Changeset 2bd45fc in git

Timestamp:

May 21, 2014, 4:26:43 PM (9 years ago)

Author:

Oleksandr Motsak <motsak@…>

Branches:

(u'spielwiese', '8e0ad00ce244dfd0756200662572aef8402f13d5')

Children:

cdb69cbf8fbe6c0d249a439d3049448352edd0b0

Parents:

fff643cc11aac90dbe5f19791aac378c1eef37bb6c524f33f553f9d0a11c9984e32c98732e50abb5

Message:

Merge pull request #589 from surface-smoothers/test.for.emtpy.charseries

added a test for empty char series

Files:

• Singular/LIB/ring.lib (modified) (5 diffs)
• Tst/Buch/Example_4_6_26.res.gz.uu (modified) (1 diff)
• Tst/Buch/Example_4_6_26.stat (modified) (1 diff)
• Tst/Long/primdec_l.res.gz.uu (modified) (1 diff)
• Tst/Long/primdec_l.stat (modified) (1 diff)
• Tst/Short/bug_15.res.gz.uu (modified) (1 diff)
• Tst/Short/bug_15.stat (modified) (1 diff)
• Tst/Short/bug_charseries.res.gz.uu (modified) (1 diff)
• Tst/Short/bug_charseries.stat (modified) (1 diff)
• Tst/Short/bug_charseries.tst (modified) (2 diffs)
• Tst/Short/charseries.res.gz.uu (modified) (1 diff)
• Tst/Short/charseries.stat (modified) (1 diff)
• Tst/Short/charseries.tst (modified) (1 diff)
• Tst/Short/charseries_p.res.gz.uu (modified) (1 diff)
• Tst/Short/charseries_p.stat (modified) (1 diff)
• Tst/Short/charseries_p.tst (modified) (1 diff)
• Tst/Short/primdec_s.res.gz.uu (modified) (1 diff)
• Tst/Short/primdec_s.stat (modified) (1 diff)
• factory/cfCharSets.cc (modified) (5 diffs)
• factory/cfCharSets.h (modified) (1 diff)
• factory/cfCharSetsUtil.cc (modified) (7 diffs)
• factory/cf_generator.cc (modified) (2 diffs)
• factory/cf_generator.h (modified) (1 diff)
• factory/facAlgExt.cc (modified) (4 diffs)
• factory/facAlgFunc.cc (modified) (6 diffs)
• factory/facAlgFuncUtil.cc (modified) (3 diffs)
• factory/facAlgFuncUtil.h (modified) (1 diff)

Singular/LIB/ring.lib

@@ -4 +4 @@
 info="
 LIBRARY:  ring.lib      Manipulating Rings and Maps
+AUTHORS: Singular team
 
 PROCEDURES:
@@ -28 +29 @@
  hasGlobalOrdering(rng)   global versus mixed/local monomial ordering
  hasMixedOrdering()       mixed versus global/local ordering
+ hasFieldCoefficient(rng) coefficients are a field
+ isQuotientRing(rng)      ring is a qotient ring
  isSubModule(I,J)         check if I is in J as submodule
 ";
@@ -955 +958 @@
 {
   ring rng = integer,x,dp;
-  hasFieldCoefficientRing(rng); //no
+  hasFieldCoefficient(rng); //no
   // if a certain method supports only rings with integer coefficients,
   // then a parameter test could be performed:
@@ -989 +992 @@
   return (size(rl)==4);
 }
+example
+{
+ ring r=0,(x,y,z),dp;
+ hasCommutativeVars(r);
+}
 
 proc hasNumericCoeffs(rng)
@@ -1009 +1017 @@
   else
   { return(size(reduce(I,groebner(J),1)==0)); }
+}
+example
+{
+  ring r=0,x,dp;
+  ideal I1=x2;
+  ideal I2=x3;
+  isSubModule(I1,I2);
+  isSubModule(I2,I1);
 }
 

Tst/Buch/Example_4_6_26.res.gz.uu

@@ -1 +1 @@
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 `
 end

Tst/Buch/Example_4_6_26.stat

@@ -1 @@
-1 >> tst_memory_0 :: 1399646713:4.0.0, 32 bit:4.0.0:i686-Linux:mamawutz:175096
-1 >> tst_memory_1 :: 1399646713:4.0.0, 32 bit:4.0.0:i686-Linux:mamawutz:2240344
-1 >> tst_memory_2 :: 1399646713:4.0.0, 32 bit:4.0.0:i686-Linux:mamawutz:2281316
-1 >> tst_timer_1 :: 1399646713:4.0.0, 32 bit:4.0.0:i686-Linux:mamawutz:18
+1 >> tst_memory_0 :: 1400667008:4.0.0, 32 bit:4.0.0:i686-Linux:mamawutz:175096
+1 >> tst_memory_1 :: 1400667008:4.0.0, 32 bit:4.0.0:i686-Linux:mamawutz:2240344
+1 >> tst_memory_2 :: 1400667008:4.0.0, 32 bit:4.0.0:i686-Linux:mamawutz:2281316
+1 >> tst_timer_1 :: 1400667008:4.0.0, 32 bit:4.0.0:i686-Linux:mamawutz:12

