# calculus v0.1.0

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## High Dimensional Numerical and Symbolic Calculus

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.

# 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.

https://emanueleguidotti.dev/calculus

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

## Functions in calculus

 Name Description 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 No Results!