Changeset 078a4a in git for Singular/LIB/arnoldclassify.lib

Timestamp:

Jan 18, 2019, 10:34:56 AM (5 years ago)

Author:

Hans Schoenemann <hannes@…>

Branches:

(u'spielwiese', 'fe61d9c35bf7c61f2b6cbf1b56e25e2f08d536cc')

Children:

2986f2519b013685239f8f01cce4e34349a4a8b4937c89ec020469703d18b67056c4ad5c6dbf4459

Parents:

69b0fe5724f956a5da5de2c12339c615ec66a644

Message:

fix: doc (arnoldclassify.lib)

File:

• Singular/LIB/arnoldclassify.lib (modified) (20 diffs)

Singular/LIB/arnoldclassify.lib

@@ -66 +66 @@
 proc arnoldClassify( poly fPoly )
 "USAGE:   arnoldClassify (f); f poly
-ASSUME:  The basering is local of characteristic at most 13 and f defines an
+ASSUME:  The basering is local of characteristic 0 and f defines an
          isolated singularity from Arnol'd's list of corank at most 2.
-COMPUTE: singularity class respect to right equivalence and
+COMPUTE: singularity class with respect to right equivalence and
          invariants used in the process of classification
 RETURN:  Singularity class of f of type singclass containing
@@ -178 +178 @@
 {
 //* Classifies Singularities of Corank 2; Series D,J,E,W,X,Y,Z
- def br = basering;
 
 //* Zero 4-jet is no listed singularity
@@ -227 +226 @@
 
   //* Reduce number of variables
-  def br = basering;
-  list L = ringlist(br);
+  def @br = basering;
+  list L = ringlist(@br);
   if( size(L[1]) == 0 )
-  { ring redbr = char(basering), (x(1..f.Corank)), (c,ds); }
+  { ring red@br = char(basering), (x(1..f.Corank)), (c,ds); }
   else{
     number m = leadcoef(L[1][4][1]);
-    ring redbr = (char(basering),t), (x(1..f.Corank)), (c,ds);
-    number m = imap(br, m);
+    ring red@br = (char(basering),t), (x(1..f.Corank)), (c,ds);
+    number m = imap(@br, m);
     minpoly = m;
   }
-   map MapReduce = br, maxideal(1);
+   map MapReduce = @br, maxideal(1);
   poly fPoly = MapReduce( fPoly );
  }
@@ -411 +410 @@
    f.Class = "Y["+string(f.k)+","+string(f.r)+","+string(f.s)+"]";
    f.Modality = 3*f.k - 2;
+   f.NormalForm, f.Restrictions = NormalFormAndRestrictionsDB(f.Series);
    return( f );
   }
@@ -427 +427 @@
    f.Class = "Y["+string(f.k)+","+string(f.r)+","+string(f.s)+"]";
    f.Modality = 3*f.k - 2;
+   f.NormalForm, f.Restrictions = NormalFormAndRestrictionsDB(f.Series);
    return( f );
   }
@@ -895 +896 @@
 ASSUME:  base ring is local, f in maxideal(2) has isolated critical point at 0
 COMPUTE: result of Splitting Lemma applied to f
-RETURN:  poly g in maxideal(3) right equivalent to f
+RETURN:  polynomial g in maxideal(3) right equivalent to f
 EXAMPLE: example arnoldMorseSplit; shows an example
 "
 {
 //* save basering
- def br = basering;
+ def @br = basering;
  int n = nvars(basering);
 
@@ -914 +915 @@
 //* requirement for procedure morse_arnold
  ring ring_ext = char(basering), (x(1..n)), (c, ds);
- map Phi = br, maxideal(1);
+ map Phi = @br, maxideal(1);
 
 
@@ -921 +922 @@
 
 //* Define inverse map to map f back into original ring
- setring br;
+ setring @br;
  map Phi_inverse = ring_ext, maxideal(1);
 
@@ -950 +951 @@
 
 //* save basering;
- def br = basering;
+ def @br = basering;
  n = nvars(basering);
 