Tst/Long/primdec_l.res.gz.uu

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 `
 end

Tst/Long/primdec_l.stat

@@ -1 @@
-1 >> tst_memory_0 :: 1394792891:4.0.0, 32 bit:4.0.0:i686-Linux:mamawutz:1557536
-1 >> tst_memory_1 :: 1394792891:4.0.0, 32 bit:4.0.0:i686-Linux:mamawutz:4800512
-1 >> tst_memory_2 :: 1394792891:4.0.0, 32 bit:4.0.0:i686-Linux:mamawutz:4935680
-1 >> tst_timer_1 :: 1394792891:4.0.0, 32 bit:4.0.0:i686-Linux:mamawutz:3242
+1 >> tst_memory_0 :: 1400677521:4.0.0, 32 bit:4.0.0:i686-Linux:mamawutz:1560168
+1 >> tst_memory_1 :: 1400677521:4.0.0, 32 bit:4.0.0:i686-Linux:mamawutz:4800512
+1 >> tst_memory_2 :: 1400677521:4.0.0, 32 bit:4.0.0:i686-Linux:mamawutz:4935680
+1 >> tst_timer_1 :: 1400677521:4.0.0, 32 bit:4.0.0:i686-Linux:mamawutz:3369

Tst/Short/bug_15.res.gz.uu

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 `
 end

Tst/Short/bug_15.stat

@@ -1 @@
-1 >> tst_memory_0 :: 1399642556:4.0.0, 32 bit:4.0.0:i686-Linux:mamawutz:317748
-1 >> tst_memory_1 :: 1399642556:4.0.0, 32 bit:4.0.0:i686-Linux:mamawutz:2387968
-1 >> tst_memory_2 :: 1399642556:4.0.0, 32 bit:4.0.0:i686-Linux:mamawutz:2517208
-1 >> tst_timer_1 :: 1399642556:4.0.0, 32 bit:4.0.0:i686-Linux:mamawutz:43
+1 >> tst_memory_0 :: 1400667038:4.0.0, 32 bit:4.0.0:i686-Linux:mamawutz:317948
+1 >> tst_memory_1 :: 1400667038:4.0.0, 32 bit:4.0.0:i686-Linux:mamawutz:2383872
+1 >> tst_memory_2 :: 1400667038:4.0.0, 32 bit:4.0.0:i686-Linux:mamawutz:2517212
+1 >> tst_timer_1 :: 1400667038:4.0.0, 32 bit:4.0.0:i686-Linux:mamawutz:43

Tst/Short/bug_charseries.res.gz.uu

@@ -1 @@
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+M4XN\:]`J#S\OV\!VEG'7>:NUZ#_3A)BC*NC:G&*:95U/D\N[ZCK%WCZ,1E]'
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+MBJ9WOU<Q&VU?S);!S)6C=*7C>HK646,PHCE(5BD;43PLDO1_^H?VE'^8ZV07
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+M)%A3:/KX]-,8*#U9T>,A512476=@>^_&XV^?'PS7SBGW?)'<Q?QA?Q"OX8;C
+MD1[B_$/:`*TJNQ'IVSTB].Q51-)%8Q/_:-'3O^5]=^UE+=J997AFLW]*]L,X
+0)`9I]#_4_@+[[>`RB08`````
 `
 end

Tst/Short/bug_charseries.stat

@@ -1 @@
-1 >> tst_memory_0 :: 1400599075:4.0.0, 64 bit:4.0.0:x86_64-Linux:nepomuck:272136
-1 >> tst_memory_1 :: 1400599075:4.0.0, 64 bit:4.0.0:x86_64-Linux:nepomuck:2342912
-1 >> tst_memory_2 :: 1400599075:4.0.0, 64 bit:4.0.0:x86_64-Linux:nepomuck:2375984
-1 >> tst_timer_1 :: 1400599075:4.0.0, 64 bit:4.0.0:x86_64-Linux:nepomuck:3
+1 >> tst_memory_0 :: 1400659407:4.0.0, 64 bit:4.0.0:x86_64-Linux:andr:409520
+1 >> tst_memory_1 :: 1400659407:4.0.0, 64 bit:4.0.0:x86_64-Linux:andr:2502656
+1 >> tst_memory_2 :: 1400659407:4.0.0, 64 bit:4.0.0:x86_64-Linux:andr:2555904
+1 >> tst_timer_1 :: 1400659407:4.0.0, 64 bit:4.0.0:x86_64-Linux:andr:11

Tst/Short/bug_charseries.tst

@@ -4 +4 @@
 
 LIB "primdec.lib";
+LIB("ehv.lib");
 ring r = 0,(x,y,z),lp;
 def p=z^2 + 1;
@@ -27 +28 @@
 sage31;
 
+// empty char series
+
+ideal I = -3*y^2-3, -3*x^2+1, -x*y+2*z^2;
+def L1 = primdecGTZ(I);
+def L2 = primdecSY(I);
+ASSUME(0, primDecsAreEquivalent(L1, L2) );
+L2;
+
 tst_status(1);$

Tst/Short/charseries.res.gz.uu

@@ -1 +1 @@
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 `
 end

Tst/Short/charseries.stat

@@ -1 @@
-1 >> tst_memory_0 :: 1399642133:4.0.0, 32 bit:4.0.0:i686-Linux:mamawutz:1170504
-1 >> tst_memory_1 :: 1399642133:4.0.0, 32 bit:4.0.0:i686-Linux:mamawutz:15392768
-1 >> tst_memory_2 :: 1399642133:4.0.0, 32 bit:4.0.0:i686-Linux:mamawutz:15392768
-1 >> tst_timer_1 :: 1399642133:4.0.0, 32 bit:4.0.0:i686-Linux:mamawutz:8632
+1 >> tst_memory_0 :: 1400667171:4.0.0, 32 bit:4.0.0:i686-Linux:mamawutz:956804
+1 >> tst_memory_1 :: 1400667171:4.0.0, 32 bit:4.0.0:i686-Linux:mamawutz:11124736
+1 >> tst_memory_2 :: 1400667171:4.0.0, 32 bit:4.0.0:i686-Linux:mamawutz:11124736
+1 >> tst_timer_1 :: 1400667171:4.0.0, 32 bit:4.0.0:i686-Linux:mamawutz:3556

