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Galileo library

The Galileo math library currently has the following mathematical objects:

  • Number
  • Constant
  • Variable
  • Sum, Product and Fraction
  • Exp and Log
  • Trigonometric functions: CosF1, SinF1, TanF1 and their inverse: ACosF1, ASinF1, ATanF1
  • Matrix, with methods solve, LU factorization (implemented in method _lup)
  • Specific matrix implementations for sparse matrices and matrices with special structures:
    • LowerTriangularMatrix
    • UpperTriangularMatrix
    • OnesMatrix
    • EyeMatrix
    • DiagMatrix
  • Tensor. The tensor object is written with a view towards physics applications. The following operations are supported:
    • Raising and lowering of indices
    • Coordinate transformations
    • Templated creation for several common metrics (two sphere, three sphere, Schwarzschild, Minkowski...)
    • Differential geometry features include calculation of Ricci tensor, Ricci curvature, Riemann tensor, Weyl tensor; Christoffel symbols (first and second kind)

All of these objects implement the generic Expr trait.

Sample projects that use the Galileo library are available here: