Changeset e5d267 in git

Timestamp:

Jul 4, 2011, 4:22:10 PM (12 years ago)

Author:

Frank Seelisch <seelisch@…>

Branches:

(u'jengelh-datetime', 'ceac47cbc86fe4a15902392bdbb9bd2ae0ea02c6')(u'spielwiese', 'f875bbaccd0831e36aaed09ff6adeb3eb45aeb94')

Children:

da49bc5ede2940b54c1e9f92022763151efa76e6

Parents:

df43d9eede47de2604d4c0ff334af81427c1ec57

git-author:

Frank Seelisch <seelisch@mathematik.uni-kl.de>2011-07-04 16:22:10+02:00

git-committer:

Mohamed Barakat <mohamed.barakat@rwth-aachen.de>2011-11-09 12:39:11+01:00

Message:

cancellation of gcd in rat. funct. fields

Location:

libpolys

Files:

• coeffs/longrat.cc (modified) (1 diff)
• polys/ext_fields/transext.cc (modified) (38 diffs)
• polys/ext_fields/transext.h (modified) (1 diff)
• polys/monomials/p_polys.cc (modified) (1 diff)
• tests/polys_test.h (modified) (4 diffs)

libpolys/coeffs/longrat.cc

@@ -2603 +2603 @@
   r->cfDBTest=nlDBTest;
 #endif
+#ifdef HAVE_FACTORY
+  r->convSingNFactoryN=nlConvSingNFactoryN;
+  r->convFactoryNSingN=nlConvFactoryNSingN;
+#endif
 
   // the variables: general stuff (required)

libpolys/polys/ext_fields/transext.cc

@@ -25 +25 @@
 #include <polys/monomials/p_polys.h>
 #include <polys/simpleideals.h>
+
+#ifdef HAVE_FACTORY
+#include <polys/clapsing.h>
+#endif
 
 #include <polys/ext_fields/transext.h>
@@ -74 +78 @@
   assume(getCoeffType(cf) == ntID);
   fraction t = (fraction)a;
-  if (is0(t)) return TRUE;
-  assume(num(t) != NULL);   /**< t != 0 ==> numerator(t) != 0 */
-  p_Test(num(t), ntRing);
-  if (!denIs1(t)) p_Test(den(t), ntRing);
+  if (IS0(t)) return TRUE;
+  assume(NUM(t) != NULL);   /**< t != 0 ==> numerator(t) != 0 */
+  p_Test(NUM(t), ntRing);
+  if (!DENIS1(t)) p_Test(DEN(t), ntRing);
   return TRUE;
 }
@@ -103 +107 @@
 {
   ntTest(a);
-  return (is0(a));
+  return (IS0(a));
 }
 
@@ -109 +113 @@
 {
   fraction f = (fraction)(*a);
-  if (is0(f)) return;
-  p_Delete(&num(f), ntRing);
-  if (!denIs1(f)) p_Delete(&den(f), ntRing);
+  if (IS0(f)) return;
+  p_Delete(&NUM(f), ntRing);
+  if (!DENIS1(f)) p_Delete(&DEN(f), ntRing);
   omFreeBin((ADDRESS)f, fractionObjectBin);
   *a = NULL;
@@ -122 +126 @@
   /// simple tests
   if (a == b) return TRUE;
-  if ((is0(a)) && (!is0(b))) return FALSE;
-  if ((is0(b)) && (!is0(a))) return FALSE;
+  if ((IS0(a)) && (!IS0(b))) return FALSE;
+  if ((IS0(b)) && (!IS0(a))) return FALSE;
   
