Changeset 91fc5e in git

Timestamp:

Mar 20, 2002, 8:55:39 PM (21 years ago)

Author:

Mathias Schulze <mschulze@…>

Branches:

(u'jengelh-datetime', 'ceac47cbc86fe4a15902392bdbb9bd2ae0ea02c6')(u'spielwiese', '0604212ebb110535022efecad887940825b97c3f')

Children:

dd2be3b773d286f5e2f5502c780f11d141c04458

Parents:

26a4bbca17dbbf5ab25f7eb164a6615485df5606

Message:

*mschulze: changed doc


git-svn-id: file:///usr/local/Singular/svn/trunk@6022 2c84dea3-7e68-4137-9b89-c4e89433aadc

Location:

Singular/LIB

Files:

• gaussman.lib (modified) (9 diffs)
• linalg.lib (modified) (2 diffs)

Singular/LIB/gaussman.lib

@@ -1 +1 @@
 ///////////////////////////////////////////////////////////////////////////////
-version="$Id: gaussman.lib,v 1.78 2002-03-20 14:03:00 mschulze Exp $";
+version="$Id: gaussman.lib,v 1.79 2002-03-20 19:55:38 mschulze Exp $";
 category="Singularities";
 
@@ -13 +13 @@
 PROCEDURES:
  gmsring(t,s);              Gauss-Manin system of t with variable s
- gmsnf(p,K);                Gauss-Manin system normal form of p
- gmscoeffs(p,K);            Gauss-Manin system basis representation of p
- monodromy(t);              Jordan data of monodromy of t
+ gmsnf(p,K);                Gauss-Manin normal form of p
+ gmscoeffs(p,K);            Gauss-Manin basis representation of p
+ monodromy(t);              Jordan data of complex monodromy of t
  spectrum(t);               singularity spectrum of t
  sppairs(t);                spectral pairs of t
@@ -22 +22 @@
  vfilt(t);                  V-filtration of t on Brieskorn lattice
  vwfilt(t);                 weighted V-filtration of t on Brieskorn lattice
- tmatrix(t);                t-matrix on Brieskorn lattice
+ tmatrix(t);                C{{s}}-matrix of t on Brieskorn lattice
  endvfilt(V);               endomorphism V-filtration on Jacobian algebra
  spprint(sp);               print spectrum sp
@@ -31 +31 @@
  spissemicont(sp[,opt]);    semicontinuity test of spectrum sp
  spsemicont(sp0,sp[,opt]);  semicontinuous combinations of spectra sp0 in sp
- spmilnor(sp);              milnor number of spectrum sp
+ spmilnor(sp);              Milnor number of spectrum sp
  spgeomgenus(sp);           geometrical genus of spectrum sp
  spgamma(sp);               gamma invariant of spectrum sp
@@ -121 +121 @@
   int gmsmaxdeg;  maximal weight of variables
 @end format
+NOTE:     gmsbasis is a C{{s}}-basis of H'' and [t,s]=s^2
 KEYWORDS: singularities; Gauss-Manin connection; Brieskorn lattice
 EXAMPLE:  example gmsring; shows examples
@@ -218 +219 @@
 @format
 list nf;
-  ideal nf[1];  projection of p to gmsbasis mod s^(K+1)
-  ideal nf[2];  p=nf[1]+nf[2]
+  ideal nf[1];  projection of p to C{{s}}*gmsbasis mod s^(K+1)
+  ideal nf[2];  p==nf[1]+nf[2]
 @end format
-NOTE:     the computation can be continued by setting p=nf[2]
+NOTE:     computation can be continued by setting p=nf[2]
 KEYWORDS: singularities; Gauss-Manin connection; Brieskorn lattice
 EXAMPLE:  example gmsnf; shows examples
@@ -298 +299 @@
 @format
 list l;
-  matrix l[1];  gmsbasis representation of p mod s^(K+1)
-  ideal l[2];  p=matrix(gmsbasis)*l[1]+l[2]
+  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:     the computation can be continued by setting p=l[2]
+NOTE:     computation can be continued by setting p=l[2]
 KEYWORDS: singularities; Gauss-Manin connection; Brieskorn lattice
 EXAMPLE:  example gmscoeffs; shows examples
@@ -920 +921 @@
 list v;  V-filtration on H''/s*H''
   ideal v[1];
-    number v[1][i];  V-filtration index of i-th spectral pair
+    number v[1][i];  V-filtration index of i-th spectral number
   intvec v[2];
-    int v[2][i];  multiplicity of i-th spectral pair
+    int v[2][i];  multiplicity of i-th spectral number
   list v[3];
     module v[3][i];  vector space of i-th graded part in terms of v[4]
@@ -1068 +1069 @@
 ASSUME:   characteristic 0; local degree ordering;
           isolated critical point 0 of t
-RETURN:   list A;  matrix A[1]+s*A[2] of t on H''
+RETURN:
+@format
+list A;  C{{s}}-matrix A[1]+s*A[2] of t on H''
+  matrix A[1];
+  matrix A[2];
+@end format
 KEYWORDS: singularities; Gauss-Manin connection; Brieskorn lattice;
           mixed Hodge structure; opposite Hodge filtration; V-filtration

Singular/LIB/linalg.lib

@@ -1 +1 @@
 //GMG last modified: 04/25/2000
 //////////////////////////////////////////////////////////////////////////////
-version="$Id: linalg.lib,v 1.29 2002-03-20 14:03:00 mschulze Exp $";
+version="$Id: linalg.lib,v 1.30 2002-03-20 19:55:39 mschulze Exp $";
 category="Linear Algebra";
 info="
@@ -1591 +1591 @@
 @format
 list l:
-  module l[1];  Jordan normal form inverse(l[1])*M*l[1]
+  module l[1];  inverse(l[1])*M*l[1] in Jordan normal form
   intvec l[2]; 
     int l[2][i];  weight filtration index of l[1][i]