Changeset 8fc505d in git

Timestamp:

Oct 6, 2010, 9:19:00 AM (14 years ago)

Author:

Frank Seelisch <seelisch@…>

Branches:

(u'spielwiese', 'fe61d9c35bf7c61f2b6cbf1b56e25e2f08d536cc')

Children:

20aed372f6f3570345cfae02b1f372ebf5f1c0fa

Parents:

a1f90e40f6eb4bdcfaf9ef62b43cfc9c02f4f093

Message:

update by Wolfram

git-svn-id: file:///usr/local/Singular/svn/trunk@13398 2c84dea3-7e68-4137-9b89-c4e89433aadc

File:

• Singular/LIB/integralbasis.lib (modified) (3 diffs)

Singular/LIB/integralbasis.lib

@@ -9 +9 @@
           F. Seelisch, seelisch@mathematik.uni-kl.de
 
+OVERVIEW:
+Given an irreducible polynomial f in two variables defining a plane curve, 
+this library implements an algorithm to compute an integral basis of the 
+integral closure of the affine coordinate ring in the algebraic function 
+field via normalization.@*
+The user can choose whether the algorithm will do the computation globally 
+or (this is the default) compute in the localization at each component of 
+the singular locus and put everything together.
+
 PROCEDURES:
  integralBasis(f, intVar);     Integral basis of an algebraic function field
@@ -24 +33 @@
         must be monic as polynomial in the intVar-th variable.@*
         Optional parameters in list choose (can be entered in any order):@*
-        Algorithm:@*
+        Parameters for selecting the algorithm:@*
         - \"global\" -> computes the integral basis by computing the
         normalization of R/<f>, where R is the base ring.@*
@@ -31 +40 @@
         locus of R/<f>, and then putting everything together.
         This is the default option.@*
-        Other:@*
+        Other parameters:@*
         - \"isIrred\" -> assumes that the input polynomial f is irreducible,
-        and therefore will not check it. If this option is given but f is not
+        and therefore will not check this. If this option is given but f is not
         irreducible, the output might be wrong.@*
         - list(\"inputJ\", ideal inputJ) -> takes as initial test ideal the
         ideal inputJ. This option is only for use in other procedures. Using 
         this option, the result might not be the integral basis.@*
-        (When this option is given the global option will be used.)@*         
+        (When this option is given, the global option will be used.)@*         
         - list(\"inputC\", ideal inputC) -> takes as initial conductor the 
         ideal inputC. This option is only for use in other procedures. Using 
         this option, the result might not be the integral basis.@*
-        (When this option is given the global option will be used.)@*         
+        (When this option is given, the global option will be used.)@*         
 RETURN: a list, say l, of size 2.
-@format l[1] is an ideal I and l[2] is a polynomial D such that the integral
+        l[1] is an ideal I and l[2] is a polynomial D such that the integral
         basis is b_0 = I[1] / D, b_1 = I[2] / D, ..., b_{n-1} = I[n] / D.@*
         That is, the integral closure of k[x] in the algebraic function 
         field k(x,y) is @* 
         k[x] b_0 + k[x] b_1 + ... + k[x] b_{n-1},@*
-        where we assume that x is the trascendental variable, y is the integral 
+        where we assume that x is the transcendental variable, y is the integral 
         element (indicated by intVar), f gives the integral equation and n is 
         the degree of f as a polynomial in y.@*
-@end format
+
 THEORY:  We compute the integral basis of the integral closure of k[x] in k(x,y)
          by computing the normalization of the affine ring k[x,y]/<f> and