Tst/Short/charseries.tst

@@ -77 +77 @@
 kill r;
 
-ring r=3,(x1,x2,x3,x4,x5,y),lp;
-poly f6= ((y+x1*x3+x2+1)*(y+x3*x4+x1*x3)*(y^3+x3*x4+x1*x3));
-ideal I=x1^2+1, x2^2+x1+1, x3^2+x2+1, x4^2+x3+x2+2;
-ideal K=I,f6;
-char_series (K);
+// examples from J. Kroeker
+ring r=0,(x,y,z),dp;
+ideal I = -3*y^2-3, -3*x^2+1, -x*y+2*z^2;
+char_series (I);
+
+kill r;
+
+ring r=0,(z,y,x),dp;
+ideal I = -3*y^2-3, -3*x^2+1, -x*y+2*z^2;
+char_series (I);
+
 
 tst_status(1);$

Tst/Short/charseries_p.res.gz.uu

@@ -1 +1 @@
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+)/V2*&7J/)@``
 `
 end

Tst/Short/charseries_p.stat

@@ -1 @@
-1 >> tst_memory_0 :: 1399642375:4.0.0, 32 bit:4.0.0:i686-Linux:mamawutz:664412
-1 >> tst_memory_1 :: 1399642375:4.0.0, 32 bit:4.0.0:i686-Linux:mamawutz:2465792
-1 >> tst_memory_2 :: 1399642375:4.0.0, 32 bit:4.0.0:i686-Linux:mamawutz:2465792
-1 >> tst_timer_1 :: 1399642375:4.0.0, 32 bit:4.0.0:i686-Linux:mamawutz:2344
+1 >> tst_memory_0 :: 1400667270:4.0.0, 32 bit:4.0.0:i686-Linux:mamawutz:618652
+1 >> tst_memory_1 :: 1400667270:4.0.0, 32 bit:4.0.0:i686-Linux:mamawutz:2384368
+1 >> tst_memory_2 :: 1400667270:4.0.0, 32 bit:4.0.0:i686-Linux:mamawutz:2425340
+1 >> tst_timer_1 :: 1400667270:4.0.0, 32 bit:4.0.0:i686-Linux:mamawutz:480

Tst/Short/charseries_p.tst

@@ -144 +144 @@
 char_series (J);
 
+kill r;
+
+ring r=3,(x1,x2,x3,x4,x5,y),lp;
+poly f6= ((y+x1*x3+x2+1)*(y+x3*x4+x1*x3)*(y^3+x3*x4+x1*x3));
+ideal I=x1^2+1, x2^2+x1+1, x3^2+x2+1, x4^2+x3+x2+2;
+ideal K=I,f6;
+char_series (K);
+
 
 

Tst/Short/primdec_s.res.gz.uu

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+M@&5!>ZZ*Q@2:F?P)25A@I\0:/4B'2LB80-<&'1&)&S7-UNE/NP?BAO1WU*Q)
+MVY<)H$F;_JI:;)"^,K).B'1E\%2&0>6I4R3G[L'CZ)PKL^#]C7/('KB]&4H%
+M[[C3O1H<2@6ON6$_$SUBX;N>V#7`?R'H%PSA2;V2)IOU"8;`FWO%ML?]&AQR
+M]Y*&K/0*!B]ATGV;]0H&[UR&\]KLNP"ZO1[:0:YXNF^[.Q\2VE">)>.]E_0+
+M*O^V1[LC(^$55:YQCX4;!VSV"2I_NL^&"-KL%^T=HO=4P0VL@:![2,1U(ZH=
+M*=RJS.8.8I$=;X>QBH_4CWTQ=Q@QLQ$5[=R@,1NLI1S$'';,]>`*)^9ZH$%X
+M'*UIGCH;.G;7AC?M44YFSUAXJ$\,;=<C/?C+[=8#(N-!#B84&8_TM:$(^0RN
+M-A0ECX0((U'R*$2S=Y0\`'P%(^23$6(P-CX9Q`8CHB7I;<V6",=`>P?NB]YZ
+MAVB=%;2<W7L9S>!UC,;W%L;NG0M%-5Z_H)I*6VK7.FO):5<$M6+N/N2:D7>,
+MM&/PG6WU[DGM@KL/A<4J)$OF0;(3F<42C[O-+LK(9J&^6O?8];KS9>VCZB?"
+M-@OKSB)BLXAI):(VDQH*^XF8.)H!I%_N!_F37_E/&^6_9?S]X0R=O_O3['^-
+'(SFUZE$`````
 `
 end

Tst/Short/primdec_s.stat

@@ -1 @@
-1 >> tst_memory_0 :: 1399642925:4.0.0, 32 bit:4.0.0:i686-Linux:mamawutz:631708
-1 >> tst_memory_1 :: 1399642925:4.0.0, 32 bit:4.0.0:i686-Linux:mamawutz:2621440
-1 >> tst_memory_2 :: 1399642925:4.0.0, 32 bit:4.0.0:i686-Linux:mamawutz:3133440
-1 >> tst_timer_1 :: 1399642925:4.0.0, 32 bit:4.0.0:i686-Linux:mamawutz:436
+1 >> tst_memory_0 :: 1400667354:4.0.0, 32 bit:4.0.0:i686-Linux:mamawutz:631864
+1 >> tst_memory_1 :: 1400667354:4.0.0, 32 bit:4.0.0:i686-Linux:mamawutz:2621440
+1 >> tst_memory_2 :: 1400667354:4.0.0, 32 bit:4.0.0:i686-Linux:mamawutz:3133440
+1 >> tst_timer_1 :: 1400667354:4.0.0, 32 bit:4.0.0:i686-Linux:mamawutz:430

