How can I use ReplaceRepeated (//.) in this case?

Question

Consider the following case:

(a^3*b) //. {a^2 -> c, a*b -> d}

instead of c d the output is:

(*a^3*b*)

How can I get what I want?

Simplify[a^3 b, {a^2 == c, a b == d}] will return c d. Replacement rules will look for a pattern match, and won't really consider the underlying math. Since Power[a, 2] is not present as such in Times[Power[a,3], b], it does not get replaced. — MarcoB, Jan 27 '17 at 17:36

score 3 · Accepted Answer · answered Jan 27 '17 at 18:13

3

In general, you want to make the left hand sides of your rules as simple as possible. A simple way of doing what you want is

(a^3*b) //. {a -> Sqrt[c], b -> d/a}
(* c d *)

answered Jan 27 '17 at 18:13

mikado

score 1 · Answer 2 · answered Jan 27 '17 at 18:49

1

How about

Last@PolynomialReduce[a^3*b, {a^2 - c, a*b - d}, {a, b}]

c d

Or a more tricky

a^3*b //. {a^n_ :> c*Quotient[n, 2]*a^Mod[n, 2], 
  Times[r1___, a, b, r2___] :> Times[d, r1, r2]}

c d

answered Jan 27 '17 at 18:49

corey979

2 Answers2