My Project
Data Structures | Functions
transext.h File Reference
#include "coeffs/coeffs.h"
#include "polys/monomials/ring.h"

Go to the source code of this file.

Data Structures

struct  TransExtInfo
 struct for passing initialization parameters to naInitChar More...
 

Functions

nMapFunc ntSetMap (const coeffs src, const coeffs dst)
 Get a mapping function from src into the domain of this type (n_transExt) More...
 
BOOLEAN ntInitChar (coeffs cf, void *infoStruct)
 Initialize the coeffs object. More...
 
number ntDiff (number a, number d, const coeffs cf)
 
int ntIsParam (number, const coeffs)
 if m == var(i)/1 => return i, More...
 
poly gcd_over_Q (poly f, poly g, const ring r)
 helper routine for calling singclap_gcd_r More...
 

Data Structure Documentation

◆ TransExtInfo

struct TransExtInfo

struct for passing initialization parameters to naInitChar

Definition at line 88 of file transext.h.

Data Fields
ring r

Function Documentation

◆ gcd_over_Q()

poly gcd_over_Q ( poly  f,
poly  g,
const ring  r 
)

helper routine for calling singclap_gcd_r

Definition at line 275 of file transext.cc.

276 {
277  poly res;
278  f=p_Copy(f,r);
279  p_Cleardenom(f, r);
280  g=p_Copy(g,r);
281  p_Cleardenom(g, r);
282  res=singclap_gcd_r(f,g,r);
283  p_Delete(&f, r);
284  p_Delete(&g, r);
285  return res;
286 }
g
Definition: cfModGcd.cc:4090
FILE * f
Definition: checklibs.c:9
poly singclap_gcd_r(poly f, poly g, const ring r)
Definition: clapsing.cc:68
CanonicalForm res
Definition: facAbsFact.cc:60
poly p_Cleardenom(poly p, const ring r)
Definition: p_polys.cc:2910
static void p_Delete(poly *p, const ring r)
Definition: p_polys.h:903
static poly p_Copy(poly p, const ring r)
returns a copy of p
Definition: p_polys.h:848

◆ ntDiff()

number ntDiff ( number  a,
number  d,
const coeffs  cf 
)

Definition at line 897 of file transext.cc.

898 {
899  //check_N(a,cf);
900  //check_N(d,cf);
901  ntTest(a);
902  ntTest(d);
903 
904  if (IS0(d))
905  {
906  WerrorS("ringvar expected");
907  return NULL;
908  }
909  fraction t = (fraction) d;
910  if (!DENIS1(t))
911  {
912  WerrorS("expected differentiation by a variable");
913  return NULL;
914  }
915  int k=p_Var(NUM(t),ntRing);
916  if (k==0)
917  {
918  WerrorS("expected differentiation by a variable");
919  return NULL;
920  }
921 
922  if (IS0(a)) return ntCopy(a, cf);
923 
924  fraction fa = (fraction)a;
925  fraction result = (fraction)omAlloc0Bin(fractionObjectBin);
926  if (DENIS1(fa))
927  {
928  NUM(result) = p_Diff(NUM(fa),k,ntRing);
929  //DEN(result) = NULL; // done by ..Alloc0..
930  if (NUM(result)==NULL)
931  {
933  return(NULL);
934  }
936  //check_N((number)result,cf);
937  ntTest((number)result);
938  return (number)result;
939  }
940 
941  poly fg = p_Mult_q(p_Copy(DEN(fa),ntRing),p_Diff(NUM(fa),k,ntRing),ntRing);
942  poly gf = p_Mult_q(p_Copy(NUM(fa),ntRing),p_Diff(DEN(fa),k,ntRing),ntRing);
943  NUM(result) = p_Sub(fg,gf,ntRing);
944  if (NUM(result)==NULL) return(NULL);
945  DEN(result) = pp_Mult_qq(DEN(fa), DEN(fa), ntRing);
946  COM(result) = COM(fa) + COM(fa) + DIFF_COMPLEXITY;
948 
949  //check_N((number)result,cf);
950  ntTest((number)result);
951  return (number)result;
952 }
void * ADDRESS
Definition: auxiliary.h:119
int k
Definition: cfEzgcd.cc:99
CanonicalForm cf
Definition: cfModGcd.cc:4083
BOOLEAN fa(leftv res, leftv args)
Definition: cohomo.cc:4369
return result
Definition: facAbsBiFact.cc:75
void WerrorS(const char *s)
Definition: feFopen.cc:24
#define omAlloc0Bin(bin)
Definition: omAllocDecl.h:206
#define omFreeBin(addr, bin)
Definition: omAllocDecl.h:259
#define NULL
Definition: omList.c:12
poly p_Diff(poly a, int k, const ring r)
Definition: p_polys.cc:1894
int p_Var(poly m, const ring r)
Definition: p_polys.cc:4772
poly p_Sub(poly p1, poly p2, const ring r)
Definition: p_polys.cc:1986
static poly p_Mult_q(poly p, poly q, const ring r)
Definition: p_polys.h:1116
static poly pp_Mult_qq(poly p, poly q, const ring r)
Definition: p_polys.h:1153
@ NUM
Definition: readcf.cc:170
static void heuristicGcdCancellation(number a, const coeffs cf)
forward declarations
Definition: transext.cc:1398
#define ntRing
Definition: transext.cc:80
#define COM(f)
Definition: transext.cc:69
static number ntCopy(number a, const coeffs cf)
Definition: transext.cc:372
#define ntTest(a)
Definition: transext.cc:76
VAR omBin fractionObjectBin
Definition: transext.cc:89
#define DIFF_COMPLEXITY
complexity increase due to diff
Definition: transext.cc:63