factory/cfCharSets.cc

@@ -401 +401 @@
 }
 
+CFList
+modCharSet (const CFList& PS, bool removeContents)
+{
+  StoreFactors tmp;
+  return modCharSet (PS, tmp, removeContents);
+}
+
 ListCFList
 charSeries (const CFList& L)
@@ -518 +525 @@
     }
     else
-      qs= CFFList (CFFactor (i.getItem(), 1));
+      qs= CFFList (CFFactor (normalize (i.getItem()), 1));
 
     if ((qs.length() >= 2 ) || (qs.getFirst().exp() > 1))
@@ -556 +563 @@
   }
   for (CFFListIterator k= qs; k.hasItem(); k++)
-    ts.append (k.getItem().factor());
+    ts.append (normalize (k.getItem().factor()));
   return ts;
 }
@@ -577 +584 @@
       sqrf *= iter2.getItem().factor();
     sqrf= normalize (sqrf);
-    L= Union (L, CFList (sqrf));
+    L= Union (CFList (sqrf), L);
   }
 
@@ -613 +620 @@
 
     StoreFactors StoredFactors;
-    cs= charSetViaModCharSet (qs, StoredFactors);
+    if (qs.length() - 3 < highestlevel)
+      cs= modCharSet (qs, StoredFactors, false);
+    else
+      cs= charSetN (qs);
     cs= removeContent (cs, StoredFactors);
 
     factorset= StoredFactors.FS1;
 
-    if (cs.getFirst().level() > 0)
+    if (!cs.isEmpty() && cs.getFirst().level() > 0)
     {
       ts= irredAS (cs, indexRed, reducible);

factory/cfCharSets.h

@@ -39 +39 @@
 modCharSet (const CFList& PS, StoreFactors& StoredFactors,
             bool removeContents= true);
+
+CFList
+modCharSet (const CFList& PS, bool removeContents);
 
 /// modified characteristic set, i.e. a characteristic set with certain

factory/cfCharSetsUtil.cc

@@ -384 +384 @@
 }
 
+int minLevel (const CFList& L)
+{
+  if (L.isEmpty())
+    return 0;
+  int min= size (L.getFirst());
+  return min;
+}
+
 /// sort in descending order of length of elements
 void
@@ -398 +406 @@
       m= j;
       m++;
-      if (j.getItem().length() < m.getItem().length())
+      if ((j.getItem().length() < m.getItem().length()) ||
+          (j.getItem().length() == m.getItem().length() &&
+           minLevel (j.getItem()) > minLevel (m.getItem())))
       {
         buf= m.getItem();
@@ -709 +719 @@
     if (isRat)
       On (SW_RATIONAL);
+    if (lc(G) < 0)
+      G= -G;
     return G;
   }
@@ -887 +899 @@
     else
       cF= 0;
+    F= normalize (F);
 
     return;
@@ -934 +947 @@
     testlist.append (CanonicalForm (Variable (i)));
 
+  // remove already removed factors
   for (j= StoredFactors.FS1; j.hasItem(); j++)
   {
     while (fdivides (j.getItem(), r, quot))
     {
-      if (!quot.inCoeffDomain())
-        r= quot;
-      else
-        break;
-    }
-  }
-
-  // remove already removed factors
+      r= quot;
+    }
+  }
+
   for (j= StoredFactors.FS2; j.hasItem(); j++)
   {
     divides= false;
-    while (fdivides (j.getItem(), r, quot))
-    {
-      if (!quot.inCoeffDomain())
+    if (j.getItem() != r)
+    {
+      while (fdivides (j.getItem(), r, quot))
       {
         divides= true;
         r= quot;
       }
-      else
-        break;
-    }
-    if (divides)
-      removedFactors= Union (removedFactors, CFList (j.getItem()));
+      if (divides)
+        removedFactors= Union (removedFactors, CFList (j.getItem()));
+    }
   }
   r= normalize (r);
@@ -967 +975 @@
   for (j= testlist; j.hasItem() && !r.isOne(); j++)
   {
-    while (fdivides (j.getItem(), r, quot))
-    {
-      if (!quot.inCoeffDomain())
+    divides= false;
+    if (j.getItem() != r)
+    {
+      while (fdivides (j.getItem(), r, quot))
+      {
+        divides= true;
         r= quot;
-      else
-        break;
-      removedFactors= Union (removedFactors, CFList (j.getItem()));
-    }
-  }
+      }
+      if (divides)
+        removedFactors= Union (removedFactors, CFList (j.getItem()));
+     }
+  }
+  r= normalize (r);
 }
 
@@ -994 +1006 @@
     if (cc.level() > 0 )
     {
-      output.append (elem / cc);
-      StoredFactors.FS1 = Union (CFList (cc), StoredFactors.FS1);
+      output.append (normalize (elem / cc));
+      StoredFactors.FS1 = Union (CFList (normalize (cc)), StoredFactors.FS1);
     }
     else
-      output.append(elem);
+      output.append(normalize (elem));
   }
   return output;

factory/cf_generator.cc

@@ -12 +12 @@
 #include "gfops.h"
 #include "ffops.h"
+
+bool IntGenerator::hasItems() const
+{
+    return 1;
+}
+
+CanonicalForm IntGenerator::item() const
+{
+  return mapinto (CanonicalForm (current));
+}
+
+void IntGenerator::next()
+{
+    current++;
+}
+
+CFGenerator * IntGenerator::clone () const
+{
+    return new IntGenerator();
+}
 
 bool FFGenerator::hasItems() const
@@ -201 +221 @@
 CFGenerator * CFGenFactory::generate()
 {
-    ASSERT( getCharacteristic() > 0, "not a finite field" );
-    if ( getGFDegree() > 1 )
+    if (getCharacteristic() == 0)
+        return new IntGenerator();
+    else if ( getGFDegree() > 1 )
         return new GFGenerator();
     else

