Singular Manual: Example of use of Letterplace

| ### 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.

User manual for Singular version 4-1-1p4, 2018, generated by texi2html.