Changeset 9ccaaf in git


Ignore:
Timestamp:
Jan 23, 2017, 6:11:28 PM (7 years ago)
Author:
Hans Schoenemann <hannes@…>
Branches:
(u'spielwiese', 'fe61d9c35bf7c61f2b6cbf1b56e25e2f08d536cc')
Children:
061eacd047c9477bf1592c43bca9e3c4772a682c
Parents:
6664a6665d5668b38e850926f691ded30e00daa9
Message:
transext.c: use static, removed unused routines etc.
Files:
2 edited

Legend:

Unmodified
Added
Removed

  • Tst/Short/absfact.res.gz.uu

    r6664a66 r9ccaaf  
    11begin 640 absfact.res.gz
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    5858end

  • libpolys/polys/ext_fields/transext.cc

    r6664a66 r9ccaaf  
    6868#define NUMIS1(f) (p_IsOne(NUM(f), cf->extRing))
    6969
    70 #define COM(f) f->complexity
     70#define COM(f) (f)->complexity
    7171
    7272
    7373#ifdef LDEBUG
    74 BOOLEAN  ntDBTest(number a, const char *f, const int l, const coeffs r);
     74static BOOLEAN  ntDBTest(number a, const char *f, const int l, const coeffs r);
    7575#endif
    7676
    … …  
    9191
    9292/// forward declarations
    93 BOOLEAN  ntGreaterZero(number a, const coeffs cf);
    94 BOOLEAN  ntGreater(number a, number b, const coeffs cf);
    95 BOOLEAN  ntEqual(number a, number b, const coeffs cf);
    96 BOOLEAN  ntIsOne(number a, const coeffs cf);
    97 BOOLEAN  ntIsMOne(number a, const coeffs cf);
    98 BOOLEAN  ntIsZero(number a, const coeffs cf);
    99 number   ntInit(long i, const coeffs cf);
    100 long     ntInt(number &a, const coeffs cf);
    101 number   ntNeg(number a, const coeffs cf);
    102 number   ntInvers(number a, const coeffs cf);
    103 number   ntAdd(number a, number b, const coeffs cf);
    104 number   ntSub(number a, number b, const coeffs cf);
    105 number   ntMult(number a, number b, const coeffs cf);
    106 number   ntDiv(number a, number b, const coeffs cf);
    107 void     ntPower(number a, int exp, number *b, const coeffs cf);
    108 number   ntCopy(number a, const coeffs cf);
    109 void     ntWriteLong(number a, const coeffs cf);
    110 void     ntWriteShort(number a, const coeffs cf);
    111 number   ntRePart(number a, const coeffs cf);
    112 number   ntImPart(number a, const coeffs cf);
    113 number   ntGetDenom(number &a, const coeffs cf);
    114 number   ntGetNumerator(number &a, const coeffs cf);
    115 number   ntGcd(number a, number b, const coeffs cf);
    116 number   ntNormalizeHelper(number a, number b, const coeffs cf);
    117 int      ntSize(number a, const coeffs cf);
    118 void     ntDelete(number * a, const coeffs cf);
    119 void     ntCoeffWrite(const coeffs cf, BOOLEAN details);
    120 const char * ntRead(const char *s, number *a, const coeffs cf);
    121 static BOOLEAN ntCoeffIsEqual(const coeffs cf, n_coeffType n, void * param);
    122 
    123 void heuristicGcdCancellation(number a, const coeffs cf);
    124 void definiteGcdCancellation(number a, const coeffs cf,
     93static void heuristicGcdCancellation(number a, const coeffs cf);
     94static void definiteGcdCancellation(number a, const coeffs cf,
    12595                             BOOLEAN simpleTestsHaveAlreadyBeenPerformed);
    126 void handleNestedFractionsOverQ(fraction f, const coeffs cf);
    12796
    12897/* test routine, usualy disabled *
    … …  
    170139
    171140#ifdef LDEBUG
    172 BOOLEAN ntDBTest(number a, const char *f, const int l, const coeffs cf)
     141static BOOLEAN ntDBTest(number a, const char *f, const int l, const coeffs cf)
    173142{
    174143  assume(getCoeffType(cf) == n_transExt);
    … …  
    323292}
    324293
    325 BOOLEAN ntIsZero(number a, const coeffs cf)
     294static BOOLEAN ntIsZero(number a, const coeffs cf)
    326295{
    327296  //check_N(a,cf);
    … …  
    330299}
    331300
    332 void ntDelete(number * a, const coeffs cf)
     301static void ntDelete(number * a, const coeffs cf)
    333302{
    334303  //check_N(*a,cf);
    … …  
    343312}
    344313
    345 BOOLEAN ntEqual(number a, number b, const coeffs cf)
     314static BOOLEAN ntEqual(number a, number b, const coeffs cf)
    346315{
    347316  //check_N(a,cf);
    … …  
    389358}
    390359
    391 number ntCopy(number a, const coeffs cf)
     360static number ntCopy(number a, const coeffs cf)
    392361{
    393362  //check_N(a,cf);
    … …  
    404373  ntTest((number)result);
    405374  return (number)result;
    406 }
    407 
    408 /// TODO: normalization of a!?
    409 number ntGetNumerator(number &a, const coeffs cf)
    410 {
    411   //check_N(a,cf);
    412   ntTest(a);
    413   if (IS0(a)) return NULL;
    414 
    415   definiteGcdCancellation(a, cf, FALSE);
    416 
    417   fraction f = (fraction)a;
    418   fraction result = (fraction)omAlloc0Bin(fractionObjectBin);
    419 
    420   const BOOLEAN denis1= DENIS1 (f);
    421 
    422   if (getCoeffType (ntCoeffs) == n_Q && !denis1)
    423     handleNestedFractionsOverQ (f, cf);
    424 
    425   if (getCoeffType (ntCoeffs) == n_Q && denis1)
    426   {
    427     assume( DEN (f) == NULL );
    428 
    429     number g;
    430     // TODO/NOTE: the following should not be necessary (due to
    431     // Hannes!) as NUM (f) should be over Z!!!
    432     CPolyCoeffsEnumerator itr(NUM(f));
    433 
    434 
    435     n_ClearDenominators(itr, g, ntCoeffs);
    436 
    437     if( !n_GreaterZero(g, ntCoeffs) )
    438     {
    439       NUM (f) = p_Neg(NUM (f), ntRing);
    440       g = n_InpNeg(g, ntCoeffs);
    441     }
    442 
    443     // g should be a positive integer now!
    444     assume( n_GreaterZero(g, ntCoeffs) );
    445 
    446     if( !n_IsOne(g, ntCoeffs) )
    447     {
    448       DEN (f) = p_NSet(g, ntRing);
    449       COM (f) ++;
    450       assume( DEN (f) != NULL );
    451     }
    452     else
    453       n_Delete(&g, ntCoeffs);
    454 
    455     ntTest(a);
    456   }
    457 
    458   // Call ntNormalize instead of above?!?
    459 
    460   NUM (result) = p_Copy (NUM (f), ntRing); // ???
    461   //DEN (result) = NULL; // done by ..Alloc0..
    462   //COM (result) = 0; // done by ..Alloc0..
    463 
    464   ntTest((number)result);
    465   //check_N((number)result,cf);
    466   return (number)result;
    467 }
    468 
    469 /// TODO: normalization of a!?
    470 number ntGetDenom(number &a, const coeffs cf)
    471 {
    472   //check_N(a,cf);
    473   ntTest(a);
    474 
    475   fraction result = (fraction)omAlloc0Bin(fractionObjectBin);
    476   //DEN (result)= NULL; // done by ..Alloc0..
    477   //COM (result)= 0; // done by ..Alloc0..
    478 
    479   if (IS0(a))
    480   {
    481     NUM (result) = p_One(ntRing);
    482     return (number)result;
    483   }
    484 
    485   definiteGcdCancellation(a, cf, FALSE);
    486 
    487   fraction f = (fraction)a;
    488 
    489   assume( !IS0(f) );
    490 
    491   const BOOLEAN denis1 = DENIS1 (f);
    492 
    493   if( denis1 && (getCoeffType (ntCoeffs) != n_Q) ) // */1 or 0
    494   {
    495     NUM (result)= p_One(ntRing);
    496     ntTest((number)result);
    497     return (number)result;
    498   }
    499 
    500   if (!denis1) // */* / Q
    501   {
    502     assume( DEN (f) != NULL );
    503 
    504     if (getCoeffType (ntCoeffs) == n_Q)
    505       handleNestedFractionsOverQ (f, cf);
    506 
    507     ntTest(a);
    508 
    509     if( DEN (f) != NULL ) // is it ?? // 1 now???
    510     {
    511       assume( !p_IsOne(DEN (f), ntRing) );
    512 
    513       NUM (result) = p_Copy (DEN (f), ntRing);
    514       ntTest((number)result);
    515       return (number)result;
    516     }
    517 //    NUM (result) = p_One(ntRing); // NOTE: just in order to be sure...
    518   }
    519 
    520   // */1 / Q
    521   assume( getCoeffType (ntCoeffs) == n_Q );
    522   assume( DEN (f) == NULL );
    523 
    524   number g;
    525 //    poly num= p_Copy (NUM (f), ntRing); // ???
    526 
    527 
    528   // TODO/NOTE: the following should not be necessary (due to
    529   // Hannes!) as NUM (f) should be over Z!!!