factory/cf_generator.h

@@ -20 +20 @@
     virtual void next() {};
     virtual CFGenerator * clone() const { return new CFGenerator();}
+};
+
+class IntGenerator : public CFGenerator
+{
+private:
+    int current;
+public:
+    IntGenerator() : current(0) {}
+    ~IntGenerator() {}
+    bool hasItems() const;
+    void reset() { current = 0; }
+    CanonicalForm item() const;
+    void next();
+    void operator++ () { next(); }
+    void operator++ ( int ) { next(); }
+    CFGenerator * clone() const;
 };
 

factory/facAlgExt.cc

@@ -50 +50 @@
 }
 
-// i is an integer such that Norm (F (x-i*alpha)) is squarefree
-CanonicalForm sqrfNorm (const CanonicalForm& F, const Variable& alpha, int& i)
+CanonicalForm Norm (const CanonicalForm& F, const Variable& alpha)
 {
   Variable x= Variable (F.level() + 1);
@@ -69 +68 @@
     norm= resultant (g, mipo, x);
   TIMING_END_AND_PRINT (fac_alg_resultant, "time to compute resultant0: ");
+  return norm;
+}
+
+// i is an integer such that Norm (F (x-i*alpha)) is squarefree
+CanonicalForm sqrfNorm (const CanonicalForm& F, const Variable& alpha, int& i)
+{
+  Variable x= Variable (F.level() + 1);
+  Variable y= F.mvar();
+  CanonicalForm g= F (x, alpha);
+  CanonicalForm mipo= getMipo (alpha);
+  mipo= mipo (x, alpha);
+  mipo *= bCommonDen (mipo);
+
+  int degg= degree (g);
+  int degmipo= degree (mipo);
+  CanonicalForm norm;
+  TIMING_START (fac_alg_resultant);
+  if (degg >= 8 || degmipo >= 8)
+    norm= resultantZ (g, mipo, x);
+  else
+    norm= resultant (g, mipo, x);
+  TIMING_END_AND_PRINT (fac_alg_resultant, "time to compute resultant0: ");
 
   i= 0;
@@ -115 +136 @@
 
 CFList
+AlgExtSqrfFactorize (const CanonicalForm& F, const Variable& alpha)
+{
+  ASSERT (F.isUnivariate(), "univariate input expected");
+  ASSERT (getCharacteristic() == 0, "characteristic 0 expected");
+
+  bool save_rat=!isOn (SW_RATIONAL);
+  On (SW_RATIONAL);
+  CanonicalForm f= F*bCommonDen (F);
+  Variable y= f.mvar();
+  int shift= 0, k= 0, count= 0;
+  CanonicalForm norm, buf, factor, oldF;
+  CFFList normFactors;
+  bool save_sort= !isOn (SW_USE_NTL_SORT);
+  CFList factors, tmp, tmp2;
+  CFFListIterator i;
+  CFListIterator iter;
+  bool shiftBuf= false;
+
+  tmp.append (f);
+  do
+  {
+    tmp2= CFList();
+    for (iter= tmp; iter.hasItem(); iter++)
+    {
+      oldF= iter.getItem()*bCommonDen (iter.getItem());
+      if (shift == 0)
+        f= oldF;
+      else
+        f= oldF (y - shift*alpha, y);
+      TIMING_START (fac_alg_norm);
+      norm= Norm (f, alpha);
+      TIMING_END_AND_PRINT (fac_alg_norm, "time to compute sqrf norm: ");
+      ASSERT (degree (norm, alpha) <= 0, "wrong norm computed");
+
+      TIMING_START (fac_alg_factor_norm);
+      On (SW_USE_NTL_SORT);
+      normFactors= factorize (norm);
+      if (save_sort)
+        Off (SW_USE_NTL_SORT);
+      TIMING_END_AND_PRINT (fac_alg_factor_norm, "time to factor norm: ");
+
+      if (normFactors.getFirst().factor().inCoeffDomain())
+        normFactors.removeFirst();
+      if (normFactors.length() < 2 && normFactors.getLast().exp() == 1)
+      {
+        factors.append (oldF);
+        continue;
+      }
+
+      i= normFactors;
+      shiftBuf= false;
+      if (!(normFactors.length() == 2 &&
+            degree (i.getItem().factor()) <= degree (f)))
+      {
+        TIMING_START (fac_alg_time_shift);
+        if (shift != 0)
+          buf= f;
+        else
+          buf= oldF;
+        shiftBuf= true;
+        TIMING_END_AND_PRINT (fac_alg_time_shift, "time to shift: ");
+      }
+      else
+        buf= oldF;
+
+      count= 0;
+      for (; i.hasItem(); i++)
+      {
+        TIMING_START (fac_alg_gcd);
+        if (shiftBuf)
+          factor= gcd (buf, i.getItem().factor());
+        else
+        {
+          if (shift == 0)
+            factor= gcd (buf, i.getItem().factor());
+          else
+            factor= gcd (buf, i.getItem().factor() (y + shift*alpha, y));
+        }
+        buf /= factor;
+        if (shiftBuf)
+        {
+          if (shift != 0)
+            factor= factor (y + shift*alpha, y);
+        }
+        TIMING_END_AND_PRINT (fac_alg_gcd, "time to recover factors: ");
+        if (i.getItem().exp() == 1 || degree (factor) == 1)
+          factors.append (factor);
+        else
+          tmp2.append (factor);
+        count++;
+        if (normFactors.length() - 1 == count)
+        {
+          if (shiftBuf)
+          {
+            if (normFactors.getLast().exp() == 1)
+              factors.append (buf (y + shift*alpha, y));
+            else
+              tmp2.append (buf (y + shift*alpha, y));
+          }
+          else
+          {
+            if (normFactors.getLast().exp() == 1)
+              factors.append (buf);
+            else
+              tmp2.append (buf);
+          }
+          buf= 1;
+          break;
+        }
+      }
+    }
+    k++;
+    if (shift == 0)
+    {
+      shift++;
+      k= 1;
+    }
+    if (k == 2)
+      shift= -shift;
+    if (k == 3)
+    {
+      shift= -shift;
+      shift++;
+      k= 1;
+    }
+    tmp= tmp2;
+  }
+  while (!tmp.isEmpty());
+
+  if (save_rat) Off(SW_RATIONAL);
+  return factors;
+}
+
+
+/*CFList
 AlgExtSqrfFactorize (const CanonicalForm& F, const Variable& alpha)
 {
@@ -195 +351 @@
   if (save_rat) Off(SW_RATIONAL);
   return factors;
-}
+}*/
 
