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cs.SC2021
Automatic Differentiation With Higher Infinitesimals, or Computational Smooth Infinitesimal Analysis in Weil Algebra
Hiromi Ishii
We propose an algorithm to compute the -ring structure of arbitrary Weil algebra. It allows us to do some analysis with higher infinitesimals numerically and symbolically…
cs.SC2021
A Succinct Multivariate Lazy Multivariate Tower AD for Weil Algebra Computation
Hiromi Ishii
We propose a functional implementation of \emph{Multivariate Tower Automatic Differentiation}. Our implementation is intended to be used in implementing -structure comput…
cs.SC2018★ 3 cited
A Purely Functional Computer Algebra System Embedded in Haskell
Hiromi Ishii
We demonstrate how methods in Functional Programming can be used to implement a computer algebra system. As a proof-of-concept, we present the computational-algebra package. It is…