I just saw that Singular has a disclaimer:
> ring R = integer, (x,y), dp;
// ** You are using coefficient rings which are not fields.
// ** Please note that only limited functionality is available
// ** for these coefficients.
// **
// ** The following commands are meant to work:
// ** - basic polynomial arithmetic
// ** - std
// ** - syz
// ** - lift
// ** - reduce

So, they do not claim that slimgb works over the integers.

Anyway, it's annoying.

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