Changeset f75297 in git for Singular/LIB/fpadim.lib

Timestamp:

Mar 4, 2011, 1:01:27 AM (13 years ago)

Author:

Viktor Levandovskyy <levandov@…>

Branches:

(u'spielwiese', 'fe61d9c35bf7c61f2b6cbf1b56e25e2f08d536cc')

Children:

8eea069dd83d32f7e8b90cd5e5ec75124c7d7903

Parents:

a8f29f505ce6c0d6ff17e0e4d9637d320299deee

Message:

*levandov: checkin from Aachen, bugfixes and improvements

git-svn-id: file:///usr/local/Singular/svn/trunk@13924 2c84dea3-7e68-4137-9b89-c4e89433aadc

File:

• Singular/LIB/fpadim.lib (modified) (9 diffs)

Singular/LIB/fpadim.lib

@@ -38 +38 @@
 @*      on. The monomial x_1*x_3*x_2 for example will be stored as (1,3,2).
 @*      Multiplication is concatenation. Note that there is no algorithm for
-@*      computing the normal form yet, but for our case it is not needed.
+@*      computing the normal form needed for our case.
 @*
 
@@ -64 +64 @@
 ivHilbert(L,n[,d]);        computes the Hilbert series of A/<L> in intvec format
 ivKDim(L,n[,d]);           computes the K-dimension of A/<L> in intvec format
+ivMis2Base(M);             computes a K-basis of the factor algebra
 ivMis2Dim(M);              computes the K-dimension of the factor algebra
 ivOrdMisLex(M);            orders a list of intvecs lexicographically
@@ -74 +75 @@
 lpDimCheck(G);             checks if the K-dimension of A/<G> is infinite
 lpKDim(G[,d,n]);           computes the K-dimension of A/<G> in lp format
+lpMis2Base(M);             computes a K-basis of the factor algebra
 lpMis2Dim(M);              computes the K-dimension of the factor algebra
 lpOrdMisLex(M);            orders an ideal of lp-monomials lexicographically
@@ -164 +166 @@
 "PURPOSE:checks, if all entries in M are variable-related
 "
-{int i,j;
+{if ((nrows(M) == 1) && (ncols(M) == 1)) {if (M[1,1] == 0){return(0);}}
+ int i,j;
   for (i = 1; i <= nrows(M); i++)
   {for (j = 1; j <= ncols(M); j++)
@@ -1229 +1232 @@
 }
 
+proc ivMis2Base(list M)
+"USAGE: ivMis2Base(M); M a list of intvecs
+RETURN: ideal, a K-base of the given algebra
+PURPOSE:Computing the K-base out of given mistletoes
+ASSUME: - The mistletoes have to be ordered lexicographically -> OrdMisLex.
+@*        Otherwise there might some elements missing.
+@*      - basering is a Letterplace ring.
+EXAMPLE: example ivMis2Base; shows examples
+"
+{
+//checkAssumptions(0,M);
+  intvec L,A;
+  if (size(M) == 0){ERROR("There are no mistletoes, so it appears your dimension is infinite!");}
+  if (isInList(L,M) > 0) {print("1 is a mistletoe, therefore 1 is the only basis element"); return(list(intvec(0)));}
+  int i,j,d,s;
+  list Rt;
+  Rt[1] = intvec(0);
+  L = M[1];
+  for (i = size(L); 1 <= i; i--) {Rt = insert(Rt,intvec(L[1..i]));}
+  for (i = 2; i <= size(M); i++)
+  {A = M[i]; L = M[i-1];
+   s = size(A);
+   if (s > size(L))
+   {d = size(L);
+    for (j = s; j > d; j--) {Rt = insert(Rt,intvec(A[1..j]));}
+    A = A[1..d];
+   }
+   if (size(L) > s){L = L[1..s];}
+   while (A <> L)
+   {Rt = insert(Rt, intvec(A));
+    if (size(A) > 1)
+    {A = A[1..(size(A)-1)];
+     L = L[1..(size(L)-1)];
+    }
+    else {break;}
+   }
+  }
+  return(Rt);
+}
+example
+{
+  "EXAMPLE:"; echo = 2;
+  ring r = 0,(x,y),dp;
+  def R = makeLetterplaceRing(5); // constructs a Letterplace ring
+  R;
+  setring R; // sets basering to Letterplace ring
+  intvec i1 = 1,2; intvec i2 = 2,1,2;
+  // the mistletoes are xy and yxy, which are already ordered lexicographically
+  list L = i1,i2;
+  ivMis2Base(L); // returns the basis of the factor algebra
+}
+
+
 proc ivMis2Dim(list M)
 "USAGE: ivMis2Dim(M); M a list of intvecs
@@ -1595 +1651 @@
 @*        degbound <= attrib(basering,uptodeg) holds.
 NOTE: - If L is the list returned, then L[1] is an integer, the K-dimension,
-@*      L[2] is an intvec, the Hilbert series and L[3] is an ideal,
+@*      L[2] is an intvec, the Hilbert series and L[3] is an ideal, 
 @*      the mistletoes
 @*    - If degbound is set, there will be a degree bound added. 0 means no
@@ -1729 +1785 @@
   // ring is not necessary
   lpKDim(G,0); // procedure without any degree bound
+}
+
+proc lpMis2Base(ideal M)
+"USAGE: lpMis2Base(M); M an ideal
+RETURN: ideal, a K-basis of the factor algebra
+PURPOSE:Computing a K-basis out of given mistletoes
+ASSUME: - basering is a Letterplace ring.
+@*      - M contains only monomials
+NOTE:   - The mistletoes have to be ordered lexicographically -> OrdMisLex.
+EXAMPLE: example lpMis2Base; shows examples
+"
+{list L;
+  L = lpId2ivLi(M);
+  return(ivL2lpI(ivMis2Base(L)));
+}
+example
+{
+  "EXAMPLE:"; echo = 2;
+  ring r = 0,(x,y),dp;
+  def R = makeLetterplaceRing(5); // constructs a Letterplace ring
+  setring R; // sets basering to Letterplace ring
+  ideal L = x(1)*y(2),y(1)*x(2)*y(3);
+  // ideal containing the mistletoes
+  lpMis2Base(L); // returns the K-basis of the factor algebra
 }
 
@@ -1968 +2048 @@
   example ivHilbert;
   example ivKDim;
+  example ivMis2Base;
   example ivMis2Dim;
   example ivOrdMisLex;
@@ -1978 +2059 @@
   example lpDimCheck;
   example lpKDim;
+  example lpMis2Base;
   example lpMis2Dim;
   example lpOrdMisLex;