    530   CPolyCoeffsEnumerator itr(NUM(f));
    531 
    532   n_ClearDenominators(itr, g, ntCoeffs); // may return -1 :(((
    533 
    534   if( !n_GreaterZero(g, ntCoeffs) )
    535   {
    536 //     NUM (f) = p_Neg(NUM (f), ntRing); // Ugly :(((
    537 //     g = n_InpNeg(g, ntCoeffs);
    538     NUM (f) = p_Neg(NUM (f), ntRing); // Ugly :(((
    539     g = n_InpNeg(g, ntCoeffs);
    540   }
    541 
    542   // g should be a positive integer now!
    543   assume( n_GreaterZero(g, ntCoeffs) );
    544 
    545   if( !n_IsOne(g, ntCoeffs) )
    546   {
    547     assume( n_GreaterZero(g, ntCoeffs) );
    548     assume( !n_IsOne(g, ntCoeffs) );
    549 
    550     DEN (f) = p_NSet(g, ntRing); // update COM(f)???
    551     assume( DEN (f) != NULL );
    552     COM (f) ++;
    553 
    554     NUM (result)= p_Copy (DEN (f), ntRing);
    555   }
    556   else
    557   { // common denom == 1?
    558     NUM (result)= p_NSet(g, ntRing); // p_Copy (DEN (f), ntRing);
    559 //  n_Delete(&g, ntCoeffs);
    560   }
    561 
    562 //    if (!p_IsConstant (num, ntRing) && pNext(num) != NULL)
    563 //    else
    564 //      g= p_GetAllDenom (num, ntRing);
    565 //    result= (fraction) ntSetMap (ntCoeffs, cf) (g, ntCoeffs, cf);
    566 
    567   ntTest((number)result);
    568   //check_N((number)result,cf);
    569   return (number)result;
    570 }
    571 
    572 BOOLEAN ntIsOne(number a, const coeffs cf)
    573 {
    574   //check_N(a,cf);
    575   ntTest(a); // !!!
    576   definiteGcdCancellation(a, cf, FALSE);
    577   fraction f = (fraction)a;
    578   return (f!=NULL) && DENIS1(f) && NUMIS1(f);
    579 }
    580 
    581 BOOLEAN ntIsMOne(number a, const coeffs cf)
    582 {
    583   //check_N(a,cf);
    584   ntTest(a);
    585   definiteGcdCancellation(a, cf, FALSE);
    586   fraction f = (fraction)a;
    587   if ((f==NULL) || (!DENIS1(f))) return FALSE;
    588   poly g = NUM(f);
    589   if (!p_IsConstant(g, ntRing)) return FALSE;
    590   return n_IsMOne(p_GetCoeff(g, ntRing), ntCoeffs);
    591 }
    592 
    593 /// this is in-place, modifies a
    594 number ntNeg(number a, const coeffs cf)
    595 {
    596   //check_N(a,cf);
    597   ntTest(a);
    598   if (!IS0(a))
    599   {
    600     fraction f = (fraction)a;
    601     NUM(f) = p_Neg(NUM(f), ntRing);
    602   }
    603   ntTest(a);
    604   return a;
    605 }
    606 
    607 number ntImPart(number a, const coeffs cf)
    608 {
    609   ntTest(a);
    610   return NULL;
    611 }
    612 
    613 number ntInit(long i, const coeffs cf)
    614 {
    615   if (i != 0)
    616   {
    617     poly p=p_ISet(i, ntRing);
    618     if (p!=NULL)
    619     {
    620       fraction result = (fraction)omAlloc0Bin(fractionObjectBin);
    621       NUM(result) = p;
    622       //DEN(result) = NULL; // done by omAlloc0Bin
    623       //COM(result) = 0; // done by omAlloc0Bin
    624       ntTest((number)result);
    625       //check_N((number)result,cf);
    626       return (number)result;
    627     }
    628   }
    629   return NULL;
    630 }
    631 
    632 
    633 /// takes over p!
    634 number ntInit(poly p, const coeffs cf)
    635 {
    636   if (p == NULL) return NULL;
    637 
    638   p_Test( p, ntRing);
    639   fraction f = (fraction)omAlloc0Bin(fractionObjectBin);
    640 
    641   if (nCoeff_is_Q(ntCoeffs))
    642   {
    643     number g;
    644     // the following is necessary because
    645     // NUM (f) should be over Z,
    646     // while p may be over Q
    647     CPolyCoeffsEnumerator itr(p);
    648 
    649     n_ClearDenominators(itr, g, ntCoeffs);
    650 
    651     if( !n_GreaterZero(g, ntCoeffs) )
    652     {
    653       p = p_Neg(p, ntRing);
    654       g = n_InpNeg(g, ntCoeffs);
    655     }
    656 
    657     // g should be a positive integer now!
    658     assume( n_GreaterZero(g, ntCoeffs) );
    659 
    660     if( !n_IsOne(g, ntCoeffs) )
    661     {
    662       DEN (f) = p_NSet(g, ntRing);
    663       p_Normalize(DEN(f), ntRing);
    664       assume( DEN (f) != NULL );
    665     }
    666     else
    667     {
    668       //DEN(f) = NULL; // done by omAlloc0
    669       n_Delete(&g, ntCoeffs);
    670     }
    671   }
    672 
    673   p_Normalize(p, ntRing);
    674   NUM(f) = p;
    675   //COM(f) = 0; // done by omAlloc0
    676 
    677   //check_N((number)f,cf);
    678   ntTest((number)f);
    679   return (number)f;
    680 }
    681 
    682 long ntInt(number &a, const coeffs cf)
    683 {
    684   //check_N(a,cf);
    685   ntTest(a);
    686   if (IS0(a)) return 0;
    687   definiteGcdCancellation(a, cf, FALSE);
    688   fraction f = (fraction)a;
    689   if (!DENIS1(f)) return 0;
    690 
    691   const poly aAsPoly = NUM(f);
    692 
    693   if(aAsPoly == NULL)
    694     return 0;
    695 
    696   if (!p_IsConstant(aAsPoly, ntRing))
    697     return 0;
    698 
    699   assume( aAsPoly != NULL );
    700 
    701   return n_Int(p_GetCoeff(aAsPoly, ntRing), ntCoeffs);
    702 }
    703 
    704 /* This method will only consider the numerators of a and b, without
    705    cancelling gcd's before.
    706    Moreover it may return TRUE only if one or both numerators
    707    are zero or if their degrees are equal. Then TRUE is returned iff
    708    coeff(numerator(a)) > coeff(numerator(b));
    709    In all other cases, FALSE will be returned. */
    710 BOOLEAN ntGreater(number a, number b, const coeffs cf)
    711 {
    712   //check_N(a,cf);
    713   //check_N(b,cf);
    714   ntTest(a);
    715   ntTest(b);
    716   number aNumCoeff = NULL; int aNumDeg = 0;
    717   number aDenCoeff = NULL; int aDenDeg = 0;
    718   number bNumCoeff = NULL; int bNumDeg = 0;
    719   number bDenCoeff = NULL; int bDenDeg = 0;
    720   if (!IS0(a))
    721   {
    722     fraction fa = (fraction)a;
    723     aNumDeg = p_Totaldegree(NUM(fa), ntRing);
    724     aNumCoeff = p_GetCoeff(NUM(fa), ntRing);
    725     if (DEN(fa)!=NULL)
    726     {
    727       aDenDeg = p_Totaldegree(DEN(fa), ntRing);
    728       aDenCoeff=p_GetCoeff(DEN(fa),ntRing);
    729     }
    730   }
    731   else return !(ntGreaterZero (b,cf));
    732   if (!IS0(b))
    733   {
    734     fraction fb = (fraction)b;
    735     bNumDeg = p_Totaldegree(NUM(fb), ntRing);
    736     bNumCoeff = p_GetCoeff(NUM(fb), ntRing);
    737     if (DEN(fb)!=NULL)
    738     {
    739       bDenDeg = p_Totaldegree(DEN(fb), ntRing);
    740       bDenCoeff=p_GetCoeff(DEN(fb),ntRing);
    741     }
    742   }
    743   else return ntGreaterZero(a,cf);
    744   if (aNumDeg-aDenDeg > bNumDeg-bDenDeg) return TRUE;
    745   if (aNumDeg-aDenDeg < bNumDeg-bDenDeg) return FALSE;
    746   number aa;
    747   number bb;
    748   if (bDenCoeff==NULL) aa=n_Copy(aNumCoeff,ntCoeffs);
    749   else                 aa=n_Mult(aNumCoeff,bDenCoeff,ntCoeffs);
    750   if (aDenCoeff==NULL) bb=n_Copy(bNumCoeff,ntCoeffs);
    751   else                 bb=n_Mult(bNumCoeff,aDenCoeff,ntCoeffs);
    752   BOOLEAN rr= n_Greater(aa, bb, ntCoeffs);
    753   n_Delete(&aa,ntCoeffs);
    754   n_Delete(&bb,ntCoeffs);
    755   return rr;
    756 }
    757 
    758 /* this method will only consider the numerator of a, without cancelling
    759    the gcd before;
    760    returns TRUE iff the leading coefficient of the numerator of a is > 0
    761                     or the leading term of the numerator of a is not a
    762                     constant */
    763 BOOLEAN ntGreaterZero(number a, const coeffs cf)
    764 {
    765   //check_N(a,cf);
    766   ntTest(a);
    767   if (IS0(a)) return FALSE;
    768   fraction f = (fraction)a;
    769   poly g = NUM(f);
    770   return (!p_LmIsConstant(g,ntRing)|| n_GreaterZero(pGetCoeff(g), ntCoeffs));
    771 }
    772 
    773 void ntCoeffWrite(const coeffs cf, BOOLEAN details)
    774 {
    775   assume( cf != NULL );
    776 
    777   const ring A = cf->extRing;
    778 
    779   assume( A != NULL );
    780   assume( A->cf != NULL );
    781 
    782   n_CoeffWrite(A->cf, details);
    783 
    784 //  rWrite(A);
    785 
    786   const int P = rVar(A);
    787   assume( P > 0 );
    788 
    789   PrintS("(");
    790 
    791   for (int nop=0; nop < P; nop ++)
    792   {
    793     Print("%s", rRingVar(nop, A));
    794     if (nop!=P-1) PrintS(", ");
    795   }
    796 
    797   PrintS(")");
    798 
    799   assume( A->qideal == NULL );
    800 
    801 /*
    802   PrintS("//   Coefficients live in the rational function field\n");
    803   Print("//   K(");
    804   for (int i = 0; i < rVar(ntRing); i++)
    805   {
    806     if (i > 0) PrintS(" ");
    807     Print("%s", rRingVar(i, ntRing));
    808   }
    809   PrintS(") with\n");
    810   PrintS("//   K: "); n_CoeffWrite(cf->extRing->cf);
    811 */
    812 }
    813 
    814 number ntDiff(number a, number d, const coeffs cf)
    815 {
    816   //check_N(a,cf);
    817   //check_N(d,cf);
    818   ntTest(a);
    819   ntTest(d);
    820 
    821   if (IS0(d))
    822   {
    823     WerrorS("ringvar expected");
    824     return NULL;
    825   }
    826   fraction t = (fraction) d;
    827   if (!DENIS1(t))
    828   {
    829     WerrorS("expected differentiation by a variable");
    830     return NULL;
    831   }
    832   int k=p_Var(NUM(t),ntRing);
    833   if (k==0)
    834   {
    835     WerrorS("expected differentiation by a variable");
    836     return NULL;
    837   }
    838 
    839   if (IS0(a)) return ntCopy(a, cf);
    840 
    841   fraction fa = (fraction)a;
    842   fraction result = (fraction)omAlloc0Bin(fractionObjectBin);
    843   if (DENIS1(fa))
    844   {
    845      NUM(result) = p_Diff(NUM(fa),k,ntRing);
    846      //DEN(result) = NULL; // done by ..Alloc0..
