Changeset 44651b in git for factory/facFqFactorize.cc

Timestamp:

Jun 17, 2010, 6:19:12 PM (14 years ago)

Author:

Hans Schoenemann <hannes@…>

Branches:

(u'spielwiese', 'fe61d9c35bf7c61f2b6cbf1b56e25e2f08d536cc')

Children:

e558c41b132228287898863201fbd5c35b4231fd

Parents:

d52c121e17973d80d9181edd4a487916a0741038

Message:

index fixed

git-svn-id: file:///usr/local/Singular/svn/trunk@12883 2c84dea3-7e68-4137-9b89-c4e89433aadc

File:

• factory/facFqFactorize.cc (modified) (111 diffs)

factory/facFqFactorize.cc

@@ -1 +1 @@
 /*****************************************************************************\
- * Computer Algebra System SINGULAR    
+ * Computer Algebra System SINGULAR
 \*****************************************************************************/
 /** @file facFqFactorize.cc
- * 
+ *
  * This file implements functions for factoring a multivariate polynomial over
- * a finite field. 
- * 
- * ABSTRACT: "Efficient Multivariate Factorization over Finite Fields" by 
- * L. Bernardin & M. Monagon.  
+ * a finite field.
+ *
+ * ABSTRACT: "Efficient Multivariate Factorization over Finite Fields" by
+ * L. Bernardin & M. Monagon.
  *
  * @author Martin Lee
@@ -40 +40 @@
 
 static inline
-CanonicalForm 
+CanonicalForm
 listGCD (const CFList& L);
 
 static inline
-CanonicalForm 
+CanonicalForm
 myContent (const CanonicalForm& F)
 {
@@ -58 +58 @@
     if (GF)
     {
-      return swapvar (GCD_GF (L.getFirst(), L.getLast()), F.mvar(), 
+      return swapvar (GCD_GF (L.getFirst(), L.getLast()), F.mvar(),
                       Variable (1));
     }
     else if (!GF && algExt)
     {
-      return swapvar (GCD_Fp_extension (L.getFirst(), L.getLast(), alpha), 
+      return swapvar (GCD_Fp_extension (L.getFirst(), L.getLast(), alpha),
                                        F.mvar(), Variable (1));
     }
     else
-      return swapvar (GCD_small_p (L.getFirst(), L.getLast()), F.mvar(), 
+      return swapvar (GCD_small_p (L.getFirst(), L.getLast()), F.mvar(),
                      Variable (1));
   }
@@ -78 +78 @@
 
 static inline
-CanonicalForm 
+CanonicalForm
 listGCD (const CFList& L)
 {
@@ -91 +91 @@
       return GCD_GF (L.getFirst(), L.getLast());
     }
-    else if (!GF && (hasFirstAlgVar (L.getFirst(), alpha) || 
+    else if (!GF && (hasFirstAlgVar (L.getFirst(), alpha) ||
                      hasFirstAlgVar (L.getLast(), alpha)))
     {
@@ -107 +107 @@
     int j= 0;
     for (CFListIterator i= L; j < length; i++, j++)
-      lHi.append (i.getItem());    
+      lHi.append (i.getItem());
     lLo= Difference (L, lHi);
     resultHi= listGCD (lHi);
@@ -117 +117 @@
       return GCD_GF (resultHi, resultLo);
     }
-    else if (!GF && (hasFirstAlgVar (resultHi, alpha) || 
+    else if (!GF && (hasFirstAlgVar (resultHi, alpha) ||
                      hasFirstAlgVar (resultLo, alpha)))
     {
@@ -158 +158 @@
     {
       if (swap)
-        return swapvar(GCD_Fp_extension (L.getFirst(), L.getLast(), alpha), 
+        return swapvar(GCD_Fp_extension (L.getFirst(), L.getLast(), alpha),
                                          F.mvar(), x);
       else
@@ -166 +166 @@
     {
       if (swap)
-        return swapvar (GCD_small_p (L.getFirst(), L.getLast()), F.mvar(), 
+        return swapvar (GCD_small_p (L.getFirst(), L.getLast()), F.mvar(),
                         x);
       else
@@ -194 +194 @@
     if (GF)
       return (F/GCD_GF (F, G))*G;
-    else if (!GF && (hasFirstAlgVar (F, alpha) || 
+    else if (!GF && (hasFirstAlgVar (F, alpha) ||
                      hasFirstAlgVar (G, alpha)))
       return (F/GCD_Fp_extension (F, G, alpha))*G;
@@ -203 +203 @@
 
 
-static inline 
+static inline
 CanonicalForm myCompress (const CanonicalForm& F, CFMap& N)
 {
@@ -210 +210 @@
   int ** swap;
   swap= new int* [n + 1];
-  for (int i= 0; i <= n; i++) 
+  for (int i= 0; i <= n; i++)
   {
     degsf[i]= 0;
     swap [i]= new int [2];
+    swap [i] [0]= 0;
     swap [i] [1]= 0;
-    swap [i] [2]= 0;
   }
   int i= 1;
-  n= 1;  
+  n= 1;
   degsf= degrees (F, degsf);
 
   CanonicalForm result= F;
-  while ( i <= F.level() ) 
+  while ( i <= F.level() )
   {
     while( degsf[i] == 0 ) i++;
-    swap[n][1]= i;
-    swap[n][2]= degsf[i]; 
+    swap[n][0]= i;
+    swap[n][1]= degsf[i];
     if (i != n)
       result= swapvar (result, Variable (n), Variable(i));
@@ -235 +235 @@
   n--;
 
-  for (i= 1; i < n; i++) 
-  {
-    for (int j= 1; j < n - i + 1; j++) 
-    {
-      if (swap[j][2] < swap[j + 1][2]) 
-      {
-        buf1= swap [j + 1] [1];
-        buf2= swap [j + 1] [2];
+  for (i= 1; i < n; i++)
+  {
+    for (int j= 1; j < n - i + 1; j++)
+    {
+      if (swap[j][1] < swap[j + 1][1])
+      {
+        buf1= swap [j + 1] [0];
+        buf2= swap [j + 1] [1];
+        swap[j + 1] [0]= swap[j] [0];
         swap[j + 1] [1]= swap[j] [1];
-        swap[j + 1] [2]= swap[j] [2];
-        swap[j][1]= buf1;
-        swap[j][2]= buf2;
+        swap[j][0]= buf1;
+        swap[j][1]= buf2;
         result= swapvar (result, Variable (j + 1), Variable (j));
-      }     
-    }
-  }
-
-  for (i= n; i > 0; i--) 
-  {
-    if (i != swap[i] [1])
-      N.newpair (Variable (i), Variable (swap[i] [1]));
+      }
+    }
+  }
+
+  for (i= n; i > 0; i--)
+  {
+    if (i != swap[i] [0])
+      N.newpair (Variable (i), Variable (swap[i] [0]));
   }
 
@@ -266 +266 @@
   return result;
 }
- 
-CFList 
+
+CFList
 monicFactorRecombi (const CFList& factors,const CanonicalForm& F, const
-                    CanonicalForm& M, const DegreePattern& degs) 
+                    CanonicalForm& M, const DegreePattern& degs)
 {
-  if (degs.getLength() == 1) 
-    return CFList(F); 
+  if (degs.getLength() == 1)
+    return CFList(F);
 
   CFList T, S;
-  
+
   T= factors;
 
