|
7.6.4 Example of use of LETTERPLACE
First, define a commutative ring
in SINGULAR and equip it with
a degree well-ordering. Then, decide what should be the degree bound
and
run the procedure makeLetterplaceRing(d) from the library freegb_lib.
This procedure creates a Letterplace ring with an ordering, induced from the given commutative ring
.
In this
-algebra, define an ideal I as a list of polynomials in the
free algebra (x*y and y*x are different) and run std . The answer is a two-sided Groebner bases of
the two-sided ideal
.
We illustrate the approach with the following example:
| LIB "freegb.lib";
ring r = 0,(x,y,z),dp;
def R = makeLetterplaceRing(4); // with degree bound 4
setring R;
ideal I = x*y + y*z, x*x + x*y - y*x - y*y;
ideal J = std(I);
J;
==> J[1]=x*y+y*z
==> J[2]=x*x-y*x-y*y-y*z
==> J[3]=y*y*y-y*y*z+y*z*y-y*z*z
==> J[4]=y*y*x+y*y*z+y*z*x+y*z*z
==> J[5]=y*z*y*y-y*z*y*z+y*z*z*y-y*z*z*z
==> J[6]=y*z*y*x+y*z*y*z+y*z*z*x+y*z*z*z
==> J[7]=y*y*z*y-y*y*z*z+y*z*z*y-y*z*z*z
==> J[8]=2*y*y*z*x+2*y*y*z*z-y*z*y*x-y*z*y*z+y*z*z*x+y*z*z*z
|
There are various conversion routines in the library freegb_lib (see freegb_lib).
Many algebras are predefined in the library fpalgebras_lib (see fpalgebras_lib).
We work further on implementing more algorithms for non-commutative ideals and modules over free associative algebra.
|