mpz_ptr *x, mpz_ptr *q, int rl, mpz_ptr *C, const ring R)
#define omFreeSize(addr, size)
Definition: omAllocDecl.h:260
#define omAlloc(size)
Definition: omAllocDecl.h:210

◆ naClearContent()

static void naClearContent ( ICoeffsEnumerator numberCollectionEnumerator,
number &  c,
const coeffs  cf 
)
static

Definition at line 1102 of file algext.cc.

1103 {
1104  assume(cf != NULL);
1106  assume(nCoeff_is_Q_algext(cf)); // only over (Q[a]/m(a)), while the default impl. is used over Zp[a]/m(a) !
1107 
1108  const ring R = cf->extRing;
1109  assume(R != NULL);
1110  const coeffs Q = R->cf;
1111  assume(Q != NULL);
1112  assume(nCoeff_is_Q(Q));
1113 
1114  numberCollectionEnumerator.Reset();
1115 
1116  if( !numberCollectionEnumerator.MoveNext() ) // empty zero polynomial?
1117  {
1118  c = n_Init(1, cf);
1119  return;
1120  }
1121 
1122  naTest(numberCollectionEnumerator.Current());
1123 
1124  // part 1, find a small candidate for gcd
1125  int s1; int s=2147483647; // max. int
1126 
1127  const BOOLEAN lc_is_pos=naGreaterZero(numberCollectionEnumerator.Current(),cf);
1128 
1129  int normalcount = 0;
1130 
1131  poly cand1, cand;
1132 
1133  do
1134  {
1135  number& n = numberCollectionEnumerator.Current();
1136  naNormalize(n, cf); ++normalcount;
1137 
1138  naTest(n);
1139 
1140  cand1 = (poly)n;
1141 
1142  s1 = p_Deg(cand1, R); // naSize?
1143  if (s>s1)
1144  {
1145  cand = cand1;
1146  s = s1;
1147  }
1148  } while (numberCollectionEnumerator.MoveNext() );
1149 
1150 // assume( nlGreaterZero(cand,cf) ); // cand may be a negative integer!
1151 
1152  cand = p_Copy(cand, R);
1153  // part 2: compute gcd(cand,all coeffs)
1154 
1155  numberCollectionEnumerator.Reset();
1156 
1157  int length = 0;
1158  while (numberCollectionEnumerator.MoveNext() )
1159  {
1160  number& n = numberCollectionEnumerator.Current();
1161  ++length;
1162 
1163  if( (--normalcount) <= 0)
1164  naNormalize(n, cf);
1165 
1166  naTest(n);
1167 
1168 // p_InpGcd(cand, (poly)n, R);
1169 
1170  { // R->cf is QQ
1171  poly tmp=gcd_over_Q(cand,(poly)n,R);
1172  p_Delete(&cand,R);
1173  cand=tmp;
1174  }
1175 
1176 // cand1 = p_Gcd(cand,(poly)n, R); p_Delete(&cand, R); cand = cand1;
1177 
1178  assume( naGreaterZero((number)cand, cf) ); // ???
1179 /*
1180  if(p_IsConstant(cand,R))
1181  {
1182  c = cand;
1183 
1184  if(!lc_is_pos)
1185  {
1186  // make the leading coeff positive
1187  c = nlNeg(c, cf);
1188  numberCollectionEnumerator.Reset();
1189 
1190  while (numberCollectionEnumerator.MoveNext() )
1191  {
1192  number& nn = numberCollectionEnumerator.Current();
1193  nn = nlNeg(nn, cf);
1194  }
1195  }
1196  return;
1197  }
1198 */
1199 
1200  }
1201 
1202 
1203  // part3: all coeffs = all coeffs / cand
1204  if (!lc_is_pos)
1205  cand = p_Neg(cand, R);
1206 
1207  c = (number)cand; naTest(c);
1208 
1209  poly cInverse = (poly)naInvers(c, cf);
1210  assume(cInverse != NULL); // c is non-zero divisor!?
1211 
1212 
1213  numberCollectionEnumerator.Reset();
1214 
1215 
1216  while (numberCollectionEnumerator.MoveNext() )
1217  {
1218  number& n = numberCollectionEnumerator.Current();
1219 
1220  assume( length > 0 );
1221 
1222  if( --length > 0 )
1223  {
1224  assume( cInverse != NULL );
1225  n = (number) p_Mult_q(p_Copy(cInverse, R), (poly)n, R);
1226  }
1227  else
1228  {
1229  n = (number) p_Mult_q(cInverse, (poly)n, R);
1230  cInverse = NULL;
1231  assume(length == 0);
1232  }
1233 
1234  definiteReduce((poly &)n, naMinpoly, cf);
1235  }
1236 
1237  assume(length == 0);
1238  assume(cInverse == NULL); // p_Delete(&cInverse, R);
1239 
1240  // Quick and dirty fix for constant content clearing... !?
1241  CRecursivePolyCoeffsEnumerator<NAConverter> itr(numberCollectionEnumerator); // recursively treat the numbers as polys!
1242 
1243  number cc;
1244 
1245  n_ClearContent(itr, cc, Q); // TODO: get rid of (-LC) normalization!?
1246 
1247  // over alg. ext. of Q // takes over the input number
1248  c = (number) __p_Mult_nn( (poly)c, cc, R);
1249 // p_Mult_q(p_NSet(cc, R), , R);
1250 
1251  n_Delete(&cc, Q);
1252 
1253  // TODO: the above is not enough! need GCD's of polynomial coeffs...!
1254 /*
1255  // old and wrong part of p_Content
1256  if (rField_is_Q_a(r) && !CLEARENUMERATORS) // should not be used anymore if CLEARENUMERATORS is 1
1257  {
1258  // we only need special handling for alg. ext.
1259  if (getCoeffType(r->cf)==n_algExt)
1260  {
1261  number hzz = n_Init(1, r->cf->extRing->cf);
1262  p=ph;
1263  while (p!=NULL)
1264  { // each monom: coeff in Q_a
1265  poly c_n_n=(poly)pGetCoeff(p);
1266  poly c_n=c_n_n;
1267  while (c_n!=NULL)
1268  { // each monom: coeff in Q
1269  d=n_NormalizeHelper(hzz,pGetCoeff(c_n),r->cf->extRing->cf);
1270  n_Delete(&hzz,r->cf->extRing->cf);
1271  hzz=d;
1272  pIter(c_n);
1273  }
1274  pIter(p);
1275  }
1276  // hzz contains the 1/lcm of all denominators in c_n_n
1277  h=n_Invers(hzz,r->cf->extRing->cf);
1278  n_Delete(&hzz,r->cf->extRing->cf);
1279  n_Normalize(h,r->cf->extRing->cf);
1280  if(!n_IsOne(h,r->cf->extRing->cf))
1281  {
1282  p=ph;
1283  while (p!=NULL)
1284  { // each monom: coeff in Q_a
1285  poly c_n=(poly)pGetCoeff(p);
1286  while (c_n!=NULL)
1287  { // each monom: coeff in Q
1288  d=n_Mult(h,pGetCoeff(c_n),r->cf->extRing->cf);
1289  n_Normalize(d,r->cf->extRing->cf);
1290  n_Delete(&pGetCoeff(c_n),r->cf->extRing->cf);
1291  pGetCoeff(c_n)=d;
1292  pIter(c_n);
1293  }
1294  pIter(p);
1295  }
1296  }
1297  n_Delete(&h,r->cf->extRing->cf);
1298  }
1299  }
1300 */
1301 
1302 
1303 // c = n_Init(1, cf); assume(FALSE); // TODO: NOT YET IMPLEMENTED!!!
1304 }
#define naMinpoly
Definition: algext.cc:70
void naNormalize(number &a, const coeffs cf)
Definition: algext.cc:742
number naInvers(number a, const coeffs cf)
Definition: algext.cc:818
int BOOLEAN
Definition: auxiliary.h:87
const CanonicalForm const CanonicalForm const CanonicalForm const CanonicalForm & cand
Definition: cfModGcd.cc:69
go into polynomials over an alg. extension recursively
virtual reference Current()=0
Gets the current element in the collection (read and write).
virtual void Reset()=0
Sets the enumerator to its initial position: -1, which is before the first element in the collection.
virtual bool MoveNext()=0
Advances the enumerator to the next element of the collection. returns true if the enumerator was suc...
@ n_algExt
used for all algebraic extensions, i.e., the top-most extension in an extension tower is algebraic
Definition: coeffs.h:36
static FORCE_INLINE BOOLEAN nCoeff_is_Q_algext(const coeffs r)
is it an alg. ext. of Q?
Definition: coeffs.h:938
static FORCE_INLINE n_coeffType getCoeffType(const coeffs r)
Returns the type of coeffs domain.
Definition: coeffs.h:422
static FORCE_INLINE void n_Delete(number *p, const coeffs r)
delete 'p'
Definition: coeffs.h:456
static FORCE_INLINE number n_Init(long i, const coeffs r)
a number representing i in the given coeff field/ring r
Definition: coeffs.h:539
static FORCE_INLINE void n_ClearContent(ICoeffsEnumerator &numberCollectionEnumerator, number &c, const coeffs r)
Computes the content and (inplace) divides it out on a collection of numbers number c is the content ...
Definition: coeffs.h:952
static BOOLEAN length(leftv result, leftv arg)
Definition: interval.cc:257
STATIC_VAR jList * Q
Definition: janet.cc:30
The main handler for Singular numbers which are suitable for Singular polynomials.
long p_Deg(poly a, const ring r)
Definition: p_polys.cc:582
static poly p_Neg(poly p, const ring r)
Definition: p_polys.h:1067
static poly p_Mult_q(poly p, poly q, const ring r)
Definition: p_polys.h:1074
static void p_Delete(poly *p, const ring r)
Definition: p_polys.h:861
#define __p_Mult_nn(p, n, r)
Definition: p_polys.h:931
poly gcd_over_Q(poly f, poly g, const ring r)
helper routine for calling singclap_gcd_r
Definition: transext.cc:275

