Changeset 607fc7 in git

Timestamp:

Feb 18, 2011, 2:15:02 PM (13 years ago)

Author:

Hans Schoenemann <hannes@…>

Branches:

(u'spielwiese', '8e0ad00ce244dfd0756200662572aef8402f13d5')

Children:

c1dff83921acf6b85f3e88171ce4371c322c7a68

Parents:

7abf40bdd915198def06568f9d06325c0e1cdf08

Message:

format

git-svn-id: file:///usr/local/Singular/svn/trunk@13866 2c84dea3-7e68-4137-9b89-c4e89433aadc

Location:

Singular/LIB

Files:

• gmspoly.lib (modified) (4 diffs)
• gmssing.lib (modified) (3 diffs)

Singular/LIB/gmspoly.lib

@@ -1 +1 @@
 ///////////////////////////////////////////////////////////////////////////////
-version="$Id: gmspoly.lib 12529 2010-02-08 15:57:48Z seelisch $";
+version="$Id$";
 category="Singularities";
 
@@ -8 +8 @@
 AUTHOR:   Mathias Schulze, mschulze at mathematik.uni-kl.de
 
-OVERVIEW: 
-A library for computing the Gauss-Manin system of a cohomologically tame 
-polynomial f. Schulze's algorithm [Sch05], based on Sabbah's theory [Sab98], 
-is used to compute a good basis of (the Brieskorn lattice of) the Gauss-Manin system and the differential operation of f in terms of this basis. 
+OVERVIEW:
+A library for computing the Gauss-Manin system of a cohomologically tame
+polynomial f. Schulze's algorithm [Sch05], based on Sabbah's theory [Sab98],
+is used to compute a good basis of (the Brieskorn lattice of) the Gauss-Manin system and the differential operation of f in terms of this basis.
 In addition, there is a test for tameness in the sense of Broughton.
-Tame polynomials can be considered as an affine algebraic analogue of local 
-analytic isolated hypersurface singularities. They have only finitely many 
-citical points, and those at infinity do not give rise to atypical values 
-in a sense depending on the precise notion of tameness considered. Well-known 
-notions of tameness like tameness, M-tameness, Malgrange-tameness, and 
-cohomological tameness, and their relations, are reviewed in [Sab98,§8]. 
-For ordinary tameness, see Broughton [Bro88,§3].
-Sabbah [Sab98] showed that the Gauss-Manin system, the D-module direct image 
-of the structure sheaf, of a cohomologically tame polynomial carries a 
-similar structure as in the isolated singularity case, coming from a Mixed 
-Hodge structure on the cohomology of the Milnor (typical) fibre (see 
+Tame polynomials can be considered as an affine algebraic analogue of local
+analytic isolated hypersurface singularities. They have only finitely many
+citical points, and those at infinity do not give rise to atypical values
+in a sense depending on the precise notion of tameness considered. Well-known
+notions of tameness like tameness, M-tameness, Malgrange-tameness, and
+cohomological tameness, and their relations, are reviewed in [Sab98,8].
+For ordinary tameness, see Broughton [Bro88,3].
+Sabbah [Sab98] showed that the Gauss-Manin system, the D-module direct image
+of the structure sheaf, of a cohomologically tame polynomial carries a
+similar structure as in the isolated singularity case, coming from a Mixed
+Hodge structure on the cohomology of the Milnor (typical) fibre (see
 gmssing.lib). The data computed by this library encodes the differential structure of the Gauss-Manin system, and the Mixed Hodge structure of the Milnor fibre over the complex numbers. As a consequence, it yields the Hodge numbers, spectral pairs, and monodromy at infinity.
 
 REFERENCES:
-[Bro88] S. Broughton: Milnor numbers and the topology of polynomial 
+[Bro88] S. Broughton: Milnor numbers and the topology of polynomial
         hypersurfaces. Inv. Math. 92 (1988) 217-241.
-[Sab98] C. Sabbah: Hypergeometric periods for a tame polynomial. 
+[Sab98] C. Sabbah: Hypergeometric periods for a tame polynomial.
         arXiv.org math.AG/9805077.
-[Sch05] M. Schulze: Good bases for tame polynomials. 
+[Sch05] M. Schulze: Good bases for tame polynomials.
         J. Symb. Comp. 39,1 (2005), 103-126.
 
@@ -83 +83 @@
 @format
 int k=
-  1;  if f is tame in the sense of Broughton [Bro88,§3]
+  1;  if f is tame in the sense of Broughton [Bro88,3]
   0;  if f is not tame
 @end format
@@ -450 +450 @@
 proc goodBasis(poly f)
 "USAGE:    goodBasis(f); poly f
-ASSUME:   f is cohomologically tame in the sense of Sabbah [Sab98,§8]
+ASSUME:   f is cohomologically tame in the sense of Sabbah [Sab98,8]
 RETURN:
 @format

Singular/LIB/gmssing.lib

@@ -1 +1 @@
 ///////////////////////////////////////////////////////////////////////////////
-version="$Id: gmssing.lib 13548 2010-10-19 07:45:40Z hannes $";
+version="$Id$";
 category="Singularities";
 
@@ -8 +8 @@
 AUTHOR:  Mathias Schulze, mschulze at mathematik.uni-kl.de
 
-OVERVIEW: 
-A library for computing invariants related to the Gauss-Manin system of an 
+OVERVIEW:
+A library for computing invariants related to the Gauss-Manin system of an
 isolated hypersurface singularity.
 
 REFERENCES:
-[Sch01] M. Schulze: Algorithms for the Gauss-Manin connection. J. Symb. Comp. 
+[Sch01] M. Schulze: Algorithms for the Gauss-Manin connection. J. Symb. Comp.
         32,5 (2001), 549-564.
-[Sch02] M. Schulze: The differential structure of the Brieskorn lattice. 
-        In: A.M. Cohen et al.: Mathematical Software - ICMS 2002. 
+[Sch02] M. Schulze: The differential structure of the Brieskorn lattice.
+        In: A.M. Cohen et al.: Mathematical Software - ICMS 2002.
         World Scientific (2002).
-[Sch03] M. Schulze: Monodromy of Hypersurface Singularities. 
+[Sch03] M. Schulze: Monodromy of Hypersurface Singularities.
         Acta Appl. Math. 75 (2003), 3-13.
-[Sch04] M. Schulze: A normal form algorithm for the Brieskorn lattice. 
+[Sch04] M. Schulze: A normal form algorithm for the Brieskorn lattice.
         J. Symb. Comp. 38,4 (2004), 1207-1225.
 
@@ -50 +50 @@
 KEYWORDS: singularities; Gauss-Manin system; Brieskorn lattice;
           mixed Hodge structure; V-filtration; weight filtration;
-          Bernstein-Sato polynomial; monodromy; spectrum; spectral pairs; 
+          Bernstein-Sato polynomial; monodromy; spectrum; spectral pairs;
           good basis
 ";