Symbolics.symplify must be invoked twice 2cos(x) - sin(2x)/sin(x)

General Usage
,
1

Dear all, why do I have to invoke symplify twice?

using Symbolics # v6.29.2, julia 1.11.4
@variables x
v = 2cos(x) - sin(2x)/sin(x)
va = simplify(v)  # not simplified
vb = simplify(va) # 0
1 Like
2

This is similar to Mathematica’s Simplify vs FullSimplify. A rule-based simplifier just runs through its set of rules. If you want to run it to convergence we could put a fixed point iteration on it with a separate full_simplify function, though it’s not guaranteed to converge.

3

Here is a simple fixed point combinator

fix(f, eq) = x -> let y = f(x)
                      while !eq(x, y)
                          x, y = y, f(y)
                      end
                      y
                  end

and it’s application:

julia> v |> fix(simplify, isequal)
0
2 Likes