@@ -290 +290 @@
   int subsetDeg;
   DegreePattern bufDegs1= degs, bufDegs2;
-  TT= copy (factors); 
-  while (T.length() >= 2*s) 
-  {
-    while (noSubset == false) 
-    {
-      if (T.length() == s) 
+  TT= copy (factors);
+  while (T.length() >= 2*s)
+  {
+    while (noSubset == false)
+    {
+      if (T.length() == s)
       {
         result.append (prodMod (T, M));
@@ -303 +303 @@
       if (noSubset) break;
       subsetDeg= subsetDegree (S);
-      if (!degs.find (subsetDeg)) 
+      if (!degs.find (subsetDeg))
         continue;
-      else 
-      { 
+      else
+      {
         g= prodMod0 (S, M);
         gg= mod (g*LCBuf, M); //univariate polys
@@ -324 +324 @@
             bufDegs2= DegreePattern (T);
             bufDegs1.intersect (bufDegs2);
-            bufDegs1.refine (); 
-            if (T.length() < 2*s || T.length() == s || 
-                bufDegs1.getLength() == 1) 
+            bufDegs1.refine ();
+            if (T.length() < 2*s || T.length() == s ||
+                bufDegs1.getLength() == 1)
             {
-              result.append (prodMod (T, M)); 
-              return result; 
+              result.append (prodMod (T, M));
+              return result;
             }
             TT= copy (T);
             indexUpdate (v, s, T.length(), noSubset);
-            if (noSubset) break; 
+            if (noSubset) break;
           }
         }
@@ -339 +339 @@
     }
     s++;
-    if (T.length() < 2*s || T.length() == s) 
+    if (T.length() < 2*s || T.length() == s)
     {
       result.append (prodMod (T, M));
@@ -349 +349 @@
     noSubset= false;
   }
-  if (T.length() < 2*s) 
-    result.append (prodMod (T, M)); 
-
-  return result; 
-} 
-
-CFList 
-earlyMonicFactorDetect (CanonicalForm& F, CFList& factors, 
+  if (T.length() < 2*s)
+    result.append (prodMod (T, M));
+
+  return result;
+}
+
+CFList
+earlyMonicFactorDetect (CanonicalForm& F, CFList& factors,
                         int& adaptedLiftBound, DegreePattern& degs,
                         bool& success, int deg, const int bound)
@@ -371 +371 @@
   int e= 0;
   adaptedLiftBound= 0;
-  for (CFListIterator i= factors; i.hasItem(); i++) 
+  for (CFListIterator i= factors; i.hasItem(); i++)
   {
     if (!bufDegs1.find (degree (i.getItem(), 1)))
@@ -392 +392 @@
           d -= degree (gg) + degree (LC (gg, 1));
           e= tmax (e, degree (gg) + degree (LC (gg, 1)));
-          LCBuf= LC (buf, Variable (1)); 
+          LCBuf= LC (buf, Variable (1));
           T= Difference (T, CFList (i.getItem()));
 
@@ -398 +398 @@
           bufDegs2= DegreePattern (T);
           bufDegs1.intersect (bufDegs2);
-          bufDegs1.refine (); 
+          bufDegs1.refine ();
           if (bufDegs1.getLength() <= 1)
           {
-            result.append (prodMod (T, M)); 
+            result.append (prodMod (T, M));
             break;
           }
@@ -410 +410 @@
   adaptedLiftBound= d;
 
-  if (adaptedLiftBound < deg) 
+  if (adaptedLiftBound < deg)
   {
     factors= T;
@@ -457 +457 @@
 
 CFList biFactorizer (const CanonicalForm& F, const Variable& alpha,
-                     CanonicalForm& bivarEval, int& liftBound) 
+                     CanonicalForm& bivarEval, int& liftBound)
 {
   CanonicalForm A= F;
   bool GF= (CFFactory::gettype() == GaloisFieldDomain);
 
-  if (A.isUnivariate())  
+  if (A.isUnivariate())
     return uniFactorizer (F, alpha, GF);
-  
+
 
   CFMap N;
@@ -482 +482 @@
   //trivial case
   CFList factors;
-  if (A.inCoeffDomain()) 
+  if (A.inCoeffDomain())
   {
     append (factors, contentAyFactors);
@@ -489 +489 @@
     return factors;
   }
-  else if (A.isUnivariate()) 
-  {
-    if (A.mvar() == x) 
+  else if (A.isUnivariate())
+  {
+    if (A.mvar() == x)
       factors= uniFactorizer (A, alpha, GF);
     append (factors, contentAyFactors);
@@ -503 +503 @@
   DegreePattern degs;
   DegreePattern bufDegs;
- 
+
   int factorNums= 5;
-  if (factorNums < (int) ceil (log (totaldegree (A)))) 
+  if (factorNums < (int) ceil (log (totaldegree (A))))
     factorNums= (int) ceil (log (totaldegree (A)));
-  for (int i= 0; i < factorNums; i++) 
-  {
-    if (i == 0) 
+  for (int i= 0; i < factorNums; i++)
+  {
+    if (i == 0)
       Aeval= A (bivarEval, y);
     else if (i > 0 && contentAx.inCoeffDomain())
     {
-      Aeval= A; 
+      Aeval= A;
       evaluation= evalPoint (A, Aeval, alpha, list, GF, fail);
     }
- 
-    if (fail && (i != 0)) 
+
+    if (fail && (i != 0))
       break;
 
@@ -523 +523 @@
     uniFactors= uniFactorizer (Aeval, alpha, GF);
 
-    if (uniFactors.length() == 1) 
-    { 
+    if (uniFactors.length() == 1)
+    {
       append (factors, contentAyFactors);
       if (contentAyFactors.isEmpty())
         factors.append (F/lc(F));
-      else 
+      else
       {
         A= A (y - bivarEval, y);
@@ -537 +537 @@
           (void) extgcd (LC (A, 1), power (y, liftBound), s, t);
           A *= s;
-          A= mod (A, power (y, liftBound)); 
+          A= mod (A, power (y, liftBound));
         }
         factors.append (A);
       }
       decompress (factors, N);
-      bivarEval= N (bivarEval); 
+      bivarEval= N (bivarEval);
       return factors;
     }
@@ -549 +549 @@
     degs= DegreePattern (uniFactors);
 
-    if (i == 0) 
+    if (i == 0)
     {
       bufAeval= Aeval;
@@ -558 +558 @@
         break;
     }
-    else 
-    {
-      bufDegs.intersect (degs); 
-      if (uniFactors.length() < bufUniFactors.length()) 
-      { 
+    else
+    {
+      bufDegs.intersect (degs);
+      if (uniFactors.length() < bufUniFactors.length())
+      {
         bufUniFactors= uniFactors;
         bufAeval= Aeval;
@@ -574 +574 @@
       if (contentAyFactors.isEmpty())
         factors.append (F/lc(F));
-      else 
+      else
       {
         A= A (y - bivarEval, y);
@@ -583 +583 @@
           (void) extgcd (LC (A, 1), power (y, liftBound), s, t);
           A *= s;
-          A= mod (A, power (y, liftBound)); 
+          A= mod (A, power (y, liftBound));
         }
         factors.append (A);
       }
       decompress (factors, N);
-      bivarEval= N (bivarEval); 
+      bivarEval= N (bivarEval);
       return factors;
     }
@@ -600 +600 @@
   // Hensel lifting
   CFList diophant;
-  CFMatrix M= CFMatrix (liftBound, bufUniFactors.length() - 1); 
+  CFMatrix M= CFMatrix (liftBound, bufUniFactors.length() - 1);
   CFArray Pi;
   bool earlySuccess= false;
@@ -639 +639 @@
                           1, Pi, diophant, M);
       earlyFactors= earlyMonicFactorDetect (A, bufUniFactors, newLiftBound,
-                                             bufDegs, earlySuccess, 
+                                             bufDegs, earlySuccess,
                                              degree (A, y) + 1, liftBound);
       if (bufDegs.getLength() > 1 && !earlySuccess)
       {
-        if (newLiftBound > degree (A, y) + 1)
-        {
+        if (newLiftBound > degree (A, y) + 1)
+        {
           if (newLiftBound < newLiftBound)
-            liftBound= newLiftBound;
-          bufUniFactors.insert (LC(A, x));
-          henselLiftResume12 (A, bufUniFactors, degree (A, y) + 1, liftBound,
+            liftBound= newLiftBound;
+          bufUniFactors.insert (LC(A, x));
+          henselLiftResume12 (A, bufUniFactors, degree (A, y) + 1, liftBound,
                               Pi, diophant, M);
-        }
+        }
       }
       else if (earlySuccess)
@@ -667 +667 @@
     factors= monicFactorRecombi (bufUniFactors, A, MODl, bufDegs);
 
