115 citations · 468 across the 26 of their papers we have counts for
27 papers
The integro-differential closure of a commutative differential ring
Clemens G. Raab, Georg Regensburger
An integro-differential ring is a differential ring that is closed under an integration operation satisfying the fundamental theorem of calculus. Via the Newton--Leibniz formula, a…
Nested Integrals and Rationalizing Transformations
Clemens G. Raab
A brief overview of some computer algebra methods for computations with nested integrals is given. The focus is on nested integrals over integrands involving square roots. Rewrite…
The fundamental theorem of calculus in differential rings
Clemens G. Raab, Georg Regensburger
In this paper, we study the consequences of the fundamental theorem of calculus from an algebraic point of view. For functions with singularities, this leads to a generalized notio…
Universal truth of operator statements via ideal membership
Clemens Hofstadler, Clemens G. Raab, Georg Regensburger
We introduce a framework for proving statements about linear operators by verification of ideal membership in a free algebra. More specifically, arbitrary first-order statements ab…
Computing elements of certain form in ideals to prove properties of operators
Clemens Hofstadler, Clemens G. Raab, Georg Regensburger
Proving statements about linear operators expressed in terms of identities often leads to finding elements of certain form in noncommutative polynomial ideals. We illustrate this b…
Algebraic proof methods for identities of matrices and operators: improvements of Hartwig's triple reverse order law
Dragana S. Cvetković-Ilić, Clemens Hofstadler, Jamal Hossein Poor +3
When improving results about generalized inverses, the aim often is to do this in the most general setting possible by eliminating superfluous assumptions and by simplifying some o…