    847      if (NUM(result)==NULL)
    848      {
    849        omFreeBin((ADDRESS)result, fractionObjectBin);
    850        return(NULL);
    851      }
    852      COM(result) = COM(fa);
    853      //check_N((number)result,cf);
    854      ntTest((number)result);
    855      return (number)result;
    856   }
    857 
    858   poly fg = p_Mult_q(p_Copy(DEN(fa),ntRing),p_Diff(NUM(fa),k,ntRing),ntRing);
    859   poly gf = p_Mult_q(p_Copy(NUM(fa),ntRing),p_Diff(DEN(fa),k,ntRing),ntRing);
    860   NUM(result) = p_Sub(fg,gf,ntRing);
    861   if (NUM(result)==NULL) return(NULL);
    862   DEN(result) = pp_Mult_qq(DEN(fa), DEN(fa), ntRing);
    863   COM(result) = COM(fa) + COM(fa) + DIFF_COMPLEXITY;
    864   heuristicGcdCancellation((number)result, cf);
    865 
    866   //check_N((number)result,cf);
    867   ntTest((number)result);
    868   return (number)result;
    869 }
    870 
    871 
    872 number ntAdd(number a, number b, const coeffs cf)
    873 {
    874   //check_N(a,cf);
    875   //check_N(b,cf);
    876   ntTest(a);
    877   ntTest(b);
    878   if (IS0(a)) return ntCopy(b, cf);
    879   if (IS0(b)) return ntCopy(a, cf);
    880 
    881   fraction fa = (fraction)a;
    882   fraction fb = (fraction)b;
    883 
    884   poly g = p_Copy(NUM(fa), ntRing);
    885   if (!DENIS1(fb)) g = p_Mult_q(g, p_Copy(DEN(fb), ntRing), ntRing);
    886   poly h = p_Copy(NUM(fb), ntRing);
    887   if (!DENIS1(fa)) h = p_Mult_q(h, p_Copy(DEN(fa), ntRing), ntRing);
    888   g = p_Add_q(g, h, ntRing);
    889 
    890   if (g == NULL) return NULL;
    891 
    892   poly f;
    893   if      (DENIS1(fa) && DENIS1(fb))  f = NULL;
    894   else if (!DENIS1(fa) && DENIS1(fb)) f = p_Copy(DEN(fa), ntRing);
    895   else if (DENIS1(fa) && !DENIS1(fb)) f = p_Copy(DEN(fb), ntRing);
    896   else /* both denom's are != 1 */    f = p_Mult_q(p_Copy(DEN(fa), ntRing),
    897                                                    p_Copy(DEN(fb), ntRing),
    898                                                    ntRing);
    899 
    900   fraction result = (fraction)omAllocBin(fractionObjectBin);
    901   NUM(result) = g;
    902   DEN(result) = f;
    903   COM(result) = COM(fa) + COM(fb) + ADD_COMPLEXITY;
    904   heuristicGcdCancellation((number)result, cf);
    905 
    906 //  ntTest((number)result);
    907 
    908   //check_N((number)result,cf);
    909   ntTest((number)result);
    910   return (number)result;
    911 }
    912 
    913 number ntSub(number a, number b, const coeffs cf)
    914 {
    915   //check_N(a,cf);
    916   //check_N(b,cf);
    917   ntTest(a);
    918   ntTest(b);
    919   if (IS0(a)) return ntNeg(ntCopy(b, cf), cf);
    920   if (IS0(b)) return ntCopy(a, cf);
    921 
    922   fraction fa = (fraction)a;
    923   fraction fb = (fraction)b;
    924 
    925   poly g = p_Copy(NUM(fa), ntRing);
    926   if (!DENIS1(fb)) g = p_Mult_q(g, p_Copy(DEN(fb), ntRing), ntRing);
    927   poly h = p_Copy(NUM(fb), ntRing);
    928   if (!DENIS1(fa)) h = p_Mult_q(h, p_Copy(DEN(fa), ntRing), ntRing);
    929   g = p_Add_q(g, p_Neg(h, ntRing), ntRing);
    930 
    931   if (g == NULL) return NULL;
    932 
    933   poly f;
    934   if      (DENIS1(fa) && DENIS1(fb))  f = NULL;
    935   else if (!DENIS1(fa) && DENIS1(fb)) f = p_Copy(DEN(fa), ntRing);
    936   else if (DENIS1(fa) && !DENIS1(fb)) f = p_Copy(DEN(fb), ntRing);
    937   else /* both den's are != 1 */      f = p_Mult_q(p_Copy(DEN(fa), ntRing),
    938                                                    p_Copy(DEN(fb), ntRing),
    939                                                    ntRing);
    940 
    941   fraction result = (fraction)omAllocBin(fractionObjectBin);
    942   NUM(result) = g;
    943   DEN(result) = f;
    944   COM(result) = COM(fa) + COM(fb) + ADD_COMPLEXITY;
    945   heuristicGcdCancellation((number)result, cf);
    946 //  ntTest((number)result);
    947   //check_N((number)result,cf);
    948   ntTest((number)result);
    949   return (number)result;
    950 }
    951 
    952 number ntMult(number a, number b, const coeffs cf)
    953 {
    954   //check_N(a,cf);
    955   //check_N(b,cf);
    956   ntTest(a); // !!!?
    957   ntTest(b); // !!!?
    958 
    959   if (IS0(a) || IS0(b)) return NULL;
    960 
    961   fraction fa = (fraction)a;
    962   fraction fb = (fraction)b;
    963 
    964   const poly g = pp_Mult_qq(NUM(fa), NUM(fb), ntRing);
    965 
    966   if (g == NULL) return NULL; // may happen due to zero divisors???
    967 
    968   fraction result = (fraction)omAllocBin(fractionObjectBin);
    969 
    970   NUM(result) = g;
    971 
    972   const poly da = DEN(fa);
    973   const poly db = DEN(fb);
    974 
    975 
    976   //check_N((number)result,cf);
    977   if (db == NULL)
    978   {
    979     // b = ? // NULL
    980 
    981     if(da == NULL)
    982     { // both fa && fb are ?? // NULL!
    983       assume (da == NULL && db == NULL);
    984       DEN(result) = NULL;
    985       COM(result) = 0;
    986     }
    987     else
    988     {
    989       assume (da != NULL && db == NULL);
    990       DEN(result) = p_Copy(da, ntRing);
    991       COM(result) = COM(fa) + MULT_COMPLEXITY;
    992       heuristicGcdCancellation((number)result, cf);
    993       //check_N((number)result,cf);
    994     }
    995   }
    996   else
    997   { // b = ?? / ??
