Changeset 4f461c in git for Singular/LIB

Timestamp:

Mar 5, 2010, 2:28:28 PM (14 years ago)

Author:

Hans Schönemann <hannes@…>

Branches:

(u'fieker-DuVal', '117eb8c30fc9e991c4decca4832b1d19036c4c65')(u'spielwiese', '4bd32dfef92ec9f5ed8dceee82d14318ae147107')

Children:

24c3680c7cb6e7c29e4766bc33d10684a0c2e1f2

Parents:

8a7e767173900998af700bab01a16d332d191b3d

Message:

format

git-svn-id: file:///usr/local/Singular/svn/trunk@12599 2c84dea3-7e68-4137-9b89-c4e89433aadc

File:

• Singular/LIB/dmodvar.lib (modified) (8 diffs)

Singular/LIB/dmodvar.lib

@@ -4 +4 @@
 info="
 LIBRARY: dmodvar.lib     Algebraic D-modules for varieties
+
 AUTHORS: Daniel Andres,          daniel.andres@math.rwth-aachen.de
-@*       Viktor Levandovskyy,    levandov@math.rwth-aachen.de
-@*       Jorge Martin-Morales,   jorge@unizar.es
+       Viktor Levandovskyy,    levandov@math.rwth-aachen.de
+       Jorge Martin-Morales,   jorge@unizar.es
 
 THEORY: Let K be a field of characteristic 0. Given a polynomial ring
-@*      R = K[x_1,...,x_n] and a set of polynomial f_1,..., f_r in R, define
-@*      F = f_1 * ... * f_r and F^s:=f_1^s_1*...*f_r^s_r for symbolic discrete
-@*      (that is shiftable) variables s_1,..., s_r.
-@*      The module R[1/F]*F^s has a structure of a D<S>-module, where 
-@*      D<S> := D(R) tensored with S over K, 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>
-@*      - S is the universal enveloping algebra of gl_r, generated by s_{ij}, where s_{ii}=s_i.
-@* One is interested in the following data:
-@* - the left ideal Ann F^s in D<S>, usually denoted by LD in the output
-@* - global Bernstein polynomial in one variable s = s_1 + ...+ s_r, 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
-@* - an r-tuple of operators in D<S>, denoted by PS, such that the functional equality
-@*     sum(k=1 to k=r) P_k*f_k*F^s = bs*F^s holds in R[1/F]*F^s.
+      R = K[x_1,...,x_n] and a set of polynomial f_1,..., f_r in R, define
+      F = f_1 * ... * f_r and F^s:=f_1^s_1*...*f_r^s_r for symbolic discrete
+      (that is shiftable) variables s_1,..., s_r.
+      The module R[1/F]*F^s has a structure of a D<S>-module, where
+      D<S> := D(R) tensored with S over K, 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>
+      - S is the universal enveloping algebra of gl_r, generated by s_{ij}, where s_{ii}=s_i.
+ One is interested in the following data:
+ - the left ideal Ann F^s in D<S>, usually denoted by LD in the output
+ - global Bernstein polynomial in one variable s = s_1 + ...+ s_r, 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
+ - an r-tuple of operators in D<S>, denoted by PS, such that the functional equality
+     sum(k=1 to k=r) P_k*f_k*F^s = bs*F^s holds in R[1/F]*F^s.
 
 REFERENCES:
-@*      (BMS06) Budur, Mustata, Saito: Bernstein-Sato polynomials of arbitrary varieties (2006).
-@*      (ALM09) Andres, Levandovskyy, Martin-Morales : Principal Intersection and Bernstein-Sato Polynomial of an Affine Variety (2009).
+  (BMS06) Budur, Mustata, Saito: Bernstein-Sato polynomials of arbitrary varieties (2006).
+  (ALM09) Andres, Levandovskyy, Martin-Morales : Principal Intersection and Bernstein-Sato Polynomial of an Affine Variety (2009).
 
 MAIN PROCEDURES:
@@ -166 +167 @@
           // the case: given ORD, given engine
           eng = int(#[2]);
-        } 
+        }
         else
         {
@@ -197 +198 @@
   int ppl = printlevel-voice+2;
   // returns a list with a ring and an ideal LD in it
-  // save, N, P and the indices are already defined 
+  // save, N, P and the indices are already defined
   int Nnew = 2*N+P+P^2;
   list RL = ringlist(basering);
@@ -328 +329 @@
   intvec iv = P+1..Nnew;
   tmpM = imap(@R@,@D);
-  kill @R@; 
+  kill @R@;
   LordM = submat(tmpM,iv,iv);
   matrix @D2 = LordM;
@@ -548 +549 @@
   // Name, Dname will be used further
   kill NName, TName, Name, DTName, DName;
-  // ORD already set, default ord dp; 
+  // ORD already set, default ord dp;
   L[3] = ORDstr2list(ORD,Nnew);
   // we are done with the list
@@ -605 +606 @@
 @*       Varnames of the basering do not include t(1),...,t(r) and
 @*       Dt(1),...,Dt(r), where r is the number of entries of the input ideal.
-BACKGROUND:  In this proc, the initial ideal of the multivariate Malgrange ideal 
+BACKGROUND:  In this proc, the initial ideal of the multivariate Malgrange ideal
 @*       defined by I is computed and then a system of linear equations is solved
 @*       by linear reductions following the ideas by Noro.
@@ -619 +620 @@
 @*       time.
 @*       If b<>0, @code{std} is used for GB computations in characteristic 0,
-@*       otherwise, and by default, @code{slimgb} is used. 
+@*       otherwise, and by default, @code{slimgb} is used.
 @*       If c<>0, a matrix ordering is used for GB computations, otherwise,
 @*       and by default, a block ordering is used.
@@ -838 +839 @@
   I = std(I);
 //ideal I = z(6)^2-z(3)*z(7), z(5)*z(6)-z(2)*z(7), z(5)^2-z(1)*z(7),
-//  z(4)*z(5)-z(3)*z(6), z(3)*z(5)-z(2)*z(6), z(2)*z(5)-z(1)*z(6), 
+//  z(4)*z(5)-z(3)*z(6), z(3)*z(5)-z(2)*z(6), z(2)*z(5)-z(1)*z(6),
 //  z(3)^2-z(2)*z(4), z(2)*z(3)-z(1)*z(4), z(2)^2-z(1)*z(3);
   bfctVarIn(I,1); // no result yet