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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;
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