    998     if (da == NULL)
    999     { // a == ? // NULL
    1000       assume( db != NULL && da == NULL);
    1001       DEN(result) = p_Copy(db, ntRing);
    1002       COM(result) = COM(fb) + MULT_COMPLEXITY;
    1003       heuristicGcdCancellation((number)result, cf);
    1004       //check_N((number)result,cf);
    1005     }
    1006     else /* both den's are != 1 */
    1007     {
    1008       assume (da != NULL && db != NULL);
    1009       DEN(result) = pp_Mult_qq(da, db, ntRing);
    1010       COM(result) = COM(fa) + COM(fb) + MULT_COMPLEXITY;
    1011       heuristicGcdCancellation((number)result, cf);
    1012       //check_N((number)result,cf);
    1013     }
    1014   }
    1015 
    1016 //  ntTest((number)result);
    1017 
    1018   //check_N((number)result,cf);
    1019   ntTest((number)result);
    1020   return (number)result;
    1021 }
    1022 
    1023 static void ntNormalizeDen(fraction result, const ring R)
    1024 {
    1025   if ((nCoeff_has_simple_inverse(R->cf))
    1026   && (result!=NULL)
    1027   && (DEN(result)!=NULL))
    1028   {
    1029     poly n=DEN(result);
    1030     if (!n_IsOne(pGetCoeff(n),R->cf))
    1031     {
    1032       number inv=n_Invers(pGetCoeff(n),R->cf);
    1033       DEN(result)=p_Mult_nn(n,inv,R);
    1034       NUM(result)=p_Mult_nn(NUM(result),inv,R);
    1035       n_Delete(&inv,R->cf);
    1036       if (p_IsOne(DEN(result), R))
    1037       {
    1038         n=DEN(result);
    1039         DEN(result)=NULL;
    1040         COM(result) = 0;
    1041         p_Delete(&n,R);
    1042       }
    1043     }
    1044   }
    1045 }
    1046 
    1047 number ntDiv(number a, number b, const coeffs cf)
    1048 {
    1049   //check_N(a,cf);
    1050   //check_N(b,cf);
    1051   ntTest(a);
    1052   ntTest(b);
    1053   if (IS0(a)) return NULL;
    1054   if (IS0(b)) WerrorS(nDivBy0);
    1055 
    1056   fraction fa = (fraction)a;
    1057   fraction fb = (fraction)b;
    1058 
    1059   poly g = p_Copy(NUM(fa), ntRing);
    1060   if (!DENIS1(fb)) g = p_Mult_q(g, p_Copy(DEN(fb), ntRing), ntRing);
    1061 
    1062   if (g == NULL) return NULL;   /* may happen due to zero divisors */
    1063 
    1064   poly f = p_Copy(NUM(fb), ntRing);
    1065   if (!DENIS1(fa)) f = p_Mult_q(f, p_Copy(DEN(fa), ntRing), ntRing);
    1066 
    1067   fraction result = (fraction)omAlloc0Bin(fractionObjectBin);
    1068   NUM(result) = g;
    1069   if (!n_GreaterZero(pGetCoeff(f),ntCoeffs))
    1070   {
    1071     g=p_Neg(g,ntRing);
    1072     f=p_Neg(f,ntRing);
    1073     NUM(result) = g;
    1074   }
    1075   if (!p_IsConstant(f,ntRing) || !n_IsOne(pGetCoeff(f),ntCoeffs))
    1076   {
    1077     DEN(result) = f;
    1078   }
    1079   COM(result) = COM(fa) + COM(fb) + MULT_COMPLEXITY;
    1080 //  definiteGcdCancellation((number)result, cf,FALSE);
    1081   heuristicGcdCancellation((number)result, cf);
    1082 //  ntTest((number)result);
    1083   //check_N((number)result,cf);
    1084   ntNormalizeDen(result,ntRing);
    1085   ntTest((number)result);
    1086   return (number)result;
    1087 }
    1088 
    1089 /* 0^0 = 0;
    1090    for |exp| <= 7 compute power by a simple multiplication loop;
    1091    for |exp| >= 8 compute power along binary presentation of |exp|, e.g.
    1092       p^13 = p^1 * p^4 * p^8, where we utilise that
    1093       p^(2^(k+1)) = p^(2^k) * p^(2^k);
    1094    intermediate cancellation is controlled by the in-place method
    1095    heuristicGcdCancellation; see there.
    1096 */
    1097 void ntPower(number a, int exp, number *b, const coeffs cf)
    1098 {
    1099   ntTest(a);
    1100 
    1101   /* special cases first */
    1102   if (IS0(a))
    1103   {
    1104     if (exp >= 0) *b = NULL;
    1105     else          WerrorS(nDivBy0);
    1106   }
    1107   else if (exp ==  0) { *b = ntInit(1, cf); return;}
    1108   else if (exp ==  1) { *b = ntCopy(a, cf); return;}
    1109   else if (exp == -1) { *b = ntInvers(a, cf); return;}
    1110 
    1111   int expAbs = exp; if (expAbs < 0) expAbs = -expAbs;
    1112 
    1113   /* now compute a^expAbs */
    1114   number pow; number t;
    1115   if (expAbs <= 7)
    1116   {
    1117     pow = ntCopy(a, cf);
    1118     for (int i = 2; i <= expAbs; i++)
    1119     {
    1120       t = ntMult(pow, a, cf);
    1121       ntDelete(&pow, cf);
    1122       pow = t;
    1123       heuristicGcdCancellation(pow, cf);
    1124     }
    1125   }
    1126   else
    1127   {
    1128     pow = ntInit(1, cf);
    1129     number factor = ntCopy(a, cf);
    1130     while (expAbs != 0)
    1131     {
    1132       if (expAbs & 1)
    1133       {
    1134         t = ntMult(pow, factor, cf);
    1135         ntDelete(&pow, cf);
    1136         pow = t;
    1137         heuristicGcdCancellation(pow, cf);
    1138       }
    1139       expAbs = expAbs / 2;
    1140       if (expAbs != 0)
    1141       {
    1142         t = ntMult(factor, factor, cf);
    1143         ntDelete(&factor, cf);
    1144         factor = t;
    1145         heuristicGcdCancellation(factor, cf);
    1146       }
    1147     }
    1148     ntDelete(&factor, cf);
    1149   }
    1150 
    1151   /* invert if original exponent was negative */
    1152   if (exp < 0)
    1153   {
    1154     t = ntInvers(pow, cf);
    1155     ntDelete(&pow, cf);
    1156     pow = t;
    1157   }
    1158   *b = pow;
    1159   ntTest(*b);
    1160   //check_N(*b,cf);
    1161375}
    1162376
    … …  
    1185399   calling procedure);
    1186400   modifies f */
    1187 void handleNestedFractionsOverQ(fraction f, const coeffs cf)
     401static void handleNestedFractionsOverQ(fraction f, const coeffs cf)
    1188402{
    1189403  assume(nCoeff_is_Q(ntCoeffs));
    … …  
    1273487      DEN(f) = p_Neg(DEN(f), ntRing);
    1274488    }
    1275 
     489  COM(f)=BOUND_COMPLEXITY+1;
    1276490  ntTest((number)f); // TODO!
     491}
     492
     493/// TODO: normalization of a!?
     494static number ntGetNumerator(number &a, const coeffs cf)
     495{
     496  //check_N(a,cf);
     497  ntTest(a);
     498  if (IS0(a)) return NULL;
     499
     500  definiteGcdCancellation(a, cf, FALSE);
     501
     502  fraction f = (fraction)a;
     503  fraction result = (fraction)omAlloc0Bin(fractionObjectBin);
     504
     505  const BOOLEAN denis1= DENIS1 (f);
     506
     507  if (getCoeffType (ntCoeffs) == n_Q && !denis1)
     508    handleNestedFractionsOverQ (f, cf);
     509
     510  if (getCoeffType (ntCoeffs) == n_Q && denis1)
     511  {
     512    assume( DEN (f) == NULL );
     513
     514    number g;
     515    // TODO/NOTE: the following should not be necessary (due to
     516    // Hannes!) as NUM (f) should be over Z!!!
     517    CPolyCoeffsEnumerator itr(NUM(f));
     518
     519
     520    n_ClearDenominators(itr, g, ntCoeffs);
     521
     522    if( !n_GreaterZero(g, ntCoeffs) )
     523    {
     524      NUM (f) = p_Neg(NUM (f), ntRing);
     525      g = n_InpNeg(g, ntCoeffs);
     526    }
     527
     528    // g should be a positive integer now!
     529    assume( n_GreaterZero(g, ntCoeffs) );
     530
     531    if( !n_IsOne(g, ntCoeffs) )
     532    {
     533      DEN (f) = p_NSet(g, ntRing);
     534      COM (f) ++;
     535      assume( DEN (f) != NULL );
     536    }
     537    else
     538      n_Delete(&g, ntCoeffs);
     539
     540    ntTest(a);
     541  }
     542
     543  // Call ntNormalize instead of above?!?
     544
     545  NUM (result) = p_Copy (NUM (f), ntRing); // ???
     546  //DEN (result) = NULL; // done by ..Alloc0..
     547  //COM (result) = 0; // done by ..Alloc0..
     548
     549  ntTest((number)result);
     550  //check_N((number)result,cf);
     551  return (number)result;
     552}
     553
     554/// TODO: normalization of a!?
     555static number ntGetDenom(number &a, const coeffs cf)
     556{
     557  //check_N(a,cf);
     558  ntTest(a);
     559
     560  fraction result = (fraction)omAlloc0Bin(fractionObjectBin);
     561  //DEN (result)= NULL; // done by ..Alloc0..
     562  //COM (result)= 0; // done by ..Alloc0..
     563
     564  if (IS0(a))
     565  {
     566    NUM (result) = p_One(ntRing);
     567    return (number)result;
     568  }
     569
     570  definiteGcdCancellation(a, cf, FALSE);
     571
     572  fraction f = (fraction)a;
     573
     574  assume( !IS0(f) );
     575
     576  const BOOLEAN denis1 = DENIS1 (f);
     577
     578  if( denis1 && (getCoeffType (ntCoeffs) != n_Q) ) // */1 or 0
     579  {
     580    NUM (result)= p_One(ntRing);
     581    ntTest((number)result);
     582    return (number)result;
     583  }
     584
     585  if (!denis1) // */* / Q
     586  {
     587    assume( DEN (f) != NULL );
     588
     589    if (getCoeffType (ntCoeffs) == n_Q)
     590      handleNestedFractionsOverQ (f, cf);
     591
     592    ntTest(a);
     593
     594    if( DEN (f) != NULL ) // is it ?? // 1 now???
