Replace BTree with Vec in LinComb

[eupn]

Resolves #312.

Replaced BTreeMap with Vec of pairs (var, value). Unit tests passed, although the order of sum items that was dependent on the order of keys inBTreeMap is changed.

?r @Schaeff

[Schaeff]

Awesome, let me have a look at it! It's true that the BTreeMap representation has the advantage of being deterministic so great for testing, let's see what we can do there.

[Schaeff]

I think this is moving in the right direction :)
The main suggested changes are about

• Accepting all unreduced forms (even those where some variables have a canonical coefficient of 0) to remove linear complexity in addition and subtraction
• Move canonicalisation to the edges: Display and communication with the back end (I'll have a think about the latter, maybe it's not even necessary)

[Schaeff]

@eupn I had a quick go here https://play.rust-lang.org/?version=stable&mode=debug&edition=2018&gist=07c263548f34a377c3497a8b94d62a32
maybe that can help!

[eupn]

@eupn I had a quick go here https://play.rust-lang.org/?version=stable&mode=debug&edition=2018&gist=07c263548f34a377c3497a8b94d62a32
maybe that can help!

Got it, thanks a lot!

[Schaeff]

Hey @eupn I realise we don't tell contributors to do it but we use https://github.com/rust-lang/rustfmt.
I'll add this somewhere so it's clear!

[Schaeff]

Hey @eupn I think we're getting there! just a bit of context in the last change: the breaking test on 01c4d18 was due to the fact that that equality on programs (which is being tested) is derived automatically, so two lincomb that are "equivalent" (ie have the same canonical representation) are not "equal" (as they can have different representation in a vector of pairs). Therefore instead of making the optimizer canonical, I changed the definition of equality between lincomb to canonical equivalence.

Let me know if you have any thoughts or I missed something!

[Schaeff]

@eupn and on this last change, I made sure (2*~one + 3*~one) * (...) is recognised as linear: before the change, it would not try to reduce to 5*~one as the lincomb is of size > 1. Any lincomb of pairs of the same variable is reducable to a summand (coefficient times variable), not just 1-sized (canonical) lincombs.

[Schaeff]

LGTM