 CFFList

factory/facAlgFunc.cc

@@ -197 +197 @@
 }
 
-// Trager's square free norm algorithm:
-// f a separable polynomial over K (alpha),
-// alpha is defined by the minimal polynomial Palpha
-// K need to contain more than S elements (S is defined in Messollen's thesis;
-// see also getDegOfExt)
+/// compute the norm R of f over PPalpha, g= f (x-s*alpha)
+/// if proof==true, R is squarefree and if in addition getCharacteristic() > 0
+/// the squarefree factors of R are returned.
+/// Based on Trager's sqrf_norm algorithm.
 static CFFList
-sqrf_norm_sub (const CanonicalForm & f, const CanonicalForm & PPalpha,
-               CFGenerator & myrandom, CanonicalForm & s,  CanonicalForm & g,
-               CanonicalForm & R)
+norm (const CanonicalForm & f, const CanonicalForm & PPalpha,
+      CFGenerator & myrandom, CanonicalForm & s, CanonicalForm & g,
+      CanonicalForm & R, bool proof)
 {
-  Variable y= PPalpha.mvar(),vf= f.mvar();
+  Variable y= PPalpha.mvar(), vf= f.mvar();
   CanonicalForm temp, Palpha= PPalpha, t;
   int sqfreetest= 0;
@@ -213 +212 @@
   CFFListIterator i;
 
-  myrandom.reset();
-  s= myrandom.item();
-  g= f;
-  R= CanonicalForm(0);
+  if (proof)
+  {
+    myrandom.reset();
+    s= myrandom.item();
+    g= f;
+    R= CanonicalForm(0);
+  }
+  else
+  {
+    if (getCharacteristic() == 0)
+      t= CanonicalForm (mapinto (myrandom.item()));
+    else
+      t= CanonicalForm (myrandom.item());
+    s= t;
+    g= f (vf - t*Palpha.mvar(), vf);
+  }
 
   // Norm, resultante taken with respect to y
   while (!sqfreetest)
   {
-    R= resultante(Palpha, g, y);
+    R= resultante (Palpha, g, y);
     R= R* bCommonDen(R);
     R /= content (R);
-    // sqfree check ; R is a polynomial in K[x]
-    if (getCharacteristic() == 0)
-    {
-      temp= gcd (R, R.deriv(vf));
-      if (degree(temp,vf) != 0 || temp == temp.genZero() )
-        sqfreetest= 0;
+    if (proof)
+    {
+      // sqfree check ; R is a polynomial in K[x]
+      if (getCharacteristic() == 0)
+      {
+        temp= gcd (R, R.deriv (vf));
+        if (degree(temp,vf) != 0 || temp == temp.genZero())
+          sqfreetest= 0;
+        else
+          sqfreetest= 1;
+      }
       else
+      {
+        Variable X;
+        testlist= sqrFree (R);
+
+        if (testlist.getFirst().factor().inCoeffDomain())
+          testlist.removeFirst();
         sqfreetest= 1;
+        for (i= testlist; i.hasItem(); i++)
+        {
+          if (i.getItem().exp() > 1 && degree (i.getItem().factor(),R.mvar()) > 0)
+          {
+            sqfreetest= 0;
+            break;
+          }
+        }
+      }
+      if (!sqfreetest)
+      {
+        myrandom.next();
+        if (getCharacteristic() == 0)
+          t= CanonicalForm (mapinto (myrandom.item()));
+        else
+          t= CanonicalForm (myrandom.item());
+        s= t;
+        g= f (vf - t*Palpha.mvar(), vf);
+      }
     }
     else
-    {
-      Variable X;
-      testlist= sqrFree (R);
-
-      if (testlist.getFirst().factor().inCoeffDomain())
-        testlist.removeFirst();
-      sqfreetest= 1;
-      for (i= testlist; i.hasItem(); i++)
-      {
-        if (i.getItem().exp() > 1 && degree (i.getItem().factor(),R.mvar()) > 0)
-        {
-          sqfreetest= 0;
-          break;
-        }
-      }
-    }
-    if (!sqfreetest)
-    {
-      myrandom.next();
-      if (getCharacteristic() == 0)
-        t= CanonicalForm (mapinto (myrandom.item()));
-      else
-        t= CanonicalForm (myrandom.item());
-      s= t;
-      g= f (f.mvar() - t*Palpha.mvar(), f.mvar());
-    }
+      break;
   }
   return testlist;
 }
 
