calculus: High-Dimensional Numerical and Symbolic Calculus in R

calculus: High-Dimensional Numerical and Symbolic Calculus in R

: symbolic programming, finite difference, differential operators, numerical integration, coordinate systems, Einstein summation, Taylor series, Hermite polynomials, R.

The R package calculus implements C++-optimized functions for numerical and symbolic calculus, such as the Einstein summing convention, fast computation of the LeviCivita symbol and generalized Kronecker delta, Taylor series expansion, multivariate Hermite polynomials, high-order derivatives, ordinary differential equations, differential operators and numerical integration in arbitrary orthogonal coordinate systems. The library
applies numerical methods when working with functions, or symbolic programming when
working with characters or expressions. The package handles multivariate numerical calculus in arbitrary dimensions and coordinates. It implements the symbolic counterpart
of the numerical methods whenever possible, without depending on external computer
algebra systems. Except for Rcpp, the package has no strict dependencies in order to
provide a stable self-contained toolbox that invites re-use

Emanuele Guidotti

https://www.jstatsoft.org/article/view/v104i05

University of Neuchâtel
CREST, Japan Science and Technology Agency

September 2022

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