◆ ntInitChar()

BOOLEAN ntInitChar ( coeffs  cf,
void *  infoStruct 
)

Initialize the coeffs object.

Definition at line 2636 of file transext.cc.

2637 {
2638 
2639  assume( infoStruct != NULL );
2640 
2641  TransExtInfo *e = (TransExtInfo *)infoStruct;
2642 
2643  assume( e->r != NULL); // extRing;
2644  assume( e->r->cf != NULL); // extRing->cf;
2645  assume( e->r->qideal == NULL );
2646 
2647  assume( cf != NULL );
2648  assume(getCoeffType(cf) == n_transExt); // coeff type;
2649 
2650  ring R = e->r;
2651  assume(R != NULL);
2652 
2653  rIncRefCnt(R); // increase the ref.counter for the ground poly. ring!
2654 
2655  cf->extRing = R;
2656  /* propagate characteristic up so that it becomes
2657  directly accessible in cf: */
2658  cf->ch = R->cf->ch;
2659 
2660  cf->is_field=TRUE;
2661  cf->is_domain=TRUE;
2662  cf->rep=n_rep_rat_fct;
2663 
2664  cf->factoryVarOffset = R->cf->factoryVarOffset + rVar(R);
2665 
2666  cf->cfCoeffName = naCoeffName; // FIXME? TODO? // extern char* naCoeffString(const coeffs r);
2667 
2668  cf->cfGreaterZero = ntGreaterZero;
2669  cf->cfGreater = ntGreater;
2670  cf->cfEqual = ntEqual;
2671  cf->cfIsZero = ntIsZero;
2672  cf->cfIsOne = ntIsOne;
2673  cf->cfIsMOne = ntIsMOne;
2674  cf->cfInit = ntInit;
2675  cf->cfFarey = ntFarey;
2676  cf->cfChineseRemainder = ntChineseRemainder;
2677  cf->cfInt = ntInt;
2678  cf->cfAdd = ntAdd;
2679  cf->cfInpAdd = ntInpAdd;
2680  cf->cfInpNeg = ntNeg;
2681  cf->cfSub = ntSub;
2682  cf->cfMult = ntMult;
2683  cf->cfInpMult = ntInpMult;
2684  cf->cfDiv = ntDiv;
2685  cf->cfExactDiv = ntExactDiv;
2686  cf->cfPower = ntPower;
2687  cf->cfCopy = ntCopy;
2688  cf->cfWriteLong = ntWriteLong;
2689  cf->cfRead = ntRead;
2690  cf->cfNormalize = ntNormalize;
2691  cf->cfDelete = ntDelete;
2692  cf->cfSetMap = ntSetMap;
2693  cf->cfGetDenom = ntGetDenom;
2694  cf->cfGetNumerator = ntGetNumerator;
2695  //cf->cfRePart = ntCopy;
2696  //cf->cfImPart = ntImPart;
2697  cf->cfCoeffWrite = ntCoeffWrite;
2698 #ifdef LDEBUG
2699  cf->cfDBTest = ntDBTest;
2700 #endif
2701  //cf->cfGcd = ntGcd_dummy;
2702  cf->cfSubringGcd = ntGcd;
2703  cf->cfNormalizeHelper = ntNormalizeHelper;
2704  cf->cfSize = ntSize;
2705  cf->nCoeffIsEqual = ntCoeffIsEqual;
2706  cf->cfInvers = ntInvers;
2707  cf->cfKillChar = ntKillChar;
2708  cf->cfInitMPZ = ntInitMPZ;
2709  cf->cfMPZ = ntMPZ;
2710 
2711  if( rCanShortOut(ntRing) )
2712  cf->cfWriteShort = ntWriteShort;
2713  else
2714  cf->cfWriteShort = ntWriteLong;
2715 
2716  cf->convFactoryNSingN =ntConvFactoryNSingN;
2717  cf->convSingNFactoryN =ntConvSingNFactoryN;
2718  cf->cfParDeg = ntParDeg;
2719 
2720  cf->iNumberOfParameters = rVar(R);
2721  cf->pParameterNames = (const char**)R->names;
2722  cf->cfParameter = ntParameter;
2723  cf->has_simple_Inverse= FALSE;
2724  /* cf->has_simple_Alloc= FALSE; */
2725 
2726 
2727  if( nCoeff_is_Q(R->cf) )
2728  cf->cfClearContent = ntClearContent;
2729 
2730  cf->cfClearDenominators = ntClearDenominators;
2731 
2732  return FALSE;
2733 }
char * naCoeffName(const coeffs r)
Definition: algext.cc:1345
#define TRUE
Definition: auxiliary.h:100
#define FALSE
Definition: auxiliary.h:96
@ n_transExt
used for all transcendental extensions, i.e., the top-most extension in an extension tower is transce...
Definition: coeffs.h:38
static FORCE_INLINE BOOLEAN nCoeff_is_Q(const coeffs r)
Definition: coeffs.h:806
static FORCE_INLINE n_coeffType getCoeffType(const coeffs r)
Returns the type of coeffs domain.
Definition: coeffs.h:421
@ n_rep_rat_fct
(fraction), see transext.h
Definition: coeffs.h:114
#define assume(x)
Definition: mod2.h:389
static ring rIncRefCnt(ring r)
Definition: ring.h:843
static BOOLEAN rCanShortOut(const ring r)
Definition: ring.h:587
static short rVar(const ring r)
#define rVar(r) (r->N)
Definition: ring.h:593
#define R
Definition: sirandom.c:27
static int ntSize(number a, const coeffs cf)
Definition: transext.cc:1903
static BOOLEAN ntDBTest(number a, const char *f, const int l, const coeffs r)
