On Aug 12, 4:14 pm, Robert Dodier <robert.dod...@gmail.com> wrote:
> Agreed. That's a good argument for separating units from quantities
> in an expression. Then you can tell without ambiguity which symbols
> are supposed to be units.
This is definitely not my field of expertise, but how is this "working
with units" thing any different from working in a (Laurent) polynomial
ring?
Except for the fact that using units one might want to work only with
monomials (which should make things easier, no harder), all the
operations, comparisons and so on can be just done on top of (say for
seconds, meters, grams) the ring R[s{+-1}, m^{+-1}, g^{+-1}], where R
is any ring you want your "quantities" to belong to (real, complex, or
symbolic) and the distinction between units and quantities is quite
apparent.
If complicated units are to be involved, so that there are nontrivial
relations between them, then the ring to work would be the quotient of
the former one by the (monomial) relations relating the units. Finding
a "nicer representation" can easily rely on (easy, monomial) Groebner
bases. As a different viewpoint, the whole thing can also be thought
of as a group ring where the group is the free abelian group on the
units (modulo the relations). In any case, I think there is a sound
algebraic foundation underneath to make the underlying computations
easy enough. I am not talking about the "representation" that the
common user sees, but how I think the internal implementation should
be.
Maybe I misunderstood something, but why to start from scratch when
there is already so much algebra to use?
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