Home Online Manual
Top
Back: diffAlgebraChangeOrd
Forward: difformFromPoly
FastBack:
FastForward:
Up: difform_lib
Top: Singular Manual
Contents: Table of Contents
Index: Index
About: About this document

D.15.2.6 diffAlgebraListGen

Procedure from library difform.lib (see difform_lib).

Usage:
diffAlgebraListGen(#); # list

Return:
- a list of generators of the differential algebra as module over the basering - a list of generators of a graded part of the differential algebra

Remarks:
In order to find all generators, they are counted 'binary': The generators are in 1:1 - correspondence to the dual number representations of 1 up to (2^n-1)

Note:
- if all generators of the differential algebra are needed, apply the procedure without input
- if the generator(s) of a graded part are needed, apply the procedure with an integer which specifies the wanted degree
- the list of generators is sorted with respect to the monomial ordering on the differential algebra

Example:
 
LIB "difform.lib";
ring R = 11,(x,y,z),dp;
diffAlgebra();
==> // The differential algebra Omega_R was constructed and the differential \
   forms dDx, dDy, dDz, dx, dy, dz are available.
////////////////////////////////////////////
// Generators of the differential algebra //
////////////////////////////////////////////
diffAlgebraListGen();
==> [1]:
==>    1
==> 
==> [2]:
==>    dz
==> 
==> [3]:
==>    dy
==> 
==> [4]:
==>    dx
==> 
==> [5]:
==>    dy*dz
==> 
==> [6]:
==>    dx*dz
==> 
==> [7]:
==>    dx*dy
==> 
==> [8]:
==>    dx*dy*dz
==> 
//////////////////////////////////////////
// Generators of the second graded part //
//////////////////////////////////////////
diffAlgebraListGen(2);
==> [1]:
==>    dy*dz
==> 
==> [2]:
==>    dx*dz
==> 
==> [3]:
==>    dx*dy
==> 
kill Omega_R,dx,dy,dz;