lpMult creates monomials that are not letterplace monomials

[Simon King]

I try to work in a free associative algebra using letterplace. Unfortunately, the law of distributivity does not hold when the letterplace algebra is equipped with the multiplication lpMult:

> LIB "freegb.lib";
> ring r=0,(a,b),dp;
> def R = makeLetterplaceRing(5);
> setring R;
> poly p = a(1);
> poly q = b(1);
> poly p2 = lpPower(p,2);
> lpMult(p2+q,q)-lpMult(p2,q)-lpMult(q,q);
-b(1)*b(2)+b(1)*b(3)

Aparently, in the free associative algebra, one would expect that the result is zero.

If I understand the manual chapter 7.6.3, in order to have the free associative algebra, we need to thoroughly work with letterplace monomials, i.e., a monomial with places 1,2,3,...,m. But lpMult(p2+q,q) contains a monomial b(1)*b(3) that is not a letterplace monomial. Is that a bug?

[Simon King]

Is it perhaps assumed that we thoroughly work with homogeneous data? In the homogeneous case, the implementation of lpMult seems ok to me. But the documentation does not mention the need of homogeneous data, although the examples of lpMult, lpPower and freeGBasis all happen to be homogeneous.

[Simon King]

Replying to SimonKing:

Is it perhaps assumed that we thoroughly work with homogeneous data? In the homogeneous case, the implementation of lpMult seems ok to me. But the documentation does not mention the need of homogeneous data, although the examples of lpMult, lpPower and freeGBasis all happen to be homogeneous.

Viktor Levandovskyy wrote me an e-mail, stating that my guess was correct: It is indeed assumed that all input is homogeneous.

So, one should add a check for homogeneity, and it should also be mentioned in the documentation (this is currently not the case - at least not in the documentation of freeGBasis, lpMult or freegb.lib).

[levandov]

Hi, now it has been fixed by me. The problem was that we implicitly had the homogeneity assumptions; now it works fine for any input.
Besides, I have implemented a new procedure letplaceGBasis, which is user friendlier than both system("freegb",_) call and freeGBasis (which uses alternative presentation possibilities).