   /// cheap test if gcd's have been cancelled in both numbers 
   fraction fa = (fraction)a;
   fraction fb = (fraction)b;
-  if ((c(fa) == 1) && (c(fb) == 1))
-  {
-    poly f = p_Add_q(p_Copy(num(fa), ntRing),
-                     p_Neg(p_Copy(num(fb), ntRing), ntRing),
+  if ((COM(fa) == 1) && (COM(fb) == 1))
+  {
+    poly f = p_Add_q(p_Copy(NUM(fa), ntRing),
+                     p_Neg(p_Copy(NUM(fb), ntRing), ntRing),
                      ntRing);
     if (f != NULL) { p_Delete(&f, ntRing); return FALSE; }
-    if (denIs1(fa) && denIs1(fb))  return TRUE;
-    if (denIs1(fa) && !denIs1(fb)) return FALSE;
-    if (!denIs1(fa) && denIs1(fb)) return FALSE;
-    f = p_Add_q(p_Copy(den(fa), ntRing),
-                p_Neg(p_Copy(den(fb), ntRing), ntRing),
+    if (DENIS1(fa) && DENIS1(fb))  return TRUE;
+    if (DENIS1(fa) && !DENIS1(fb)) return FALSE;
+    if (!DENIS1(fa) && DENIS1(fb)) return FALSE;
+    f = p_Add_q(p_Copy(DEN(fa), ntRing),
+                p_Neg(p_Copy(DEN(fb), ntRing), ntRing),
                 ntRing);
     if (f != NULL) { p_Delete(&f, ntRing); return FALSE; }
@@ -146 +150 @@
   /* default: the more expensive multiplication test
               a/b = c/d  <==>  a*d = b*c */
-  poly f = p_Copy(num(fa), ntRing);
-  if (!denIs1(fb)) f = p_Mult_q(f, p_Copy(den(fb), ntRing), ntRing);
-  poly g = p_Copy(num(fb), ntRing);
-  if (!denIs1(fa)) g = p_Mult_q(g, p_Copy(den(fa), ntRing), ntRing);
+  poly f = p_Copy(NUM(fa), ntRing);
+  if (!DENIS1(fb)) f = p_Mult_q(f, p_Copy(DEN(fb), ntRing), ntRing);
+  poly g = p_Copy(NUM(fb), ntRing);
+  if (!DENIS1(fa)) g = p_Mult_q(g, p_Copy(DEN(fa), ntRing), ntRing);
   poly h = p_Add_q(f, p_Neg(g, ntRing), ntRing);
   if (h == NULL) return TRUE;
@@ -162 +166 @@
 {
   ntTest(a);
-  if (is0(a)) return NULL;
-  fraction f = (fraction)a;
-  poly g = p_Copy(num(f), ntRing);
-  poly h = NULL; if (!denIs1(f)) h = p_Copy(den(f), ntRing);
+  if (IS0(a)) return NULL;
+  fraction f = (fraction)a;
+  poly g = p_Copy(NUM(f), ntRing);
+  poly h = NULL; if (!DENIS1(f)) h = p_Copy(DEN(f), ntRing);
   fraction result = (fraction)omAlloc0Bin(fractionObjectBin);
-  num(result) = g;
-  den(result) = h;
-  c(result) = c(f);
+  NUM(result) = g;
+  DEN(result) = h;
+  COM(result) = COM(f);
   return (number)result;
 }
@@ -177 +181 @@
   ntTest(a);
   definiteGcdCancellation(a, cf, FALSE);
-  if (is0(a)) return NULL;
-  fraction f = (fraction)a;
-  poly g = p_Copy(num(f), ntRing);
+  if (IS0(a)) return NULL;
+  fraction f = (fraction)a;
+  poly g = p_Copy(NUM(f), ntRing);
   fraction result = (fraction)omAlloc0Bin(fractionObjectBin);
-  num(result) = g;
-  den(result) = NULL;
-  c(result) = 0;
+  NUM(result) = g;
+  DEN(result) = NULL;
+  COM(result) = 0;
   return (number)result;
 }
@@ -193 +197 @@
   fraction f = (fraction)a;
   poly g;
-  if (is0(f) || denIs1(f)) g = p_One(ntRing);
-  else g = p_Copy(den(f), ntRing);
+  if (IS0(f) || DENIS1(f)) g = p_One(ntRing);
+  else g = p_Copy(DEN(f), ntRing);
   fraction result = (fraction)omAlloc0Bin(fractionObjectBin);
-  num(result) = g;
-  den(result) = NULL;
-  c(result) = 0;
+  NUM(result) = g;
+  DEN(result) = NULL;
+  COM(result) = 0;
   return (number)result;
 }
@@ -207 +211 @@
   definiteGcdCancellation(a, cf, FALSE);
   fraction f = (fraction)a;
-  return denIs1(f) && numIs1(f);
+  return DENIS1(f) && NUMIS1(f);
 }
 