+/// see @a norm, R is guaranteed to be squarefree
+/// Based on Trager's sqrf_norm algorithm.
 static CFFList
-sqrf_norm( const CanonicalForm & f, const CanonicalForm & PPalpha,
-           const Variable & Extension, CanonicalForm & s,  CanonicalForm & g,
-           CanonicalForm & R)
+sqrfNorm (const CanonicalForm & f, const CanonicalForm & PPalpha,
+          const Variable & Extension, CanonicalForm & s,  CanonicalForm & g,
+          CanonicalForm & R)
 {
   CFFList result;
@@ -273 +291 @@
   {
     IntGenerator myrandom;
-    result= sqrf_norm_sub (f, PPalpha, myrandom, s, g, R);
+    result= norm (f, PPalpha, myrandom, s, g, R, true);
   }
   else if (degree (Extension) > 0)
   {
     AlgExtGenerator myrandom (Extension);
-    result= sqrf_norm_sub (f, PPalpha, myrandom, s, g, R);
+    result= norm (f, PPalpha, myrandom, s, g, R, true);
   }
   else
   {
     FFGenerator myrandom;
-    result= sqrf_norm_sub (f, PPalpha, myrandom, s, g, R);
+    result= norm (f, PPalpha, myrandom, s, g, R, true);
   }
   return result;
@@ -323 +341 @@
       oldR= R;
       //TODO normalize i.getItem over K(R)?
-      (void) sqrf_norm (i.getItem(), R, Extension, s, g, R);
+      (void) sqrfNorm (i.getItem(), R, Extension, s, g, R);
 
       backSubst.insert (s);
@@ -473 +491 @@
   }
 
-  sqrfFactors= sqrf_norm (f, Rstar, vminpoly, s, g, R);
-
-  if (getCharacteristic() > 0)
-  {
-    if (sqrfFactors.getFirst().factor().inCoeffDomain())
-      sqrfFactors.removeFirst();
-
-    Variable X;
-    for (iter= sqrfFactors; iter.hasItem(); iter++)
-    {
-      if (hasFirstAlgVar (iter.getItem().factor(), X))
-      {
-        // factorize over alg.extension with X
-        tmp= factorize (iter.getItem().factor(), X);
-      }
+  CFGenerator * Gen;
+  if (getCharacteristic() == 0)
+    Gen= CFGenFactory::generate();
+  else if (degree (vminpoly) > 0)
+    Gen= AlgExtGenerator (vminpoly).clone();
+  else
+    Gen= CFGenFactory::generate();
+
+  CFFList LL= CFFList (CFFactor (f, 1));
+
+  Variable X;
+  do
+  {
+    tmp= CFFList();
+    for (iter= LL; iter.hasItem(); iter++)
+    {
+      f= iter.getItem().factor();
+      sqrfFactors= norm (f, Rstar, *Gen, s, g, R, false);
+
+      if (hasFirstAlgVar (R, X))
+        Factorlist= factorize (R, X);
       else
-      {
-        // factorize over k
-        tmp= factorize (iter.getItem().factor(), true);
-      }
-      if (tmp.getFirst().factor().inCoeffDomain())
-        tmp.removeFirst();
-      for (iter2= tmp; iter2.hasItem(); iter2++)
-        Factorlist= append (Factorlist, iter2.getItem());
-    }
-  }
-  else
-    Factorlist= factorize (R, true);
-
-  if (!Factorlist.getFirst().factor().inCoeffDomain())
-    Factorlist.insert (CFFactor (1, 1));
-  if (Factorlist.length() == 2 && Factorlist.getLast().exp() == 1)
-  {
-    f= backSubst (f, backSubsts, Astar);
-    f *= bCommonDen (f);
-    f= Prem (f, as);
-    f /= vcontent (f, as.getFirst().mvar());
-
-    L.append(CFFactor(f,1));
-  }
-  else
-  {
-    g= f;
-    for (iter= Factorlist; iter.hasItem(); iter++)
-    {
-      CanonicalForm fnew= iter.getItem().factor();
-      if (fnew.level() < Rstar.level()) //factor is a constant from the function field
-        continue;
+        Factorlist= factorize (R);
+
+      if (!Factorlist.getFirst().factor().inCoeffDomain())
+        Factorlist.insert (CFFactor (1, 1));
+      if (Factorlist.length() == 2 && Factorlist.getLast().exp() == 1)
+      {
+        f= backSubst (f, backSubsts, Astar);
+        f *= bCommonDen (f);
+        f= Prem (f, as);
+        f /= vcontent (f, as.getFirst().mvar());
+
+        L.append (CFFactor (f, 1));
+        break;
+      }
       else
       {
-        fnew= fnew (g.mvar() + s*Rstar.mvar(), g.mvar());
-        fnew= reduce (fnew, Rstar);
-      }
-
-      h= alg_gcd (g, fnew, Rstarlist);
-      numinv= QuasiInverse (Rstar, alg_LC (h, algExtLevel), Rstar.mvar());
-      h *= numinv;
-      h= Prem (h, Rstarlist);
-      h /= vcontent (h, Rstar.mvar());
-
-      if (h.level() >= Rstar.level())
-      {
-        g= divide (g, h, Rstarlist);
-        h= backSubst (h, backSubsts, Astar);
-        h= Prem (h, as);
-        h *= bCommonDen (h);
-        h /= vcontent (h, as.getFirst().mvar());
-        L.append (CFFactor (h, 1));
-      }
-    }
-    // we are not interested in a
-    // constant (over K_r, which can be a polynomial!)
-    if (degree (g, f.mvar()) > 0)
-      L.append (CFFactor (g, 1));
-  }
-  CFFList LL;
-  if (getCharacteristic() > 0) //do I really need this part?
-  {
-    CFFListIterator i=L;
-    CanonicalForm c_fac=1;
-    CanonicalForm c;
-    for(;i.hasItem(); i++ )
-    {
-      CanonicalForm ff=i.getItem().factor();
-      c=alg_lc(ff);
-      int e=i.getItem().exp();
-      ff/=c;
-      if (!ff.isOne()) LL.append(CFFactor(ff,e));
-      while (e>0) { c_fac*=c;e--; }
-    }
-    if (!c_fac.isOne()) LL.insert(CFFactor(c_fac,1));
-  }
-  else
-  {
-    LL=L;
-  }
+        g= f;
+        for (iter2= Factorlist; iter2.hasItem(); iter2++)
+        {
+          CanonicalForm fnew= iter2.getItem().factor();
+          if (fnew.level() < Rstar.level()) //factor is a constant from the function field
+            continue;
+          else
+          {
+            fnew= fnew (g.mvar() + s*Rstar.mvar(), g.mvar());
+            fnew= reduce (fnew, Rstar);
+          }
+
+          h= alg_gcd (g, fnew, Rstarlist);
+          numinv= QuasiInverse (Rstar, alg_LC (h, algExtLevel), Rstar.mvar());
+          h *= numinv;
+          h= Prem (h, Rstarlist);
+          h /= vcontent (h, Rstar.mvar());
+
+          if (h.level() >= Rstar.level())
+          {
+            g= divide (g, h, Rstarlist);
+            if (degree (h) == 1 || iter2.getItem().exp() == 1)
+            {
+              h= backSubst (h, backSubsts, Astar);
+              h= Prem (h, as);
+              h *= bCommonDen (h);
+              h /= vcontent (h, as.getFirst().mvar());
+              L.append (CFFactor (h, 1));
+            }
+            else
+              tmp.append (CFFactor (h, iter2.getItem().exp()));
+          }
+        }
+      }
+    }
+    LL= tmp;
+    (*Gen).next();
+  }
+  while (!LL.isEmpty());
 