◆ naClearDenominators()

void naClearDenominators ( ICoeffsEnumerator numberCollectionEnumerator,
number &  c,
const coeffs  cf 
)

Definition at line 1307 of file algext.cc.

1308 {
1309  assume(cf != NULL);
1311  assume(nCoeff_is_Q_algext(cf)); // only over (Q[a]/m(a)), while the default impl. is used over Zp[a]/m(a) !
1312 
1313  assume(cf->extRing != NULL);
1314  const coeffs Q = cf->extRing->cf;
1315  assume(Q != NULL);
1316  assume(nCoeff_is_Q(Q));
1317  number n;
1318  CRecursivePolyCoeffsEnumerator<NAConverter> itr(numberCollectionEnumerator); // recursively treat the numbers as polys!
1319  n_ClearDenominators(itr, n, Q); // this should probably be fine...
1320  c = (number)p_NSet(n, cf->extRing); // over alg. ext. of Q // takes over the input number
1321 }
static FORCE_INLINE void n_ClearDenominators(ICoeffsEnumerator &numberCollectionEnumerator, number &d, const coeffs r)
(inplace) Clears denominators on a collection of numbers number d is the LCM of all the coefficient d...
Definition: coeffs.h:959
poly p_NSet(number n, const ring r)
returns the poly representing the number n, destroys n
Definition: p_polys.cc:1460

◆ naCoeffIsEqual()

static BOOLEAN naCoeffIsEqual ( const coeffs  cf,
n_coeffType  n,
void *  param 
)
static

Definition at line 678 of file algext.cc.

679 {
680  if (n_algExt != n) return FALSE;
681  AlgExtInfo *e = (AlgExtInfo *)param;
682  /* for extension coefficient fields we expect the underlying
683  polynomial rings to be IDENTICAL, i.e. the SAME OBJECT;
684  this expectation is based on the assumption that we have properly
685  registered cf and perform reference counting rather than creating
686  multiple copies of the same coefficient field/domain/ring */
687  if (naRing == e->r)
688  return TRUE;
689  /* (Note that then also the minimal ideals will necessarily be
690  the same, as they are attached to the ring.) */
691 
692  // NOTE: Q(a)[x] && Q(a)[y] should better share the _same_ Q(a)...
693  if( rEqual(naRing, e->r, TRUE) ) // also checks the equality of qideals
694  {
695  const ideal mi = naRing->qideal;
696  assume( IDELEMS(mi) == 1 );
697  const ideal ii = e->r->qideal;
698  assume( IDELEMS(ii) == 1 );
699 
700  // TODO: the following should be extended for 2 *equal* rings...
701  assume( p_EqualPolys(mi->m[0], ii->m[0], naRing, e->r) );
702 
703  rDelete(e->r);
704 
705  return TRUE;
706  }
707 
708  return FALSE;
709 
710 }
BOOLEAN p_EqualPolys(poly p1, poly p2, const ring r)
Definition: p_polys.cc:4540
#define IDELEMS(i)
Definition: simpleideals.h:23

◆ naCoeffName()

char* naCoeffName ( const coeffs  r)

Definition at line 1330 of file algext.cc.

1331 {
1332  const char* const* p=n_ParameterNames(r);
1333  int l=0;
1334  int i;
1335  for(i=0; i<n_NumberOfParameters(r);i++)
1336  {
1337  l+=(strlen(p[i])+1);
1338  }
1339  STATIC_VAR char s[200];
1340  s[0]='\0';
1341  snprintf(s,10+1,"%d",r->ch); /* Fp(a) or Q(a) */
1342  char tt[2];
1343  tt[0]=',';
1344  tt[1]='\0';
1345  for(i=0; i<n_NumberOfParameters(r);i++)
1346  {
1347  strcat(s,tt);
1348  strcat(s,p[i]);
1349  }
1350  return s;
1351 }
static FORCE_INLINE int n_NumberOfParameters(const coeffs r)
Returns the number of parameters.
Definition: coeffs.h:798

◆ naCoeffWrite()

void naCoeffWrite ( const coeffs  cf,
BOOLEAN  details 
)

Definition at line 387 of file algext.cc.

388 {
389  assume( cf != NULL );
390 
391  const ring A = cf->extRing;
392 
393  assume( A != NULL );
394  assume( A->cf != NULL );
395 
396  n_CoeffWrite(A->cf, details);
397 
398 // rWrite(A);
399 
400  const int P = rVar(A);
401  assume( P > 0 );
402 
403  PrintS("[");
404 
405  for (int nop=0; nop < P; nop ++)
406  {
407  Print("%s", rRingVar(nop, A));
408  if (nop!=P-1) PrintS(", ");
409  }
410 
411  PrintS("]/(");
412 
413  const ideal I = A->qideal;
414 
415  assume( I != NULL );
416  assume( IDELEMS(I) == 1 );
417 
418 
419  if ( details )
420  {
421  p_Write0( I->m[0], A);
422  PrintS(")");
423  }
424  else
425  PrintS("...)");
426 
427 /*
428  char *x = rRingVar(0, A);
429 
430  Print("// Coefficients live in the extension field K[%s]/<f(%s)>\n", x, x);
431  Print("// with the minimal polynomial f(%s) = %s\n", x,
432  p_String(A->qideal->m[0], A));
433  PrintS("// and K: ");
434 */
435 }
static FORCE_INLINE void n_CoeffWrite(const coeffs r, BOOLEAN details=TRUE)
output the coeff description
Definition: coeffs.h:743
#define Print
Definition: emacs.cc:80
void p_Write0(poly p, ring lmRing, ring tailRing)
Definition: polys0.cc:332
static char * rRingVar(short i, const ring r)
Definition: ring.h:579

◆ naConvFactoryNSingN()

number naConvFactoryNSingN ( const CanonicalForm  n,
const coeffs  cf 
)

Definition at line 750 of file algext.cc.