     595    {
     596      assume( !p_IsOne(DEN (f), ntRing) );
     597
     598      NUM (result) = p_Copy (DEN (f), ntRing);
     599      ntTest((number)result);
     600      return (number)result;
     601    }
     602//    NUM (result) = p_One(ntRing); // NOTE: just in order to be sure...
     603  }
     604
     605  // */1 / Q
     606  assume( getCoeffType (ntCoeffs) == n_Q );
     607  assume( DEN (f) == NULL );
     608
     609  number g;
     610//    poly num= p_Copy (NUM (f), ntRing); // ???
     611
     612
     613  // TODO/NOTE: the following should not be necessary (due to
     614  // Hannes!) as NUM (f) should be over Z!!!
     615  CPolyCoeffsEnumerator itr(NUM(f));
     616
     617  n_ClearDenominators(itr, g, ntCoeffs); // may return -1 :(((
     618
     619  if( !n_GreaterZero(g, ntCoeffs) )
     620  {
     621//     NUM (f) = p_Neg(NUM (f), ntRing); // Ugly :(((
     622//     g = n_InpNeg(g, ntCoeffs);
     623    NUM (f) = p_Neg(NUM (f), ntRing); // Ugly :(((
     624    g = n_InpNeg(g, ntCoeffs);
     625  }
     626
     627  // g should be a positive integer now!
     628  assume( n_GreaterZero(g, ntCoeffs) );
     629
     630  if( !n_IsOne(g, ntCoeffs) )
     631  {
     632    assume( n_GreaterZero(g, ntCoeffs) );
     633    assume( !n_IsOne(g, ntCoeffs) );
     634
     635    DEN (f) = p_NSet(g, ntRing); // update COM(f)???
     636    assume( DEN (f) != NULL );
     637    COM (f) ++;
     638
     639    NUM (result)= p_Copy (DEN (f), ntRing);
     640  }
     641  else
     642  { // common denom == 1?
     643    NUM (result)= p_NSet(g, ntRing); // p_Copy (DEN (f), ntRing);
     644//  n_Delete(&g, ntCoeffs);
     645  }
     646
     647//    if (!p_IsConstant (num, ntRing) && pNext(num) != NULL)
     648//    else
     649//      g= p_GetAllDenom (num, ntRing);
     650//    result= (fraction) ntSetMap (ntCoeffs, cf) (g, ntCoeffs, cf);
     651
     652  ntTest((number)result);
     653  //check_N((number)result,cf);
     654  return (number)result;
     655}
     656
     657static BOOLEAN ntIsOne(number a, const coeffs cf)
     658{
     659  //check_N(a,cf);
     660  ntTest(a); // !!!
     661  definiteGcdCancellation(a, cf, FALSE);
     662  fraction f = (fraction)a;
     663  return (f!=NULL) && DENIS1(f) && NUMIS1(f);
     664}
     665
     666static BOOLEAN ntIsMOne(number a, const coeffs cf)
     667{
     668  //check_N(a,cf);
     669  ntTest(a);
     670  definiteGcdCancellation(a, cf, FALSE);
     671  fraction f = (fraction)a;
     672  if ((f==NULL) || (!DENIS1(f))) return FALSE;
     673  poly g = NUM(f);
     674  if (!p_IsConstant(g, ntRing)) return FALSE;
     675  return n_IsMOne(p_GetCoeff(g, ntRing), ntCoeffs);
     676}
     677
     678/// this is in-place, modifies a
     679static number ntNeg(number a, const coeffs cf)
     680{
     681  //check_N(a,cf);
     682  ntTest(a);
     683  if (!IS0(a))
     684  {
     685    fraction f = (fraction)a;
     686    NUM(f) = p_Neg(NUM(f), ntRing);
     687  }
     688  ntTest(a);
     689  return a;
     690}
     691
     692number ntInit(long i, const coeffs cf)
     693{
     694  if (i != 0)
     695  {
     696    poly p=p_ISet(i, ntRing);
     697    if (p!=NULL)
     698    {
     699      fraction result = (fraction)omAlloc0Bin(fractionObjectBin);
     700      NUM(result) = p;
     701      //DEN(result) = NULL; // done by omAlloc0Bin
     702      //COM(result) = 0; // done by omAlloc0Bin
     703      ntTest((number)result);
     704      //check_N((number)result,cf);
     705      return (number)result;
     706    }
     707  }
     708  return NULL;
     709}
     710
     711
     712/// takes over p!
     713number ntInit(poly p, const coeffs cf)
     714{
     715  if (p == NULL) return NULL;
     716
     717  p_Test( p, ntRing);
     718  fraction f = (fraction)omAlloc0Bin(fractionObjectBin);
     719
     720  if (nCoeff_is_Q(ntCoeffs))
     721  {
     722    number g;
     723    // the following is necessary because
     724    // NUM (f) should be over Z,
     725    // while p may be over Q
     726    CPolyCoeffsEnumerator itr(p);
     727
     728    n_ClearDenominators(itr, g, ntCoeffs);
     729
     730    if( !n_GreaterZero(g, ntCoeffs) )
     731    {
     732      p = p_Neg(p, ntRing);
     733      g = n_InpNeg(g, ntCoeffs);
     734    }
     735
     736    // g should be a positive integer now!
     737    assume( n_GreaterZero(g, ntCoeffs) );
     738
     739    if( !n_IsOne(g, ntCoeffs) )
     740    {
     741      DEN (f) = p_NSet(g, ntRing);
     742      p_Normalize(DEN(f), ntRing);
     743      assume( DEN (f) != NULL );
     744    }
     745    else
     746    {
     747      //DEN(f) = NULL; // done by omAlloc0
     748      n_Delete(&g, ntCoeffs);
     749    }
     750  }
     751
     752  p_Normalize(p, ntRing);
     753  NUM(f) = p;
     754  //COM(f) = 0; // done by omAlloc0
     755
     756  //check_N((number)f,cf);
     757  ntTest((number)f);
     758  return (number)f;
     759}
     760
     761static long ntInt(number &a, const coeffs cf)
     762{
     763  //check_N(a,cf);
     764  ntTest(a);
     765  if (IS0(a)) return 0;
     766  definiteGcdCancellation(a, cf, FALSE);
     767  fraction f = (fraction)a;
     768  if (!DENIS1(f)) return 0;
     769
     770  const poly aAsPoly = NUM(f);
     771
     772  if(aAsPoly == NULL)
     773    return 0;
     774
     775  if (!p_IsConstant(aAsPoly, ntRing))
     776    return 0;
     777
     778  assume( aAsPoly != NULL );
     779
     780  return n_Int(p_GetCoeff(aAsPoly, ntRing), ntCoeffs);
     781}
     782
     783/* this method will only consider the numerator of a, without cancelling
     784   the gcd before;
     785   returns TRUE iff the leading coefficient of the numerator of a is > 0
     786                    or the leading term of the numerator of a is not a
     787                    constant */
     788static BOOLEAN ntGreaterZero(number a, const coeffs cf)
     789{
     790  //check_N(a,cf);
     791  ntTest(a);
     792  if (IS0(a)) return FALSE;
     793  fraction f = (fraction)a;
     794  poly g = NUM(f);
     795  return (!p_LmIsConstant(g,ntRing)|| n_GreaterZero(pGetCoeff(g), ntCoeffs));
     796}
     797
     798/* This method will only consider the numerators of a and b, without
     799   cancelling gcd's before.
