Changeset 60544d in git

Timestamp:

Feb 9, 2008, 12:28:01 AM (15 years ago)

Author:

Viktor Levandovskyy <levandov@…>

Branches:

(u'spielwiese', '91fdef05f09f54b8d58d92a472e9c4a43aa4656f')

Children:

b0db25abf3084c7d7d01f25d0aba758412326e95

Parents:

093f30ed98c16ff1ec739d588efdfea696a6f4b6

Message:

*levandov: fixes and updates


git-svn-id: file:///usr/local/Singular/svn/trunk@10574 2c84dea3-7e68-4137-9b89-c4e89433aadc

Location:

Singular/LIB

Files:

• dmodapp.lib (modified) (7 diffs)
• nchomolog.lib (modified) (4 diffs)
• ratgb.lib (modified) (9 diffs)

Singular/LIB/dmodapp.lib

@@ -1 +1 @@
 //////////////////////////////////////////////////////////////////////////////
-version="$Id: dmodapp.lib,v 1.2 2008-02-05 22:44:29 levandov Exp $";
+version="$Id: dmodapp.lib,v 1.3 2008-02-08 23:28:01 levandov Exp $";
 category="Noncommutative";
 info="
@@ -25 +25 @@
 AUXILIARY PROCEDURES:
 
-Appell(a,b,c,d);      create an ideal annihilating Appel F4 function
+AppelF1();      create an ideal annihilating Appel F1 function
+AppelF2();      create an ideal annihilating Appel F2 function
+AppelF4();      create an ideal annihilating Appel F4 function
 
 SEE ALSO: dmod_lib, gmssing_lib
@@ -143 +145 @@
 
 
-proc Appel(number a,b,c,d)
-{
+proc AppelF1()
+//(number a,b,c,d)
+{
+  // Appel F1, d = b', SST p.48
+  ring @r = (0,a,b,c),(x,y,Dx,Dy),(a(0,0,1,1),dp);
+  matrix @D[4][4];
+  @D[1,3]=1; @D[2,4]=1;
+  def @S = nc_algebra(1,@D);
+  setring @S;
+  ideal IAppel1 =
+    (x*Dx)*(x*Dx+y*Dy+c-1) - x*(x*Dx+y*Dy+a)*(x*Dx+b),
+    (y*Dy)*(x*Dx+y*Dy+c-1) - y*(x*Dx+y*Dy+a)*(x*Dx+d),
+    (x-y)*Dx*Dy - d*Dx + b*Dy;
+  export IAppel1;
+  kill @r;
+  return(@S);
+}
+example
+{
+  "EXAMPLE:"; echo = 2;
+  ring r = 0,x,dp;
+  def A = AppelF1(); //(1,2,3,4);
+  setring A;
+  IAppel1;
+}
+
+proc AppelF2()
+//(number a,b,c)
+{
+  // Appel F2, c = b', SST p.85
+  ring @r = (0,a,b,c),(x,y,Dx,Dy),(a(0,0,1,1),dp);
+  matrix @D[4][4];
+  @D[1,3]=1; @D[2,4]=1;
+  def @S = nc_algebra(1,@D);
+  setring @S;
+  ideal IAppel2 =
+    (x*Dx)^2 - x*(x*Dx+y*Dy+a)*(x*Dx+b),
+    (y*Dy)^2 - y*(x*Dx+y*Dy+a)*(y*Dy+c);
+  export IAppel2;
+  kill @r;
+  return(@S);
+}
+example
+{
+  "EXAMPLE:"; echo = 2;
+  ring r = 0,x,dp;
+  def A = AppelF2(); //(1,2,3,4);
+  setring A;
+  IAppel2;
+}
+
+proc AppelF4()
+//number a,b,c,d - ?
+{
+  // Appel F4, d = c', SST, p. 39
   ring @r = (0,a,b,c,d),(x,y,Dx,Dy),(a(0,0,1,1),dp);
   matrix @D[4][4];
@@ -150 +205 @@
   def @S = nc_algebra(1,@D);
   setring @S;
-  ideal IAppel =
+  ideal IAppel4 =
     Dx*(x*Dx+c-1) - x*(x*Dx+y*Dy+a)*(x*Dx+y*Dy+b),
     Dy*(y*Dy+d-1) - y*(x*Dx+y*Dy+a)*(x*Dx+y*Dy+b);
-  export IAppel;
+  export IAppel4;
   kill @r;
   return(@S);
@@ -161 +216 @@
   "EXAMPLE:"; echo = 2;
   ring r = 0,x,dp;
-  def Ap = Appel(1,2,3,4);
-  setring Ap;
-  IAppel;
+  def A = AppelF4(); //(1,2,3,4);
+  setring A;
+  IAppel4;
 }
 