751 {
752  if (n.isZero()) return NULL;
753  poly p=convFactoryPSingP(n,naRing);
754  return (number)p;
755 }
poly convFactoryPSingP(const CanonicalForm &f, const ring r)
Definition: clapconv.cc:40
CF_NO_INLINE bool isZero() const

◆ naConvSingNFactoryN()

CanonicalForm naConvSingNFactoryN ( number  n,
BOOLEAN  ,
const coeffs  cf 
)

Definition at line 756 of file algext.cc.

757 {
758  naTest(n);
759  if (n==NULL) return CanonicalForm(0);
760 
761  return convSingPFactoryP((poly)n,naRing);
762 }
CanonicalForm convSingPFactoryP(poly p, const ring r)
Definition: clapconv.cc:136
factory's main class
Definition: canonicalform.h:86

◆ naCopy()

number naCopy ( number  a,
const coeffs  cf 
)

Definition at line 296 of file algext.cc.

297 {
298  naTest(a);
299  if (a == NULL) return NULL;
300  if (((poly)a)==naMinpoly) return a;
301  return (number)p_Copy((poly)a, naRing);
302 }

◆ naCopyTrans2AlgExt()

number naCopyTrans2AlgExt ( number  a,
const coeffs  src,
const coeffs  dst 
)

Definition at line 890 of file algext.cc.

891 {
892  assume (nCoeff_is_transExt (src));
893  assume (nCoeff_is_algExt (dst));
894  fraction fa=(fraction)a;
895  poly p, q;
896  if (rSamePolyRep(src->extRing, dst->extRing))
897  {
898  p = p_Copy(NUM(fa),src->extRing);
899  if (!DENIS1(fa))
900  {
901  q = p_Copy(DEN(fa),src->extRing);
902  assume (q != NULL);
903  }
904  }
905  else
906  {
907  assume ((strcmp(rRingVar(0,src->extRing),rRingVar(0,dst->extRing))==0) && (rVar (src->extRing) == rVar (dst->extRing)));
908 
909  nMapFunc nMap= n_SetMap (src->extRing->cf, dst->extRing->cf);
910 
911  assume (nMap != NULL);
912  p= p_PermPoly (NUM (fa), NULL, src->extRing, dst->extRing,nMap, NULL,rVar (src->extRing));
913  if (!DENIS1(fa))
914  {
915  q= p_PermPoly (DEN (fa), NULL, src->extRing, dst->extRing,nMap, NULL,rVar (src->extRing));
916  assume (q != NULL);
917  }
918  }
919  definiteReduce(p, dst->extRing->qideal->m[0], dst);
920  p_Test (p, dst->extRing);
921  if (!DENIS1(fa))
922  {
923  definiteReduce(q, dst->extRing->qideal->m[0], dst);
924  p_Test (q, dst->extRing);
925  if (q != NULL)
926  {
927  number t= naDiv ((number)p,(number)q, dst);
928  p_Delete (&p, dst->extRing);
929  p_Delete (&q, dst->extRing);
930  return t;
931  }
932  WerrorS ("mapping denominator to zero");
933  }
934  return (number) p;
935 }
number naDiv(number a, number b, const coeffs cf)
Definition: algext.cc:469
static FORCE_INLINE nMapFunc n_SetMap(const coeffs src, const coeffs dst)
set the mapping function pointers for translating numbers from src to dst
Definition: coeffs.h:723
static FORCE_INLINE BOOLEAN nCoeff_is_algExt(const coeffs r)
TRUE iff r represents an algebraic extension field.
Definition: coeffs.h:934
number(* nMapFunc)(number a, const coeffs src, const coeffs dst)
maps "a", which lives in src, into dst
Definition: coeffs.h:74
static FORCE_INLINE BOOLEAN nCoeff_is_transExt(const coeffs r)
TRUE iff r represents a transcendental extension field.
Definition: coeffs.h:942
BOOLEAN fa(leftv res, leftv args)
Definition: cohomo.cc:4390
poly p_PermPoly(poly p, const int *perm, const ring oldRing, const ring dst, nMapFunc nMap, const int *par_perm, int OldPar, BOOLEAN use_mult)
Definition: p_polys.cc:4158
@ NUM
Definition: readcf.cc:170
BOOLEAN rSamePolyRep(ring r1, ring r2)
returns TRUE, if r1 and r2 represents the monomials in the same way FALSE, otherwise this is an analo...
Definition: ring.cc:1713

◆ naDBTest()

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

Definition at line 233 of file algext.cc.

234 {
235  if (a == NULL) return TRUE;
236  p_Test((poly)a, naRing);
237  if (getCoeffType(cf)==n_algExt)
238  {
239  if((((poly)a)!=naMinpoly)
241  && (p_Totaldegree((poly)a, naRing)> 1)) // allow to output par(1)
242  {
243  dReportError("deg >= deg(minpoly) in %s:%d\n",f,l);
244  return FALSE;
245  }
246  }
247  return TRUE;
248 }
FILE * f
Definition: checklibs.c:9
int dReportError(const char *fmt,...)
Definition: dError.cc:43

◆ naDelete()

void naDelete ( number *  a,
const coeffs  cf 
)

Definition at line 278 of file algext.cc.

279 {
280  if (*a == NULL) return;
281  if (((poly)*a)==naMinpoly) { *a=NULL;return;}
282  poly aAsPoly = (poly)(*a);
283  p_Delete(&aAsPoly, naRing);
284  *a = NULL;
285 }

◆ naDiv()

number naDiv ( number  a,
number  b,
const coeffs  cf 
)

Definition at line 469 of file algext.cc.

470 {
471  naTest(a); naTest(b);
472  if (b == NULL) WerrorS(nDivBy0);
473  if (a == NULL) return NULL;
474  poly bInverse = (poly)naInvers(b, cf);
475  if(bInverse != NULL) // b is non-zero divisor!
476  {
477  poly aDivB = p_Mult_q(p_Copy((poly)a, naRing), bInverse, naRing);
478  definiteReduce(aDivB, naMinpoly, cf);
479  p_Normalize(aDivB,naRing);
480  return (number)aDivB;
481  }
482  return NULL;
483 }

◆ naEqual()

BOOLEAN naEqual ( number  a,
number  b,
const coeffs  cf 
)

simple tests

Definition at line 287 of file algext.cc.

288 {
289  naTest(a); naTest(b);
290  /// simple tests
291  if (a == NULL) return (b == NULL);
292  if (b == NULL) return (a == NULL);
293  return p_EqualPolys((poly)a,(poly)b,naRing);
294 }

◆ naFarey()

number naFarey ( number  p,
number  n,
const coeffs  cf 
)

Definition at line 1365 of file algext.cc.

1366 {
1367  // n is really a bigint
1368  poly result=p_Farey(p_Copy((poly)p,cf->extRing),n,cf->extRing);
1369  return ((number)result);
1370 }
poly p_Farey(poly p, number N, const ring r)
Definition: p_polys.cc:54

◆ naGcd()

number naGcd ( number  a,
number  b,
const coeffs  cf 
)

Definition at line 770 of file algext.cc.