Definition: transext.cc:140
static number ntParameter(const int iParameter, const coeffs cf)
return the specified parameter as a number in the given trans.ext.
Definition: transext.cc:2286
static void ntWriteLong(number a, const coeffs cf)
Definition: transext.cc:1641
static BOOLEAN ntCoeffIsEqual(const coeffs cf, n_coeffType n, void *param)
Definition: transext.cc:1727
nMapFunc ntSetMap(const coeffs src, const coeffs dst)
Get a mapping function from src into the domain of this type (n_transExt)
Definition: transext.cc:2170
static number ntSub(number a, number b, const coeffs cf)
Definition: transext.cc:1034
static long ntInt(number &a, const coeffs cf)
Definition: transext.cc:773
static void ntDelete(number *a, const coeffs cf)
Definition: transext.cc:313
static BOOLEAN ntIsOne(number a, const coeffs cf)
Definition: transext.cc:669
static BOOLEAN ntIsZero(number a, const coeffs cf)
Definition: transext.cc:306
static number ntGetNumerator(number &a, const coeffs cf)
TODO: normalization of a!?
Definition: transext.cc:506
static CanonicalForm ntConvSingNFactoryN(number n, BOOLEAN, const coeffs cf)
Definition: transext.cc:2268
static void ntClearDenominators(ICoeffsEnumerator &numberCollectionEnumerator, number &c, const coeffs cf)
Definition: transext.cc:2427
static BOOLEAN ntIsMOne(number a, const coeffs cf)
Definition: transext.cc:678
static void ntMPZ(mpz_t m, number &n, const coeffs r)
Definition: transext.cc:2619
static void ntCoeffWrite(const coeffs cf, BOOLEAN details)
Definition: transext.cc:856
static number ntGcd(number a, number b, const coeffs cf)
Definition: transext.cc:1830
static number ntConvFactoryNSingN(const CanonicalForm n, const coeffs cf)
Definition: transext.cc:2256
static void ntClearContent(ICoeffsEnumerator &numberCollectionEnumerator, number &c, const coeffs cf)
Definition: transext.cc:2334
static number ntInvers(number a, const coeffs cf)
Definition: transext.cc:1270
static number ntNormalizeHelper(number a, number b, const coeffs cf)
Definition: transext.cc:1749
static void ntPower(number a, int exp, number *b, const coeffs cf)
Definition: transext.cc:1336
number ntInit(long i, const coeffs cf)
Definition: transext.cc:704
static number ntGetDenom(number &a, const coeffs cf)
TODO: normalization of a!?
Definition: transext.cc:567
static const char * ntRead(const char *s, number *a, const coeffs cf)
Definition: transext.cc:1691
static void ntInpMult(number &a, number b, const coeffs cf)
Definition: transext.cc:1141
static void ntKillChar(coeffs cf)
Definition: transext.cc:2250
static void ntInpAdd(number &a, number b, const coeffs cf)
Definition: transext.cc:995
static void ntWriteShort(number a, const coeffs cf)
Definition: transext.cc:1666
static number ntDiv(number a, number b, const coeffs cf)
Definition: transext.cc:1224
static int ntParDeg(number a, const coeffs cf)
Definition: transext.cc:2277
static BOOLEAN ntGreaterZero(number a, const coeffs cf)
Definition: transext.cc:796
static number ntChineseRemainder(number *x, number *q, int rl, BOOLEAN, CFArray &inv_cache, const coeffs cf)
Definition: transext.cc:2571
static number ntMult(number a, number b, const coeffs cf)
Definition: transext.cc:1073
static number ntNeg(number a, const coeffs cf)
this is in-place, modifies a
Definition: transext.cc:691
static number ntAdd(number a, number b, const coeffs cf)
Definition: transext.cc:954
static number ntFarey(number p, number n, const coeffs cf)
Definition: transext.cc:2601
static void ntNormalize(number &a, const coeffs cf)
Definition: transext.cc:1701
static BOOLEAN ntEqual(number a, number b, const coeffs cf)
Definition: transext.cc:326
static BOOLEAN ntGreater(number a, number b, const coeffs cf)
Definition: transext.cc:806
static number ntExactDiv(number a, number b, const coeffs cf)
Definition: transext.cc:1719
static number ntInitMPZ(mpz_t m, const coeffs r)
Definition: transext.cc:2611
struct for passing initialization parameters to naInitChar
Definition: transext.h:88

