Changeset a0b5e2 in git for Singular/LIB

Timestamp:

Sep 20, 2010, 6:47:00 PM (14 years ago)

Author:

Hans Schoenemann <hannes@…>

Branches:

(u'fieker-DuVal', '117eb8c30fc9e991c4decca4832b1d19036c4c65')(u'spielwiese', '38dfc5131670d387a89455159ed1e071997eec94')

Children:

50b025ceafb1c25958940abd4fee0a82510cba8e

Parents:

dec1024e771ce38246bebbcab5f04dba4465e82d

Message:

the pending changes for monomial.lib

git-svn-id: file:///usr/local/Singular/svn/trunk@13231 2c84dea3-7e68-4137-9b89-c4e89433aadc

File:

• Singular/LIB/monomial.lib (modified) (18 diffs)

Singular/LIB/monomial.lib

@@ -16 +16 @@
  (radical, intersection, quotient...).
 
+LITERATURE: Miller, Ezra  and Sturmfels, Bernd: Combinatorial Commutative Algebra,
+            Springer 2004
+
 PROCEDURES:
  isMonomial(id);       checks whether an ideal id is monomial
@@ -31 +34 @@
  isirreducibleMon(id); checks whether a monomial ideal id is irreducible
  isartinianMon(id);    checks whether a monomial ideal id is artininan
- isgenericMon(id);     checks whether a monomial ideal id is generic
+ isgenericMon(id);     checks whether a monomial ideal id is generic, i.e.,
+                       no two  minimal generators of it agree in the exponent
+                       of any variable that actually appears in both of them.
  dimMon(id);           dimension of a monomial ideal id
  irreddecMon(id,..);   computes the irreducible decomposition of a monomial
@@ -47 +52 @@
 "
 USAGE:    checkIdeal (I); I ideal.
-RETURN:   1, if ideal is generated by monomials; 0, otherwise.
+RETURN:   1, if the given generators of I are monomials; 0, otherwise.
 "
 // Aqui NO estoy quitando el caso de que el ideal sea el trivial.
@@ -68 +73 @@
 USAGE:    quotientIdealMon(I,f); I ideal, f polynomial.
 RETURN:   an ideal, the quotient ideal I:(f).
-ASSUME:   I is an ideal generated by a list of monomials and f is a monomial
+ASSUME:   I is an ideal given by a list of monomials and f is a monomial
           of the basering.
 "
@@ -211 +216 @@
   // Si no tienen el mismo numero de generadores, no pueden ser iguales; ya
   // que vienen dados por el sistema minimal de generadores.
-  if (size(I) <> size(J))
+  if (ncols(I) <> ncols(J))
   {
     return(0);
@@ -507 +512 @@
 "
 USAGE:    isMinimal (I); I ideal.
-RETURN:   1, if the generators of I are the minimal ones;
+RETURN:   1, if the given generators of I are the minimal ones;
           0 & minimal generators of I, otherwise.
-ASSUME:   I is an ideal of the basering generated by monomials.
+ASSUME:   I is an ideal of the basering given by monomial generators.
 "
 {
@@ -548 +553 @@
         I = J;
         i--;
-        sizI = size(I);
+        sizI = ncols(I);
       }
     }
@@ -568 +573 @@
 RETURN:   a list, 1 & the minimal generators of I, if I is a monomial ideal;
           0, otherwise.
-ASSUME:   I is an ideal of the basering which is not generated by
+ASSUME:   I is an ideal of the basering whose given generators are not
           monomials.
 NOTE:     this procedure is NOT Grobner free and should be used only if the
-          ideal has non-monomial generators (use first checkIdeal)
+          given generators are not monomials. (use first checkIdeal)
 "
 {
@@ -685 +690 @@
 "USAGE:    minbaseMon (I); I ideal.
 RETURN:   an ideal, the minimal monomial generators of I.
-          (-1 if the generators of I are not monomials)
+          (-1 if the given generators of I are not monomials)
 ASSUME:   I is an  ideal generated by a list of monomials of the basering.
 EXAMPLE:  example minbaseMon; shows an example.
@@ -697 +702 @@
   if (control == 0)
   {
-    return (-1);
+    ERROR ("the ideal is not monomial");
   }
   // Quitamos los ceros del sistema de generadores.
@@ -945 +950 @@
 ASSUME:   I,J are monomial ideals of the basering.
 NOTE:     the minimal monomial generating set is returned.
+          USING THE SINGULAR COMMAND 'intersect' IS USUALLY FASTER
 EXAMPLE:  example intersectMon; shows some examples
 "
@@ -1069 +1075 @@
     {
       ERROR ("the second ideal is not monomial.");
-      return (-1);
     }
     else
@@ -2652 +2657 @@
   }
   // Generico
-  sizI = size(I);
+  sizI = ncols(I);
   if (genericlist[1] == 0)
   {
@@ -3080 +3085 @@
   {
     expartI = leadexp(artI[1]);
-    if (size(artI) <> 1)
-    {
-      artI = artI[2..size(artI)];
+    if (ncols(artI) <> 1)
+    {
+      artI = artI[2..ncols(artI)];
     }
     // Hay que distinguir T_1 y T_2. Para ello se comparar vectores
@@ -3553 +3558 @@
   {
     artI = sort(artI)[1];
-    int sizartI = size(artI);
+    int sizartI = ncols(artI);
     for (i = 1 ; i <= sizartI - 1 ; i ++)
     {
@@ -3577 +3582 @@
   poly comp;
   intvec exp;
-  int sizIrred = size(irredDec);
+  int sizIrred = ncols(irredDec);
   ideal auxIdeal;
   for (i = 1 ; i <= sizIrred ; i ++)
@@ -3634 +3639 @@
           (returns -1 if I is not a monomial ideal).
 ASSUME:   I is a monomial ideal of the basering k[x(1)..x(n)].
-NOTE:     This procesure returns the irreducible decomposition of I.
+NOTE:     This procedure returns the irreducible decomposition of I,
+          i.e., the unique irredundant decomposition of I into irreducible
+          monomial ideals.
           One may call the procedure with different algorithms using
           the optional argument 'alg':
@@ -3739 +3746 @@
           (returns -1 if I is not a monomial ideal).
 ASSUME:   I is a monomial ideal of the basering k[x(1)..x(n)].
-NOTE:     This procesure returns a minimal primary decomposition of I.
+NOTE:     This procedure returns a minimal primary decomposition of I.
           One may call the procedure with different algorithms using
           the optional argument 'alg':