@@ -215 +219 @@
   definiteGcdCancellation(a, cf, FALSE);
   fraction f = (fraction)a;
-  if (!denIs1(f)) return FALSE;
-  poly g = num(f);
+  if (!DENIS1(f)) return FALSE;
+  poly g = NUM(f);
   if (!p_IsConstant(g, ntRing)) return FALSE;
   return n_IsMOne(p_GetCoeff(g, ntRing), ntCoeffs);
@@ -225 +229 @@
 {
   ntTest(a);
-  if (!is0(a))
+  if (!IS0(a))
   {
     fraction f = (fraction)a;
-    num(f) = p_Neg(num(f), ntRing);
+    NUM(f) = p_Neg(NUM(f), ntRing);
   }
   return a;
@@ -245 +249 @@
   {
     fraction result = (fraction)omAlloc0Bin(fractionObjectBin);
-    num(result) = p_ISet(i, ntRing);
-    den(result) = NULL;
-    c(result) = 0;
+    NUM(result) = p_ISet(i, ntRing);
+    DEN(result) = NULL;
+    COM(result) = 0;
     return (number)result;
   }
@@ -255 +259 @@
 {
   ntTest(a);
-  if (is0(a)) return 0;
+  if (IS0(a)) return 0;
   definiteGcdCancellation(a, cf, FALSE);
   fraction f = (fraction)a;
-  if (!denIs1(f)) return 0;
-  if (!p_IsConstant(num(f), ntRing)) return 0;
-  return n_Int(p_GetCoeff(num(f), ntRing), ntCoeffs);
+  if (!DENIS1(f)) return 0;
+  if (!p_IsConstant(NUM(f), ntRing)) return 0;
+  return n_Int(p_GetCoeff(NUM(f), ntRing), ntCoeffs);
 }
 
@@ -274 +278 @@
   number aNumCoeff = NULL; int aNumDeg = 0;
   number bNumCoeff = NULL; int bNumDeg = 0;
-  if (!is0(a))
+  if (!IS0(a))
   {
     fraction fa = (fraction)a;
-    aNumDeg = p_Totaldegree(num(fa), ntRing);
-    aNumCoeff = p_GetCoeff(num(fa), ntRing);
-  }
-  if (!is0(b))
+    aNumDeg = p_Totaldegree(NUM(fa), ntRing);
+    aNumCoeff = p_GetCoeff(NUM(fa), ntRing);
+  }
+  if (!IS0(b))
   {
     fraction fb = (fraction)b;
-    bNumDeg = p_Totaldegree(num(fb), ntRing);
-    bNumCoeff = p_GetCoeff(num(fb), ntRing);
+    bNumDeg = p_Totaldegree(NUM(fb), ntRing);
+    bNumCoeff = p_GetCoeff(NUM(fb), ntRing);
   }
   if (aNumDeg != bNumDeg) return FALSE;
@@ -298 +302 @@
 {
   ntTest(a);
-  if (is0(a)) return FALSE;
-  fraction f = (fraction)a;
-  poly g = num(f);
+  if (IS0(a)) return FALSE;
+  fraction f = (fraction)a;
+  poly g = NUM(f);
   return (n_GreaterZero(p_GetCoeff(g, ntRing), ntCoeffs) ||
           (!p_LmIsConstant(g, ntRing)));
@@ -326 +330 @@
   p_Setm(p, ntRing);
   fraction result = (fraction)omAlloc0Bin(fractionObjectBin);
-  num(result) = p;
-  den(result) = NULL;
-  c(result) = 0;
+  NUM(result) = p;
+  DEN(result) = NULL;
+  COM(result) = 0;
   return (number)result;
 }
@@ -335 +339 @@
 {
   ntTest(a); ntTest(b);
-  if (is0(a)) return ntCopy(b, cf);
-  if (is0(b)) return ntCopy(a, cf);
+  if (IS0(a)) return ntCopy(b, cf);
+  if (IS0(b)) return ntCopy(a, cf);
   
   fraction fa = (fraction)a;
   fraction fb = (fraction)b;
   
-  poly g = p_Copy(num(fa), ntRing);
-  if (!denIs1(fb)) g = p_Mult_q(g, p_Copy(den(fb), ntRing), ntRing);
-  poly h = p_Copy(num(fb), ntRing);
-  if (!denIs1(fa)) h = p_Mult_q(h, p_Copy(den(fa), ntRing), ntRing);
+  poly g = p_Copy(NUM(fa), ntRing);
+  if (!DENIS1(fb)) g = p_Mult_q(g, p_Copy(DEN(fb), ntRing), ntRing);
+  poly h = p_Copy(NUM(fb), ntRing);
+  if (!DENIS1(fa)) h = p_Mult_q(h, p_Copy(DEN(fa), ntRing), ntRing);
   g = p_Add_q(g, h, ntRing);
   
