Changeset 45c67dc in git for Singular/LIB/gmssing.lib

Timestamp:

Jul 20, 2009, 12:16:04 PM (15 years ago)

Author:

Viktor Levandovskyy <levandov@…>

Branches:

(u'spielwiese', 'fe61d9c35bf7c61f2b6cbf1b56e25e2f08d536cc')

Children:

645a19587ae6d80e5d860f48654600b3300248b3

Parents:

6ae83a06bcff3f02af32f42b3606969790cda282

Message:

*levandov for mschulze: small bugfix and docu improvements


git-svn-id: file:///usr/local/Singular/svn/trunk@11990 2c84dea3-7e68-4137-9b89-c4e89433aadc

File:

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

Singular/LIB/gmssing.lib

@@ -1 +1 @@
 ///////////////////////////////////////////////////////////////////////////////
-version="$Id: gmssing.lib,v 1.12 2008-10-09 09:31:57 Singular Exp $";
+version="$Id: gmssing.lib,v 1.13 2009-07-20 10:16:04 levandov Exp $";
 category="Singularities";
 
 info="
-LIBRARY:  gmssing.lib  Gauss-Manin System of Isolated Singularities
+LIBRARY:  gaussman.lib  Gauss-Manin System of Isolated Singularities
 
 AUTHOR:   Mathias Schulze, email: mschulze@mathematik.uni-kl.de
 
-OVERVIEW: A library to compute invariants related to the Gauss-Manin system
+OVERVIEW: A library to compute invariants related to the the Gauss-Manin system
           of an isolated hypersurface singularity
 
@@ -15 +15 @@
  gmsnf(p,K);                Gauss-Manin normal form of p
  gmscoeffs(p,K);            Gauss-Manin basis representation of p
- bernstein(t);              roots of the Bernstein polynomial of t
+ bernstein(t);              Bernstein-Sato polynomial of t
  monodromy(t);              Jordan data of complex monodromy of t
  spectrum(t);               singularity spectrum of t
@@ -38 +38 @@
 KEYWORDS: singularities; Gauss-Manin system; Brieskorn lattice;
           mixed Hodge structure; V-filtration; weight filtration
-          Bernstein polynomial; monodromy; spectrum; spectral pairs;
+          Bernstein-Sato polynomial; monodromy; spectrum; spectral pairs; 
           good basis
 ";
@@ -122 +122 @@
 @end format
 NOTE:     gmsbasis is a C[[s]]-basis of H'' and [t,s]=s^2
-KEYWORDS: Gauss-Manin system; Brieskorn lattice
+KEYWORDS: singularities; Gauss-Manin system; Brieskorn lattice
 EXAMPLE:  example gmsring; shows examples
 "
@@ -194 +194 @@
 
   attrib(gmsstd,"isSB",1);
-  export gmspoly, gmsjacob, gmsstd, gmsmatrix, gmsbasis;
-  if (system("with","Namespaces")) { exportto(Top, gmsmaxdeg);}
-  else { export(gmsmaxdeg);}
+  export gmspoly,gmsjacob,gmsstd,gmsmatrix,gmsbasis,gmsmaxdeg;
 
   return(G);
@@ -220 +218 @@
 RETURN:
   list nf;
-  ideal nf[1];  projection of p to <gmsbasis>C{{s}} mod s^(K+1) @*
+  ideal nf[1];  projection of p to <gmsbasis>C{{s}} mod s^(K+1)
   ideal nf[2];  p==nf[1]+nf[2]
-NOTE:     computation can be continued by setting p to nf[2][1]
+NOTE:     computation can be continued by setting p=nf[2]
+KEYWORDS: singularities; Gauss-Manin system; Brieskorn lattice
 EXAMPLE:  example gmsnf; shows examples
 "
@@ -298 +297 @@
 @format
 list l;
-  matrix l[1];  C@{@{s@}@}-basis representation of p mod s^(K+1)
+  matrix l[1];  C{{s}}-basis representation of p mod s^(K+1)
   ideal l[2];  p==matrix(gmsbasis)*l[1]+l[2]
 @end format
-NOTE:     computation can be continued by setting p to l[2]
+NOTE:     computation can be continued by setting p=l[2]
+KEYWORDS: singularities; Gauss-Manin system; Brieskorn lattice
 EXAMPLE:  example gmscoeffs; shows examples
 "
@@ -524 +524 @@
               }
             }
-          }
+          }
         }
       }
@@ -580 +580 @@
 ASSUME:   characteristic 0; local degree ordering;
           isolated critical point 0 of t
-RETURN:   list:
-          roots of the Bernstein polynomial b (ideal) and its multiplicies
-NOTE:     the roots of b are negative rational numbers and -1 is a root of b
-KEYWORDS: Bernstein polynomial
+RETURN:
+@format
+list bs;  Bernstein-Sato polynomial b(s) of t
+  ideal bs[1];
+    number bs[1][i];  i-th root of b(s)
+  intvec bs[2];
+    int bs[2][i];  multiplicity of i-th root of b(s)
+@end format
+KEYWORDS: singularities; Gauss-Manin system; Brieskorn lattice; 
+          Bernstein-Sato polynomial
 EXAMPLE:  example bernstein; shows examples
 "
@@ -601 +607 @@
   list l=minipoly(A);
   e,m=l[1..2];
-
-  for(int i=1;i<=ncols(e);i++)
-  {
-    e[i]=-e[i];
-    if(e[i]==-1)
-    {
-      m[i]=m[i]+1;
-    }
-  }
+  e=-e;
+  l=spnf(spadd(list(e,m),list(ideal(-1),intvec(1))));
 