     800   Moreover it may return TRUE only if one or both numerators
     801   are zero or if their degrees are equal. Then TRUE is returned iff
     802   coeff(numerator(a)) > coeff(numerator(b));
     803   In all other cases, FALSE will be returned. */
     804static BOOLEAN ntGreater(number a, number b, const coeffs cf)
     805{
     806  //check_N(a,cf);
     807  //check_N(b,cf);
     808  ntTest(a);
     809  ntTest(b);
     810  number aNumCoeff = NULL; int aNumDeg = 0;
     811  number aDenCoeff = NULL; int aDenDeg = 0;
     812  number bNumCoeff = NULL; int bNumDeg = 0;
     813  number bDenCoeff = NULL; int bDenDeg = 0;
     814  if (!IS0(a))
     815  {
     816    fraction fa = (fraction)a;
     817    aNumDeg = p_Totaldegree(NUM(fa), ntRing);
     818    aNumCoeff = p_GetCoeff(NUM(fa), ntRing);
     819    if (DEN(fa)!=NULL)
     820    {
     821      aDenDeg = p_Totaldegree(DEN(fa), ntRing);
     822      aDenCoeff=p_GetCoeff(DEN(fa),ntRing);
     823    }
     824  }
     825  else return !(ntGreaterZero (b,cf));
     826  if (!IS0(b))
     827  {
     828    fraction fb = (fraction)b;
     829    bNumDeg = p_Totaldegree(NUM(fb), ntRing);
     830    bNumCoeff = p_GetCoeff(NUM(fb), ntRing);
     831    if (DEN(fb)!=NULL)
     832    {
     833      bDenDeg = p_Totaldegree(DEN(fb), ntRing);
     834      bDenCoeff=p_GetCoeff(DEN(fb),ntRing);
     835    }
     836  }
     837  else return ntGreaterZero(a,cf);
     838  if (aNumDeg-aDenDeg > bNumDeg-bDenDeg) return TRUE;
     839  if (aNumDeg-aDenDeg < bNumDeg-bDenDeg) return FALSE;
     840  number aa;
     841  number bb;
     842  if (bDenCoeff==NULL) aa=n_Copy(aNumCoeff,ntCoeffs);
     843  else                 aa=n_Mult(aNumCoeff,bDenCoeff,ntCoeffs);
     844  if (aDenCoeff==NULL) bb=n_Copy(bNumCoeff,ntCoeffs);
     845  else                 bb=n_Mult(bNumCoeff,aDenCoeff,ntCoeffs);
     846  BOOLEAN rr= n_Greater(aa, bb, ntCoeffs);
     847  n_Delete(&aa,ntCoeffs);
     848  n_Delete(&bb,ntCoeffs);
     849  return rr;
     850}
     851
     852static void ntCoeffWrite(const coeffs cf, BOOLEAN details)
     853{
     854  assume( cf != NULL );
     855
     856  const ring A = cf->extRing;
     857
     858  assume( A != NULL );
     859  assume( A->cf != NULL );
     860
     861  n_CoeffWrite(A->cf, details);
     862
     863//  rWrite(A);
     864
     865  const int P = rVar(A);
     866  assume( P > 0 );
     867
     868  PrintS("(");
     869
     870  for (int nop=0; nop < P; nop ++)
     871  {
     872    Print("%s", rRingVar(nop, A));
     873    if (nop!=P-1) PrintS(", ");
     874  }
     875
     876  PrintS(")");
     877
     878  assume( A->qideal == NULL );
     879
     880/*
     881  PrintS("//   Coefficients live in the rational function field\n");
     882  Print("//   K(");
     883  for (int i = 0; i < rVar(ntRing); i++)
     884  {
     885    if (i > 0) PrintS(" ");
     886    Print("%s", rRingVar(i, ntRing));
     887  }
     888  PrintS(") with\n");
     889  PrintS("//   K: "); n_CoeffWrite(cf->extRing->cf);
     890*/
     891}
     892
     893number ntDiff(number a, number d, const coeffs cf)
     894{
     895  //check_N(a,cf);
     896  //check_N(d,cf);
     897  ntTest(a);
     898  ntTest(d);
     899
     900  if (IS0(d))
     901  {
     902    WerrorS("ringvar expected");
     903    return NULL;
     904  }
     905  fraction t = (fraction) d;
     906  if (!DENIS1(t))
     907  {
     908    WerrorS("expected differentiation by a variable");
     909    return NULL;
     910  }
     911  int k=p_Var(NUM(t),ntRing);
     912  if (k==0)
     913  {
     914    WerrorS("expected differentiation by a variable");
     915    return NULL;
     916  }
     917
     918  if (IS0(a)) return ntCopy(a, cf);
     919
     920  fraction fa = (fraction)a;
     921  fraction result = (fraction)omAlloc0Bin(fractionObjectBin);
     922  if (DENIS1(fa))
     923  {
     924     NUM(result) = p_Diff(NUM(fa),k,ntRing);
     925     //DEN(result) = NULL; // done by ..Alloc0..
     926     if (NUM(result)==NULL)
     927     {
     928       omFreeBin((ADDRESS)result, fractionObjectBin);
     929       return(NULL);
     930     }
     931     COM(result) = COM(fa)+DIFF_COMPLEXITY;
     932     //check_N((number)result,cf);
     933     ntTest((number)result);
     934     return (number)result;
     935  }
     936
     937  poly fg = p_Mult_q(p_Copy(DEN(fa),ntRing),p_Diff(NUM(fa),k,ntRing),ntRing);
     938  poly gf = p_Mult_q(p_Copy(NUM(fa),ntRing),p_Diff(DEN(fa),k,ntRing),ntRing);
     939  NUM(result) = p_Sub(fg,gf,ntRing);
     940  if (NUM(result)==NULL) return(NULL);
     941  DEN(result) = pp_Mult_qq(DEN(fa), DEN(fa), ntRing);
     942  COM(result) = COM(fa) + COM(fa) + DIFF_COMPLEXITY;
     943  heuristicGcdCancellation((number)result, cf);
     944
     945  //check_N((number)result,cf);
     946  ntTest((number)result);
     947  return (number)result;
     948}
     949
     950static number ntAdd(number a, number b, const coeffs cf)
     951{
     952  //check_N(a,cf);
     953  //check_N(b,cf);
     954  ntTest(a);
     955  ntTest(b);
     956  if (IS0(a)) return ntCopy(b, cf);
     957  if (IS0(b)) return ntCopy(a, cf);
     958
     959  fraction fa = (fraction)a;
     960  fraction fb = (fraction)b;
     961
     962  poly g = p_Copy(NUM(fa), ntRing);
     963  if (!DENIS1(fb)) g = p_Mult_q(g, p_Copy(DEN(fb), ntRing), ntRing);
     964  poly h = p_Copy(NUM(fb), ntRing);
     965  if (!DENIS1(fa)) h = p_Mult_q(h, p_Copy(DEN(fa), ntRing), ntRing);
     966  g = p_Add_q(g, h, ntRing);
     967
     968  if (g == NULL) return NULL;
     969
     970  poly f;
     971  if      (DENIS1(fa) && DENIS1(fb))  f = NULL;
     972  else if (!DENIS1(fa) && DENIS1(fb)) f = p_Copy(DEN(fa), ntRing);
     973  else if (DENIS1(fa) && !DENIS1(fb)) f = p_Copy(DEN(fb), ntRing);
     974  else /* both denom's are != 1 */    f = p_Mult_q(p_Copy(DEN(fa), ntRing),
     975                                                   p_Copy(DEN(fb), ntRing),
     976                                                   ntRing);
     977
     978  fraction result = (fraction)omAllocBin(fractionObjectBin);
     979  NUM(result) = g;
     980  DEN(result) = f;
     981  COM(result) = COM(fa) + COM(fb) + ADD_COMPLEXITY;
     982  heuristicGcdCancellation((number)result, cf);
     983
     984//  ntTest((number)result);
     985
     986  //check_N((number)result,cf);
     987  ntTest((number)result);
     988  return (number)result;
     989}
     990
     991static number ntSub(number a, number b, const coeffs cf)
     992{
     993  //check_N(a,cf);
     994  //check_N(b,cf);
     995  ntTest(a);
     996  ntTest(b);
     997  if (IS0(a)) return ntNeg(ntCopy(b, cf), cf);
     998  if (IS0(b)) return ntCopy(a, cf);
     999
     1000  fraction fa = (fraction)a;
     1001  fraction fb = (fraction)b;
     1002
     1003  poly g = p_Copy(NUM(fa), ntRing);
     1004  if (!DENIS1(fb)) g = p_Mult_q(g, p_Copy(DEN(fb), ntRing), ntRing);
     1005  poly h = p_Copy(NUM(fb), ntRing);
     1006  if (!DENIS1(fa)) h = p_Mult_q(h, p_Copy(DEN(fa), ntRing), ntRing);
     1007  g = p_Add_q(g, p_Neg(h, ntRing), ntRing);
     1008
     1009  if (g == NULL) return NULL;
     1010
     1011  poly f;
     1012  if      (DENIS1(fa) && DENIS1(fb))  f = NULL;
     1013  else if (!DENIS1(fa) && DENIS1(fb)) f = p_Copy(DEN(fa), ntRing);
     1014  else if (DENIS1(fa) && !DENIS1(fb)) f = p_Copy(DEN(fb), ntRing);
     1015  else /* both den's are != 1 */      f = p_Mult_q(p_Copy(DEN(fa), ntRing),
     1016                                                   p_Copy(DEN(fb), ntRing),
     1017                                                   ntRing);
     1018
     1019  fraction result = (fraction)omAllocBin(fractionObjectBin);
     1020  NUM(result) = g;
     1021  DEN(result) = f;
     1022  COM(result) = COM(fa) + COM(fb) + ADD_COMPLEXITY;
     1023  heuristicGcdCancellation((number)result, cf);
     1024//  ntTest((number)result);
     1025  //check_N((number)result,cf);
     1026  ntTest((number)result);
     1027  return (number)result;
     1028}
     1029
     1030static number ntMult(number a, number b, const coeffs cf)
     1031{
     1032  //check_N(a,cf);
     1033  //check_N(b,cf);
     1034  ntTest(a); // !!!?
     1035  ntTest(b); // !!!?
     1036
     1037  if (IS0(a) || IS0(b)) return NULL;
     1038
     1039  fraction fa = (fraction)a;
     1040  fraction fb = (fraction)b;
     1041
     1042  const poly g = pp_Mult_qq(NUM(fa), NUM(fb), ntRing);
     1043
     1044  if (g == NULL) return NULL; // may happen due to zero divisors???
     1045
     1046  fraction result = (fraction)omAllocBin(fractionObjectBin);
     1047
     1048  NUM(result) = g;
     1049
     1050  const poly da = DEN(fa);
     1051  const poly db = DEN(fb);
     1052
     1053
     1054  //check_N((number)result,cf);
     1055  if (db == NULL)
     1056  {
     1057    // b = ? // NULL
     1058
     1059    if(da == NULL)
     1060    { // both fa && fb are ?? // NULL!
     1061      assume (da == NULL && db == NULL);
     1062      DEN(result) = NULL;
     1063      COM(result) = 0;
     1064    }
     1065    else
     1066    {
     1067      assume (da != NULL && db == NULL);
     1068      DEN(result) = p_Copy(da, ntRing);
     1069      COM(result) = COM(fa) + MULT_COMPLEXITY;
     1070      heuristicGcdCancellation((number)result, cf);
     1071      //check_N((number)result,cf);
     1072    }
     1073  }
     1074  else
     1075  { // b = ?? / ??
