Changeset 4a54b7 in git for Singular/LIB/ratgb.lib

Timestamp:

Oct 13, 2010, 2:37:12 PM (14 years ago)

Author:

Hans Schoenemann <hannes@…>

Branches:

(u'fieker-DuVal', '117eb8c30fc9e991c4decca4832b1d19036c4c65')(u'spielwiese', 'd08f5f0bb3329b8ca19f23b74cb1473686415c3a')

Children:

9c5f5282789f1d596251d632f870343d23c5e7c0

Parents:

e82bb379fa5d86aee55251282d46ad9638fa2ebc

Message:

format

git-svn-id: file:///usr/local/Singular/svn/trunk@13467 2c84dea3-7e68-4137-9b89-c4e89433aadc

File:

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

Singular/LIB/ratgb.lib

@@ -10 +10 @@
 The operators are usually denoted by @code{d1,..,dM}.
 
-Assume, that A is a @code{G}-algebra, then the set @code{S=R-{0}} is multiplicatively 
+Assume, that A is a @code{G}-algebra, then the set @code{S=R-{0}} is multiplicatively
 closed Ore set in A.
 That is, for any s in S and a in A, there exist t in S and b in A, such that @code{sa=bt}.
-In other words, one can transform any left fraction into the right fraction. 
+In other words, one can transform any left fraction into the right fraction.
 The algebra @code{A_S} is called an Ore localization of A with respect to S.
 
-This library provides Groebner basis procedure for A_S, performing polynomial (that is 
+This library provides Groebner basis procedure for A_S, performing polynomial (that is
 fraction-free) computations only. Note, that there is ongoing development of the
 subsystem called Singular:Locapal, which will provide yet another approach to Groebner
@@ -24 +24 @@
 We will assume that the variables @code{x1,...,xN} from above (which will become invertible
 in the localization) come as the first block in the basering.
-Moreover, the ordering on the basering must be an antiblock ordering, that is its 
+Moreover, the ordering on the basering must be an antiblock ordering, that is its
 matrix form has the left upper @code{NxN} block zero. Here is a recipy to create such
 an ordering easily: use 'a(w)' definitions of the ordering N times with intvecs @code{w_i}
@@ -31 +31 @@
 
 Guide: with this library, it is possible
-- to compute a Groebner basis of an ideal or a submodule in the 'rational' 
-  Ore localization D = A_S 
+- to compute a Groebner basis of an ideal or a submodule in the 'rational'
+  Ore localization D = A_S
 - to compute a dimension of associated graded submodule (called D-dimension)
-- to compute a vector space dimension over Quot(R) of a submodule of 
+- to compute a vector space dimension over Quot(R) of a submodule of
   D-dimension 0 (so called D-finite submodule)
 - to compute a basis over Quot(R) of a D-finite submodule
@@ -88 +88 @@
 ASSUME: the variables of basering are organized in two blocks and
 - the first block of length n contains the elements with respect to which one localizes,
-- the basering is equipped with the elimination block ordering for the variables 
+- the basering is equipped with the elimination block ordering for the variables
   in the second block
 NOTE: the output ring C is commutative. The ideal @code{rGBid} in C
@@ -359 +359 @@
   // this ordering is an antiblock ordering, as it must be
   def S = Weyl(); setring S;
-  // the ideal I below annihilates parametric Appel F4 function 
+  // the ideal I below annihilates parametric Appel F4 function
   // where we set parameters to a=-2, b=-1 and d=0
   ideal I =
@@ -464 +464 @@
   // this ordering is an antiblock ordering, as it must be
   def S = Weyl(); setring S;
-  // the ideal I below annihilates parametric Appel F4 function 
+  // the ideal I below annihilates parametric Appel F4 function
   // where we set parameters to a=-2, b=-1 and d=0
   ideal I =
@@ -470 +470 @@
     y*Dy*(y*Dy-1) - y*(x*Dx+y*Dy-2)*(x*Dx+y*Dy-1);
 
-  // the ideal J below annihilates parametric Appel F4 function 
+  // the ideal J below annihilates parametric Appel F4 function
   // where we set parameters to a=0, b=-1, c=0, d=0
 
-  ideal J = 
+  ideal J =
     x*Dx*(x*Dx-1) - x*(x*Dx+y*Dy)*(x*Dx+y*Dy-1),
     y*Dy*(y*Dy-1) - y*(x*Dx+y*Dy)*(x*Dx+y*Dy-1);
@@ -479 +479 @@
   module M = I*gen(1), J*gen(2);
 
-// harder modification: M = M, Dx*gen(1) + Dy*gen(2); 
+// harder modification: M = M, Dx*gen(1) + Dy*gen(2);
 // gives K(x,y)-dim 3