Changeset 4eba9ec in git

Timestamp:

Apr 8, 2009, 6:51:07 PM (15 years ago)

Author:

Frank Seelisch <seelisch@…>

Branches:

(u'spielwiese', 'fe61d9c35bf7c61f2b6cbf1b56e25e2f08d536cc')

Children:

21ebf68308bcf7db9c5f99b208152c3abfedece1

Parents:

e7778adedbf4b7cd363cb88f576d7b16023f2ca3

Message:

*** empty log message ***


git-svn-id: file:///usr/local/Singular/svn/trunk@11649 2c84dea3-7e68-4137-9b89-c4e89433aadc

Location:

Singular/LIB

Files:

• bfun.lib (modified) (3 diffs)
• dmod.lib (modified) (4 diffs)

Singular/LIB/bfun.lib

@@ -1 +1 @@
 //////////////////////////////////////////////////////////////////////////////
-version="$Id: bfun.lib,v 1.6 2009-03-10 16:27:55 Singular Exp $";
+version="$Id: bfun.lib,v 1.7 2009-04-08 16:51:07 seelisch Exp $";
 category="Noncommutative";
 info="
@@ -9 +9 @@
 THEORY: Given a polynomial ring R = K[x_1,...,x_n] and a polynomial F in R,
 @*      one is interested in the global b-function (also known as Bernstein-Sato
-@*      polynomial) b(s) in K[s], defined to be the monic polynomial of minimal
+@*      polynomial) b(s) in K[s], defined to be the non-zero monic polynomial of minimal
 @*      degree, satisfying a functional identity L * F^{s+1} = b(s) F^s,   
 @*      for some operator L in D[s] (* stands for the action of differential operator)
@@ -19 +19 @@
 @*      - the multiplicities of the roots.
 @*
-@*   There is a general definition of a b-function of a holonomic ideal [SST]
+@*   There is a constructive definition of a b-function of a holonomic ideal I in D
 @*   (that is, an ideal I in a Weyl algebra D, such that D/I is holonomic module)
 @*   with respect to the given weight vector w: For a poly p in D, its initial 

Singular/LIB/dmod.lib

@@ -1 +1 @@
 //////////////////////////////////////////////////////////////////////////////
-version="$Id: dmod.lib,v 1.37 2009-03-09 18:34:51 levandov Exp $";
+version="$Id: dmod.lib,v 1.38 2009-04-08 16:51:07 seelisch Exp $";
 category="Noncommutative";
 info="
@@ -144 +144 @@
 RETURN:  ring
 PURPOSE: compute the D-module structure of basering[1/f]*f^s with the algorithm 
-@*  given in S and with the Groebner basis engine given in 'eng'
+@*  given in S and with the Groebner basis engine given in ''eng''
 NOTE:  activate the output ring with the @code{setring} command.
-@*    The value of a string S can be
+@*    String S; S can be one of the following:
 @*    'bm' (default) - for the algorithm of Briancon and Maisonobe,
 @*    'ot'  - for the algorithm of Oaku and Takayama,
@@ -727 +727 @@
 proc bernsteinBM(poly F, list #)
 "USAGE:  bernsteinBM(f [,eng]);  f a poly, eng an optional int
-RETURN:  list (of roots of the Bernstein polynomial b and its multiplicies)
+RETURN:  list (of roots of the Bernstein polynomial b and their multiplicies)
 PURPOSE: compute the global Bernstein-Sato polynomial for a hypersurface, 
 @* defined by f, according to the algorithm by Briancon and Maisonobe
@@ -1603 +1603 @@
 PURPOSE: compute the B-operator and other relevant data for Ann F^s, 
 @*  using e.g. algorithm by Briancon and Maisonobe for Ann F^s and BS.
-NOTE:    activate this ring with the @code{setring} command. In this ring D[s]
+NOTE:    activate the output ring with the @code{setring} command. In the output ring D[s]
 @*       - the polynomial F is the same as the input,
 @*       - the ideal LD is the annihilator of f^s in Dn[s],