   setring(@R);
-  ideal e=imap(@G,e);
+  list l=imap(@G,l);
   kill @G,gmsmaxdeg;
 
-  return(list(e,m));
+  return(l);
 }
 example
@@ -632 +631 @@
 @format
 list l;  Jordan data jordan(M) of monodromy matrix exp(-2*pi*i*M)
-  ideal l[1];
+  ideal l[1]; 
     number l[1][i];  eigenvalue of i-th Jordan block of M
-  intvec l[2];
+  intvec l[2]; 
     int l[2][i];  size of i-th Jordan block of M
-  intvec l[3];
+  intvec l[3]; 
     int l[3][i];  multiplicity of i-th Jordan block of M
 @end format
 SEE ALSO: mondromy_lib, linalg_lib
-KEYWORDS: monodromy
+KEYWORDS: singularities; Gauss-Manin system; Brieskorn lattice; monodromy
 EXAMPLE:  example monodromy; shows examples
 "
@@ -686 +685 @@
 @end format
 SEE ALSO: spectrum_lib
-KEYWORDS: mixed Hodge structure; V-filtration; spectrum
+KEYWORDS: singularities; Gauss-Manin system; Brieskorn lattice;
+          mixed Hodge structure; V-filtration; spectrum
 EXAMPLE:  example spectrum; shows examples
 "
@@ -716 +716 @@
 @end format
 SEE ALSO: spectrum_lib
-KEYWORDS: mixed Hodge structure; V-filtration; weight filtration;
+KEYWORDS: singularities; Gauss-Manin system; Brieskorn lattice;
+          mixed Hodge structure; V-filtration; weight filtration;
           spectrum; spectral pairs
 EXAMPLE:  example sppairs; shows examples
@@ -749 +750 @@
 @end format
 SEE ALSO: spectrum_lib
-KEYWORDS: mixed Hodge structure; V-filtration; spectrum
+KEYWORDS: singularities; Gauss-Manin system; Brieskorn lattice;
+          mixed Hodge structure; V-filtration; spectrum
 EXAMPLE:  example vfilt; shows examples
 "
@@ -783 +785 @@
 @end format
 SEE ALSO: spectrum_lib
-KEYWORDS: mixed Hodge structure; V-filtration; weight filtration;
+KEYWORDS: singularities; Gauss-Manin system; Brieskorn lattice;
+          mixed Hodge structure; V-filtration; weight filtration;
           spectrum; spectral pairs
 EXAMPLE:  example vwfilt; shows examples
@@ -1033 +1036 @@
   ideal M;  monomial C-basis of H''/sH''
 @end format
-KEYWORDS: good basis
+KEYWORDS: singularities; Gauss-Manin system; Brieskorn lattice;
+          mixed Hodge structure; V-filtration; weight filtration;
+          monodromy; spectrum; spectral pairs; good basis
 EXAMPLE:  example tmatrix; shows examples
 "
@@ -1090 +1095 @@
   ideal ev[5];  standard basis of Jacobian ideal
 @end format
-KEYWORDS: V-filtration; endomorphism filtration
+KEYWORDS: singularities; Gauss-Manin system; Brieskorn lattice;
+          mixed Hodge structure; V-filtration; endomorphism filtration
 EXAMPLE:  example endvfilt; shows examples
 "
@@ -1233 +1239 @@
 proc sppnf(list sp)
 "USAGE:   sppnf(list(a,w[,m])); ideal a, intvec w, intvec m
-ASSUME:  ncols(a)==size(w)==size(m)
+ASSUME:  ncols(e)==size(w)==size(m)
 RETURN:  order (a[i][,w[i]]) with multiplicity m[i] lexicographically
 EXAMPLE: example sppnf; shows examples