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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.

Additional Resources

https://emanueleguidotti.dev/calculus

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

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Install

install.packages('calculus')

Monthly Downloads

2,427

Version

0.1.0

License

GPL-3

Maintainer

Emanuele Guidotti

Last Published

November 7th, 2019

Functions in calculus (0.1.0)

c2e

Character to Expression
cross

Numerical and Symbolic Cross Product
gradient

Numerical and Symbolic Gradient
divergence

Numerical and Symbolic Divergence
e2c

Expression to Character
%dot%

Numerical and Symbolic Dot Product
%div%

Numerical and Symbolic Division
det

Numerical and Symbolic Determinant
kronecker

Generalized Kronecker Delta
inverse

Numeric and Symbolic Matrix Inverse
%matrix%

Numerical and Symbolic Matrix Product
%outer%

Numerical and Symbolic Outer Product
diag

Tensor Diagonals
%diff%

Numerical and Symbolic Difference
%inner%

Numerical and Symbolic Inner Product
%kronecker%

Numerical and Symbolic Kronecker Product
einstein

Numerical and Symbolic Einstein Summation
evaluate

Numerical Evaluation
laplacian

Numerical and Symbolic Laplacian
levicivita

Levi-Civita Symbol
index

Einstein Notation Indices
integral

Monte Carlo Integration
hessian

Numerical and Symbolic Hessian
hermite

Hermite Polynomials
wrap

Wrap Character
trace

Tensor Contraction
%prod%

Numerical and Symbolic Product
%sum%

Numerical and Symbolic Sum
partitions

Partitions of an Integer
taylor

Taylor Series
curl

Numerical and Symbolic Curl
derivative

Numerical and Symbolic Derivatives