-  if (earlySuccess) 
+  if (earlySuccess)
     factors= Union (earlyFactors, factors);
   else if (!earlySuccess && bufDegs.getLength() == 1)
@@ -679 +679 @@
 }
 
-CFList 
-extFactorRecombination (const CFList& factors, const CanonicalForm& F, 
-                        const CFList& M, const ExtensionInfo& info,  
+CFList
+extFactorRecombination (const CFList& factors, const CanonicalForm& F,
+                        const CFList& M, const ExtensionInfo& info,
                         const CFList& evaluation)
-{ 
+{
   Variable alpha= info.getAlpha();
   Variable beta= info.getBeta();
@@ -690 +690 @@
   int k= info.getGFDegree();
   CFList source, dest;
-  if (factors.length() == 1) 
+  if (factors.length() == 1)
   {
     CanonicalForm buf= reverseShift (F, evaluation);
-    return CFList (mapDown (buf, info, source, dest)); 
-  } 
+    return CFList (mapDown (buf, info, source, dest));
+  }
   if (factors.length() < 1)
     return CFList();
@@ -711 +711 @@
   CanonicalForm buf;
   if (beta != Variable (1))
-    buf= mapDown (F, gamma, delta, alpha, source, dest); 
+    buf= mapDown (F, gamma, delta, alpha, source, dest);
   else
     buf= F;
 
-  CanonicalForm g, LCBuf= LC (buf, Variable (1)); 
+  CanonicalForm g, LCBuf= LC (buf, Variable (1));
   CanonicalForm buf2;
   int v [T.length()];
@@ -723 +723 @@
   CFArray TT;
   int subsetDeg;
-  TT= copy (factors); 
+  TT= copy (factors);
   bool recombination= false;
-  while (T.length() >= 2*s) 
-  {
-    while (noSubset == false) 
-    {
-      if (T.length() == s) 
+  while (T.length() >= 2*s)
+  {
+    while (noSubset == false)
+    {
+      if (T.length() == s)
       {
         if (recombination)
@@ -757 +757 @@
       S.removeFirst();
       g /= myContent (g);
-      if (fdivides (g, buf)) 
-      {
-        buf2= reverseShift (g, evaluation); 
+      if (fdivides (g, buf))
+      {
+        buf2= reverseShift (g, evaluation);
         buf2 /= Lc (buf2);
-        if (!k && beta == Variable (1)) 
-        {
-          if (degree (buf2, alpha) < degMipoBeta)
-          {  
-            appendTestMapDown (result, buf2, info, source, dest);
-            buf /= g;
-            LCBuf= LC (buf, Variable (1));
-            recombination= true;
-          }
-        }
-        else 
-        {
-          if (!isInExtension (buf2, delta, k))
-          {
-            appendTestMapDown (result, buf2, info, source, dest);
-            buf /= g;
-            LCBuf= LC (buf, Variable (1));
-            recombination= true;
-          }
-        }
-        T= Difference (T, S);
-
-        if (T.length() < 2*s || T.length() == s) 
-        {
-          buf= reverseShift (buf, evaluation);
+        if (!k && beta == Variable (1))
+        {
+          if (degree (buf2, alpha) < degMipoBeta)
+          {
+            appendTestMapDown (result, buf2, info, source, dest);
+            buf /= g;
+            LCBuf= LC (buf, Variable (1));
+            recombination= true;
+          }
+        }
+        else
+        {
+          if (!isInExtension (buf2, delta, k))
+          {
+            appendTestMapDown (result, buf2, info, source, dest);
+            buf /= g;
+            LCBuf= LC (buf, Variable (1));
+            recombination= true;
+          }
+        }
+        T= Difference (T, S);
+
+        if (T.length() < 2*s || T.length() == s)
+        {
+          buf= reverseShift (buf, evaluation);
           buf /= Lc (buf);
-          appendTestMapDown (result, buf, info, source, dest);
-          return result; 
-        }
-        TT= copy (T);
-        indexUpdate (v, s, T.length(), noSubset);
-        if (noSubset) break;        
+          appendTestMapDown (result, buf, info, source, dest);
+          return result;
+        }
+        TT= copy (T);
+        indexUpdate (v, s, T.length(), noSubset);
+        if (noSubset) break;
       }
     }
     s++;
-    if (T.length() < 2*s || T.length() == s) 
+    if (T.length() < 2*s || T.length() == s)
     {
       buf= reverseShift (buf, evaluation);
@@ -809 +809 @@
   if (T.length() < 2*s)
   {
-    buf= reverseShift (F, evaluation); 
-    appendMapDown (result, buf, info, source, dest); 
-  }
-
-  return result; 
-} 
-
-CFList 
-factorRecombination (const CanonicalForm& F, const CFList& factors, 
+    buf= reverseShift (F, evaluation);
+    appendMapDown (result, buf, info, source, dest);
+  }
+
+  return result;
+}
+
+CFList
+factorRecombination (const CanonicalForm& F, const CFList& factors,
                      const CFList& M)
 {
-  if (factors.length() == 1) 
+  if (factors.length() == 1)
     return CFList(F);
   if (factors.length() < 1)
@@ -839 +839 @@
   CFArray TT;
   int subsetDeg;
-  TT= copy (factors); 
+  TT= copy (factors);
   Variable y= F.level() - 1;
   bool recombination= false;
   CanonicalForm h;
-  while (T.length() >= 2*s) 
-  {
-    while (noSubset == false) 
-    {
-      if (T.length() == s) 
+  while (T.length() >= 2*s)
+  {
+    while (noSubset == false)
+    {
+      if (T.length() == s)
       {
         if (recombination)
@@ -872 +872 @@
         LCBuf= LC (buf, Variable(1));
         T= Difference (T, S);
-        if (T.length() < 2*s || T.length() == s) 
-        {
-          result.append (buf);
-          return result; 
-        }
-        TT= copy (T);
-        indexUpdate (v, s, T.length(), noSubset);
-        if (noSubset) break;        
+        if (T.length() < 2*s || T.length() == s)
+        {
+          result.append (buf);
+          return result;
+        }
+        TT= copy (T);
+        indexUpdate (v, s, T.length(), noSubset);
+        if (noSubset) break;
       }
     }
     s++;
-    if (T.length() < 2*s || T.length() == s) 
+    if (T.length() < 2*s || T.length() == s)
     {
       result.append (buf);
@@ -893 +893 @@
     noSubset= false;
   }
-  if (T.length() < 2*s) 
+  if (T.length() < 2*s)
     result.append (F);
 
