Singular

hi,
i need following computation:

let r be the polynomial ring: r=Q[a,b]
let R be the polynomial ring: R=r[x,y,z]
let I be an Ideal in R:

compute a set of generators of R/I as an free r module (if finite dimentional).

in the past i used "work-arounds" like R=(0,a,b),(x,y,z),Dp; to be able to use "kbase(I)",
but for many reasons a mathematical correct definition like R=0,(a,b,x,y,z),Dp; would help much. i've read in the online manual that such computations can be done but did not find a function doing it.

best regards,
peter

No, such a function does not exist (not every module over r is free).

In fact, what you do is computing a basis of the module over the quotient field,
which is a basis over the ring iff the module is free. In this case your way should
be the fastest possibility to compute it (except you choose random values for a and b).
Checking whether a module is free, is however another story.