@@ -172 +227 @@
   /*  for simplicity : later check attrib */
   /* returns -1 if true */
-  I = groebner(I);
+  if (attrib(I,"isSB")!=1)
+  {
+    I = groebner(I);
+  }
   matrix @M = matrix(I);
   matrix @F[1][1] = F;
@@ -196 +254 @@
 "USAGE:  DLoc(I, F);  I an ideal, F a poly
 RETURN: nothing (exports objects instead)
-ASSUME: the basering is a Weyl algebra
+ASSUME: the basering is a Weyl algebra and I is F-saturated
 PURPOSE: compute the presentation of the localization of D/I w.r.t. f^s
 NOTE:    In the basering, the following objects are exported:

Singular/LIB/nchomolog.lib

@@ -1 @@
-version="$Id: nchomolog.lib,v 1.6 2007-12-11 12:00:01 levandov Exp $";
+version="$Id: nchomolog.lib,v 1.7 2008-02-08 23:28:01 levandov Exp $";
 category="Noncommutative";
 info="
@@ -258 +258 @@
 { "EXAMPLE:"; echo = 2;
   ring R     = 0,(x,y),dp;
-  poly F    = x2-y3;
+  poly F    = x2-y2;
   def A = annfs(F);
   setring A;
   matrix M[1][size(LD)] = LD;
-  int i = 1;
-  matrix Ps = M;
-  module E1  = ncExt_R(1,M);
-  E1;
+  print(ncExt_R(1,M)); // hence the Ext^1 is zero
+  module E  = ncExt_R(2,M); // right module
+  print(E);
   def Aop = opposite(A);
   setring Aop;
-  module Psop = oppose(A,Ps);
-  module T1  = ncExt_R(1,Psop);
-  T1;
+  module Eop = oppose(A,E);
+  module T1  = ncExt_R(2,Eop);
+  setring A;
+  module T1 = oppose(Aop,T1);
+  print(T1); // this is a left module Ext^2(Ext^2(M,A),A)
 }
 
@@ -541 +542 @@
 
 proc dmodoublext(module M, list #)
-{
-  // if a list is nonempty and contains an integer N, n = N; otherwise n = nvars/2
-  // assume: basering is a Weyl algebra
-  // returns Ext^n_D(Ext^n_D(M,D),D), that is 
-  // computes the "dual" of the "dual" of a d-mod M (for n = nvars/2)
+"USAGE:   dmodoublext(M [,i]);  M module, i optional int 
+COMPUTE:  a presentation of Ext^i(Ext^i(M,D),D); for basering D
+RETURN:   left module
+NOTE: by default, i is set to the integer part of the half of number of variables of D
+@* for holonomic modules over Weyl algebra, the double ext is known to be holonomic
+EXAMPLE: example dmodoublext; shows an example
+"
+{
+  // assume: basering is a Weyl algebra?
   def save = basering; 
   setring save;
-  int n = nvars(save); n = n div 2;
+  // if a list is nonempty and contains an integer N, n = N; otherwise n = nvars/2
+  int n;
+  if (size(#) > 0)
+  {
+    //    if (typeof(#) == "int")
+    //    {
+      n = int(#[1]);
+      //    }
+//     else
+//     {
+//       ERROR("the optional argument expected to have type int");
+//     }
+  }
+  else
+  {
+    n = nvars(save); n = n div 2;
+  }
+  // returns Ext^i_D(Ext^i_D(M,D),D), that is 
+  // computes the "dual" of the "dual" of a d-mod M (for n = nvars/2)
   module Md = ncExt_R(n,M); // right module
   // no prune yet!
@@ -581 +604 @@
   ideal I = Dx*(x2-y3),Dy*(x2-y3);
   I = groebner(I);
-  print(dmodoublext(I));
+  print(dmodoublext(I,1));
+  print(dmodoublext(I,2));
 }
 

Singular/LIB/ratgb.lib

@@ -1 +1 @@
 //////////////////////////////////////////////////////////////////////////////
-version="$Id: ratgb.lib,v 1.10 2008-02-05 22:44:30 levandov Exp $";
+version="$Id: ratgb.lib,v 1.11 2008-02-08 23:28:01 levandov Exp $";
 category="Noncommutative";
 info="
@@ -15 +15 @@
 