-  return result; 
+  return result;
 }
 
@@ -913 +913 @@
   int e= 0;
   int nBuf;
-  for (CFListIterator i= factors; i.hasItem(); i++) 
-  {
-    g= mulMod (i.getItem(), LCBuf, M); 
+  for (CFListIterator i= factors; i.hasItem(); i++)
+  {
+    g= mulMod (i.getItem(), LCBuf, M);
     g /= myContent (g);
     if (fdivides (g, buf))
@@ -923 +923 @@
       e= tmax (e, nBuf);
       buf /= g;
-      LCBuf= LC (buf, Variable (1)); 
+      LCBuf= LC (buf, Variable (1));
     }
   }
   adaptedLiftBound= d;
 
-  if (adaptedLiftBound < deg) 
-  {  
+  if (adaptedLiftBound < deg)
+  {
     if (adaptedLiftBound < degree (F) + 1)
     {
@@ -939 +939 @@
           success= false;
         }
-        else 
+        else
         {
           success= true;
@@ -951 +951 @@
       {
         success= true;
-        adaptedLiftBound= deg; 
+        adaptedLiftBound= deg;
       }
     }
@@ -962 +962 @@
 }
 
-int 
-extLiftBoundAdaption (const CanonicalForm& F, const CFList& factors, bool& 
-                      success, const ExtensionInfo& info, const CFList& eval, 
+int
+extLiftBoundAdaption (const CanonicalForm& F, const CFList& factors, bool&
+                      success, const ExtensionInfo& info, const CFList& eval,
                       const int deg, const CFList& MOD, const int bound)
 {
@@ -981 +981 @@
   adaptedLiftBound= 0;
   int d= bound;
-  int e= 0; 
+  int e= 0;
   int nBuf;
   int degMipoBeta;
@@ -989 +989 @@
     degMipoBeta= degree (getMipo (beta));
 
-  for (CFListIterator i= factors; i.hasItem(); i++) 
+  for (CFListIterator i= factors; i.hasItem(); i++)
   {
     g= mulMod (i.getItem(), LCBuf, M);
@@ -997 +997 @@
       gg= reverseShift (g, eval);
       gg /= Lc (gg);
-      if (!k && beta == Variable (1)) 
+      if (!k && beta == Variable (1))
       {
         if (degree (gg, alpha) < degMipoBeta)
-        {  
-          buf /= g;
-          nBuf= degree (g, y) + degree (LC (g, Variable (1)), y);
-          d -= nBuf;
-          e= tmax (e, nBuf);
-          LCBuf= LC (buf, Variable (1));            
-        }
-      }
-      else 
-      {
-        if (!isInExtension (gg, delta, k))
         {
           buf /= g;
@@ -1019 +1008 @@
         }
       }
-    } 
+      else
+      {
+        if (!isInExtension (gg, delta, k))
+        {
+          buf /= g;
+          nBuf= degree (g, y) + degree (LC (g, Variable (1)), y);
+          d -= nBuf;
+          e= tmax (e, nBuf);
+          LCBuf= LC (buf, Variable (1));
+        }
+      }
+    }
   }
   adaptedLiftBound= d;
@@ -1034 +1034 @@
           success= false;
         }
-        else 
+        else
         {
           success= true;
@@ -1043 +1043 @@
         }
       }
-      else 
+      else
       {
         success= true;
-        adaptedLiftBound= deg; 
+        adaptedLiftBound= deg;
       }
     }
@@ -1058 +1058 @@
 }
 
-CFList 
+CFList
 earlyFactorDetect (CanonicalForm& F, CFList& factors, int& adaptedLiftBound,
-                   bool& success, const int deg, const CFList& MOD, 
+                   bool& success, const int deg, const CFList& MOD,
                    const int bound)
 {
@@ -1075 +1075 @@
   int e= 0;
   int nBuf;
-  for (CFListIterator i= factors; i.hasItem(); i++) 
+  for (CFListIterator i= factors; i.hasItem(); i++)
   {
     g= mulMod (i.getItem(), LCBuf, M);
@@ -1086 +1086 @@
       e= tmax (e, nBuf);
       buf /= g;
-      LCBuf= LC (buf, Variable (1)); 
+      LCBuf= LC (buf, Variable (1));
       T= Difference (T, CFList (i.getItem()));
     }
@@ -1092 +1092 @@
   adaptedLiftBound= d;
 
-  if (adaptedLiftBound < deg) 
+  if (adaptedLiftBound < deg)
   {
     if (adaptedLiftBound < degree (F) + 1)
@@ -1099 +1099 @@
         adaptedLiftBound= tmin (e + 1, deg);
       else
-        adaptedLiftBound= deg; 
+        adaptedLiftBound= deg;
     }
     factors= T;
@@ -1108 +1108 @@
 }
 
-CFList 
+CFList
 extEarlyFactorDetect (CanonicalForm& F, CFList& factors, int& adaptedLiftBound,
-                      bool& success, const ExtensionInfo& info, const CFList& 
+                      bool& success, const ExtensionInfo& info, const CFList&
                       eval, const int deg, const CFList& MOD, const int bound)
 {
@@ -1138 +1138 @@
     degMipoBeta= degree (getMipo (beta));
 
-  for (CFListIterator i= factors; i.hasItem(); i++) 
+  for (CFListIterator i= factors; i.hasItem(); i++)
   {
     g= mulMod (i.getItem(), LCBuf, M);
@@ -1146 +1146 @@
       gg= reverseShift (g, eval);
       gg /= Lc (gg);
-          if (!k && beta == Variable (1)) 
+          if (!k && beta == Variable (1))
           {
             if (degree (gg, alpha) < degMipoBeta)
-            {  
+            {
               appendTestMapDown (result, gg, info, source, dest);
               buf /= g;
@@ -1155 +1155 @@
               d -= nBuf;
               e= tmax (e, nBuf);
-              LCBuf= LC (buf, Variable (1));            
+              LCBuf= LC (buf, Variable (1));
             }
           }
-          else 
+          else
           {
             if (!isInExtension (gg, delta, k))
@@ -1169 +1169 @@
               LCBuf= LC (buf, Variable (1));
             }
-          } 
+          }
       T= Difference (T, CFList (i.getItem()));
     }
@@ -1182 +1182 @@
         adaptedLiftBound= tmin (e + 1, deg);
       else
-        adaptedLiftBound= deg; 
+        adaptedLiftBound= deg;
     }
     success= true;
@@ -1191 +1191 @@
 }
 
-CFList 
+CFList
 evalPoints (const CanonicalForm& F, CFList & eval, const Variable& alpha,
-            CFList& list, const bool& GF, bool& fail) 
-{  
+            CFList& list, const bool& GF, bool& fail)
+{
   int k= F.level() - 1;
   Variable x= Variable (1);
@@ -1201 +1201 @@
   GFRandom genGF;
   int p= getCharacteristic ();
-  double bound; 
-  if (alpha != Variable (1)) 
+  double bound;
+  if (alpha != Variable (1))
   {
     bound= pow ((double) p, (double) degree (getMipo(alpha)));
     bound= pow ((double) bound, (double) k);
   }
-  else if (GF) 
+  else if (GF)
   {
     bound= pow ((double) p, (double) getGFDegree());
@@ -1217 +1217 @@
   CanonicalForm random;
   CanonicalForm deriv_x, gcd_deriv;
-  do 
+  do
   {
     random= 0;
     // possible overflow if list.length() does not fit into a int
-    if (list.length() >= bound) 
-    { 
+    if (list.length() >= bound)
+    {
       fail= true;
       break;
     }
-    for (int i= 0; i < k; i++) 
-    { 
-      if (GF) 
+    for (int i= 0; i < k; i++)
+    {
+      if (GF)
       {
         result.append (genGF.generate());
         random += result.getLast()*power (x, i);
       }
-      else if (alpha != Variable(1)) 
-      {    
+      else if (alpha != Variable(1))
+      {
         AlgExtRandomF genAlgExt (alpha);
         result.append (genAlgExt.generate());
-        random += result.getLast()*power (x, i); 
-      }
-      else 
-      { 
+        random += result.getLast()*power (x, i);
+      }
+      else
+      {
         result.append (genFF.generate());
         random += result.getLast()*power (x, i);
-      } 
-    }
-    if (find (list, random)) 
+      }
+    }
+    if (find (list, random))
     {
       result= CFList();
@@ -1252 +1252 @@
     int l= F.level();
     eval.insert (F);
-    for (CFListIterator i= result; i.hasItem(); i++, l--) 
+    for (CFListIterator i= result; i.hasItem(); i++, l--)
       eval.insert (eval.getFirst()(i.getItem(), l));
 
