7.6.4 Example of use of LETTERPLACE
The input monomials must be given in a letterplace notation (though we recommend to
get used to the letterplace notation, the procedure freeGBasis from the freegb_lib
provides an alternative).
We recommend first to define a commutative ring
in SINGULAR and equip it with
a degree well-ordering. Then, decide what should be the degree bound d and
run the procedure makeLetterplaceRing(d)
from the library freegb_lib.
This procedure creates a letterplace algebra with an ordering, induced from the given commutative ring
.
In this algebra, define an ideal I as a list of polynomials in the letterplace encoding
and run the procedure letplaceGBasis . The output is given in the letterplace encoding as well.
Alternatively, one can run the procedure system("freegb",I,d,n) , where
is the number of variables of the original commutative ring which does the same computations as letplaceGBasis .
It is possible to convert the letterplace presentation of an ideal to a list of strings with the help of procedures lp2lstr and lst2str from the library freegb_lib. This is shown in the second part of the example below.
Yet another anternative is to use the procedure freeGBasis from freegb_lib in order to use a different encoding for polynomials in free algebra. No conversion tools are needed in that case.
We illustrate the approach with the following example:
There are various conversion routines in the library freegb_lib (see freegb_lib).
We work further on implementing more algorithms for non-commutative ideals and modules over free associative algebra.
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