This is a c++ math library. It provides :

• abstract mathematical objects

  groups, vector spaces, algebras, etc.

• some specific instances of such objects

  geometric algebra, which includes complex numbers, quaternions, and much more. todo : geometric transformation groups (rotations, translations, isometries, similarities).

• coordinate free geometry

  Never again write something like Vector3d{1., 2., 0.} and then the compiler doesn't know in which frame those coordinates are (and maybe you don't either). Instead, use meaningful directions like 1.*up+2.*east+0.*north. But here 0.*north is superfluous, so just write up+2*east. And if you have several frames, don't bother changing frame explicitly, just write 1.3*my_frame_x + 2.4*my_other_frame_z.

Mathematical objects and expressions are represented by c++ types. Operations on those types are made by constexpr functions. It can effectively turn your compiler into a symbolic math software. The resulting program would only print the result that have been computed at compile time.

No need to specify in advance a space in which to work, new types are generated if new dimensions appear in an expression. If you write auto a=3*x+4*y, a stores two values in a type generated from the expression "double*x+double*y". Then, writing a+2.5*z will just generate a larger type holding three values (assuming z is not a combination of x and y).

It is small because it exploits centuries of work from mathematicians. They have put many concepts into the most beautiful form they could find : both as general and as simple as possible, which means factorized and simple code. The library also uses c++17 with concepts, which provides human friendly template programming.

They are a good place to look for examples. They make sure things work as intended.