-    if (degree (eval.getFirst()) != degree (F, 1)) 
+    if (degree (eval.getFirst()) != degree (F, 1))
     {
       if (!find (list, random))
@@ -1262 +1262 @@
       eval= CFList();
       continue;
-    }     
-   
+    }
+
     deriv_x= deriv (eval.getFirst(), x);
     gcd_deriv= gcd (eval.getFirst(), deriv_x);
-    if (degree (gcd_deriv) > 0) 
-    { 
+    if (degree (gcd_deriv) > 0)
+    {
       if (!find (list, random))
         list.append (random);
@@ -1286 +1286 @@
     }
 
-    if (list.length() >= bound) 
+    if (list.length() >= bound)
     {
       fail= true;
@@ -1293 +1293 @@
   } while (find (list, random));
 
-  if (!eval.isEmpty()) 
+  if (!eval.isEmpty())
     eval.removeFirst();
 
@@ -1299 +1299 @@
 }
 
-static inline  
+static inline
 int newMainVariableSearch (CanonicalForm& A, CFList& Aeval, CFList&
-                           evaluation, const Variable& alpha, const int lev) 
-{ 
+                           evaluation, const Variable& alpha, const int lev)
+{
   Variable x= Variable (1);
   CanonicalForm derivI, buf;
@@ -1312 +1312 @@
   Aeval= CFList();
   evaluation= CFList();
-  for (int i= lev; i <= A.level(); i++) 
+  for (int i= lev; i <= A.level(); i++)
   {
     derivI= deriv (buf, Variable (i));
     if (!derivI.isZero())
     {
-      buf= swapvar (buf, x, Variable (i)); 
+      buf= swapvar (buf, x, Variable (i));
       Aeval= CFList();
       evaluation= CFList();
       fail= false;
       evaluation= evalPoints (buf, Aeval, alpha, list, GF, fail);
-      if (!fail) 
-      {
-        A= buf;
-        swapLevel= i;
-        break;
-      }
-      else 
+      if (!fail)
+      {
+        A= buf;
+        swapLevel= i;
+        break;
+      }
+      else
         buf= A;
     }
@@ -1335 +1335 @@
 }
 
-static inline 
-CanonicalForm lcmContent (const CanonicalForm& A, CFList& contentAi) 
+static inline
+CanonicalForm lcmContent (const CanonicalForm& A, CFList& contentAi)
 {
   int i= A.level();
   contentAi.append (myContent (A, i));
   contentAi.append (myContent (A, i - 1));
-  CanonicalForm result= myLcm (contentAi.getFirst(), contentAi.getLast()); 
-  for (i= i - 2; i > 0; i--) 
+  CanonicalForm result= myLcm (contentAi.getFirst(), contentAi.getLast());
+  for (i= i - 2; i > 0; i--)
   {
     contentAi.append (content (A, i));
@@ -1348 +1348 @@
   }
   return result;
-} 
- 
+}
+
 CFList
 henselLiftAndEarly (CanonicalForm& A, CFList& MOD, int*& liftBounds, bool&
                     earlySuccess, CFList& earlyFactors, const CFList& Aeval,
-                    const CFList& biFactors, const CFList& evaluation, 
+                    const CFList& biFactors, const CFList& evaluation,
                     const ExtensionInfo& info)
 {
   bool extension= info.isInExtension();
-  CFList bufFactors= biFactors; 
+  CFList bufFactors= biFactors;
   bufFactors.insert (LC (Aeval.getFirst(), 1));
 