@@ -350 +354 @@
   
   poly f;
-  if      (denIs1(fa) && denIs1(fb))  f = NULL;
-  else if (!denIs1(fa) && denIs1(fb)) f = p_Copy(den(fa), ntRing);
-  else if (denIs1(fa) && !denIs1(fb)) f = p_Copy(den(fb), ntRing);
-  else /* both denom's are != 1 */    f = p_Mult_q(p_Copy(den(fa), ntRing),
-                                                   p_Copy(den(fb), ntRing),
+  if      (DENIS1(fa) && DENIS1(fb))  f = NULL;
+  else if (!DENIS1(fa) && DENIS1(fb)) f = p_Copy(DEN(fa), ntRing);
+  else if (DENIS1(fa) && !DENIS1(fb)) f = p_Copy(DEN(fb), ntRing);
+  else /* both denom's are != 1 */    f = p_Mult_q(p_Copy(DEN(fa), ntRing),
+                                                   p_Copy(DEN(fb), ntRing),
                                                    ntRing);
   
   fraction result = (fraction)omAlloc0Bin(fractionObjectBin);
-  num(result) = g;
-  den(result) = f;
-  c(result) = c(fa) + c(fb) + ADD_COMPLEXITY;
+  NUM(result) = g;
+  DEN(result) = f;
+  COM(result) = COM(fa) + COM(fb) + ADD_COMPLEXITY;
   heuristicGcdCancellation((number)result, cf);
   return (number)result;
@@ -368 +372 @@
 {
   ntTest(a); ntTest(b);
-  if (is0(a)) return ntNeg(ntCopy(b, cf), cf);
-  if (is0(b)) return ntCopy(a, cf);
+  if (IS0(a)) return ntNeg(ntCopy(b, cf), cf);
+  if (IS0(b)) return ntCopy(a, cf);
   
   fraction fa = (fraction)a;
   fraction fb = (fraction)b;
   
-  poly g = p_Copy(num(fa), ntRing);
-  if (!denIs1(fb)) g = p_Mult_q(g, p_Copy(den(fb), ntRing), ntRing);
-  poly h = p_Copy(num(fb), ntRing);
-  if (!denIs1(fa)) h = p_Mult_q(h, p_Copy(den(fa), ntRing), ntRing);
+  poly g = p_Copy(NUM(fa), ntRing);
+  if (!DENIS1(fb)) g = p_Mult_q(g, p_Copy(DEN(fb), ntRing), ntRing);
+  poly h = p_Copy(NUM(fb), ntRing);
+  if (!DENIS1(fa)) h = p_Mult_q(h, p_Copy(DEN(fa), ntRing), ntRing);
   g = p_Add_q(g, p_Neg(h, ntRing), ntRing);
   
@@ -383 +387 @@
   
   poly f;
-  if      (denIs1(fa) && denIs1(fb))  f = NULL;
-  else if (!denIs1(fa) && denIs1(fb)) f = p_Copy(den(fa), ntRing);
-  else if (denIs1(fa) && !denIs1(fb)) f = p_Copy(den(fb), ntRing);
-  else /* both den's are != 1 */      f = p_Mult_q(p_Copy(den(fa), ntRing),
-                                                   p_Copy(den(fb), ntRing),
+  if      (DENIS1(fa) && DENIS1(fb))  f = NULL;
+  else if (!DENIS1(fa) && DENIS1(fb)) f = p_Copy(DEN(fa), ntRing);
+  else if (DENIS1(fa) && !DENIS1(fb)) f = p_Copy(DEN(fb), ntRing);
+  else /* both den's are != 1 */      f = p_Mult_q(p_Copy(DEN(fa), ntRing),
+                                                   p_Copy(DEN(fb), ntRing),
                                                    ntRing);
   
   fraction result = (fraction)omAlloc0Bin(fractionObjectBin);
-  num(result) = g;
-  den(result) = f;
-  c(result) = c(fa) + c(fb) + ADD_COMPLEXITY;
+  NUM(result) = g;
+  DEN(result) = f;
+  COM(result) = COM(fa) + COM(fb) + ADD_COMPLEXITY;
   heuristicGcdCancellation((number)result, cf);
   return (number)result;
@@ -401 +405 @@
 {
   ntTest(a); ntTest(b);
-  if (is0(a) || is0(b)) return NULL;
+  if (IS0(a) || IS0(b)) return NULL;
   
   fraction fa = (fraction)a;
   fraction fb = (fraction)b;
   
