Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Automatic Differentiation With Higher Infinitesimals, or Computational
  Smooth Infinitesimal Analysis in Weil Algebra   We propose an algorithm to compute the $C^\infty$-ring structure of arbitrary
Weil algebra. It allows us to do some analysis with higher infinitesimals
numerically and symbolically. To that end, we first give a brief description of
the (Forward-mode) automatic differentiation (AD) in terms of $C^\infty$-rings.
The notion of a $C^\infty$-ring was introduced by Lawvere and used as the
fundamental building block of smooth infinitesimal analysis and synthetic
differential geometry. We argue that interpreting AD in terms of
$C^\infty$-rings gives us a unifying theoretical framework and modular ways to
express multivariate partial derivatives. In particular, we can "package"
higher-order Forward-mode AD as a Weil algebra, and take tensor products to
compose them to achieve multivariate higher-order AD. The algorithms in the
present paper can also be used for a pedagogical purpose in learning and
studying smooth infinitesimal analysis as well.

36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