@@ -1365 +1365 @@
   CFArray Pi;
   int smallFactorDeg= 11; //tunable parameter
-  CFList result; 
+  CFList result;
   int newLiftBound= 0;
   int adaptedLiftBound= 0;
@@ -1389 +1389 @@
     {
       if (!extension)
-        earlyFactors= earlyFactorDetect 
+        earlyFactors= earlyFactorDetect
                        (buf, result, adaptedLiftBound, earlySuccess,
                         degree (buf) + 1, MOD, liftBound);
       else
-        earlyFactors= extEarlyFactorDetect 
+        earlyFactors= extEarlyFactorDetect
                        (buf, result, adaptedLiftBound, earlySuccess,
-                        info, evaluation, degree       
+                        info, evaluation, degree
                         (buf) + 1, MOD, liftBound);
     }
@@ -1406 +1406 @@
         adaptedLiftBound= extLiftBoundAdaption (buf, result, earlySuccess, info,
                                                 evaluation, degree (buf) + 1,
-                                                MOD, liftBound);       
+                                                MOD, liftBound);
     }
     if (!earlySuccess)
@@ -1413 +1413 @@
       liftBounds[1]= adaptedLiftBound;
       liftBound= adaptedLiftBound;
-      henselLiftResume (buf, result, degree (buf) + 1, liftBound, 
+      henselLiftResume (buf, result, degree (buf) + 1, liftBound,
                         Pi, diophant, Mat, MOD);
-    }  
+    }
     else
       liftBounds[1]= adaptedLiftBound;
@@ -1426 +1426 @@
     {
       if (!extension)
-        earlyFactors= earlyFactorDetect (buf, result, adaptedLiftBound,  
+        earlyFactors= earlyFactorDetect (buf, result, adaptedLiftBound,
                                          earlySuccess, smallFactorDeg, MOD,
                                          liftBound);
-      else 
+      else
         earlyFactors= extEarlyFactorDetect (buf, result, adaptedLiftBound,
                                             earlySuccess, info, evaluation,
@@ -1441 +1441 @@
       else
         adaptedLiftBound= extLiftBoundAdaption (buf, result, earlySuccess, info,
-                                                evaluation, smallFactorDeg, MOD, 
+                                                evaluation, smallFactorDeg, MOD,
                                                 liftBound);
     }
@@ -1448 +1448 @@
     {
       result.insert (LC (buf, 1));
-      henselLiftResume (buf, result, smallFactorDeg, degree (buf) + 1, 
+      henselLiftResume (buf, result, smallFactorDeg, degree (buf) + 1,
                         Pi, diophant, Mat, MOD);
       if (Aeval.length() == 2)
@@ -1459 +1459 @@
            earlyFactors= extEarlyFactorDetect (buf, result, adaptedLiftBound,
                                                earlySuccess, info, evaluation,
-                                               degree (buf) + 1, MOD, 
+                                               degree (buf) + 1, MOD,
                                                liftBound);
       }
-      else 
+      else
       {
         if (!extension)
           adaptedLiftBound= liftBoundAdaption (buf, result, earlySuccess,
-                                               degree (buf) + 1, MOD,liftBound); 
+                                               degree (buf) + 1, MOD,liftBound);
         else
-          adaptedLiftBound= extLiftBoundAdaption (buf, result, earlySuccess, 
+          adaptedLiftBound= extLiftBoundAdaption (buf, result, earlySuccess,
                                                   info, evaluation,
                                                   degree (buf) + 1, MOD,
@@ -1478 +1478 @@
         liftBounds[1]= adaptedLiftBound;
         liftBound= adaptedLiftBound;
-        henselLiftResume (buf, result, degree (buf) + 1, liftBound, 
+        henselLiftResume (buf, result, degree (buf) + 1, liftBound,
                           Pi, diophant, Mat, MOD);
       }
@@ -1499 +1499 @@
     int liftBoundsLength= Aeval.getLast().level() - 1;
     for (int i= 2; i <= liftBoundsLength && j.hasItem(); i++, j++)
-    { 
+    {
       earlySuccess= false;
       result.insert (LC (bufEval.getFirst(), 1));
@@ -1509 +1509 @@
       if (smallFactorDeg >= liftBound)
         result= henselLift (bufEval, result, MOD, diophant, Pi, Mat,
-                            liftBounds[i -  1], liftBounds[i]);
+                            liftBounds[i -  1], liftBounds[i]);
       else if (smallFactorDeg >= degree (buf) + 1)
       {
-        result= henselLift (bufEval, result, MOD, diophant, Pi, Mat,
-                            liftBounds[i -  1], degree (buf) + 1);
-
-        if (Aeval.length() == i + 1)
-        {
-          if (!extension)
-            earlyFactors= earlyFactorDetect 
+        result= henselLift (bufEval, result, MOD, diophant, Pi, Mat,
+                            liftBounds[i -  1], degree (buf) + 1);
+
+        if (Aeval.length() == i + 1)
+        {
+          if (!extension)
+            earlyFactors= earlyFactorDetect
                            (buf, result, adaptedLiftBound, earlySuccess,
                             degree (buf) + 1, MOD, liftBound);
-          else
-            earlyFactors= extEarlyFactorDetect 
+          else
+            earlyFactors= extEarlyFactorDetect
                            (buf, result, adaptedLiftBound, earlySuccess,
                             info, evaluation, degree (buf) + 1, MOD, liftBound);
-        }
-        else
-        {
-          if (!extension)
-            adaptedLiftBound= liftBoundAdaption 
+        }
+        else
+        {
+          if (!extension)
+            adaptedLiftBound= liftBoundAdaption
                                 (buf, result, earlySuccess, degree (buf)
                                  + 1,  MOD, liftBound);
-          else
-            adaptedLiftBound= extLiftBoundAdaption 
-                                (buf, result, earlySuccess, info, evaluation, 
-                                 degree (buf) + 1, MOD, liftBound);       
-        }
-
-        if (!earlySuccess)
-        {
-          result.insert (LC (buf, 1));
+          else
+            adaptedLiftBound= extLiftBoundAdaption
+                                (buf, result, earlySuccess, info, evaluation,
+                                 degree (buf) + 1, MOD, liftBound);
+        }
+
+        if (!earlySuccess)
+        {
+          result.insert (LC (buf, 1));
           liftBounds[i]= adaptedLiftBound;
           liftBound= adaptedLiftBound;
-          henselLiftResume (buf, result, degree (buf) + 1, liftBound, 
-                            Pi, diophant, Mat, MOD);
-        }  
-        else
-        {
-          liftBounds[i]= adaptedLiftBound;
-        }
+          henselLiftResume (buf, result, degree (buf) + 1, liftBound,
+                            Pi, diophant, Mat, MOD);
+        }
+        else
+        {
+          liftBounds[i]= adaptedLiftBound;
+        }
       }
       else if (smallFactorDeg < degree (buf) + 1)
       {
-        result= henselLift (bufEval, result, MOD, diophant, Pi, Mat,
-                            liftBounds[i -  1], smallFactorDeg);
-
-        if (Aeval.length() == i + 1)
-        {
-          if (!extension)
-            earlyFactors= earlyFactorDetect 
+        result= henselLift (bufEval, result, MOD, diophant, Pi, Mat,
+                            liftBounds[i -  1], smallFactorDeg);
+
+        if (Aeval.length() == i + 1)
+        {
+          if (!extension)
+            earlyFactors= earlyFactorDetect
                            (buf, result, adaptedLiftBound, earlySuccess,
                             smallFactorDeg, MOD, liftBound);
-          else
-            earlyFactors= extEarlyFactorDetect 
+          else
+            earlyFactors= extEarlyFactorDetect
                            (buf, result, adaptedLiftBound, earlySuccess,
                             info, evaluation, smallFactorDeg, MOD, liftBound);
-        }
-        else
-        {
-          if (!extension)
-            adaptedLiftBound= liftBoundAdaption 
+        }
+        else
+        {
+          if (!extension)
+            adaptedLiftBound= liftBoundAdaption
                                 (buf, result, earlySuccess,
                                  smallFactorDeg, MOD, liftBound);
-          else
-            adaptedLiftBound= extLiftBoundAdaption 
+          else
+            adaptedLiftBound= extLiftBoundAdaption
                                 (buf, result, earlySuccess, info, evaluation,
-                                 smallFactorDeg, MOD, liftBound);         
-        }
-
-        if (!earlySuccess)
-        {
-          result.insert (LC (buf, 1));
-          henselLiftResume (buf, result, smallFactorDeg, 
+                                 smallFactorDeg, MOD, liftBound);
+        }
+
+        if (!earlySuccess)
+        {
+          result.insert (LC (buf, 1));
+          henselLiftResume (buf, result, smallFactorDeg,
                             degree (buf) + 1, Pi, diophant, Mat, MOD);
-          if (Aeval.length() == i + 1)
-          {
-            if (!extension)
-              earlyFactors= earlyFactorDetect 
+          if (Aeval.length() == i + 1)
+          {
+            if (!extension)
+              earlyFactors= earlyFactorDetect
                              (buf, result, adaptedLiftBound, earlySuccess,
                               degree (buf) +  1,  MOD, liftBound);
-            else
-              earlyFactors= extEarlyFactorDetect 
+            else
+              earlyFactors= extEarlyFactorDetect
                              (buf, result, adaptedLiftBound, earlySuccess,
-                              info, evaluation, degree (buf) + 1, MOD, 
+                              info, evaluation, degree (buf) + 1, MOD,
                               liftBound);
-          }
-          else
-          {
-            if (!extension)
-              adaptedLiftBound= liftBoundAdaption 
+          }
+          else
+          {
+            if (!extension)
+              adaptedLiftBound= liftBoundAdaption
                                   (buf, result, earlySuccess, degree
                                    (buf) +  1,  MOD, liftBound);
-            else
-              adaptedLiftBound= extLiftBoundAdaption 
-                                  (buf, result, earlySuccess, info, evaluation, 
-                                   degree (buf) + 1,  MOD, liftBound);    
-          }
-
-          if (!earlySuccess)
-          {
-            result.insert (LC (buf, 1));
+            else
+              adaptedLiftBound= extLiftBoundAdaption
+                                  (buf, result, earlySuccess, info, evaluation,
+                                   degree (buf) + 1,  MOD, liftBound);
+          }
+
+          if (!earlySuccess)
+          {
+            result.insert (LC (buf, 1));
             liftBounds[i]= adaptedLiftBound;
             liftBound= adaptedLiftBound;
-            henselLiftResume (buf, result, degree (buf) + 1, liftBound, 
-                              Pi, diophant, Mat, MOD);
-          }
-          else
-            liftBounds[i]= adaptedLiftBound;
-        }
-        else
-          liftBounds[i]= adaptedLiftBound;
+            henselLiftResume (buf, result, degree (buf) + 1, liftBound,
+                              Pi, diophant, Mat, MOD);
+          }
+          else
+            liftBounds[i]= adaptedLiftBound;
+        }
+        else
+          liftBounds[i]= adaptedLiftBound;
       }
       MOD.append (power (Variable (i + 2), liftBounds[i]));
@@ -1635 +1635 @@
 }
 
-CFList 
-extFactorize (const CanonicalForm& F, const ExtensionInfo& info); 
-
-CFList 
-multiFactorize (const CanonicalForm& F, const ExtensionInfo& info) 
+CFList
+extFactorize (const CanonicalForm& F, const ExtensionInfo& info);
+
+CFList
+multiFactorize (const CanonicalForm& F, const ExtensionInfo& info)
 {
 
@@ -1659 +1659 @@
   bool GF= (CFFactory::gettype() == GaloisFieldDomain);
   //univariate case
-  if (F.isUnivariate()) 
+  if (F.isUnivariate())
   {
     if (extension == false)
       return uniFactorizer (F, alpha, GF);
-    else 
-    {  
+    else
+    {
       CFList source, dest;
       A= mapDown (F, info, source, dest);
@@ -1672 +1672 @@
 
   //bivariate case
-  if (A.level() == 2) 
-  {
-    CFList buf= biFactorize (F, info); 
+  if (A.level() == 2)
+  {
+    CFList buf= biFactorize (F, info);
     return buf;
   }
- 
+
   Variable x= Variable (1);
   Variable y= Variable (2);
- 
+
   // remove content
   CFList contentAi;
   CanonicalForm lcmCont= lcmContent (A, contentAi);
-  A /= lcmCont; 
+  A /= lcmCont;
 
   // trivial after content removal
   CFList contentAFactors;
-  if (A.inCoeffDomain()) 
-  { 
-    for (CFListIterator i= contentAi; i.hasItem(); i++) 
+  if (A.inCoeffDomain())
+  {
+    for (CFListIterator i= contentAi; i.hasItem(); i++)
     {
       if (i.getItem().inCoeffDomain())
         continue;
-      else 
+      else
       {
         lcmCont /= i.getItem();
-        contentAFactors= 
-        Union (multiFactorize (lcmCont, info), 
+        contentAFactors=
+        Union (multiFactorize (lcmCont, info),
                multiFactorize (i.getItem(), info));
         break;
@@ -1709 +1709 @@
 
   // factorize content
-  contentAFactors= multiFactorize (lcmCont, info); 
+  contentAFactors= multiFactorize (lcmCont, info);
 
   // univariate after content removal
   CFList factors;
-  if (A.isUnivariate ()) 
+  if (A.isUnivariate ())
   {
     factors= uniFactorizer (A, alpha, GF);
@@ -1728 +1728 @@
   Variable z;
   for (int i= 1; i <= A.level(); i++)
-  {  
+  {
     z= Variable (i);
     derivZ= deriv (bufA, z);
@@ -1746 +1746 @@
       }
       if (GF)
-        gcdDerivZ= GCD_GF (bufA, derivZ); 
+        gcdDerivZ= GCD_GF (bufA, derivZ);
       else if (alpha == Variable (1))
         gcdDerivZ= GCD_small_p (bufA, derivZ);
-      else 
+      else
         gcdDerivZ= GCD_Fp_extension (bufA, derivZ, alpha);
-      if (degree (gcdDerivZ) > 0 && !derivZ.isZero()) 
+      if (degree (gcdDerivZ) > 0 && !derivZ.isZero())
       {
         CanonicalForm g= bufA/gcdDerivZ;
-        CFList factorsG= 
+        CFList factorsG=
         Union (multiFactorize (g, info),
                multiFactorize (gcdDerivZ, info));
@@ -1774 +1774 @@
   CanonicalForm evalPoly;
   int lift, bufLift;
-  if (factorNums < (int) ceil (log (totaldegree (A)))) 
+  if (factorNums < (int) ceil (log (totaldegree (A))))
     factorNums= (int) ceil (log (totaldegree (A)));
-  // several bivariate factorizations 
-  for (int i= 0; i < factorNums; i++) 
+  // several bivariate factorizations
+  for (int i= 0; i < factorNums; i++)
   {
     bufA= A;
     bufAeval= CFList();
     bufEvaluation= evalPoints (bufA, bufAeval, alpha, list, GF, fail);
-    evalPoly= 0;  
-
-    if (fail && (i == 0)) 
+    evalPoly= 0;
+
+    if (fail && (i == 0))
     {
       if (!swapLevel)
-        level= 2;
-      else 
-        level= swapLevel + 1;
+        level= 2;
+      else
+        level= swapLevel + 1;
 
       swapLevel2= newMainVariableSearch (A, Aeval, evaluation, alpha, level);
 
       if (!swapLevel2) // need to pass to an extension
-      { 
-        factors= extFactorize (A, info);
-        appendSwapDecompress (factors, contentAFactors, N, swapLevel, x);
-        normalize (factors);
-        return factors;
+      {
+        factors= extFactorize (A, info);
+        appendSwapDecompress (factors, contentAFactors, N, swapLevel, x);
+        normalize (factors);
+        return factors;
       }
       else
@@ -1805 +1805 @@
         bufAeval= Aeval;
         bufA= A;
-        bufEvaluation= evaluation; 
+        bufEvaluation= evaluation;
       }
     }
@@ -1812 +1812 @@
 
     bivarEval= bufEvaluation.getLast();
-    bufEvaluation.removeLast(); 
+    bufEvaluation.removeLast();
 
     bufLift= degree (A, y) + 1 + degree (LC(A, x), y);
 
     TIMING_START (fac_bi_factorizer);
-    bufBiFactors= biFactorizer (bufAeval.getFirst(), alpha, bivarEval, bufLift); 
-    TIMING_END_AND_PRINT (fac_bi_factorizer, 
-                          "time for bivariate factorization: ");
-
-    if (bufBiFactors.length() == 1) 
-    {
-      if (extension) 
-      {
-        CFList source, dest;
-        A= mapDown (A, info, source, dest);
+    bufBiFactors= biFactorizer (bufAeval.getFirst(), alpha, bivarEval, bufLift);
+    TIMING_END_AND_PRINT (fac_bi_factorizer,
+                          "time for bivariate factorization: ");
+
+    if (bufBiFactors.length() == 1)
+    {
+      if (extension)
+      {
+        CFList source, dest;
+        A= mapDown (A, info, source, dest);
       }
       factors.append (A);
       appendSwapDecompress (factors, contentAFactors, N, swapLevel,
-                            swapLevel2, x);
+                            swapLevel2, x);
       normalize (factors);
       return factors;
@@ -1845 +1845 @@
     else
     {
-      if (bufBiFactors.length() < biFactors.length() || 
+      if (bufBiFactors.length() < biFactors.length() ||
           ((bufLift < lift) && (bufBiFactors.length() == biFactors.length())))
       {
@@ -1857 +1857 @@
     for (CFListIterator j= bufEvaluation; j.hasItem(); j++, k++)
       evalPoly += j.getItem()*power (x, k);
-    list.append (evalPoly);  
+    list.append (evalPoly);
   }
 
