MathExpr.jl

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MathExpr.jl provides (1) parser parseexpr for mathematical expressions using Julia's parser, and (2) exact methods for determinant and inverse for matrices (determinant and inverse).

Expressions supported by the parser include:

• Unary operations: + and -
• Binary operations: +, -, *, /, //, \, ^
• Mathematical functions
  • cos, sin, tan
  • cosh, sinh, tanh
  • exp, cis
  • cospi, sinpi, cispi
  • sqrt
  • log
  • abs, abs2, sign
  • conj, real, imag, angle
• Mathematical constants
  • i, im
  • pi, π

julia> using MathExpr

julia> parseexpr("cos(0.75π)+i*sin(0.5*pi)")
 -0.7071067811865475 + 1.0im

julia> parseexpr("[cos(0.1) sin(0.1); -sin(0.1) cos(0.1)]")
2×2 Array{Float64,2}:
  0.995004   0.0998334
 -0.0998334  0.995004

"Exact" determinant and inverse support matrices of integers and rational numbers.

julia> inverse([2 0; 1 2])
2×2 Array{Rational{Int64},2}:
  1//2  0//1
 -1//6  1//3

julia> determinant([2 0; 1 3])
6

Note that determinant and inverse are also defined for floating points. They simply call LinearAlgebra's det and inv.

julia> det([2.0 0.0; 1.0 3.0])
6.0

julia> inv([2.0 0.0; 1.0 3.0])
2×2 Array{Float64,2}:
  0.5       0.0
 -0.166667  0.333333