771 {
772  if (a==NULL) return naCopy(b,cf);
773  if (b==NULL) return naCopy(a,cf);
774 
775  poly ax=(poly)a;
776  poly bx=(poly)b;
777  if (pNext(ax)!=NULL)
778  return (number)p_Copy(ax, naRing);
779  else
780  {
781  if(nCoeff_is_Zp(naRing->cf))
782  return naInit(1,cf);
783  else
784  {
785  number x = n_Copy(pGetCoeff((poly)a),naRing->cf);
786  if (n_IsOne(x,naRing->cf))
787  return (number)p_NSet(x,naRing);
788  while (pNext(ax)!=NULL)
789  {
790  pIter(ax);
791  number y = n_SubringGcd(x, pGetCoeff(ax), naRing->cf);
792  n_Delete(&x,naRing->cf);
793  x = y;
794  if (n_IsOne(x,naRing->cf))
795  return (number)p_NSet(x,naRing);
796  }
797  do
798  {
799  number y = n_SubringGcd(x, pGetCoeff(bx), naRing->cf);
800  n_Delete(&x,naRing->cf);
801  x = y;
802  if (n_IsOne(x,naRing->cf))
803  return (number)p_NSet(x,naRing);
804  pIter(bx);
805  }
806  while (bx!=NULL);
807  return (number)p_NSet(x,naRing);
808  }
809  }
810 #if 0
811  naTest(a); naTest(b);
812  const ring R = naRing;
813  return (number) singclap_gcd_r((poly)a, (poly)b, R);
814 #endif
815 // return (number)p_Gcd((poly)a, (poly)b, naRing);
816 }
poly singclap_gcd_r(poly f, poly g, const ring r)
Definition: clapsing.cc:45
static FORCE_INLINE number n_Copy(number n, const coeffs r)
return a copy of 'n'
Definition: coeffs.h:452
static FORCE_INLINE BOOLEAN nCoeff_is_Zp(const coeffs r)
Definition: coeffs.h:824
static FORCE_INLINE number n_SubringGcd(number a, number b, const coeffs r)
Definition: coeffs.h:689
static FORCE_INLINE BOOLEAN n_IsOne(number n, const coeffs r)
TRUE iff 'n' represents the one element.
Definition: coeffs.h:469
const CanonicalForm int const CFList const Variable & y
Definition: facAbsFact.cc:53
#define pIter(p)
Definition: monomials.h:37
#define pNext(p)
Definition: monomials.h:36

◆ naGenMap()

number naGenMap ( number  a,
const coeffs  cf,
const coeffs  dst 
)

Definition at line 972 of file algext.cc.

973 {
974  if (a==NULL) return NULL;
975 
976  const ring rSrc = cf->extRing;
977  const ring rDst = dst->extRing;
978 
979  const nMapFunc nMap=n_SetMap(rSrc->cf,rDst->cf);
980  poly f = (poly)a;
981  poly g = prMapR(f, nMap, rSrc, rDst);
982 
983  n_Test((number)g, dst);
984  return (number)g;
985 }
g
Definition: cfModGcd.cc:4092
#define n_Test(a, r)
BOOLEAN n_Test(number a, const coeffs r)
Definition: coeffs.h:736
poly prMapR(poly src, nMapFunc nMap, ring src_r, ring dest_r)
Definition: prCopy.cc:45

◆ naGenTrans2AlgExt()

number naGenTrans2AlgExt ( number  a,
const coeffs  cf,
const coeffs  dst 
)

Definition at line 987 of file algext.cc.

988 {
989  if (a==NULL) return NULL;
990 
991  const ring rSrc = cf->extRing;
992  const ring rDst = dst->extRing;
993 
994  const nMapFunc nMap=n_SetMap(rSrc->cf,rDst->cf);
995  fraction f = (fraction)a;
996  poly g = prMapR(NUM(f), nMap, rSrc, rDst);
997 
998  number result=NULL;
999  poly h = NULL;
1000 
1001  if (!DENIS1(f))
1002  h = prMapR(DEN(f), nMap, rSrc, rDst);
1003 
1004  if (h!=NULL)
1005  {
1006  result=naDiv((number)g,(number)h,dst);
1007  p_Delete(&g,dst->extRing);
1008  p_Delete(&h,dst->extRing);
1009  }
1010  else
1011  result=(number)g;
1012 
1013  n_Test((number)result, dst);
1014  return (number)result;
1015 }
STATIC_VAR Poly * h
Definition: janet.cc:971

◆ naGetDenom()

number naGetDenom ( number &  a,
const coeffs  cf 
)

Definition at line 309 of file algext.cc.

310 {
311  naTest(a);
312  return naInit(1, cf);
313 }

◆ naGetNumerator()

number naGetNumerator ( number &  a,
const coeffs  cf 
)

Definition at line 304 of file algext.cc.

305 {
306  return naCopy(a, cf);
307 }

◆ naGreater()

BOOLEAN naGreater ( number  a,
number  b,
const coeffs  cf 
)

Definition at line 358 of file algext.cc.

359 {
360  naTest(a); naTest(b);
361  if (naIsZero(a, cf))
362  {
363  if (naIsZero(b, cf)) return FALSE;
364  return !n_GreaterZero(pGetCoeff((poly)b),naCoeffs);
365  }
366  if (naIsZero(b, cf))
367  {
368  return n_GreaterZero(pGetCoeff((poly)a),naCoeffs);
369  }
370  int aDeg = p_Totaldegree((poly)a, naRing);
371  int bDeg = p_Totaldegree((poly)b, naRing);
372  if (aDeg>bDeg) return TRUE;
373  if (aDeg<bDeg) return FALSE;
374  return n_Greater(pGetCoeff((poly)a),pGetCoeff((poly)b),naCoeffs);
375 }
#define naCoeffs
Definition: algext.cc:67
static FORCE_INLINE BOOLEAN n_GreaterZero(number n, const coeffs r)
ordered fields: TRUE iff 'n' is positive; in Z/pZ: TRUE iff 0 < m <= roundedBelow(p/2),...
Definition: coeffs.h:495
static FORCE_INLINE BOOLEAN n_Greater(number a, number b, const coeffs r)
ordered fields: TRUE iff 'a' is larger than 'b'; in Z/pZ: TRUE iff la > lb, where la and lb are the l...
Definition: coeffs.h:512

◆ naGreaterZero()

BOOLEAN naGreaterZero ( number  a,
const coeffs  cf 
)

forward declarations

Definition at line 378 of file algext.cc.

379 {
380  naTest(a);
381  if (a == NULL) return FALSE;
382  if (n_GreaterZero(p_GetCoeff((poly)a, naRing), naCoeffs)) return TRUE;
383  if (p_Totaldegree((poly)a, naRing) > 0) return TRUE;
384  return FALSE;
385 }
#define p_GetCoeff(p, r)
Definition: monomials.h:50

◆ naInit()

number naInit ( long  i,
const coeffs  cf 
)

Definition at line 339 of file algext.cc.

340 {
341  if (i == 0) return NULL;
342  else return (number)p_ISet(i, naRing);
343 }
poly p_ISet(long i, const ring r)
returns the poly representing the integer i
Definition: p_polys.cc:1292

◆ naInitChar()

BOOLEAN naInitChar ( coeffs  cf,
void *  infoStruct 
)

Initialize the coeffs object.

first check whether cf->extRing != NULL and delete old ring???

Definition at line 1373 of file algext.cc.

