  We consider a class of monotone operators which are appropriate for symbolic
representation and manipulation within a computer algebra system. Various
structural properties of the class (e.g., closure under taking inverses,
resolvents) are investigated as well as the role played by maximal monotonicity
within the class. In particular, we show that there is a natural correspondence
between our class of monotone operators and the subdifferentials of convex
functions belonging to a class of convex functions deemed suitable for symbolic
computation of Fenchel conjugates which were previously studied by Bauschke &
von Mohrenschildt and by Borwein & Hamilton. A number of illustrative examples
utilizing the introduced class of operators are provided including computation
of proximity operators, recovery of a convex penalty function associated with
the hard thresholding operator, and computation of superexpectations,
superdistributions and superquantiles with specialization to risk measures.
