Changeset 0be039 in git

Timestamp:

Mar 16, 2018, 6:27:45 PM (5 years ago)

Author:

Karim Abou Zeid <karim23697@…>

Branches:

(u'spielwiese', '0d6b7fcd9813a1ca1ed4220cfa2b104b97a0a003')

Children:

52ac0882b123798821765bb16d5ba4b371ced4cd

Parents:

95a42a2dacdcadb5c004cb3520b5c252dfe8e784df09c0184ffc4aaf31c02b8691e68734f25fc3b3

Message:

Merge branch 'lpDivision' into stable

Location:

Singular/LIB

Files:

• fpadim.lib (modified) (3 diffs)
• fpaprops.lib (modified) (13 diffs)
• freegb.lib (modified) (2 diffs)

Singular/LIB/fpadim.lib

@@ -2378 +2378 @@
   return (words);
 }
-example {
+example
+{
   "EXAMPLE:"; echo = 2;
   ring r = 0,(a,b,c),dp;
@@ -2399 +2400 @@
   return(ivL2lpI(ivMaxIdeal(d, donly)));
 }
-example {
+example
+{
   "EXAMPLE:"; echo = 2;
   ring r = 0,(a,b,c),dp;
@@ -2489 +2491 @@
   return(I);
 }
-example {
+example
+{
   "EXAMPLE:"; echo = 2;
   ring r = 0,(x,y),dp;

Singular/LIB/fpaprops.lib

@@ -19 +19 @@
 PROCEDURES:
   lpNoetherian(<GB>);     check whether A/<GB> is (left/right) noetherian
-  lpIsSemiPrime(<GB>);    check whether A/<GB> is semi prime
-  lpIsPrime(<GB>);        check whether A/<GB> is prime
+  lpIsSemiPrime(<GB>);    check whether A/<LM(GB)> is semi prime
+  lpIsPrime(<GB>);        check whether A/<LM(GB)> is prime
   lpGkDim(<GB>);          compute the Gelfand Kirillov dimension of A/<GB>
   lpGlDimBound(<GB>);     compute an upper bound for the global dimension of A/<GB>
@@ -37 +37 @@
 @*      2 right noetherian
 @*      3 noetherian
-PURPOSE: Check whether R/<G> is (left/right) noetherian, where R is the basering
+PURPOSE: Check whether A/<G> is (left/right) noetherian
 ASSUME: - basering is a Letterplace ring
 @*      - G is a Groebner basis
@@ -108 +108 @@
   return (3 - inFlag - outFlag);
 }
-example {
+example
+{
   "EXAMPLE:"; echo = 2;
   ring r = 0,(x,y),dp;
@@ -198 +199 @@
 "USAGE: lpIsSemiPrime(G); G an ideal in a Letterplace ring
 RETURN: boolean
-PURPOSE: Check whether R/<G> is semi prime, where R is the basering
+PURPOSE: Check whether A/<LM(G)> is semi prime, that is when p * (A/<LM(G)>) * p != 0 for all p in (A/<LM(G)> - {0}).
 ASSUME: - basering is a Letterplace ring
       - G is a Groebner basis
@@ -249 +250 @@
   return (1);
 }
-example {
+example
+{
   "EXAMPLE:"; echo = 2;
   ring r = 0,(x1,x2),dp;
@@ -298 +300 @@
 "USAGE: lpIsPrime(G); G an ideal in a Letterplace ring
 RETURN: boolean
-PURPOSE: Check whether R/<G> is prime, where R is the basering
+PURPOSE: Check whether A/<LM(G)> is prime, that is when p1 * (A/<LM(G)>) * p2 != 0 for all p1, p2 in (A/<LM(G)> - {0}).
 ASSUME: - basering is a Letterplace ring
       - G is a Groebner basis
@@ -362 +364 @@
   return (1);
 }
-example {
+example
+{
   "EXAMPLE:"; echo = 2;
   ring r = 0,(x,y),dp;
@@ -681 +684 @@
   return (UG);
 }
-example {
+example
+{
   "EXAMPLE:"; echo = 2;
   ring r = 0,(x,y,z),dp;
@@ -1047 +1051 @@
     for (int j = 1; j <= size(ivfi); j++) {
       int varindex = ivfi[j];
-      int subindex = lpIndexOf(s1, var(varindex));
-      if (subindex > 0) {
-        s2[subindex] = lpNF(s2[subindex],G);
-        fis = lpMult(fis, s2[subindex]);
-      } else {
-        fis = lpMult(fis, lpNF(iv2lp(varindex),G));
-      }
-      /*fis = lpNF(fis,G);*/
-      kill varindex; kill subindex;
+      if (varindex > 0) {
+        int subindex = lpIndexOf(s1, var(varindex));
+        if (subindex > 0) {
+          s2[subindex] = lpNF(s2[subindex],G);
+          fis = lpMult(fis, s2[subindex]);
+        } else {
+          fis = lpMult(fis, lpNF(iv2lp(varindex),G));
+        }
+        /*fis = lpNF(fis,G);*/
+        kill subindex;
+      }
+      kill varindex;
     } kill j;
     kill ivfi;
@@ -1065 +1072 @@
   return (fs);
 }
-example {
+example
+{
+  "EXAMPLE:"; echo = 2;
   //////// EXAMPLE A ////////
   ring r = 0,(x,y,z),dp;
@@ -1144 +1153 @@
     for (int j = 1; j <= size(ivfi); j++) {
       int varindex = ivfi[j];
-      int subindex = lpIndexOf(s1, var(varindex));
-      if (subindex > 0) {
-        tmpDegBound = tmpDegBound + deg(s2[subindex]);
-      } else {
-        tmpDegBound = tmpDegBound + 1;
-      }
-      kill varindex; kill subindex;
+      if (varindex > 0) {
+        int subindex = lpIndexOf(s1, var(varindex));
+        if (subindex > 0) {
+          tmpDegBound = tmpDegBound + deg(s2[subindex]);
+        } else {
+          tmpDegBound = tmpDegBound + 1;
+        }
+        kill subindex;
+      }
+      kill varindex;
     } kill j;
     if (tmpDegBound > maxDegBound) {
@@ -1160 +1172 @@
   // increase degbound by 50% when ideal is provided
   // needed for lpNF
-  maxDegBound = maxDegBound + maxDegBound/2;
+  maxDegBound = maxDegBound + (maxDegBound div 2);
 
   return (maxDegBound);
 }
-example {
+example
+{
   // see lpSubstitute()
 }
@@ -1187 +1200 @@
   return (maxDegBound);
 }
-example {
+example
+{
   // see lpSubstitute()
 }

Singular/LIB/freegb.lib

@@ -51 +51 @@
 LIB "qhmoduli.lib"; // for Max
 LIB "bfun.lib"; // for inForm
+LIB "fpadim.lib"; // for intvec conversion
 
 proc tstfreegb()
@@ -3278 +3279 @@
 }
 
+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);
+  } kill 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);
+  } kill 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));
+
+        kill left;
+        kill right;
+        kill summand;
+        break;
+      }
+    } kill j;
+    kill iv;
+  } kill i;
+
+  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
 ////////////////////////////////////////////////////////