Changeset e7d857 in git for Singular/LIB/freegb.lib

Timestamp:

Mar 9, 2018, 1:34:25 PM (6 years ago)

Author:

Karim Abou Zeid <karim23697@…>

Branches:

(u'spielwiese', 'fe61d9c35bf7c61f2b6cbf1b56e25e2f08d536cc')

Children:

ce5d1bd5855860c909fa9377861c9d1b7a8e52ba

Parents:

1af34f3a9d6f48f7bc59d937c310ee496a6c7258

Message:

Add lpDivision() proc to freegb

File:

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

Singular/LIB/freegb.lib

@@ -49 +49 @@
 LIB "qhmoduli.lib"; // for Max
 LIB "bfun.lib"; // for inForm
+LIB "fpadim.lib"; // for intvec conversion
 
 proc tstfreegb()
@@ -3276 +3277 @@
 }
 
+proc lpDivision(poly p, ideal I)
+"ASSUME: I is a Groebner basis G = {g1,...,gN}, the original ring of the Letterplace ring has the name 'r' and no variable is called 'tag_i' for i in 1...N
+RETURN: list L
+NOTE: - L[1] NF(p,I)
+      - L[2] list of expressions [i,l_{ij},r_{ij}] with \sum_{i,j} l_{ij} g_i r_{ij} = p - NF(p,I)
+"
+{
+  if (p == 0 || size(I) == 0) {
+    list L = 0;
+    list empty;
+    L[2] = empty;
+    return (L);
+  }
+  poly pNF = lpNF(p,I);
+  p = p - pNF;
+
+  // make new ring
+  def save = basering;
+  int norigvars = nvars(r);
+  string tagvarstr = "(tag_1";
+  for (int i = 2; i <= size(I); i++) {
+    tagvarstr = tagvarstr + ",tag_" + string(i);
+  }
+  tagvarstr = tagvarstr + ")";
+  string field = string(ringlist(r)[1]);
+  execute("ring @tags = " + field + "," + tagvarstr + ",dp;");
+  ring @tagged = (r + @tags);
+  def @R = makeLetterplaceRing(attrib(save,"uptodeg")); setring @R;
+
+  // restore vars
+  poly p = imap(save, p);
+  poly pNF = imap(save, pNF);
+  ideal I = imap(save, I);
+  for (int i = 1; i <= size(I); i++) {
+    I[i] = I[i] + var(norigvars + i);
+  }
+
+  list summands;
+  list L = pNF;
+  poly pTaggedNF = lpNF(p,I);
+  pTaggedNF = pTaggedNF * leadcoef(p); // somehow pTaggedNF gets normalized
+  for (int i = 1; i <= size(pTaggedNF); i++) {
+    intvec iv = lp2iv(pTaggedNF[i]);
+    for (int j = 1; j <= size(iv); j++) {
+      if (iv[j] > norigvars) {
+        intvec left;
+        intvec right;
+        if (j > 1) {
+          left = iv[1..(j-1)];
+        }
+        if (j < size(iv)) {
+          right = iv[(j+1)..size(iv)];
+        }
+        list summand = (iv[j] - norigvars), leadcoef(pTaggedNF[i])*iv2lp(left), iv2lp(right);
+        summands = insert(summands, summand, size(summands));
+        break;
+      }
+    }
+  }
+
+  L[2] = summands;
+
+  setring save;
+  list L = imap(@R,L);
+  return(L);
+}
+
+proc lpGBPres2Poly(list L, ideal I)
+"ASSUME: L is a valid Groebner presentation as for example the result of lpDivision
+RETURN: poly
+NOTE: computes p = \sum_{i,j} l_{ij} g_i r_{ij} + NF(p,I) = \sum_{i} L[2][i][2] I[L[2][i][1]] L[2][i][3] + L[1]
+"
+{
+  poly p;
+  for (int i = 1; i <= size(L[2]); i++) {
+    p = p + lpMult(lpMult(L[2][i][2], I[L[2][i][1]]), L[2][i][3]);
+  }
+  p = p + L[1];
+  return (p);
+}
+
 //procedures to convert monomials into the DVec representation, all static
 ////////////////////////////////////////////////////////