1374 {
1375  assume( infoStruct != NULL );
1376 
1377  AlgExtInfo *e = (AlgExtInfo *)infoStruct;
1378  /// first check whether cf->extRing != NULL and delete old ring???
1379 
1380  assume(e->r != NULL); // extRing;
1381  assume(e->r->cf != NULL); // extRing->cf;
1382 
1383  assume((e->r->qideal != NULL) && // minideal has one
1384  (IDELEMS(e->r->qideal) == 1) && // non-zero generator
1385  (e->r->qideal->m[0] != NULL) ); // at m[0];
1386 
1387  assume( cf != NULL );
1388  assume(getCoeffType(cf) == n_algExt); // coeff type;
1389 
1390  rIncRefCnt(e->r); // increase the ref.counter for the ground poly. ring!
1391  const ring R = e->r; // no copy!
1392  cf->extRing = R;
1393 
1394  /* propagate characteristic up so that it becomes
1395  directly accessible in cf: */
1396  cf->ch = R->cf->ch;
1397 
1398  cf->is_field=TRUE;
1399  cf->is_domain=TRUE;
1400  cf->rep=n_rep_poly;
1401 
1402  #ifdef LDEBUG
1403  p_Test((poly)naMinpoly, naRing);
1404  #endif
1405 
1406  cf->cfCoeffName = naCoeffName;
1407 
1408  cf->cfGreaterZero = naGreaterZero;
1409  cf->cfGreater = naGreater;
1410  cf->cfEqual = naEqual;
1411  cf->cfIsZero = naIsZero;
1412  cf->cfIsOne = naIsOne;
1413  cf->cfIsMOne = naIsMOne;
1414  cf->cfInit = naInit;
1415  cf->cfFarey = naFarey;
1416  cf->cfChineseRemainder= naChineseRemainder;
1417  cf->cfInt = naInt;
1418  cf->cfInpNeg = naNeg;
1419  cf->cfAdd = naAdd;
1420  cf->cfSub = naSub;
1421  cf->cfMult = naMult;
1422  cf->cfDiv = naDiv;
1423  cf->cfExactDiv = naDiv;
1424  cf->cfPower = naPower;
1425  cf->cfCopy = naCopy;
1426 
1427  cf->cfWriteLong = naWriteLong;
1428 
1429  if( rCanShortOut(naRing) )
1430  cf->cfWriteShort = naWriteShort;
1431  else
1432  cf->cfWriteShort = naWriteLong;
1433 
1434  cf->cfRead = naRead;
1435  cf->cfDelete = naDelete;
1436  cf->cfSetMap = naSetMap;
1437  cf->cfGetDenom = naGetDenom;
1438  cf->cfGetNumerator = naGetNumerator;
1439  cf->cfRePart = naCopy;
1440  cf->cfCoeffWrite = naCoeffWrite;
1441  cf->cfNormalize = naNormalize;
1442  cf->cfKillChar = naKillChar;
1443 #ifdef LDEBUG
1444  cf->cfDBTest = naDBTest;
1445 #endif
1446  cf->cfGcd = naGcd;
1447  cf->cfNormalizeHelper = naLcmContent;
1448  cf->cfSize = naSize;
1449  cf->nCoeffIsEqual = naCoeffIsEqual;
1450  cf->cfInvers = naInvers;
1451  cf->convFactoryNSingN=naConvFactoryNSingN;
1452  cf->convSingNFactoryN=naConvSingNFactoryN;
1453  cf->cfParDeg = naParDeg;
1454 
1455  cf->iNumberOfParameters = rVar(R);
1456  cf->pParameterNames = (const char**)R->names;
1457  cf->cfParameter = naParameter;
1458  cf->has_simple_Inverse= R->cf->has_simple_Inverse;
1459  /* cf->has_simple_Alloc= FALSE; */
1460 
1461  if( nCoeff_is_Q(R->cf) )
1462  {
1463  cf->cfClearContent = naClearContent;
1464  cf->cfClearDenominators = naClearDenominators;
1465  }
1466 
1467  return FALSE;
1468 }
void naPower(number a, int exp, number *b, const coeffs cf)
Definition: algext.cc:493
void naCoeffWrite(const coeffs cf, BOOLEAN details)
Definition: algext.cc:387
char * naCoeffName(const coeffs r)
Definition: algext.cc:1330
number naMult(number a, number b, const coeffs cf)
Definition: algext.cc:459
const char * naRead(const char *s, number *a, const coeffs cf)
Definition: algext.cc:606
static BOOLEAN naCoeffIsEqual(const coeffs cf, n_coeffType n, void *param)
Definition: algext.cc:678
@ n_rep_poly
(poly), see algext.h
Definition: coeffs.h:114

◆ naInt()

long naInt ( number &  a,
const coeffs  cf 
)

Definition at line 345 of file algext.cc.

346 {
347  naTest(a);
348  poly aAsPoly = (poly)a;
349  if(aAsPoly == NULL)
350  return 0;
351  if (!p_IsConstant(aAsPoly, naRing))
352  return 0;
353  assume( aAsPoly != NULL );
354  return n_Int(p_GetCoeff(aAsPoly, naRing), naCoeffs);
355 }
static FORCE_INLINE long n_Int(number &n, const coeffs r)
conversion of n to an int; 0 if not possible in Z/pZ: the representing int lying in (-p/2 ....
Definition: coeffs.h:548

◆ naInvers()

number naInvers ( number  a,
const coeffs  cf 
)

Definition at line 818 of file algext.cc.

819 {
820  naTest(a);
821  if (a == NULL) WerrorS(nDivBy0);
822 
823  poly aFactor = NULL; poly mFactor = NULL; poly theGcd = NULL;
824 // singclap_extgcd!
825  const BOOLEAN ret = singclap_extgcd ((poly)a, naMinpoly, theGcd, aFactor, mFactor, naRing);
826 
827  assume( !ret );
828 
829 // if( ret ) theGcd = p_ExtGcd((poly)a, aFactor, naMinpoly, mFactor, naRing);
830 
831  naTest((number)theGcd); naTest((number)aFactor); naTest((number)mFactor);
832  p_Delete(&mFactor, naRing);
833 
834  // /* the gcd must be 1 since naMinpoly is irreducible and a != NULL: */
835  // assume(naIsOne((number)theGcd, cf));
836 
837  if( !naIsOne((number)theGcd, cf) )
838  {
839  WerrorS("zero divisor found - your minpoly is not irreducible");
840  p_Delete(&aFactor, naRing); aFactor = NULL;
841  }
842  p_Delete(&theGcd, naRing);
843 
844  return (number)(aFactor);
845 }
BOOLEAN singclap_extgcd(poly f, poly g, poly &res, poly &pa, poly &pb, const ring r)
Definition: clapsing.cc:455

◆ naIsMOne()

BOOLEAN naIsMOne ( number  a,
const coeffs  cf 
)

Definition at line 323 of file algext.cc.

324 {
325  naTest(a);
326  poly aAsPoly = (poly)a;
327  if ((a==NULL) || (!p_IsConstant(aAsPoly, naRing))) return FALSE;
328  return n_IsMOne(p_GetCoeff(aAsPoly, naRing), naCoeffs);
329 }
static FORCE_INLINE BOOLEAN n_IsMOne(number n, const coeffs r)
TRUE iff 'n' represents the additive inverse of the one element, i.e. -1.
Definition: coeffs.h:473

◆ naIsOne()

BOOLEAN naIsOne ( number  a,
const coeffs  cf 
)

Definition at line 315 of file algext.cc.

316 {
317  naTest(a);
318  poly aAsPoly = (poly)a;
319  if ((a==NULL) || (!p_IsConstant(aAsPoly, naRing))) return FALSE;
320  return n_IsOne(p_GetCoeff(aAsPoly, naRing), naCoeffs);
321 }

◆ naIsParam()

int naIsParam ( number  m,
const coeffs  cf 
)

if m == var(i)/1 => return i,

Definition at line 1091 of file algext.cc.

1092 {
1094 
1095  const ring R = cf->extRing;
1096  assume( R != NULL );
1097 
1098  return p_Var( (poly)m, R );
1099 }
int m
Definition: cfEzgcd.cc:128
int p_Var(poly m, const ring r)
Definition: p_polys.cc:4684

◆ naIsZero()

BOOLEAN naIsZero ( number  a,
const coeffs  cf 
)

Definition at line 272 of file algext.cc.

273 {
274  naTest(a);
275  return (a == NULL);
276 }

◆ naKillChar()

void naKillChar ( coeffs  cf)

Definition at line 1323 of file algext.cc.

1324 {
1325  rDecRefCnt(cf->extRing);
1326  if(cf->extRing->ref<0)
1327  rDelete(cf->extRing);
1328 }
static void rDecRefCnt(ring r)
Definition: ring.h:845

◆ naLcmContent()

number naLcmContent ( number  a,
number  b,
const coeffs  cf 
)

Definition at line 643 of file algext.cc.

