Hi,

I'm new to sage, and so far I like it!

Just my two cents here: it seems that the sage interface to singular
is not aware that Singular handles multivariate polynomial rings with
coefficients in a fraction field.

sage: from sage.rings.polynomial.polynomial_singular_interface import
can_convert_to_singular
sage: r=Frac(QQ['a,b'])['x,y']
sage: can_convert_to_singular(r)
False

However, it is possible to define it in Singular: in this case, it
would be

ring R=(0,a,b),(x,y),dp;

(following the syntax 2. given at 
http://www.singular.uni-kl.de/Manual/latest/sing_30.htm#SEC40)

In particular, Gröbner basis can be computed by Singular in these
polynomial rings more efficiently than the toy algorithm currently
used.


I hope this can help!

Best regards,


Guillaume


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