◆ ntIsParam()

int ntIsParam ( number  m,
const  coeffs 
)

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

Definition at line 2308 of file transext.cc.

2309 {
2310  ntTest(m);
2312 
2313  const ring R = cf->extRing;
2314  assume( R != NULL );
2315 
2316  fraction f = (fraction)m;
2317 
2318  if( DEN(f) != NULL )
2319  return 0;
2320 
2321  return p_Var( NUM(f), R );
2322 }
int m
Definition: cfEzgcd.cc:128

◆ ntSetMap()

nMapFunc ntSetMap ( const coeffs  src,
const coeffs  dst 
)

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

Q or Z --> Q(T)

Z --> K(T)

Z/p --> Q(T)

Q --> Z/p(T)

Z/p --> Z/p(T)

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

Z/p --> Z/p(T)

K(T') --> K(T)

K(T') --> K'(T)

K(T') --> K(T)

K(T') --> K'(T)

default

Definition at line 2170 of file transext.cc.

2171 {
2172  /* dst is expected to be a rational function field */
2173  assume(getCoeffType(dst) == n_transExt);
2174 
2175  int h = 0; /* the height of the extension tower given by dst */
2176  coeffs bDst = nCoeff_bottom(dst, h); /* the bottom field in the tower dst */
2177  coeffs bSrc = nCoeff_bottom(src, h); /* the bottom field in the tower src */
2178 
2179  /* for the time being, we only provide maps if h = 1 and if b is Q or
2180  some field Z/pZ: */
2181  if (h==0)
2182  {
2183  if (((src->rep==n_rep_gap_rat) || (src->rep==n_rep_gap_gmp))
2184  && (nCoeff_is_Q(dst->extRing->cf) || nCoeff_is_Z(dst->extRing->cf)))
2185  return ntMap00; /// Q or Z --> Q(T)
2186  if (src->rep==n_rep_gmp)
2187  return ntMapZ0; /// Z --> K(T)
2188  if (nCoeff_is_Zp(src) && nCoeff_is_Q(bDst))
2189  return ntMapP0; /// Z/p --> Q(T)
2190  if (nCoeff_is_Q_or_BI(src) && nCoeff_is_Zp(bDst))
2191  return ntMap0P; /// Q --> Z/p(T)
2192  if (nCoeff_is_Zp(src) && nCoeff_is_Zp(bDst))
2193  {
2194  if (src->ch == dst->ch) return ntMapPP; /// Z/p --> Z/p(T)
2195  else return ntMapUP; /// Z/u --> Z/p(T)
2196  }
2197  if (nCoeff_is_Zn(src) && nCoeff_is_Zn(bDst))
2198  {
2199  if (mpz_cmp(src->modNumber,bDst->modNumber)==0) return ntMapPP; /// Z/p --> Z/p(T)
2200  }
2201  }
2202  if (h != 1) return NULL;
2203  //if ((!nCoeff_is_Zp(bDst)) && (!nCoeff_is_Q(bDst))) return NULL;
2204 
2205  /* Let T denote the sequence of transcendental extension variables, i.e.,
2206  K[t_1, ..., t_s] =: K[T];
2207  Let moreover, for any such sequence T, T' denote any subsequence of T
2208  of the form t_1, ..., t_w with w <= s. */
2209 
2210  if (rVar(src->extRing) > rVar(dst->extRing))
2211  return NULL;
2212 
2213  for (int i = 0; i < rVar(src->extRing); i++)
2214  if (strcmp(rRingVar(i, src->extRing), rRingVar(i, dst->extRing)) != 0)
2215  return NULL;
2216 
2217  if (src->type==n_transExt)
2218  {
2219  if (src->extRing->cf==dst->extRing->cf)
2220  return ntCopyMap; /// K(T') --> K(T)
2221  else
2222  return ntGenMap; /// K(T') --> K'(T)
2223  }
2224  else
2225  {
2226  if (src->extRing->cf==dst->extRing->cf)
2227  return ntCopyAlg; /// K(T') --> K(T)
2228  else
2229  return ntGenAlg; /// K(T') --> K'(T)
2230  }
2231 
2232  return NULL; /// default
2233 }
int i
Definition: cfEzgcd.cc:132
static FORCE_INLINE BOOLEAN nCoeff_is_Z(const coeffs r)
Definition: coeffs.h:816
static FORCE_INLINE BOOLEAN nCoeff_is_Q_or_BI(const coeffs r)
Definition: coeffs.h:829
static FORCE_INLINE BOOLEAN nCoeff_is_Zn(const coeffs r)
Definition: coeffs.h:826
static FORCE_INLINE BOOLEAN nCoeff_is_Zp(const coeffs r)
Definition: coeffs.h:800
@ n_rep_gap_rat
(number), see longrat.h
Definition: coeffs.h:111
@ n_rep_gap_gmp
(), see rinteger.h, new impl.
Definition: coeffs.h:112
@ n_rep_gmp
(mpz_ptr), see rmodulon,h
Definition: coeffs.h:115
STATIC_VAR Poly * h
Definition: janet.cc:971
The main handler for Singular numbers which are suitable for Singular polynomials.
static char * rRingVar(short i, const ring r)
Definition: ring.h:578
static number ntCopyAlg(number a, const coeffs cf, const coeffs dst)
Definition: transext.cc:2092
static number ntMapPP(number a, const coeffs src, const coeffs dst)
Definition: transext.cc:2133
static number ntMapZ0(number a, const coeffs src, const coeffs dst)
Definition: transext.cc:1954
static number ntMap0P(number a, const coeffs src, const coeffs dst)
Definition: transext.cc:2109
static number ntMapP0(number a, const coeffs src, const coeffs dst)
Definition: transext.cc:1968
static number ntMapUP(number a, const coeffs src, const coeffs dst)
Definition: transext.cc:2148
static number ntGenMap(number a, const coeffs cf, const coeffs dst)
Definition: transext.cc:2013
static number ntMap00(number a, const coeffs src, const coeffs dst)
Definition: transext.cc:1930
static number ntGenAlg(number a, const coeffs cf, const coeffs dst)
Definition: transext.cc:2099
static number ntCopyMap(number a, const coeffs cf, const coeffs dst)
Definition: transext.cc:1984
static coeffs nCoeff_bottom(const coeffs r, int &height)
Definition: transext.cc:292