Changeset 36b837d in git

Timestamp:

Jul 4, 2022, 8:21:10 PM (22 months ago)

Author:

slap <slaplagne@…>

Branches:

(u'spielwiese', 'fe61d9c35bf7c61f2b6cbf1b56e25e2f08d536cc')

Children:

167a156d1776640d18beeb0a98abf41bf1c8081a

Parents:

a96a75d78ee43e8f2bef3aa36791cf8761509e21

Message:

Changes in documentation

Algorithm and strategy interchanged.

File:

• Singular/LIB/integralbasis.lib (modified) (6 diffs)

Singular/LIB/integralbasis.lib

@@ -13 +13 @@
 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
+this library implements algorithms for computing 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.
+field.@*
 
 PROCEDURES:
@@ -43 +40 @@
         must be monic as polynomial in the intVar-th variable.@*
         Optional parameters in list choose (can be entered in any order):@*
-        Strategy:@*
-        - \"global\" -> computes the integral basis by global algorithms. This
-        forces \"normal\" option. @*
-        - \"local\" -> computes the integral basis by computing the
-        local contribution at each component of the singular
-        locus of R/<f>, and then putting everything together. (Default option.)
-        @*Algorithm:@*
-        - \"normal\" -> the integral bases are computed using the normalization
-        algorithm.@*
-        - \"hensel\" -> the integral bases are computed using a special
-        algorithm, based on Hensel lifting. (Default option.)
+        Algorithm:@*
+        - \"normal\" -> the integral basis is computed using the general
+        normalization algorithm.@*
+        - \"hensel\" -> the integral bases is computed using an algorithm 
+        based on Puiseux expansions and Hensel lifting. (Default option.)
+        @*Options for normal algorithm:@*
+        - \"global\" -> computes the normalization of R / <f> and put the
+        results in integral basis shape.@*
+        - \"local\" -> computes the normalization at each component of
+        the singular locus of R/<f> and puts everything together. 
+        (Default option for normal algorithm.)
+        @*Other options:@*
         - \"modular\" -> uses modular algorithms for computing Groebner bases,
         radicals and decompositions whenever possible. Can be used together
@@ -61 +59 @@
         - \"nonModular\" -> do not uses modular algorithms. (Default option for
         ground fields of positive charecteristic.)@*
-        - \"rotation\" -> apply a rotation when there are singularities
-        with the same X-coordinate @*
-        - \"noRotation\" -> does not apply a rotation when there are singularities
-        with the same X-coordinate (Default option.)@*
-        Other options:@*
         - \"atOrigin\" -> will compute the local contribution at the origin
         to the integral basis, assuming that the curve has a singularity at
@@ -94 +87 @@
         element (indicated by intVar), f gives the integral equation and n is
         the degree of f as a polynomial in y.@*
-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
-         converting the k[x,y]-module generators into a k[x]-basis.@*
+THEORY:  We compute the integral basis of the integral closure of k[x] in k(x,y).
+         When option \"normal\" is selected, the normalization of the affine 
+         ring k[x,y]/<f> is computed using procedure normal from normal.lib,
+         which implements a general algorithm for normalization of rings
+         by G. Greuel, S. Laplagne and F. Seelisch, and the k[x,y]-module 
+         generators are converted into a k[x]-basis.
+         When option \"Hensel\" is selected, the algorithm by J. Boehm, W. Decker, 
+         S. Laplagne and G. Pfister is used. @*
 KEYWORDS: integral basis; normalization.
 SEE ALSO: normal.
@@ -140 +138 @@
     if ( typeof(#[i]) == "string" )
     {
+      if (#[i]=="normal"){
+        algorithm = "normal";
+      }
+      if (#[i]=="hensel"){
+        algorithm = "hensel";
+      }
       if (#[i]=="local"){
         strategy = "local";
@@ -152 +156 @@
         modular = 0;
       }
-      if (#[i]=="rotation"){
-        useRotation = 1;
-      }
-      if (#[i]=="noRotation"){
-        useRotation = 0;
-      }
-      if (#[i]=="normal"){
-        algorithm = "normal";
-      }
-      if (#[i]=="hensel"){
-        algorithm = "hensel";
-      }
+// Not implemented
+//      if (#[i]=="rotation"){
+//        useRotation = 1;
+//      }
+//      if (#[i]=="noRotation"){
+//        useRotation = 0;
+//      }
       if (#[i]=="atOrigin"){
         compType = "inputJ";