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math.RA2025
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…
math.RA2024
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…