alg.math does concise formulas for custom types. Similar to operator overloading in other languages.

I'm making this for a private project which needs to do various types of algebraic math. Unless Alg takes on a life of its own, things will mostly be implemented whent I need them. Also I'm new to Zig and things are likely to not be idiomatic. Issues, comments, and requests are welcome, but will only be acted upon as I see fit.

Example:

var a = alg.mat.Matrix(f32, 2, 1).lit(.{
    1,
    2,
});
var b = alg.mat.Matrix(f32, 1, 2).lit(.{
    3, 4,
});
var c: f32 = 5;
var result = alg.math("a * b * c", .{
    .a = a,
    .b = b,
    .c = c,
});
try expectEqual(alg.mat.Matrix(f32, 2, 2).lit(.{
    15, 20,
    30, 40,
}), result);

Current limitations:

• Only a limited number of operations implemented so far.
• There is no order of operations. All chained operations must be the same. Use parethesis to determine order. Eg, "(a * b) + c".
• Chained operations are always carried out left to right. This may be inefficient for some equations, and not standard for others (eg, raising to a power).

All more complex types have a single underlying type, and all operations require the same underlying type between operands. Eg you can't add a matrix backed by floats with one backed by integers.

Implemented:

• Matrices:
  • Define matrix in terms of rows, and columns.
  • Addition between matrices of the same size.
  • Multiplication with compatible shaped matricies resulting in a third, possibly differently shapped, matrix.
  • Multiplication with scaler values, which multiplies each value in the matrix by the scaler.
• Imaginary Numbers:
  • Define in terms of real and imaginary parts.
  • Addition and Multiplication with other imaginary numbers.

Feature Wishlist:

• Types:
  • Floats
  • Integers
  • Comptime float and integers
  • Vectory / Array
  • Matrix
  • Affine Matrix
  • Geometic Algebra
  • Maybe custom functions?
  • Imaginary Numbers
  • Quaternion
• Operations
  • Add
  • multiply
  • dot
  • etc.
• Built in values?
  • e
  • pi
  • Identity matrix? Is this useful?
• Make parse errors actually useful.
• Pairwise conversion of underlying type.