@@ -1866 +1866 @@
   int liftBoundsLength= F.level() - 1;
   liftBounds= liftingBounds (A, lift);
-  
+
   CFList MOD;
   bool earlySuccess;
   CFList earlyFactors;
   TIMING_START (fac_hensel_lift);
-  CFList liftedFactors= henselLiftAndEarly 
+  CFList liftedFactors= henselLiftAndEarly
                         (A, MOD, liftBounds, earlySuccess, earlyFactors,
                          Aeval, biFactors, evaluation, info);
   TIMING_END_AND_PRINT (fac_hensel_lift, "time for hensel lifting: ");
 
-  if (!extension) 
+  if (!extension)
   {
     TIMING_START (fac_factor_recombination);
     factors= factorRecombination (A, liftedFactors, MOD);
-    TIMING_END_AND_PRINT (fac_factor_recombination, 
+    TIMING_END_AND_PRINT (fac_factor_recombination,
                           "time for factor recombination: ");
   }
-  else 
+  else
   {
     TIMING_START (fac_factor_recombination);
     factors= extFactorRecombination (liftedFactors, A, MOD, info, evaluation);
-    TIMING_END_AND_PRINT (fac_factor_recombination, 
-                          "time for factor recombination: "); 
+    TIMING_END_AND_PRINT (fac_factor_recombination,
+                          "time for factor recombination: ");
   }
 
@@ -1894 +1894 @@
     factors= Union (factors, earlyFactors);
 
-  if (!extension) 
+  if (!extension)
   {
     for (CFListIterator i= factors; i.hasItem(); i++)
@@ -1908 +1908 @@
   }
 
-  swap (factors, swapLevel, swapLevel2, x); 
+  swap (factors, swapLevel, swapLevel2, x);
   append (factors, contentAFactors);
   decompress (factors, N);
@@ -1919 +1919 @@
 
 /// multivariate factorization over an extension of the initial field
-CFList 
-extFactorize (const CanonicalForm& F, const ExtensionInfo& info) 
+CFList
+extFactorize (const CanonicalForm& F, const ExtensionInfo& info)
 {
   CanonicalForm A= F;
@@ -1936 +1936 @@
   {
     CFList factors;
-    bool extension= true;         
+    bool extension= true;
     int p= getCharacteristic();
     if (p*p < (1<<16)) // pass to GF if possible
-    { 
+    {
       setCharacteristic (getCharacteristic(), 2, 'Z');
       ExtensionInfo info= ExtensionInfo (extension);
@@ -1947 +1947 @@
       Variable vBuf= rootOf (gf_mipo);
       setCharacteristic (getCharacteristic());
-      for (CFListIterator j= factors; j.hasItem(); j++) 
-        j.getItem()= GF2FalphaRep (j.getItem(), vBuf);
+      for (CFListIterator j= factors; j.hasItem(); j++)
+        j.getItem()= GF2FalphaRep (j.getItem(), vBuf);
     }
     else  // not able to pass to GF, pass to F_p(\alpha)
@@ -1959 +1959 @@
   }
   else if (!GF && (alpha != w)) // we are in F_p(\alpha)
-  { 
+  {
     if (k == 1) // need factorization over F_p
     {
       int extDeg= degree (getMipo (alpha));
-      extDeg++; 
+      extDeg++;
       CanonicalForm mipo= randomIrredpoly (extDeg + 1, Variable (1));
       Variable v= rootOf (mipo);
@@ -1969 +1969 @@
       factors= biFactorize (A, info);
     }
-    else 
+    else
     {
       if (beta == Variable (1))
@@ -1985 +1985 @@
 
         CFList source, dest;
-        CanonicalForm bufA= mapUp (A, alpha, v, primElem, imPrimElem, 
+        CanonicalForm bufA= mapUp (A, alpha, v, primElem, imPrimElem,
                                    source, dest);
         ExtensionInfo info= ExtensionInfo (v, alpha, imPrimElem, primElem);
@@ -2014 +2014 @@
   }
   else // we are in GF (p^k)
-  { 
+  {
     int p= getCharacteristic();
     int extensionDeg= getGFDegree();
     bool extension= true;
     if (k == 1) // need factorization over F_p
-    { 
+    {
       extensionDeg++;
-      if (pow ((double) p, (double) extensionDeg) < (1<<16)) 
+      if (pow ((double) p, (double) extensionDeg) < (1<<16))
       // pass to GF(p^k+1)
-      { 
+      {
         setCharacteristic (p);
-        Variable vBuf= rootOf (gf_mipo);
-        A= GF2FalphaRep (A, vBuf);
-        setCharacteristic (p, extensionDeg, 'Z');
+        Variable vBuf= rootOf (gf_mipo);
+        A= GF2FalphaRep (A, vBuf);
+        setCharacteristic (p, extensionDeg, 'Z');
         ExtensionInfo info= ExtensionInfo (extension);
-        factors= multiFactorize (A.mapinto(), info);
+        factors= multiFactorize (A.mapinto(), info);
       }
       else // not able to pass to another GF, pass to F_p(\alpha)
-      { 
-        setCharacteristic (p);
-        Variable vBuf= rootOf (gf_mipo);
-        A= GF2FalphaRep (A, vBuf);
-        Variable v= chooseExtension (A, beta);
+      {
+        setCharacteristic (p);
+        Variable vBuf= rootOf (gf_mipo);
+        A= GF2FalphaRep (A, vBuf);
+        Variable v= chooseExtension (A, beta);
         ExtensionInfo info= ExtensionInfo (v, extension);
-        factors= multiFactorize (A, info);
+        factors= multiFactorize (A, info);
       }
     }
     else // need factorization over GF (p^k)
     {
-      if (pow ((double) p, (double) 2*extensionDeg) < (1<<16)) 
+      if (pow ((double) p, (double) 2*extensionDeg) < (1<<16))
       // pass to GF(p^2k)
-      { 
-        setCharacteristic (p, 2*extensionDeg, 'Z');
+      {
+        setCharacteristic (p, 2*extensionDeg, 'Z');
         ExtensionInfo info= ExtensionInfo (k, cGFName, extension);
-        factors= multiFactorize (GFMapUp (A, extensionDeg), info); 
-        setCharacteristic (p, extensionDeg, cGFName);
+        factors= multiFactorize (GFMapUp (A, extensionDeg), info);
+        setCharacteristic (p, extensionDeg, cGFName);
       }
       else // not able to pass to GF (p^2k), pass to F_p (\alpha)
-      { 
-        setCharacteristic (p);
-        Variable v1= rootOf (gf_mipo);
-        A= GF2FalphaRep (A, v1);
-        Variable v2= chooseExtension (A, v1); 
+      {
+        setCharacteristic (p);
+        Variable v1= rootOf (gf_mipo);
+        A= GF2FalphaRep (A, v1);
+        Variable v2= chooseExtension (A, v1);
         CanonicalForm primElem, imPrimElem;
         bool primFail= false;
@@ -2070 +2070 @@
         }
         CFList source, dest;
-        CanonicalForm bufA= mapUp (A, alpha, beta, primElem, imPrimElem, 
+        CanonicalForm bufA= mapUp (A, alpha, beta, primElem, imPrimElem,
                                      source, dest);
         ExtensionInfo info= ExtensionInfo (v2, v1, imPrimElem, primElem);
-        factors= multiFactorize (bufA, info); 
-        setCharacteristic (p, k, cGFName);
-        for (CFListIterator i= factors; i.hasItem(); i++) 
-          i.getItem()= Falpha2GFRep (i.getItem());
+        factors= multiFactorize (bufA, info);
+        setCharacteristic (p, k, cGFName);
+        for (CFListIterator i= factors; i.hasItem(); i++)
+          i.getItem()= Falpha2GFRep (i.getItem());
       }
     }