-  poly g = p_Copy(num(fa), ntRing);
-  poly h = p_Copy(num(fb), ntRing);
+  poly g = p_Copy(NUM(fa), ntRing);
+  poly h = p_Copy(NUM(fb), ntRing);
   g = p_Mult_q(g, h, ntRing);
   
@@ -413 +417 @@
   
   poly f;
-  if      (denIs1(fa) && denIs1(fb))  f = NULL;
-  else if (!denIs1(fa) && denIs1(fb)) f = p_Copy(den(fa), ntRing);
-  else if (denIs1(fa) && !denIs1(fb)) f = p_Copy(den(fb), ntRing);
-  else /* both den's are != 1 */      f = p_Mult_q(p_Copy(den(fa), ntRing),
-                                                   p_Copy(den(fb), ntRing),
+  if      (DENIS1(fa) && DENIS1(fb))  f = NULL;
+  else if (!DENIS1(fa) && DENIS1(fb)) f = p_Copy(DEN(fa), ntRing);
+  else if (DENIS1(fa) && !DENIS1(fb)) f = p_Copy(DEN(fb), ntRing);
+  else /* both den's are != 1 */      f = p_Mult_q(p_Copy(DEN(fa), ntRing),
+                                                   p_Copy(DEN(fb), ntRing),
                                                    ntRing);
   
   fraction result = (fraction)omAlloc0Bin(fractionObjectBin);
-  num(result) = g;
-  den(result) = f;
-  c(result) = c(fa) + c(fb) + MULT_COMPLEXITY;
+  NUM(result) = g;
+  DEN(result) = f;
+  COM(result) = COM(fa) + COM(fb) + MULT_COMPLEXITY;
   heuristicGcdCancellation((number)result, cf);
   return (number)result;
@@ -431 +435 @@
 {
   ntTest(a); ntTest(b);
-  if (is0(a)) return NULL;
-  if (is0(b)) WerrorS(nDivBy0);
+  if (IS0(a)) return NULL;
+  if (IS0(b)) WerrorS(nDivBy0);
   
   fraction fa = (fraction)a;
   fraction fb = (fraction)b;
   
-  poly g = p_Copy(num(fa), ntRing);
-  if (!denIs1(fb)) g = p_Mult_q(g, p_Copy(den(fb), ntRing), ntRing);
+  poly g = p_Copy(NUM(fa), ntRing);
+  if (!DENIS1(fb)) g = p_Mult_q(g, p_Copy(DEN(fb), ntRing), ntRing);
   
   if (g == NULL) return NULL;   /* may happen due to zero divisors */
   
-  poly f = p_Copy(num(fb), ntRing);
-  if (!denIs1(fa)) f = p_Mult_q(f, p_Copy(den(fa), ntRing), ntRing);
+  poly f = p_Copy(NUM(fb), ntRing);
+  if (!DENIS1(fa)) f = p_Mult_q(f, p_Copy(DEN(fa), ntRing), ntRing);
   
   fraction result = (fraction)omAlloc0Bin(fractionObjectBin);
-  num(result) = g;
-  den(result) = f;
-  c(result) = c(fa) + c(fb) + MULT_COMPLEXITY;
+  NUM(result) = g;
+  DEN(result) = f;
+  COM(result) = COM(fa) + COM(fb) + MULT_COMPLEXITY;
   heuristicGcdCancellation((number)result, cf);
   return (number)result;
@@ -466 +470 @@
   
