Changeset ac7280 in git

Timestamp:

Sep 12, 1997, 3:33:29 PM (27 years ago)

Author:

Hans Schönemann <hannes@…>

Branches:

(u'spielwiese', 'fe61d9c35bf7c61f2b6cbf1b56e25e2f08d536cc')

Children:

8c38a0e3c9888fd679d68714485e7ebc514f933b

Parents:

2a99baf62f13066b86adaabc31f813ac7023eacf

Message:

* hannes: removed the first codim from  sing.lib


git-svn-id: file:///usr/local/Singular/svn/trunk@723 2c84dea3-7e68-4137-9b89-c4e89433aadc

File:

• Singular/LIB/sing.lib (modified) (2 diffs)

Singular/LIB/sing.lib

@@ -1 @@
-// $Id: sing.lib,v 1.5 1997-09-12 10:29:48 pohl Exp $
+// $Id: sing.lib,v 1.6 1997-09-12 13:33:29 Singular Exp $
 //system("random",787422842);
 //(GMG/BM, last modified 26.06.96)
@@ -26 +26 @@
 LIB "inout.lib";
 LIB "random.lib";
-///////////////////////////////////////////////////////////////////////////////
-
-proc codim (id1, id2)
-USAGE:   codim(id1,id2); id1,id2 ideal or module
-ASSUME:  both must be standard bases w.r.t. ordering ds or Ds or homogeneous
-         and standardbases w.r.t. ordering dp or Dp
-RETURN:  int, which is:
-         1. the codimension of id2 in id1, i.e. the vectorspace dimension of
-            id1/id2 if id2 is contained in id1 and if this number is finite
-         2. -1 if the dimension of id1/id2 is infinite
-         3. -2 if id2 is not contained in id1,
-COMPUTE: consider the two hilberseries iv1(t) and iv2(t), then, in case 1.,
-         q(t)=(iv2(t)-iv1(t))/(1-t)^n must be rational, and the result is the
-         sum of the coefficients of q(t) (n number of variables)
-NOTE:    As always, id1 and id2 must be consider as ideals in the localization
-         of the polynomial ring w.r.t. the monomial ordering
-EXAMPLE: example codim; shows an example
-{
-   ideal le1, le2;
-   intvec iv1, iv2, iv;
-   int i, d1, d2, dd, i1, i2, ia, ie;
-  //--------------------------- check id2 < id1 -------------------------------
-   le1 = lead(id1);
-   if (attrib(id1,"isSB") != 0)
-   {
-     attrib(le1,"isSB",1);
-   }
-   le2 = lead(id2);
-   if (attrib(id2,"isSB") != 0)
-   {
-     attrib(le2,"isSB",1);
-   }
-   i = size(NF(le2,le1));
-   if ( i > 0 )
-   {
-     return(-2);
-   }
-  //--------------------------- 1. check finiteness ---------------------------
-   i1 = dim(le1);
-   i2 = dim(le2);
-   if (i1 <= 0)
-   {
-     if (i2 <= 0)
-     {
-       return(vdim(le2)-vdim(le1)); 
-     }
-     else
-     {
-       return(-1);
-     }
-   }
-   if (i2 != i1)
-   {
-     return(-1);
-   }
-   if (mult(le2) != mult(le1))
-   {
-     return(-1);
-   }
-  //--------------------------- module ---------------------------------------
-   d1 = nrows(le1);
-   d2 = nrows(le2);
-   dd = 0;
-   if (d1 > d2)
-   {
-     le2=le2,maxideal(1)*gen(d1);
-     dd = -1;
-   }
-   if (d2 > d1)
-   {
-     le1=le1,maxideal(1)*gen(d2);
-     dd = 1;
-   }
-  //--------------------------- compute first hilbertseries ------------------
-   iv1 = hilb(id1,1);
-   i1 = size(iv1);
-   iv2 = hilb(id2,1);
-   i2 = size(iv2);
-   kill le1,le2;
-  //--------------------------- difference of hilbertseries ------------------
-   if (i2 > i1)
-   {
-     for ( i=1; i<=i1; i=i+1)
-     {
-       iv2[i] = iv2[i]-iv1[i];
-     }
-     ie = i2;
-     iv = iv2;
-   }
-   else
-   {
-     for ( i=1; i<=i2; i=i+1)
-     {
-       iv1[i] = iv2[i]-iv1[i];
-     }
-     iv = iv1;
-     for (ie=i1;ie>=0;ie=ie-1)
-     {
-       if (ie == 0)
-       {
-         return(0);
-       }
-       if (iv[ie] != 0)
-       {
-         break;
-       }
-     }
-   }
-   ia = 1;
-   while (iv[ia] == 0) { ia=ia+1; }
-  //--------------------------- ia <= nonzeros <= ie -------------------------
-   iv1 = iv[ia];
-   for(i=ia+1;i<=ie;i=i+1)
-   {
-     iv1=iv1,iv[i];
-   }
-  //--------------------------- compute second hilbertseries -----------------
-   iv2 = hilb(iv1);
-  //--------------------------- check finitenes ------------------------------
-   i2 = size(iv2);
-   i1 = ie - ia + 1 - i2;
-   if (i1 != nvars(basering))
-   {
-     return(-1);
-   }
-  //--------------------------- compute result -------------------------------
-   i1 = 0;
-   for ( i=1; i<=i2; i=i+1)
-   {
-     i1 = i1 + iv2[i];
-   }
-   return(i1+dd);
-}
-example
-{ "EXAMPLE:"; echo = 2;
-   ring r  = 0,(x,y,z),dp;
-   ideal j = y6,x4;
-   ideal m = x,y;
-   attrib(m,"isSB",1);  //let Singular know that ideals are a standard basis
-   attrib(j,"isSB",1);  
-   codim(m,j);          // should be 23 (Milnor number -1 of y7-x5)
-}
 ///////////////////////////////////////////////////////////////////////////////