@@ -993 +994 @@
 
    //* Find coordinate change Phi2 such that Q(0) != 0
-   Phi2 = br, maxideal(1);  //* Identity
+   Phi2 = @br, maxideal(1);  //* Identity
    while( Q == 0 && i<n && k <= n ){
     B2 = maxideal(1);
     B2[k]= var(k)+ var(i);
-    Phi2 = br, B2;
+    Phi2 = @br, B2;
     imagef = Phi2( f );
     Q = Coeff( jet(imagef,2), var(i), var(i)^2);
@@ -1012 +1013 @@
      B2 = maxideal(1);
      B2[i] = var(i) - P;
-     Phi2 = br, B2;
+     Phi2 = @br, B2;
      f = Phi2(f);
      f = jet(f, Determinacy);
@@ -1022 +1023 @@
  i = i+1;
  }
- Phi = br, B1;
+ Phi = @br, B1;
  f = Phi(f);
  return( f );
@@ -1060 +1061 @@
 
 //* save basering;
- def br = basering;
+ def @br = basering;
  n = nvars(basering);
 
@@ -1081 +1082 @@
 
 //* Reorder variables
- map Phi = br, B;
+ map Phi = @br, B;
  return (Phi(f));
 }
@@ -1148 +1149 @@
 proc arnoldDeterminacy( I, list # )
 "USAGE:   arnoldDeterminacy( I[, m]); I poly or ideal, m int.
-ASSUME:  the basering is local, I is (the Jacobian ideal of) a poly f
+ASSUME:  the basering is local, I is the Jacobian ideal of a polynomial f
          with isolated critical point at 0, m is the Milnor number of f
 COMPUTE: determinacy bound k for f w.r.t. right equivalence
-RETURN:  int k s.th. f is right-k-determined, -1 for infinity
+RETURN:  integer k s.th. f is right-k-determined, -1 for infinity
 NOTE:    uses [Cor. A.9.7,GP12]
 EXAMPLE: example arnoldDeterminacy; shows an example"
@@ -1422 +1423 @@
   if(size(polys) == 0 ){
     //* Define ring for the NF; NF given in C(x,y)
-    def br = basering;
+    def @br = basering;
       if(defined(RingNF) != 0 ) { kill RingNF; }
     ring RingNF=char(basering),(x,y),(c, ds);
-    map Conv = br,maxideal(1);
+    map Conv = @br,maxideal(1);
 
     string nf_str = specialformDB(Series);
@@ -1439 +1440 @@
 
    //* Define ring for the NF; NF given in C(x,y)
-    def br = basering;
+    def @br = basering;
      if(defined(RingNF) != 0 ) { kill RingNF; }
      ring RingNF=char(basering),(x,y),(c, ds);
-     map Conv = br,maxideal(1);
+     map Conv = @br,maxideal(1);
 
    //* Map Polynomial parameter
@@ -1479 +1480 @@
 
  //* Map poly nf back to basering;
- setring br;
+ setring @br;
  map ConvBack = RingNF, maxideal(1);
   return( ConvBack(nf) );
@@ -1739 +1740 @@
         f.SpecialForm = \"((x + y^k)^2 + y^(2*k+s))*(x2 + y^(2*k+r))\";
         f.Restrictions = \"(jet(a,0)!=0)&&(deg(a)<=(k-2))&&(k>1)&&(jet(b,0)!=0)
-        &&(1<=s)&&(s<=7)\";";
+        &&(1<=s)&&(s<=r)\";";
         write(l, "Y[k,r,s]", s);
 
@@ -1751 +1752 @@
         f.NormalForm = \" x^(4+r)+ a(y)*x2*y2 + y^(4+s)\";
         f.SpecialForm = \" x^(4+r)+ x2*y2 + y^(4+s)\";
-        f.Restrictions = \"(deg(a)==0)&&(jet(a,0)!=0)&&(1<=s)&&(s<=7)\";";
+        f.Restrictions = \"(deg(a)==0)&&(jet(a,0)!=0)&&(1<=s)&&(s<=r)\";";
         write(l, "Y[1,r,s]", s);