Ivory: Indeterminates
TODO
- Adjoin with an indeterminate
v, which is commutative - Start with
univariate-monomial, i.e. individual powersv^0,v^1,v^2,v^3, etc. - These don’t collapse since there are no identities like
d^2 = 0, etc. - Technically an infinite-dimensional vector space. Is this useful to our implementation?
- Introduce other indeterminates
v1,v2, etc. to get general monomials - Introduce “degree”, and
homogeneouspolynomials which sum monomials of the same degree - Useful for projective geometry, etc.
Beyond the number lines
In the geometric level we found values which do not
appear on a simple “number line”, but instead inhabit a larger space
full of interesting geometrical structure such as rotations. This
structure could be neatly described using our existing notions of
arithmetic, if we allow some extra values like i₀,
d₂, etc.