 //static 
-proc rm_content_id(ideal J)
-"USAGE:  rm_content_id(I);  I an ideal
-RETURN:  ideal
+proc rm_content_id(def J)
+"USAGE:  rm_content_id(I);  I an ideal/module
+RETURN:  the same type as input
 PURPOSE: remove the content of every generator of I
 EXAMPLE: example rm_content_id; shows examples
 "
 {
-  ideal I = J;
+  def  I = J;
   int i;
-  int s = size(I);
+  int s = ncols(I);
   for (i=1; i<=s; i++)
   {
@@ -41 +41 @@
   I;
   rm_content_id(I);
-}
-
-proc ratstd(ideal I, int is)
-"USAGE:  ratstd(I, n);  I an ideal, n an integer
+  module M = I[1]*gen(1), I[2]*gen(2);
+  print(rm_content_id(M));
+}
+
+proc ratstd(def I, int is)
+"USAGE:  ratstd(I, n);  I an ideal/module, n an integer
 RETURN:  ring
 PURPOSE: compute the Groebner basis of I in the Ore localization of
@@ -154 +156 @@
   // 2. preprocess input with rm_content_id
   setring @RAT;
-  ideal CI = imap(save,I);
+  dbprint(ppl-1, @RAT);
+  //  ideal CI = imap(save,I);
+  def CI = imap(save,I);
   CI = rm_content_id(CI);
+  dbprint(ppl-1, CI);
 
   dbprint(ppl,"// -3- running groebner");
   // 3. compute G = GB(I) wrt. the elim. ord. for D
   setring save;
-  ideal CI = imap(@RAT,CI);
+  //  ideal CI = imap(@RAT,CI);
+  def CI = imap(@RAT,CI);
   option(redSB);
   option(redTail);
-  ideal G = groebner(CI); // although slimgb looks better
+  //  ideal G = groebner(CI); // although slimgb looks better
+  def G = groebner(CI);
   G = simplify(G,2); // to be sure there are no 0's
+  dbprint(ppl-1, G);
 
   dbprint(ppl,"// -4- postprocessing with content");
   // 4. postprocess the output with 1) rm_content_id,  2) lm-minimization;
   setring @RAT;
-  ideal CG = imap(save,G);
+  // ideal CG = imap(save,G);
+  def CG = imap(save,G);
   CG = rm_content_id(CG);
   CG = simplify(CG,2);
+  dbprint(ppl-1, CG);
 
   // warning: a bugfarm! in this ring, the ordering might change!!! (see appelF4)
@@ -181 +191 @@
   G = imap(@RAT,CG);
   int sG  = ncols(G);
-  ideal LG;
-  for (i=1; i<= sG; i++)
-  {
-    LG[i] = lead(G[i]);
-  }
+  //  ideal LG;
+  def LG = G;
+   for (i=1; i<= sG; i++)
+   {
+     LG[i] = lead(G[i]);
+   }
   // compute the D-dimension of the ideal in the ring @RAT
   setring @RAT;
-  ideal LG = imap(save,LG);
-  ideal LGG = groebner(LG); // cosmetics
+  //  ideal LG = imap(save,LG);
+  def LG = imap(save,LG);
+  //  ideal LGG = groebner(LG); // cosmetics
+  def LGG = groebner(LG); // cosmetics
   int d = dim(LGG);
   int Ddim = d;
@@ -199 +212 @@
     printf("the K-dimension is %s",d);
   }
-  ideal SLG = simplify(LG,8+32); //contains zeros
-  setring save;
-  ideal SLG = imap(@RAT,SLG);
+  //  ideal SLG = simplify(LG,8+32); //contains zeros
+  def SLG = simplify(LG,8+32); //contains zeros
+  setring save;
+  //  ideal SLG = imap(@RAT,SLG);
+  def SLG = imap(@RAT,SLG);
   // simplify(LG,8+32); //contains zeros
   intvec islg;
@@ -229 +244 @@
   //  G = imap(@RAT,CG);
   // return the result
-  ideal pGBid = G;
+  //  ideal pGBid = G;
+  def pGBid = G;
   export pGBid;
   //  export Ddim;
   //  export Dvdim;
   setring @RAT;
-  ideal rGBid = imap(save,G);
+  //  ideal rGBid = imap(save,G);
+  def rGBid = imap(save,G);
   // CG;
   export rGBid;
@@ -245 +262 @@
 {
   "EXAMPLE:"; echo = 2;
-  ring r = 0,(k,n,K,N),(a(0,0,1,1),dp);
+  ring r = 0,(k,n,K,N),(a(0,1),dp);
   matrix D[4][4];
   D[1,3] = K;
@@ -252 +269 @@
   setring S;
   ideal I = (k+1)*K - (n-k), (n-k+1)*N - (n+1);
-  int is = 2;
+  int is = 1;
   def A  = ratstd(I,is);
   pGBid; // polynomial form