   if (!isRat && getCharacteristic() == 0)
     Off (SW_RATIONAL);
 
-  return LL;
+  delete Gen;
+
+  return L;
 }
 
@@ -816 +817 @@
     factor= M (factor);
     transform.append (factor);
-    transform= charSetViaModCharSet (transform, false);
+    transform= modCharSet (transform, false);
     for (i= transform; i.hasItem(); i++)
     {

factory/facAlgFuncUtil.cc

@@ -20 +20 @@
 #include "cf_assert.h"
 
+#include "canonicalform.h"
 #include "facAlgFuncUtil.h"
 #include "cfCharSetsUtil.h"
@@ -93 +94 @@
 }
 
-// // missing class: IntGenerator:
-bool IntGenerator::hasItems() const
-{
-    return 1;
-}
-
-CanonicalForm IntGenerator::item() const
-//int IntGenerator::item() const
-{
-  //return current; //CanonicalForm( current );
-  return mapinto (CanonicalForm (current));
-}
-
-void IntGenerator::next()
-{
-    current++;
-}
-
 CanonicalForm alg_lc (const CanonicalForm & f)
 {
@@ -140 +123 @@
   CFListIterator j= b;
   CanonicalForm result= f, tmp, powj;
-  for (CFListIterator i= a; i.hasItem() && j.hasItem(); i++, j++)
-  {
-    if (!isFunctionField)
-      result= result (j.getItem(), i.getItem().mvar());
-    else
-    {
-      tmp= j.getItem();
-      j++;
-      powj= power (j.getItem(), degree (result, i.getItem().mvar()));
-      result= evaluate (result, tmp, j.getItem(), powj, i.getItem().mvar());
-
-      if (fdivides (powj, result, tmp))
-        result= tmp;
-
-      result /= vcontent (result, Variable (i.getItem().level() + 1));
+  CFListIterator i= a;
+  int length= a.length();
+  int count= 0;
+  for (; i.hasItem() && j.hasItem(); i++, j++, count++)
+  {
+    if (length - count == 2)
+    {
+      if (!isFunctionField)
+      {
+        result= result (b.getLast(), a.getLast().mvar());
+        result= result (j.getItem(), i.getItem().mvar());
+        break;
+      }
+      else
+      {
+        tmp= b.getLast();
+        j++;
+        j++;
+        powj= power (tmp, degree (result, a.getLast().mvar()));
+        result= evaluate (result, j.getItem(), tmp, powj, a.getLast().mvar());
+
+        if (fdivides (powj, result, tmp))
+          result= tmp;
+
+        result /= vcontent (result, Variable (a.getLast().level() + 1));
+        j--;
+        j--;
+        tmp= j.getItem();
+        j++;
+        powj= power (j.getItem(), degree (result, i.getItem().mvar()));
+        result= evaluate (result, tmp, j.getItem(), powj, i.getItem().mvar());
+
+        if (fdivides (powj, result, tmp))
+          result= tmp;
+
+        result /= vcontent (result, Variable (i.getItem().level() + 1));
+        break;
+      }
+    }
+    else
+    {
+      if (!isFunctionField)
+        result= result (j.getItem(), i.getItem().mvar());
+      else
+      {
+        tmp= j.getItem();
+        j++;
+        powj= power (j.getItem(), degree (result, i.getItem().mvar()));
+        result= evaluate (result, tmp, j.getItem(), powj, i.getItem().mvar());
+
+        if (fdivides (powj, result, tmp))
+          result= tmp;
+
+        result /= vcontent (result, Variable (i.getItem().level() + 1));
+      }
     }
   }

factory/facAlgFuncUtil.h

@@ -18 +18 @@
 #ifndef FAC_ALG_FUNC_UTIL_H
 #define FAC_ALG_FUNC_UTIL_H
-
-#include "cf_generator.h"
-
-
-// missing class: IntGenerator:
-class IntGenerator : public CFGenerator
-{
-private:
-    int current;
-public:
-    IntGenerator() : current(0) {}
-    ~IntGenerator() {}
-    bool hasItems() const;
-    void reset() { current = 0; }
-    CanonicalForm item() const;
-    void next();
-    void operator++ () { next(); }
-    void operator++ ( int ) { next(); }
-};
 
 CFFList