     1076    if (da == NULL)
     1077    { // a == ? // NULL
     1078      assume( db != NULL && da == NULL);
     1079      DEN(result) = p_Copy(db, ntRing);
     1080      COM(result) = COM(fb) + MULT_COMPLEXITY;
     1081      heuristicGcdCancellation((number)result, cf);
     1082      //check_N((number)result,cf);
     1083    }
     1084    else /* both den's are != 1 */
     1085    {
     1086      assume (da != NULL && db != NULL);
     1087      DEN(result) = pp_Mult_qq(da, db, ntRing);
     1088      COM(result) = COM(fa) + COM(fb) + MULT_COMPLEXITY;
     1089      heuristicGcdCancellation((number)result, cf);
     1090      //check_N((number)result,cf);
     1091    }
     1092  }
     1093
     1094//  ntTest((number)result);
     1095
     1096  //check_N((number)result,cf);
     1097  ntTest((number)result);
     1098  return (number)result;
     1099}
     1100
     1101static void ntNormalizeDen(fraction result, const ring R)
     1102{
     1103  if ((nCoeff_has_simple_inverse(R->cf))
     1104  && (result!=NULL)
     1105  && (DEN(result)!=NULL))
     1106  {
     1107    poly n=DEN(result);
     1108    if (!n_IsOne(pGetCoeff(n),R->cf))
     1109    {
     1110      number inv=n_Invers(pGetCoeff(n),R->cf);
     1111      DEN(result)=p_Mult_nn(n,inv,R);
     1112      NUM(result)=p_Mult_nn(NUM(result),inv,R);
     1113      n_Delete(&inv,R->cf);
     1114      if (p_IsOne(DEN(result), R))
     1115      {
     1116        n=DEN(result);
     1117        DEN(result)=NULL;
     1118        COM(result) = 0;
     1119        p_Delete(&n,R);
     1120      }
     1121    }
     1122  }
     1123}
     1124
     1125static number ntDiv(number a, number b, const coeffs cf)
     1126{
     1127  //check_N(a,cf);
     1128  //check_N(b,cf);
     1129  ntTest(a);
     1130  ntTest(b);
     1131  if (IS0(a)) return NULL;
     1132  if (IS0(b)) WerrorS(nDivBy0);
     1133
     1134  fraction fa = (fraction)a;
     1135  fraction fb = (fraction)b;
     1136
     1137  poly g = p_Copy(NUM(fa), ntRing);
     1138  if (!DENIS1(fb)) g = p_Mult_q(g, p_Copy(DEN(fb), ntRing), ntRing);
     1139
     1140  if (g == NULL) return NULL;   /* may happen due to zero divisors */
     1141
     1142  poly f = p_Copy(NUM(fb), ntRing);
     1143  if (!DENIS1(fa)) f = p_Mult_q(f, p_Copy(DEN(fa), ntRing), ntRing);
     1144
     1145  fraction result = (fraction)omAlloc0Bin(fractionObjectBin);
     1146  NUM(result) = g;
     1147  if (!n_GreaterZero(pGetCoeff(f),ntCoeffs))
     1148  {
     1149    g=p_Neg(g,ntRing);
     1150    f=p_Neg(f,ntRing);
     1151    NUM(result) = g;
     1152  }
     1153  if (!p_IsConstant(f,ntRing) || !n_IsOne(pGetCoeff(f),ntCoeffs))
     1154  {
     1155    DEN(result) = f;
     1156  }
     1157  COM(result) = COM(fa) + COM(fb) + MULT_COMPLEXITY;
     1158//  definiteGcdCancellation((number)result, cf,FALSE);
     1159  heuristicGcdCancellation((number)result, cf);
     1160//  ntTest((number)result);
     1161  //check_N((number)result,cf);
     1162  ntNormalizeDen(result,ntRing);
     1163  ntTest((number)result);
     1164  return (number)result;
     1165}
     1166
     1167static number ntInvers(number a, const coeffs cf)
     1168{
     1169  //check_N(a,cf);
     1170  ntTest(a);
     1171  if (IS0(a))
     1172  {
     1173    WerrorS(nDivBy0);
     1174    return NULL;
     1175  }
     1176  fraction f = (fraction)a;
     1177  assume( f != NULL );
     1178
     1179  fraction result = (fraction)omAlloc0Bin(fractionObjectBin);
     1180
     1181  assume( NUM(f) != NULL );
     1182  const poly den = DEN(f);
     1183
     1184  if (den == NULL)
     1185    NUM(result) = p_One(ntRing);
     1186  else
     1187    NUM(result) = p_Copy(den, ntRing);
     1188
     1189  if( !NUMIS1(f) )
     1190  {
     1191    poly num_f=NUM(f);
     1192    BOOLEAN neg= !n_GreaterZero(pGetCoeff(num_f),ntCoeffs);
     1193    if (neg)
     1194    {
     1195      num_f=p_Neg(p_Copy(num_f, ntRing), ntRing);
     1196      NUM(result)=p_Neg(NUM(result), ntRing);
     1197    }
     1198    else
     1199    {
     1200      num_f=p_Copy(num_f, ntRing);
     1201    }
     1202    DEN(result) = num_f;
     1203    COM(result) = COM(f);
     1204    if (neg)
     1205    {
     1206      if (p_IsOne(num_f, ntRing))
     1207      {
     1208        DEN(result)=NULL;
     1209        //COM(result) = 0;
     1210        p_Delete(&num_f,ntRing);
     1211      }
     1212    }
     1213  }
     1214  //else// Alloc0
     1215  //{
     1216  //  DEN(result) = NULL;
     1217  //  COM(result) = 0;
     1218  //}
     1219  ntNormalizeDen(result,ntRing);
     1220  ntTest((number)result); // !!!!
     1221  //check_N((number)result,cf);
     1222  return (number)result;
     1223}
     1224
     1225/* 0^0 = 0;
     1226   for |exp| <= 7 compute power by a simple multiplication loop;
     1227   for |exp| >= 8 compute power along binary presentation of |exp|, e.g.
     1228      p^13 = p^1 * p^4 * p^8, where we utilise that
     1229      p^(2^(k+1)) = p^(2^k) * p^(2^k);
     1230   intermediate cancellation is controlled by the in-place method
     1231   heuristicGcdCancellation; see there.
     1232*/
     1233static void ntPower(number a, int exp, number *b, const coeffs cf)
     1234{
     1235  ntTest(a);
     1236
     1237  /* special cases first */
     1238  if (IS0(a))
     1239  {
     1240    if (exp >= 0) *b = NULL;
     1241    else          WerrorS(nDivBy0);
     1242  }
     1243  else if (exp ==  0) { *b = ntInit(1, cf); return;}
     1244  else if (exp ==  1) { *b = ntCopy(a, cf); return;}
     1245  else if (exp == -1) { *b = ntInvers(a, cf); return;}
     1246
     1247  int expAbs = exp; if (expAbs < 0) expAbs = -expAbs;
     1248
     1249  /* now compute a^expAbs */
     1250  number pow; number t;
     1251  if (expAbs <= 7)
     1252  {
     1253    pow = ntCopy(a, cf);
     1254    for (int i = 2; i <= expAbs; i++)
     1255    {
     1256      t = ntMult(pow, a, cf);
     1257      ntDelete(&pow, cf);
     1258      pow = t;
     1259      heuristicGcdCancellation(pow, cf);
     1260    }
     1261  }
     1262  else
     1263  {
     1264    pow = ntInit(1, cf);
     1265    number factor = ntCopy(a, cf);
     1266    while (expAbs != 0)
     1267    {
     1268      if (expAbs & 1)
     1269      {
     1270        t = ntMult(pow, factor, cf);
     1271        ntDelete(&pow, cf);
     1272        pow = t;
     1273        heuristicGcdCancellation(pow, cf);
     1274      }
     1275      expAbs = expAbs / 2;
     1276      if (expAbs != 0)
     1277      {
     1278        t = ntMult(factor, factor, cf);
     1279        ntDelete(&factor, cf);
     1280        factor = t;
     1281        heuristicGcdCancellation(factor, cf);
     1282      }
     1283    }
     1284    ntDelete(&factor, cf);
     1285  }
     1286
     1287  /* invert if original exponent was negative */
     1288  if (exp < 0)
     1289  {
     1290    t = ntInvers(pow, cf);
     1291    ntDelete(&pow, cf);
     1292    pow = t;
     1293  }
     1294  *b = pow;
     1295  ntTest(*b);
     1296  //check_N(*b,cf);
    12771297}
    12781298
    12791299/* modifies a */
    12801300/* this is an intermediate simplification routine - not a comple "normalize" */
    1281 void heuristicGcdCancellation(number a, const coeffs cf)
     1301static void heuristicGcdCancellation(number a, const coeffs cf)
    12821302{
    12831303  if (IS0(a)) return;
    … …  
    13641384
    13651385/// modifies a
    1366 void definiteGcdCancellation(number a, const coeffs cf,
     1386static void definiteGcdCancellation(number a, const coeffs cf,
    13671387                             BOOLEAN simpleTestsHaveAlreadyBeenPerformed)
    13681388{
    … …  
    13721392
    13731393  if (IS0(a)) return;
     1394  if (COM(f)==0) return;
    13741395  if (DENIS1(f) || NUMIS1(f)) { COM(f) = 0; ntTest(a); return; }
    13751396  if (!simpleTestsHaveAlreadyBeenPerformed)
    … …  
    14411462
    14421463  /* here we assume: NUM(f), DEN(f) !=NULL, in Z_a reqp. Z/p_a */
     1464  //StringSetS("");ntWriteLong(a,cf);
