Changeset cad507 in git for Singular/LIB/dmod.lib

Timestamp:

Mar 6, 2009, 10:05:54 PM (15 years ago)

Author:

Viktor Levandovskyy <levandov@…>

Branches:

(u'spielwiese', '8e0ad00ce244dfd0756200662572aef8402f13d5')

Children:

55a8282afcb99a7a85304b3f8ecf99062c4dd376

Parents:

fda698647a5a06bd263906206d3ce89a87b42c0d

Message:

*levandov: dmod enhanced, docu, examples etc.


git-svn-id: file:///usr/local/Singular/svn/trunk@11523 2c84dea3-7e68-4137-9b89-c4e89433aadc

File:

• Singular/LIB/dmod.lib (modified) (5 diffs)

Singular/LIB/dmod.lib

@@ -1 +1 @@
 //////////////////////////////////////////////////////////////////////////////
-version="$Id: dmod.lib,v 1.35 2009-02-12 20:25:22 levandov Exp $";
+version="$Id: dmod.lib,v 1.36 2009-03-06 21:05:54 levandov Exp $";
 category="Noncommutative";
 info="
@@ -7 +7 @@
 @*             Jorge Martin Morales,    jorge@unizar.es
 
-THEORY: Given a polynomial ring R = K[x_1,...,x_n] and a polynomial F in R,
-@*      one is interested in the R[1/F]-module of rank one, generated by F^s
-@*      for a natural number s.
+THEORY: Let K be a field of characteristic 0. Given a polynomial ring 
+@*      R = K[x_1,...,x_n] and a polynomial F in R,
+@*      one is interested in the R[1/F]-module of rank one, generated by 
+@*      the symbol F^s for a symbolic discrete variable s.
 @* In fact, the module R[1/F]*F^s has a structure of a D(R)[s]-module, where D(R)
 @* is an n-th Weyl algebra K<x_1,...,x_n,d_1,...,d_n | d_j x_j = x_j d_j +1> and
@@ -18 +19 @@
 @* One is interested in the following data:
 @* - Ann F^s = I = I(F^s) in D(R)[s], denoted by LD in the output
-@* - global Bernstein polynomial in K[s], denoted by bs, its minimal integer root s0 and
-@*   the list of all roots of bs, which are rational, with their multiplicities is denoted by BS
-@* - Ann F^s0 = I(F^s0) in D(R), denoted by LD0 in the output (LD0 is a holonomic ideal in D(R))
+@* - global Bernstein polynomial in K[s], denoted by bs, 
+@* - its minimal integer root s0, the list of all roots of bs, which are known
+@*   to be rational, with their multiplicities, which is denoted by BS
+@* - Ann F^s0 = I(F^s0) in D(R), denoted by LD0 in the output 
+@*   (LD0 is a holonomic ideal in D(R))
 @* - Ann^(1) F^s in D(R)[s], denoted by LD1 (logarithmic derivations)
-@* - an operator in D(R)[s], denoted by PS, such that PS*F^(s+1) = bs*F^s holds in K[x_1,...,x_n,1/F^s].
+@* - an operator in D(R)[s], denoted by PS, such that the functional equality
+@*     PS*F^(s+1) = bs*F^s holds in K[x_1,...,x_n,1/F]*F^s.
 
 @* We provide the following implementations:
-@* OT) the classical Ann F^s algorithm from Oaku and Takayama (J. Pure
-        Applied Math., 1999),
+@* OT) the classical Ann F^s algorithm from Oaku and Takayama (Journal of 
+@* Pure and Applied Math., 1999),
 @* LOT) Levandovskyy's modification of the Oaku-Takayama algorithm (ISSAC 2007)
 @* BM) the Ann F^s algorithm by Briancon and Maisonobe (Remarques sur
-        l'ideal de Bernstein associe a des polynomes, preprint, 2002)
+@*        l'ideal de Bernstein associe a des polynomes, preprint, 2002)
 
 GUIDE:
-@* - Ann F^s = I = I(F^s) = LD in D(R)[s] can be computed by SannfsBM, SannfsOT, SannfsLOT
+@* - Ann F^s = I(F^s) = LD in D(R)[s] can be computed by Sannfs [BM, OT, LOT]
 @* - Ann^(1) F^s in D(R)[s] can be computed by Sannfslog
-@* - global Bernstein polynomial bs resp. BS in K[s] can be computed by bernsteinBM
-@* - Ann F^s0 = I(F^s0) = LD0 in D(R) can be computed by annfs0, annfsBM, annfsOT, annfsLOT, annfs2
-@* - all the relevant data (LD, LD0, bs, PS) are computed by operatorBM
+@* - global Bernstein polynomial bs in K[s] can be computed by bernsteinBM
+@* - Ann F^s0 = I(F^s0) = LD0 in D(R) can be computed by annfs0, annfs, annfsBM,
+@*    annfsOT, annfsLOT, annfs2, annfsRB etc.
+@* - all the relevant data to F^s (LD, LD0, bs, PS) are computed by operatorBM
+@*
+@* - annihilator of F^{s1} for a number s1 is computed with annfspecial
+@* - annihilator of F_1^s_1 * ... * F_p^s_p is computed with annfsBMI
+@* - computing the multiplicity of a rational number r in the Bernstein poly
+@*   of a given ideal goes with checkRoot
+@* - check, whether a given univariate polynomial divides the Bernstein poly
+@*   goes with checkFactor
+
 
 MAIN PROCEDURES:
@@ -78 +91 @@
 LIB "matrix.lib"; // for submat
 LIB "nctools.lib";
-LIB "elim.lib";
+LIB "elim.lib"; // for nselect
 LIB "qhmoduli.lib"; // for Max
 LIB "gkdim.lib";
@@ -237 +250 @@
   poly F = z*x^2+y^3;
   def A  = annfs(F); // here, the default BM algorithm will be used
-  setring A;
-  LD;
-  BS;
+  setring A; // the Weyl algebra in (x,y,z,Dx,Dy,Dz)
+  LD; //the annihilator of F^{-1} over A
+  BS; // roots with multiplicities of BS polynomial
 }