Rule List

[lukebhan]

This list will serve as a thread for new rules that are to be implemented. This is more of a larger goal todo then a specific issue, but I think organizing our future ideas can't hurt. I will update this list when a new rule idea is posted (also, this would be easier if one day github should support tex rending in issues and PRs) :

Addition

• [x] x+0 => x

  Subtraction

  • [x] x - 0 => x

    Multiplication

• [ ] x*1 => x
• [ ] ax+ay => a(x+y)

  Division

• [ ] x/1 => x

  Factoring/Cancellation

• [ ] handle polynomial factoring (x^2 + x) / x => x + 1

  Exponent Rules

• [ ] (x^a)*(x^b) => x^(a+b)
• [ ] (x^a)/(x^b) => x^(a-b)
• [ ] (x^a)/(y^a) => (x/y)^a
• [ ] (x^a)*(y^a) => (xy)^a
• [ ] (x^a)^b => x^(a*b)
• [ ] b_root ( x ^ a) => x^(a/b)
• [ ] x^0 => 1
• [ ] x^1 => x
• [ ] 1^a => 1
• [ ] 0^a => 0 for a > 0 ;)
• [ ] -1^n => 1 n even or -1 n odd - this could be far in the future

[ayazhafiz]

@luke-bhan there a large number of trivial rules (aka can be represented in the string form “lhs -> rhs”) that we can add. we should figure out some way to aggregate some mathematical identities and add them, or just add these trivial rules as we think of them.

For example, x^a*x^b -> x^(a+b)

[lukebhan]

I added some to get us started. I think if we were to find and aggregate list that'd be perfect.

[ayazhafiz]

https://www.researchgate.net/publication/2450227_A_Complete_Term_Rewriting_System_for_Decimal_Integer_Arithmetic