    14431465  poly pGcd = singclap_gcd_and_divide(NUM(f), DEN(f), ntRing);
    14441466  //PrintS("gcd= ");p_wrp(pGcd,ntRing);PrintLn();
    … …  
    14931515  }
    14941516  p_Delete(&pGcd, ntRing);
     1517//  StringAppendS(" -> ");ntWriteLong(a,cf);StringAppendS("\n");{ char* s = StringEndS(); Print("%s", s); omFree(s); }
    14951518  COM(f) = 0;
    14961519
    … …  
    15131536}
    15141537
    1515 void ntWriteLong(number a, const coeffs cf)
     1538static void ntWriteLong(number a, const coeffs cf)
    15161539{
    15171540  ntTest(a);
    … …  
    15381561}
    15391562
    1540 void ntWriteShort(number a, const coeffs cf)
     1563static void ntWriteShort(number a, const coeffs cf)
    15411564{
    15421565  ntTest(a);
    … …  
    15631586}
    15641587
    1565 const char * ntRead(const char *s, number *a, const coeffs cf)
     1588static const char * ntRead(const char *s, number *a, const coeffs cf)
    15661589{
    15671590  poly p;
    … …  
    15731596}
    15741597
    1575 void ntNormalize (number &a, const coeffs cf)
     1598static void ntNormalize (number &a, const coeffs cf)
    15761599{
    15771600  if ( /*(*/ a!=NULL /*)*/ )
    … …  
    15791602    //PrintS("num=");p_wrp(NUM(a),ntRing);
    15801603    //PrintS(" den=");p_wrp(DEN(a),ntRing);PrintLn();
    1581     definiteGcdCancellation(a, cf, FALSE);
     1604    if (COM((fraction)a)>0) definiteGcdCancellation(a, cf, FALSE);
    15821605    if ((DEN((fraction)a)!=NULL)
    15831606    &&(!n_GreaterZero(pGetCoeff(DEN((fraction)a)),ntCoeffs)))
    … …  
    16141637}
    16151638
    1616 number ntNormalizeHelper(number a, number b, const coeffs cf)
     1639static number ntNormalizeHelper(number a, number b, const coeffs cf)
    16171640{
    16181641  ntTest(a);
    … …  
    17021725}
    17031726
    1704 number ntGcd(number a, number b, const coeffs cf)
     1727static number ntGcd(number a, number b, const coeffs cf)
    17051728{
    17061729  ntTest(a);
    … …  
    17781801//}
    17791802
    1780 int ntSize(number a, const coeffs cf)
     1803static int ntSize(number a, const coeffs cf)
    17811804{
    17821805  ntTest(a);
    … …  
    18051828}
    18061829
    1807 number ntInvers(number a, const coeffs cf)
    1808 {
    1809   //check_N(a,cf);
    1810   ntTest(a);
    1811   if (IS0(a))
    1812   {
    1813     WerrorS(nDivBy0);
    1814     return NULL;
    1815   }
    1816   fraction f = (fraction)a;
    1817   assume( f != NULL );
    1818 
    1819   fraction result = (fraction)omAlloc0Bin(fractionObjectBin);
    1820 
    1821   assume( NUM(f) != NULL );
    1822   const poly den = DEN(f);
    1823 
    1824   if (den == NULL)
    1825     NUM(result) = p_One(ntRing);
    1826   else
    1827     NUM(result) = p_Copy(den, ntRing);
    1828 
    1829   if( !NUMIS1(f) )
    1830   {
    1831     poly num_f=NUM(f);
    1832     BOOLEAN neg= !n_GreaterZero(pGetCoeff(num_f),ntCoeffs);
    1833     if (neg)
    1834     {
    1835       num_f=p_Neg(p_Copy(num_f, ntRing), ntRing);
    1836       NUM(result)=p_Neg(NUM(result), ntRing);
    1837     }
    1838     else
    1839     {
    1840       num_f=p_Copy(num_f, ntRing);
    1841     }
    1842     DEN(result) = num_f;
    1843     COM(result) = COM(f);
    1844     if (neg)
    1845     {
    1846       if (p_IsOne(num_f, ntRing))
    1847       {
    1848         DEN(result)=NULL;
    1849         //COM(result) = 0;
    1850         p_Delete(&num_f,ntRing);
    1851       }
    1852     }
    1853   }
    1854   //else// Alloc0
    1855   //{
    1856   //  DEN(result) = NULL;
    1857   //  COM(result) = 0;
    1858   //}
    1859   ntNormalizeDen(result,ntRing);
    1860   ntTest((number)result); // !!!!
    1861   //check_N((number)result,cf);
    1862   return (number)result;
    1863 }
    1864 
    18651830/* assumes that src = Q or Z, dst = Q(t_1, ..., t_s) */
    1866 number ntMap00(number a, const coeffs src, const coeffs dst)
     1831static number ntMap00(number a, const coeffs src, const coeffs dst)
    18671832{
    18681833  n_Test(a, src);
    … …  
    18881853}
    18891854
    1890 number ntMapZ0(number a, const coeffs src, const coeffs dst)
     1855static number ntMapZ0(number a, const coeffs src, const coeffs dst)
    18911856{
    18921857  n_Test(a, src);
    … …  
    19021867
    19031868/* assumes that src = Z/p, dst = Q(t_1, ..., t_s) */
    1904 number ntMapP0(number a, const coeffs src, const coeffs dst)
     1869static number ntMapP0(number a, const coeffs src, const coeffs dst)
    19051870{
    19061871  n_Test(a, src);
    … …  
    19181883
    19191884 /* assumes that either src = K(t_1, ..., t_s), dst = K(t_1, ..., t_s) */
    1920 number ntCopyMap(number a, const coeffs cf, const coeffs dst)
     1885static number ntCopyMap(number a, const coeffs cf, const coeffs dst)
    19211886{
    19221887  ntTest(a);
    … …  
    19471912}
    19481913
    1949 number ntGenMap(number a, const coeffs cf, const coeffs dst)
     1914static number ntGenMap(number a, const coeffs cf, const coeffs dst)
    19501915{
    19511916  ntTest(a);
    … …  
    20261991}
    20271992
    2028 number ntCopyAlg(number a, const coeffs cf, const coeffs dst)
     1993static number ntCopyAlg(number a, const coeffs cf, const coeffs dst)
    20291994{
    20301995  n_Test(a, cf) ;
    … …  
    20331998}
    20341999
    2035 number ntGenAlg(number a, const coeffs cf, const coeffs dst)
     2000static number ntGenAlg(number a, const coeffs cf, const coeffs dst)
    20362001{
    20372002  n_Test(a, cf) ;
    … …  
    20432008
    20442009/* assumes that src = Q, dst = Z/p(t_1, ..., t_s) */
    2045 number ntMap0P(number a, const coeffs src, const coeffs dst)
     2010static number ntMap0P(number a, const coeffs src, const coeffs dst)
    20462011{
    20472012  n_Test(a, src) ;
    … …  
    20672032
    20682033/* assumes that src = Z/p, dst = Z/p(t_1, ..., t_s) */
    2069 number ntMapPP(number a, const coeffs src, const coeffs dst)
     2034static number ntMapPP(number a, const coeffs src, const coeffs dst)
    20702035{
    20712036  n_Test(a, src) ;
    … …  
    20822047
    20832048/* assumes that src = Z/u, dst = Z/p(t_1, ..., t_s), where u != p */
    2084 number ntMapUP(number a, const coeffs src, const coeffs dst)
     2049static number ntMapUP(number a, const coeffs src, const coeffs dst)
    20852050{
    20862051  n_Test(a, src) ;
    … …  
    21812146#endif
    21822147
    2183 void ntKillChar(coeffs cf)
     2148static void ntKillChar(coeffs cf)
    21842149{
    21852150  if ((--cf->extRing->ref) == 0)
    21862151    rDelete(cf->extRing);
    21872152}
    2188 number ntConvFactoryNSingN( const CanonicalForm n, const coeffs cf)
     2153static number ntConvFactoryNSingN( const CanonicalForm n, const coeffs cf)
    21892154{
    21902155  if (n.isZero()) return NULL;
    … …  
    21982163  return (number)result;
    21992164}
    2200 CanonicalForm ntConvSingNFactoryN( number n, BOOLEAN /*setChar*/, const coeffs cf )
     2165static CanonicalForm ntConvSingNFactoryN( number n, BOOLEAN /*setChar*/, const coeffs cf )
    22012166{
    22022167  ntTest(n);
    … …  
    24972462}
    24982463
    2499 number ntChineseRemainder(number *x, number *q,int rl, BOOLEAN /*sym*/,CFArray &inv_cache,const coeffs cf)
     2464static number ntChineseRemainder(number *x, number *q,int rl, BOOLEAN /*sym*/,CFArray &inv_cache,const coeffs cf)
    25002465{
    25012466  fraction result = (fraction)omAlloc0Bin(fractionObjectBin);
    … …  
    25272492}
    25282493
    2529 number ntFarey(number p, number n, const coeffs cf)
     2494static number ntFarey(number p, number n, const coeffs cf)
    25302495{
    25312496  // n is really a bigint
    … …  
    25952560  cf->cfGetDenom     = ntGetDenom;
    25962561  cf->cfGetNumerator = ntGetNumerator;
    2597   cf->cfRePart       = ntCopy;
    2598   cf->cfImPart       = ntImPart;
     2562  //cf->cfRePart       = ntCopy;
     2563  //cf->cfImPart       = ntImPart;
    25992564  cf->cfCoeffWrite   = ntCoeffWrite;
    26002565#ifdef LDEBUG
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