Efficient C++ optimized functions for numerical and symbolic calculus.

The R package **calculus** implements C++ optimized
functions for numerical and symbolic calculus, such as the Einstein
summing convention, fast computation of the Levi-Civita
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 and 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.

Install the package.

`install.packages("calculus")`

Load the package.

`library(calculus)`

Read or browse the documentation and the vignettes.

The package provides a unified interface to work with mathematical
objects in R. The library applies numerical methods when working with
`functions`

or symbolic programming when working with
`characters`

or `expressions`

. To describe
multidimensional objects such as vectors, matrices, and tensors, the
package uses the class `array`

regardless of the dimension.
This is done to prevent unwanted results due to operations among
different classes such as `vector`

for unidimensional objects
or `matrix`

for bidimensional objects.

The package integrates seamlessly with cubature for efficient numerical integration in C. However, except for Rcpp, the package has no strict dependencies in order to provide a stable self-contained toolbox that invites re-use.

Several unit tests are implemented via the standard framework offered by testthat and run via continuous integration.

Report a bug and star the repository.

Guidotti E (2022). “calculus: High-Dimensional Numerical and Symbolic
Calculus in R.” *Journal of Statistical Software*,
*104*(5), 1-37. doi:10.18637/jss.v104.i05

A BibTeX entry for LaTeX users is

```
@Article{calculus,
title = {{calculus}: High-Dimensional Numerical and Symbolic Calculus in {R}},
author = {Emanuele Guidotti},
journal = {Journal of Statistical Software},
year = {2022},
volume = {104},
number = {5},
pages = {1--37},
doi = {10.18637/jss.v104.i05},
}
```