   /* special cases first */
-  if (is0(a))
+  if (IS0(a))
   {
     if (exp >= 0) *b = NULL;
@@ -529 +533 @@
 {
   ntTest(a);
-  if (is0(a)) return;
-  
-  fraction f = (fraction)a;
-  if (denIs1(f) || numIs1(f)) { c(f) = 0; return; }
-  
-  /* check whether num(f) = den(f), and - if so - replace 'a' by 1 */
-  poly difference = p_Add_q(p_Copy(num(f), ntRing),
-                            p_Neg(p_Copy(den(f), ntRing), ntRing),
-                            ntRing);
-  if (difference == NULL)
-  { /* we also know that numerator and denominator are both != 1 */
-    p_Delete(&num(f), ntRing); num(f) = p_ISet(1, ntRing);
-    p_Delete(&den(f), ntRing); den(f) = NULL;
-    c(f) = 0;
+  if (IS0(a)) return;
+  
+  fraction f = (fraction)a;
+  if (DENIS1(f) || NUMIS1(f)) { COM(f) = 0; return; }
+  
+  /* check whether NUM(f) = DEN(f), and - if so - replace 'a' by 1 */
+  if (p_EqualPolys(NUM(f), DEN(f), ntRing))
+  { /* numerator and denominator are both != 1 */
+    p_Delete(&NUM(f), ntRing); NUM(f) = p_ISet(1, ntRing);
+    p_Delete(&DEN(f), ntRing); DEN(f) = NULL;
+    COM(f) = 0;
     return;
   }
-  else p_Delete(&difference, ntRing);
-  
-  if (c(f) <= BOUND_COMPLEXITY) return;
+  
+  if (COM(f) <= BOUND_COMPLEXITY) return;
   else definiteGcdCancellation(a, cf, TRUE);
 }
@@ -561 +561 @@
   if (!skipSimpleTests)
   {
-    if (is0(a)) return;
-    if (denIs1(f) || numIs1(f)) { c(f) = 0; return; }
-  
-    /* check whether num(f) = den(f), and - if so - replace 'a' by 1 */
-    poly difference = p_Add_q(p_Copy(num(f), ntRing),
-                              p_Neg(p_Copy(den(f), ntRing), ntRing),
-                              ntRing);
-    if (difference == NULL)
-    { /* we also know that numerator and denominator are both != 1 */
-      p_Delete(&num(f), ntRing); num(f) = p_ISet(1, ntRing);
-      p_Delete(&den(f), ntRing); den(f) = NULL;
-      c(f) = 0;
+    if (IS0(a)) return;
+    if (DENIS1(f) || NUMIS1(f)) { COM(f) = 0; return; }
+  
+    /* check whether NUM(f) = DEN(f), and - if so - replace 'a' by 1 */
+    if (p_EqualPolys(NUM(f), DEN(f), ntRing))
+    { /* numerator and denominator are both != 1 */
+      p_Delete(&NUM(f), ntRing); NUM(f) = p_ISet(1, ntRing);
+      p_Delete(&DEN(f), ntRing); DEN(f) = NULL;
+      COM(f) = 0;
       return;
     }
-    else p_Delete(&difference, ntRing);
-  }
-  
-  /* TO BE IMPLEMENTED!
-     for the time being, cancellation of gcd's does not take place */
-  Print("// TO BE IMPLEMENTED: transext.cc:definiteGcdCancellation\n");
-  Print("// (complexity of number = %d, bound = %d)\n",
-        c(f), BOUND_COMPLEXITY);
-}
-
+  }
+  
+#ifdef HAVE_FACTORY
+  /* singclap_gcd destroys its arguments. We hence need copies: */
+  poly pNum = p_Copy(NUM(f), ntRing);
+  poly pDen = p_Copy(DEN(f), ntRing);
+  poly pGcd = singclap_gcd(pNum, pDen, cf->extRing);
+  if (p_IsConstant(pGcd, ntRing) &&
+      n_IsOne(p_GetCoeff(pGcd, ntRing), ntCoeffs))
+  {
+      /* gcd = 1; nothing to cancel */
+  }
+  else
+  {
+      poly newNum = singclap_pdivide(NUM(f), pGcd, ntRing);
+      p_Delete(&NUM(f), ntRing);
+      NUM(f) = newNum;
+      poly newDen = singclap_pdivide(DEN(f), pGcd, ntRing);
+      p_Delete(&DEN(f), ntRing);
+      if (p_IsConstant(newDen, ntRing) &&
+          n_IsOne(p_GetCoeff(newDen, ntRing), ntCoeffs))
+      {
+        /* newDen = 1 needs to be represented by NULL */
+        p_Delete(&newDen, ntRing);
+        newDen = NULL;
+      }
+      DEN(f) = newDen;