644 {
645  if (nCoeff_is_Zp(naRing->cf)) return naCopy(a,cf);
646 #if 0
647  else {
648  number g = ndGcd(a, b, cf);
649  return g;
650  }
651 #else
652  {
653  a=(number)p_Copy((poly)a,naRing);
654  number t=napNormalizeHelper(b,cf);
655  if(!n_IsOne(t,naRing->cf))
656  {
657  number bt, rr;
658  poly xx=(poly)a;
659  while (xx!=NULL)
660  {
661  bt = n_SubringGcd(t, pGetCoeff(xx), naRing->cf);
662  rr = n_Mult(t, pGetCoeff(xx), naRing->cf);
663  n_Delete(&pGetCoeff(xx),naRing->cf);
664  pGetCoeff(xx) = n_Div(rr, bt, naRing->cf);
665  n_Normalize(pGetCoeff(xx),naRing->cf);
666  n_Delete(&bt,naRing->cf);
667  n_Delete(&rr,naRing->cf);
668  pIter(xx);
669  }
670  }
671  n_Delete(&t,naRing->cf);
672  return (number) a;
673  }
674 #endif
675 }
number napNormalizeHelper(number b, const coeffs cf)
Definition: algext.cc:629
static FORCE_INLINE number n_Mult(number a, number b, const coeffs r)
return the product of 'a' and 'b', i.e., a*b
Definition: coeffs.h:637
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...
Definition: coeffs.h:616
static FORCE_INLINE void n_Normalize(number &n, const coeffs r)
inplace-normalization of n; produces some canonical representation of n;
Definition: coeffs.h:579
number ndGcd(number, number, const coeffs r)
Definition: numbers.cc:169

◆ naMap00()

number naMap00 ( number  a,
const coeffs  src,
const coeffs  dst 
)

Definition at line 848 of file algext.cc.

849 {
850  if (n_IsZero(a, src)) return NULL;
851  assume(src->rep == dst->extRing->cf->rep);
852  poly result = p_One(dst->extRing);
853  p_SetCoeff(result, n_Copy(a, src), dst->extRing);
854  return (number)result;
855 }
static FORCE_INLINE BOOLEAN n_IsZero(number n, const coeffs r)
TRUE iff 'n' represents the zero element.
Definition: coeffs.h:465
poly p_One(const ring r)
Definition: p_polys.cc:1308
static number p_SetCoeff(poly p, number n, ring r)
Definition: p_polys.h:412

◆ naMap0P()

number naMap0P ( number  a,
const coeffs  src,
const coeffs  dst 
)

Definition at line 938 of file algext.cc.

939 {
940  if (n_IsZero(a, src)) return NULL;
941  // int p = rChar(dst->extRing);
942 
943  number q = nlModP(a, src, dst->extRing->cf); // FIXME? TODO? // extern number nlModP(number q, const coeffs Q, const coeffs Zp); // Map q \in QQ \to pZ
944 
945  poly result = p_NSet(q, dst->extRing);
946 
947  return (number)result;
948 }
number nlModP(number q, const coeffs, const coeffs Zp)
Definition: longrat.cc:1538

◆ naMapP0()

number naMapP0 ( number  a,
const coeffs  src,
const coeffs  dst 
)

Definition at line 870 of file algext.cc.

871 {
872  if (n_IsZero(a, src)) return NULL;
873  /* mapping via intermediate int: */
874  int n = n_Int(a, src);
875  number q = n_Init(n, dst->extRing->cf);
876  poly result = p_One(dst->extRing);
877  p_SetCoeff(result, q, dst->extRing);
878  return (number)result;
879 }

◆ naMapPP()

number naMapPP ( number  a,
const coeffs  src,
const coeffs  dst 
)

Definition at line 951 of file algext.cc.

952 {
953  if (n_IsZero(a, src)) return NULL;
954  assume(src == dst->extRing->cf);
955  poly result = p_One(dst->extRing);
956  p_SetCoeff(result, n_Copy(a, src), dst->extRing);
957  return (number)result;
958 }

◆ naMapUP()

number naMapUP ( number  a,
const coeffs  src,
const coeffs  dst 
)

Definition at line 961 of file algext.cc.

962 {
963  if (n_IsZero(a, src)) return NULL;
964  /* mapping via intermediate int: */
965  int n = n_Int(a, src);
966  number q = n_Init(n, dst->extRing->cf);
967  poly result = p_One(dst->extRing);
968  p_SetCoeff(result, q, dst->extRing);
969  return (number)result;
970 }

◆ naMapZ0()

number naMapZ0 ( number  a,
const coeffs  src,
const coeffs  dst 
)

Definition at line 858 of file algext.cc.

859 {
860  if (n_IsZero(a, src)) return NULL;
861  poly result = p_One(dst->extRing);
862  nMapFunc nMap=n_SetMap(src,dst->extRing->cf);
863  p_SetCoeff(result, nMap(a, src, dst->extRing->cf), dst->extRing);
864  if (n_IsZero(pGetCoeff(result),dst->extRing->cf))
865  p_Delete(&result,dst->extRing);
866  return (number)result;
867 }

◆ naMult()

number naMult ( number  a,
number  b,
const coeffs  cf 
)

Definition at line 459 of file algext.cc.

460 {
461  naTest(a); naTest(b);
462  if ((a == NULL)||(b == NULL)) return NULL;
463  poly aTimesB = pp_Mult_qq((poly)a, (poly)b, naRing);
464  definiteReduce(aTimesB, naMinpoly, cf);
465  p_Normalize(aTimesB,naRing);
466  return (number)aTimesB;
467 }

◆ naNeg()

number naNeg ( number  a,
const coeffs  cf 
)

this is in-place, modifies a

Definition at line 332 of file algext.cc.

333 {
334  naTest(a);
335  if (a != NULL) a = (number)p_Neg((poly)a, naRing);
336  return a;
337 }

◆ naNormalize()

void naNormalize ( number &  a,
const coeffs  cf 
)

Definition at line 742 of file algext.cc.

743 {
744  poly aa=(poly)a;
745  if (aa!=naMinpoly)
747  a=(number)aa;
748 }

◆ naParameter()

number naParameter ( const int  iParameter,
const coeffs  cf 
)

return the specified parameter as a number in the given alg. field

Definition at line 1076 of file algext.cc.

1077 {
1079 
1080  const ring R = cf->extRing;
1081  assume( R != NULL );
1082  assume( 0 < iParameter && iParameter <= rVar(R) );
1083 
1084  poly p = p_One(R); p_SetExp(p, iParameter, 1, R); p_Setm(p, R);
1085 
1086  return (number) p;
1087 }
static unsigned long p_SetExp(poly p, const unsigned long e, const unsigned long iBitmask, const int VarOffset)
set a single variable exponent @Note: VarOffset encodes the position in p->exp
Definition: p_polys.h:488
static void p_Setm(poly p, const ring r)
Definition: p_polys.h:233

◆ naParDeg()

int naParDeg ( number  a,
const coeffs  cf 
)

Definition at line 1068 of file algext.cc.

1069 {
1070  if (a == NULL) return -1;
1071  poly aa=(poly)a;
1072  return cf->extRing->pFDeg(aa,cf->extRing);
1073 }

◆ napNormalizeHelper()

number napNormalizeHelper ( number  b,
const coeffs  cf 
)

Definition at line 629 of file algext.cc.

630 {
631  number h=n_Init(1,naRing->cf);
632  poly bb=(poly)b;
633  number d;
634  while(bb!=NULL)
635  {
636  d=n_NormalizeHelper(h,pGetCoeff(bb), naRing->cf);
637  n_Delete(&h,naRing->cf);
638  h=d;
639  pIter(bb);
640  }
641  return h;
642 }
static FORCE_INLINE number n_NormalizeHelper(number a, number b, const coeffs r)
assume that r is a quotient field (otherwise, return 1) for arguments (a1/a2,b1/b2) return (lcm(a1,...
Definition: coeffs.h:718

◆ naPower()

void naPower ( number  a,
int  exp,
number *  b,
const coeffs  cf 
)

Definition at line 493 of file algext.cc.

