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High Dimensional Numerical and Symbolic Calculus in R

Efficient C++ optimized functions for numerical and symbolic calculus. It includes basic symbolic arithmetic, tensor calculus, Einstein summing convention, fast computation of the Levi-Civita symbol and generalized Kronecker delta, Taylor series expansion, multivariate Hermite polynomials, accurate high-order derivatives, differential operators (Gradient, Jacobian, Hessian, Divergence, Curl, Laplacian) and Monte Carlo integration in arbitrary orthogonal coordinate systems: cartesian, polar, spherical, cylindrical, parabolic or user defined by custom scale factors.

Quickstart

# Install calculus
install.packages('calculus')

# Load calculus
require('calculus')

Documentation

https://calculus.r-package.org

https://cran.r-project.org/package=calculus

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Version

Install

install.packages('calculus')

Monthly Downloads

2,520

Version

0.1.1

License

GPL-3

Maintainer

Emanuele Guidotti

Last Published

November 11th, 2019

Functions in calculus (0.1.1)

det

Numerical and Symbolic Determinant
derivative

Numerical and Symbolic Derivatives
einstein

Numerical and Symbolic Einstein Summation
divergence

Numerical and Symbolic Divergence
cross

Numerical and Symbolic Cross Product
evaluate

Numerical Evaluation
%div%

Numerical and Symbolic Division
inverse

Numeric and Symbolic Matrix Inverse
%dot%

Numerical and Symbolic Dot Product
gradient

Numerical and Symbolic Gradient
%matrix%

Numerical and Symbolic Matrix Product
kronecker

Generalized Kronecker Delta
%outer%

Numerical and Symbolic Outer Product
%diff%

Numerical and Symbolic Difference
%kronecker%

Numerical and Symbolic Kronecker Product
hessian

Numerical and Symbolic Hessian
%sum%

Numerical and Symbolic Sum
%prod%

Numerical and Symbolic Product
%inner%

Numerical and Symbolic Inner Product
hermite

Hermite Polynomials
partitions

Partitions of an Integer
taylor

Taylor Series
laplacian

Numerical and Symbolic Laplacian
trace

Tensor Contraction
wrap

Wrap Character
levicivita

Levi-Civita Symbol
integral

Monte Carlo Integration
index

Einstein Notation Indices
c2e

Character to Expression
e2c

Expression to Character
curl

Numerical and Symbolic Curl
diag

Tensor Diagonals