extended simplify function rules to include fractions with coefficients

[luckyayush777]

Added a couple of new rules for expression parsing in case of fractions with coefficients. The expression mentioned in #2594 simplifies correctly now. Multi variable functional expressions with coefficients don't simplify yet. Don't know yet if there is a way to parse both single and multi variable (for instance 'w/5-(2w+3 + 2z)/2-3w/5') using a single rule. Probably not.

[josdejong]

Thanks Ayush.

Two things:

1. Can you add a couple of unit tests to validate that the rule works (and keeps working) as intended?
2. It indeed feels to me that the rule is still quite specific. In general, I think we would like to extract the constant part from the section inside parenthesis. So maybe a simpler rule is s: '(n1+c2)/c3 -> (n1/c3)+c2/c3'. But you have all the variations of what can be inside the parenthesis: (n1+c2)/c3, (n1-c2)/c3, (n1+n2+c2)/c3, etc. Basically: any constant part inside the numerator of a division. I think we cannot write that as a rule. What we can do is write a function (node) => node instead where we match the pattern we're looking for ourselves by looking at the expression tree (see docs). What do you think?

[josdejong]

@luckyayush777 did you see my feedbacks?

[gwhitney]

Thanks for finding these expressions that help with #2594. I am slightly confused by them -- there are two sign variants, but the sign is changed in two places. Are the other two possibilities where only one sign is changed instead of both needed? Why not? (Also I am unclear on the need for associativity in this identity; it seems to use only the distributive property, but I think we always assume that, I don't think there is a separate assumption for that.) Conversely, is there any way that these expressions can be merged into one -- that would help slow the ongoing growth of complication in simplify. I know there is a step where signs are merged into constants -- could this simplification possibly work with a single sign variant at a differentlocation? As another idea, would casting the rule as

(c1*v +c2)/c3 -> ((c1/c3)*v + c2/c3)

(this would now need a commutative assumption) perform any better, as it coalesces constants? Just some thoughts, I haven't tried any alternatives. Thanks for considering.

[gwhitney]

Ah, sorry, I hadn't focused entirely on Jos's feedback, which is excellent. Did you try his suggestion (n1+c2)/c3 -> n1/c3 + c2/c3? That might work well, especially in a place where all signs have been absorbed into constants so that there isn't any such thing as n1-c2 at that point. That might avoid the need for a function as Jos suggests because perhaps all of the "other stuff" that could be in the numerator that Jos mentions could be absorbed into the n1 term. Or possibly it could help to write it as (c2+n1)/c3 -> c2/c3 + n1/c3 because the simplifier prefers to match on the beginnings of terms? It is true and unfortunate that its operation is a bit finicky... Thanks for following up on these ideas if you can, and I was just about to add the comment about tests when I saw Jos already had.

[gwhitney]

Given the time since there's been a response and my interest in simplification, I am willing to try the changes proposed in this discussion.

[josdejong]

Thanks 👍