Dual d(x) such that d(v) * v = I See: eq 124 of PGA4CS

Dual d(x) such that v * d(v) = sign * I where sign = e * ~e and e = v.nondegenerate()

Retrieve the minimal integer dtype for holding a given integer value

Retrieve a bivector step, or integrated-rate variable, from relative body motor states

Should only hit this with degenerate components present

Iteratively solve the quadratic equations prod(x, s, x) = 1, for the inverse square root x, using a newton iteration: https://en.wikipedia.org/w

Put an array of blades in canonical order, as defined by this factory

Parse an algebra description in string format Parameters ---------- description: str Returns ------- names : Tuple[str] signature: Tuple[Sign

Given a string like 'yx' parse it into recognized basis tokens

Verlet post integration step; deduce rates from change in motors, after constraint relaxation

Verlet pre integration step; inertial update of the bodies, ignoring constraints

b onto a

l * r.pseudoscalar_negation()

Generalized Euler's rotation equation forque = d/dt momentum momentum = Inertia(rate) Thats all there is to it really.

Restrict i to o; drop terms not in o

l * ~r

Dual d(x) such that v * d(v) = I See: eq 124 of PGA4CS

l * r.scalar_negation()

Scalar product (l * r)<0>; only grade-0 part of geometric product

Subspace selection The returned multivector contains all components inside the selected subspace. Those components not present in the input multi

Simplex inertia via uniform random sampling of the simplex

Compute barycentric weighting matrix, mapping uniform density simplex, to its equivalent vertex-lumped-mass simplex

split point-pair bivector into two vector-valued points

Jax specific part of main loop, to be compiled

Jax specific part of main loop, to be compiled

Conjugation; or combined reversion and involution

l * r.study_conjugate()

Sum over a broadcastable axis

Sum over a broadcastable axis

x * x.conjugate()

x * x.involute()

Compute (~R * v) * R, while preserving the outermorphism That is, transform(R, v) ^ transform(R, u) == transform(R, v ^ u) Note; R is assumed norm

velocity-Relax the constraint set for one step

solve for velocity impulse exchange

Wedge product, or outer product