+  }
+  COM(f) = 0;
+  p_Delete(&pGcd, ntRing);
+#endif /* HAVE_FACTORY */
+}
+
+/* modifies a */
 void ntWrite(number &a, const coeffs cf)
 {
   ntTest(a);
   definiteGcdCancellation(a, cf, FALSE);
-  if (is0(a))
+  if (IS0(a))
     StringAppendS("0");
   else
   {
     fraction f = (fraction)a;
-    BOOLEAN useBrackets = !(p_IsConstant(num(f), ntRing)) && (!denIs1(f));
+    BOOLEAN useBrackets = (!p_IsConstant(NUM(f), ntRing)) && (!DENIS1(f));
     if (useBrackets) StringAppendS("(");
-    p_String0(num(f), ntRing, ntRing);
+    p_String0(NUM(f), ntRing, ntRing);
     if (useBrackets) StringAppendS(")");
-    if (!denIs1(f))
+    if (!DENIS1(f))
     {
       StringAppendS("/");
-      useBrackets = !p_IsConstant(den(f), ntRing);
+      useBrackets = !p_IsConstant(DEN(f), ntRing);
       if (useBrackets) StringAppendS("(");
-      p_String0(den(f), ntRing, ntRing);
+      p_String0(DEN(f), ntRing, ntRing);
       if (useBrackets) StringAppendS(")");
     }
@@ -617 +638 @@
   {
     fraction f = (fraction)omAlloc0Bin(fractionObjectBin);
-    num(f) = p;
-    den(f) = NULL;
-    c(f) = 0;
+    NUM(f) = p;
+    DEN(f) = NULL;
+    COM(f) = 0;
     *a = (number)f;
     return result;
@@ -659 +680 @@
 {
   ntTest(a);
-  if (is0(a)) return -1;
+  if (IS0(a)) return -1;
   /* this has been taken from the old implementation of field extensions,
      where we computed the sum of the degrees and the numbers of terms in
@@ -665 +686 @@
      time being */
   fraction f = (fraction)a;
-  poly p = num(f);
+  poly p = NUM(f);
   int noOfTerms = 0;
   int numDegree = 0;
@@ -678 +699 @@
   }
   int denDegree = 0;
-  if (!denIs1(f))
-  {
-    p = den(f);
+  if (!DENIS1(f))
+  {
+    p = DEN(f);
     while (p != NULL)
     {
@@ -697 +718 @@
 {
   ntTest(a);
-  if (is0(a)) WerrorS(nDivBy0);
+  if (IS0(a)) WerrorS(nDivBy0);
   fraction f = (fraction)a;
   fraction result = (fraction)omAlloc0Bin(fractionObjectBin);
   poly g;
-  if (denIs1(f)) g = p_One(ntRing);
-  else           g = p_Copy(den(f), ntRing);
-  num(result) = g;
-  den(result) = p_Copy(num(f), ntRing);
-  c(result) = c(f);
+  if (DENIS1(f)) g = p_One(ntRing);
+  else           g = p_Copy(DEN(f), ntRing);
+  NUM(result) = g;
+  DEN(result) = p_Copy(NUM(f), ntRing);
+  COM(result) = COM(f);
   return (number)result;
 }
@@ -717 +738 @@
   p_SetCoeff(p, ntCopy(a, src), dst->extRing);
   fraction f = (fraction)omAlloc0Bin(fractionObjectBin);
-  num(f) = p; den(f) = NULL; c(f) = 0;
+  NUM(f) = p; DEN(f) = NULL; COM(f) = 0;
   return (number)f;
 }
@@ -737 +758 @@
   p_SetCoeff(p, q, dst->extRing);
   fraction f = (fraction)omAlloc0Bin(fractionObjectBin);
-  num(f) = p; den(f) = NULL; c(f) = 0;
+  NUM(f) = p; DEN(f) = NULL; COM(f) = 0;
   return (number)f;
 }
@@ -764 +785 @@
   p_SetCoeff(g, q, dst->extRing);
   fraction f = (fraction)omAlloc0Bin(fractionObjectBin);
-  num(f) = g; den(f) = NULL; c(f) = 0;
+  NUM(f) = g; DEN(f) = NULL; COM(f) = 0;
   return (number)f;
 }
@@ -776 +797 @@
   p_SetCoeff(p, ntCopy(a, src), dst->extRing);
   fraction f = (fraction)omAlloc0Bin(fractionObjectBin);
-  num(f) = p; den(f) = NULL; c(f) = 0;
+  NUM(f) = p; DEN(f) = NULL; COM(f) = 0;
   return (number)f;
 }
@@ -796 +817 @@
   p_SetCoeff(p, q, dst->extRing);
   fraction f = (fraction)omAlloc0Bin(fractionObjectBin);
-  num(f) = p; den(f) = NULL; c(f) = 0;
+  NUM(f) = p; DEN(f) = NULL; COM(f) = 0;
   return (number)f;
 }
@@ -907 +928 @@
   cf->cfIntDiv       = ntDiv;
   
+#ifndef HAVE_FACTORY
+  PrintS("// Warning: The 'factory' module is not available.\n");
+  PrintS("//          Hence gcd's cannot be cancelled in any\n");
+  PrintS("//          computed fraction!\n");
+#endif
+  
   return FALSE;
 }

libpolys/polys/ext_fields/transext.h

@@ -59 +59 @@
 
 /* some useful accessors for fractions: */
-#define is0(f) (f == NULL) /**< TRUE iff n represents 0 in K(t_1, .., t_s) */
-#define num(f) f->numerator
-#define den(f) f->denominator
-#define denIs1(f) (f->denominator == NULL) /**< TRUE iff den. represents 1 */
-#define numIs1(f) (p_IsConstant(f->numerator, cf->extRing) && \
-                   n_IsOne(p_GetCoeff(num(f), cf->extRing), cf->extRing->cf))
+#define IS0(f) (f == NULL) /**< TRUE iff n represents 0 in K(t_1, .., t_s) */
+#define NUM(f) f->numerator
+#define DEN(f) f->denominator
+#define DENIS1(f) (f->denominator == NULL) /**< TRUE iff den. represents 1 */
+#define NUMIS1(f) (p_IsConstant(f->numerator, cf->extRing) && \
+                   n_IsOne(p_GetCoeff(f->numerator, cf->extRing), \
+                           cf->extRing->cf))
                    /**< TRUE iff num. represents 1 */
-#define c(f) f->complexity
+#define COM(f) f->complexity
 
 /// Get a mapping function from src into the domain of this type (n_transExt)

libpolys/polys/monomials/p_polys.cc

@@ -1310 +1310 @@
 }
 /*2
-* assumes that the head term of b is a multiple of the head term of a
-* and return the multiplicant *m
-* Frank's observation: If LM(b) = LM(a)*m, then we may actually set
-* negative(!) exponents in the below loop. I suspect that the correct
-* comment should be "assumes that LM(a) = LM(b)*m, for some monomial m..."
+* assumes that LM(a) = LM(b)*m, for some monomial m,
+* returns the multiplicant m,
+* leaves a and b unmodified
 */
 poly p_Divide(poly a, poly b, const ring r)

libpolys/tests/polys_test.h

@@ -233 +233 @@
   }
   /* assumes that cf represents a rational function field;
-     does NOT copy p, i.e. uses p directly inside the resulting number */
+     uses a copy of p inside the resulting number */
   number toFractionNumber(poly p, const coeffs cf)
   {
@@ -239 +239 @@
     fraction f = (fraction)n;
     p_Delete(&(f->numerator), cf->extRing);
-    f->numerator = p;
+    f->numerator = p_Copy(p, cf->extRing);
     return n;
   }
@@ -953 +953 @@
     number v_n = toFractionNumber(v, cf);
     PrintSized(v_n, cf);
-    poly w = NULL;
-    plusTerm(w, 1, 1, 1, cf->extRing);        // s
-    plusTerm(w, 1, 1, 0, cf->extRing);        // s + 1
+    poly w1 = NULL;
+    plusTerm(w1, 1, 1, 1, cf->extRing);       // s
+    plusTerm(w1, 1, 1, 0, cf->extRing);       // s + 1
+    poly w2 = NULL;
+    plusTerm(w2, 3, 1, 1, cf->extRing);       // 3s
+    plusTerm(w2, -7, 2, 1, cf->extRing);       // 3s - 7t
+    poly w = p_Mult_q(w1, w2, cf->extRing);   // (s + 1) * (3s - 7t)
     number w_n = toFractionNumber(w, cf);
     PrintSized(w_n, cf);
@@ -972 +976 @@
       clog << i << ". "; PrintSized(nn, cf);
     }
+    
     n_Delete(&prod, cf); n_Delete(&nn, cf);
     n_Delete(&v_n, cf); n_Delete(&w_n, cf);