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math.AC2023★ 2 cited
Signature Gröbner bases in free algebras over rings
Clemens Hofstadler, Thibaut Verron
We generalize signature Gröbner bases, previously studied in the free algebra over a field or polynomial rings over a ring, to ideals in the mixed algebra $R[x_1,...,x_k]\langle y_…
cs.SC2023
Transcendence Certificates for D-finite Functions
Manuel Kauers, Christoph Koutschan, Thibaut Verron
Although in theory we can decide whether a given D-finite function is transcendental, transcendence proofs remain a challenge in practice. Typically, transcendence is certified by…
cs.SC2023
Short proofs of ideal membership
Clemens Hofstadler, Thibaut Verron
A cofactor representation of an ideal element, that is, a representation in terms of the generators, can be considered as a certificate for ideal membership. Such a representation…