494 {
495  naTest(a);
496 
497  /* special cases first */
498  if (a == NULL)
499  {
500  if (exp >= 0) *b = NULL;
501  else WerrorS(nDivBy0);
502  return;
503  }
504  else if (exp == 0) { *b = naInit(1, cf); return; }
505  else if (exp == 1) { *b = naCopy(a, cf); return; }
506  else if (exp == -1) { *b = naInvers(a, cf); return; }
507 
508  int expAbs = exp; if (expAbs < 0) expAbs = -expAbs;
509 
510  /* now compute a^expAbs */
511  poly pow; poly aAsPoly = (poly)a;
512  if (expAbs <= 7)
513  {
514  pow = p_Copy(aAsPoly, naRing);
515  for (int i = 2; i <= expAbs; i++)
516  {
517  pow = p_Mult_q(pow, p_Copy(aAsPoly, naRing), naRing);
519  }
521  }
522  else
523  {
524  pow = p_ISet(1, naRing);
525  poly factor = p_Copy(aAsPoly, naRing);
526  while (expAbs != 0)
527  {
528  if (expAbs & 1)
529  {
532  }
533  expAbs = expAbs / 2;
534  if (expAbs != 0)
535  {
538  }
539  }
542  }
543 
544  /* invert if original exponent was negative */
545  number n = (number)pow;
546  if (exp < 0)
547  {
548  number m = naInvers(n, cf);
549  naDelete(&n, cf);
550  n = m;
551  }
552  *b = n;
553 }
Rational pow(const Rational &a, int e)
Definition: GMPrat.cc:411
void heuristicReduce(poly &p, poly reducer, const coeffs cf)
Definition: algext.cc:560
CanonicalForm factor
Definition: facAbsFact.cc:97

◆ naRead()

const char * naRead ( const char *  s,
number *  a,
const coeffs  cf 
)

Definition at line 606 of file algext.cc.

607 {
608  poly aAsPoly;
609  const char * result = p_Read(s, aAsPoly, naRing);
610  if (aAsPoly!=NULL) definiteReduce(aAsPoly, naMinpoly, cf);
611  *a = (number)aAsPoly;
612  return result;
613 }

◆ naSetMap()

nMapFunc naSetMap ( const coeffs  src,
const coeffs  dst 
)

Get a mapping function from src into the domain of this type (n_algExt)

Q or Z --> Q(a)

Z --> Q(a)

Z/p --> Q(a)

Q --> Z/p(a)

Z --> Z/p(a)

Z/p --> Z/p(a)

Z/u --> Z/p(a)

default

Definition at line 1017 of file algext.cc.

1018 {
1019  /* dst is expected to be an algebraic field extension */
1020  assume(getCoeffType(dst) == n_algExt);
1021 
1022  int h = 0; /* the height of the extension tower given by dst */
1023  coeffs bDst = nCoeff_bottom(dst, h); /* the bottom field in the tower dst */
1024  coeffs bSrc = nCoeff_bottom(src, h); /* the bottom field in the tower src */
1025 
1026  /* for the time being, we only provide maps if h = 1 or 0 */
1027  if (h==0)
1028  {
1029  if ((src->rep==n_rep_gap_rat) && nCoeff_is_Q(bDst))
1030  return naMap00; /// Q or Z --> Q(a)
1031  if ((src->rep==n_rep_gap_gmp) && nCoeff_is_Q(bDst))
1032  return naMapZ0; /// Z --> Q(a)
1033  if (nCoeff_is_Zp(src) && nCoeff_is_Q(bDst))
1034  return naMapP0; /// Z/p --> Q(a)
1035  if (nCoeff_is_Q_or_BI(src) && nCoeff_is_Zp(bDst))
1036  return naMap0P; /// Q --> Z/p(a)
1037  if ((src->rep==n_rep_gap_gmp) && nCoeff_is_Zp(bDst))
1038  return naMapZ0; /// Z --> Z/p(a)
1039  if (nCoeff_is_Zp(src) && nCoeff_is_Zp(bDst))
1040  {
1041  if (src->ch == dst->ch) return naMapPP; /// Z/p --> Z/p(a)
1042  else return naMapUP; /// Z/u --> Z/p(a)
1043  }
1044  }
1045  if (h != 1) return NULL;
1046  if ((!nCoeff_is_Zp(bDst)) && (!nCoeff_is_Q(bDst))) return NULL;
1047  if ((!nCoeff_is_Zp(bSrc)) && (!nCoeff_is_Q_or_BI(bSrc))) return NULL;
1048 
1049  nMapFunc nMap=n_SetMap(src->extRing->cf,dst->extRing->cf);
1050  if (rSamePolyRep(src->extRing, dst->extRing) && (strcmp(rRingVar(0, src->extRing), rRingVar(0, dst->extRing)) == 0))
1051  {
1052  if (src->type==n_algExt)
1053  return ndCopyMap; // naCopyMap; /// K(a) --> K(a)
1054  else
1055  return naCopyTrans2AlgExt;
1056  }
1057  else if ((nMap!=NULL) && (strcmp(rRingVar(0,src->extRing),rRingVar(0,dst->extRing))==0) && (rVar (src->extRing) == rVar (dst->extRing)))
1058  {
1059  if (src->type==n_algExt)
1060  return naGenMap; // naCopyMap; /// K(a) --> K'(a)
1061  else
1062  return naGenTrans2AlgExt;
1063  }
1064 
1065  return NULL; /// default
1066 }
number naMap00(number a, const coeffs src, const coeffs dst)
Definition: algext.cc:848
number naGenMap(number a, const coeffs cf, const coeffs dst)
Definition: algext.cc:972
number naCopyTrans2AlgExt(number a, const coeffs src, const coeffs dst)
Definition: algext.cc:890
number naMap0P(number a, const coeffs src, const coeffs dst)
Definition: algext.cc:938
number naGenTrans2AlgExt(number a, const coeffs cf, const coeffs dst)
Definition: algext.cc:987
number naMapPP(number a, const coeffs src, const coeffs dst)
Definition: algext.cc:951
number naMapP0(number a, const coeffs src, const coeffs dst)
Definition: algext.cc:870
static coeffs nCoeff_bottom(const coeffs r, int &height)
Definition: algext.cc:258
number naMapZ0(number a, const coeffs src, const coeffs dst)
Definition: algext.cc:858
number naMapUP(number a, const coeffs src, const coeffs dst)
Definition: algext.cc:961
number ndCopyMap(number a, const coeffs src, const coeffs dst)
Definition: numbers.cc:259
static FORCE_INLINE BOOLEAN nCoeff_is_Q_or_BI(const coeffs r)
Definition: coeffs.h:853
@ n_rep_gap_rat
(number), see longrat.h
Definition: coeffs.h:112
@ n_rep_gap_gmp
(), see rinteger.h, new impl.
Definition: coeffs.h:113

◆ naSize()

int naSize ( number  a,
const coeffs  cf 
)

Definition at line 712 of file algext.cc.

713 {
714  if (a == NULL) return 0;
715  poly aAsPoly = (poly)a;
716  int theDegree = 0; int noOfTerms = 0;
717  while (aAsPoly != NULL)
718  {
719  noOfTerms++;
720  int d = p_GetExp(aAsPoly, 1, naRing);
721  if (d > theDegree) theDegree = d;
722  pIter(aAsPoly);
723  }
724  return (theDegree +1) * noOfTerms;
725 }
STATIC_VAR int theDegree
Definition: cf_char.cc:26

◆ naSub()

number naSub ( number  a,
number  b,
const coeffs  cf 
)

Definition at line 448 of file algext.cc.

449 {
450  naTest(a); naTest(b);
451  if (b == NULL) return naCopy(a, cf);
452  poly minusB = p_Neg(p_Copy((poly)b, naRing), naRing);
453  if (a == NULL) return (number)minusB;
454  poly aMinusB = p_Add_q(p_Copy((poly)a, naRing), minusB, naRing);
455  //definiteReduce(aMinusB, naMinpoly, cf);
456  return (number)aMinusB;
457 }

◆ naWriteLong()

void naWriteLong ( number  a,
const coeffs  cf 
)

Definition at line 570 of file algext.cc.

