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.

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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

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
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Details

Type Package
License GPL-3
URL https://emanueleguidotti.dev/calculus/
BugReports https://github.com/emanuele-guidotti/calculus/issues/
LinkingTo Rcpp
RoxygenNote 6.1.1
NeedsCompilation yes
Packaged 2019-11-05 06:33:45 UTC; Emanuele
Repository CRAN
Date/Publication 2019-11-07 10:00:02 UTC
imports Rcpp (>= 1.0.1)
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