High Dimensional Numerical and Symbolic Calculus
Characters to Expressions
calculus: High Dimensional Numerical and Symbolic Calculus
Numerical and Symbolic Tensor Contraction
Numerical and Symbolic Cross Product
Numerical and Symbolic Curl
Generalized Kronecker Delta
Numerical and Symbolic Derivatives
Tensor Diagonals
Numerical and Symbolic Divergence
Expressions to Characters
Numerical and Symbolic Einstein Summation
Levi-Civita Symbol
Evaluate Characters and Expressions
Numerical and Symbolic Gradient
Numerical and Symbolic Difference
Numerical and Symbolic Division
Numerical and Symbolic Dot Product
Numerical and Symbolic Inner Product
Numerical and Symbolic Kronecker Product
Numerical and Symbolic Outer Product
Numerical and Symbolic Product
Numerical and Symbolic Sum
Hermite Polynomials
Numerical and Symbolic Hessian
Tensor Indices
Numerical Integration
Numerical and Symbolic Jacobian
Numerical and Symbolic Laplacian
Numerical and Symbolic Matrix Product
Numerical and Symbolic Determinant
Numerical and Symbolic Matrix Inverse
Numerical and Symbolic Matrix Trace
Ordinary Differential Equations
Integer Partitions
Taylor Series Expansion
Wrap Characters in Parentheses
Efficient C++ optimized functions for numerical and symbolic calculus as described in Guidotti (2022) <doi:10.18637/jss.v104.i05>. It includes basic arithmetic, tensor calculus, 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 (Gradient, Jacobian, Hessian, Divergence, Curl, Laplacian) and numerical integration in arbitrary orthogonal coordinate systems: cartesian, polar, spherical, cylindrical, parabolic or user defined by custom scale factors.