571 {
572  naTest(a);
573  if (a == NULL)
574  StringAppendS("0");
575  else
576  {
577  poly aAsPoly = (poly)a;
578  /* basically, just write aAsPoly using p_Write,
579  but use brackets around the output, if a is not
580  a constant living in naCoeffs = cf->extRing->cf */
581  BOOLEAN useBrackets = !(p_IsConstant(aAsPoly, naRing));
582  if (useBrackets) StringAppendS("(");
583  p_String0Long(aAsPoly, naRing, naRing);
584  if (useBrackets) StringAppendS(")");
585  }
586 }
void p_String0Long(const poly p, ring lmRing, ring tailRing)
print p in a long way
Definition: polys0.cc:203
void StringAppendS(const char *st)
Definition: reporter.cc:107

◆ naWriteShort()

void naWriteShort ( number  a,
const coeffs  cf 
)

Definition at line 588 of file algext.cc.

589 {
590  naTest(a);
591  if (a == NULL)
592  StringAppendS("0");
593  else
594  {
595  poly aAsPoly = (poly)a;
596  /* basically, just write aAsPoly using p_Write,
597  but use brackets around the output, if a is not
598  a constant living in naCoeffs = cf->extRing->cf */
599  BOOLEAN useBrackets = !(p_IsConstant(aAsPoly, naRing));
600  if (useBrackets) StringAppendS("(");
601  p_String0Short(aAsPoly, naRing, naRing);
602  if (useBrackets) StringAppendS(")");
603  }
604 }
void p_String0Short(const poly p, ring lmRing, ring tailRing)
print p in a short way, if possible
Definition: polys0.cc:184

◆ nCoeff_bottom()

static coeffs nCoeff_bottom ( const coeffs  r,
int &  height 
)
static

Definition at line 258 of file algext.cc.

259 {
260  assume(r != NULL);
261  coeffs cf = r;
262  height = 0;
263  while (nCoeff_is_Extension(cf))
264  {
265  assume(cf->extRing != NULL); assume(cf->extRing->cf != NULL);
266  cf = cf->extRing->cf;
267  height++;
268  }
269  return cf;
270 }
static FORCE_INLINE BOOLEAN nCoeff_is_Extension(const coeffs r)
Definition: coeffs.h:870

◆ p_ExtGcd()

poly p_ExtGcd ( poly  p,
poly &  pFactor,
poly  q,
poly &  qFactor,
ring  r 
)

assumes that p and q are univariate polynomials in r, mentioning the same variable; assumes a global monomial ordering in r; assumes that not both p and q are NULL; returns the gcd of p and q; moreover, afterwards pFactor and qFactor contain appropriate factors such that gcd(p, q) = p * pFactor + q * qFactor; leaves p and q unmodified

Definition at line 216 of file algext.cc.

217 {
218  assume((p != NULL) || (q != NULL));
219  poly a = p; poly b = q; BOOLEAN aCorrespondsToP = TRUE;
220  if (p_Deg(a, r) < p_Deg(b, r))
221  { a = q; b = p; aCorrespondsToP = FALSE; }
222  a = p_Copy(a, r); b = p_Copy(b, r);
223  poly aFactor = NULL; poly bFactor = NULL;
224  poly theGcd = p_ExtGcdHelper(a, aFactor, b, bFactor, r);
225  if (aCorrespondsToP) { pFactor = aFactor; qFactor = bFactor; }
226  else { pFactor = bFactor; qFactor = aFactor; }
227  return theGcd;
228 }
static poly p_ExtGcdHelper(poly &p, poly &pFactor, poly &q, poly &qFactor, ring r)
Definition: algext.cc:183

◆ p_ExtGcdHelper()

static poly p_ExtGcdHelper ( poly &  p,
poly &  pFactor,
poly &  q,
poly &  qFactor,
ring  r 
)
inlinestatic

Definition at line 183 of file algext.cc.

185 {
186  if (q == NULL)
187  {
188  qFactor = NULL;
189  pFactor = p_ISet(1, r);
190  p_SetCoeff(pFactor, n_Invers(p_GetCoeff(p, r), r->cf), r);
191  p_Monic(p, r);
192  return p;
193  }
194  else
195  {
196  poly pDivQ = p_PolyDiv(p, q, TRUE, r);
197  poly ppFactor = NULL; poly qqFactor = NULL;
198  poly theGcd = p_ExtGcdHelper(q, qqFactor, p, ppFactor, r);
199  pFactor = ppFactor;
200  qFactor = p_Add_q(qqFactor,
201  p_Neg(p_Mult_q(pDivQ, p_Copy(ppFactor, r), r), r),
202  r);
203  return theGcd;
204  }
205 }
static void p_Monic(poly p, const ring r)
returns NULL if p == NULL, otherwise makes p monic by dividing by its leading coefficient (only done ...
Definition: algext.cc:120

◆ p_Gcd()

static poly p_Gcd ( const poly  p,
const poly  q,
const ring  r 
)
inlinestatic

Definition at line 165 of file algext.cc.

166 {
167  assume((p != NULL) || (q != NULL));
168 
169  poly a = p; poly b = q;
170  if (p_Deg(a, r) < p_Deg(b, r)) { a = q; b = p; }
171  a = p_Copy(a, r); b = p_Copy(b, r);
172 
173  /* We have to make p monic before we return it, so that if the
174  gcd is a unit in the ground field, we will actually return 1. */
175  a = p_GcdHelper(a, b, r);
176  p_Monic(a, r);
177  return a;
178 }
static poly p_GcdHelper(poly &p, poly &q, const ring r)
see p_Gcd; additional assumption: deg(p) >= deg(q); must destroy p and q (unless one of them is retur...
Definition: algext.cc:145

◆ p_GcdHelper()

static poly p_GcdHelper ( poly &  p,
poly &  q,
const ring  r 
)
inlinestatic

see p_Gcd; additional assumption: deg(p) >= deg(q); must destroy p and q (unless one of them is returned)

Definition at line 145 of file algext.cc.

146 {
147  while (q != NULL)
148  {
149  p_PolyDiv(p, q, FALSE, r);
150  // swap p and q:
151  poly& t = q;
152  q = p;
153  p = t;
154 
155  }
156  return p;
157 }

◆ p_Monic()

static void p_Monic ( poly  p,
const ring  r 
)
inlinestatic

returns NULL if p == NULL, otherwise makes p monic by dividing by its leading coefficient (only done if this is not already 1); this assumes that we are over a ground field so that division is well-defined; modifies p

assumes that p and q are univariate polynomials in r, mentioning the same variable; assumes a global monomial ordering in r; assumes that not both p and q are NULL; returns the gcd of p and q; leaves p and q unmodified

Definition at line 120 of file algext.cc.

121 {
122  if (p == NULL) return;
123  number n = n_Init(1, r->cf);
124  if (p->next==NULL) { p_SetCoeff(p,n,r); return; }
125  poly pp = p;
126  number lc = p_GetCoeff(p, r);
127  if (n_IsOne(lc, r->cf)) return;
128  number lcInverse = n_Invers(lc, r->cf);
129  p_SetCoeff(p, n, r); // destroys old leading coefficient!
130  pIter(p);
131  while (p != NULL)
132  {
133  number n = n_Mult(p_GetCoeff(p, r), lcInverse, r->cf);
134  n_Normalize(n,r->cf);
135  p_SetCoeff(p, n, r); // destroys old leading coefficient!
136  pIter(p);
137  }
138  n_Delete(&lcInverse, r->cf);
139  p = pp;
140 }
CanonicalForm lc(const CanonicalForm &f)
CanonicalForm pp(const CanonicalForm &)
CanonicalForm pp ( const CanonicalForm & f )
Definition: cf_gcd.cc:676