Issue with creating rule for even and odd function of cos and sin

[yewalenikhil65]

using SymbolicUtils
@syms z
r  = @acrule(cos(-1(~x)) => 1*cos(~x))

gives as expected

julia> r(cos(-z))
cos(z)

but for following, it doesn't work

julia> r(cos(-2z))

gives nothing

Can any one help me to generalise this rule ?

[NilsNiggemann]

Why was this closed as completed?
As far as I can see, this is still not working and in particular one cannot use it to simplify expressions in Symbolics.jl.

julia> r  = @acrule(cos(-1(~x)) => 1*cos(~x))
ACRule(cos(-1 * ~x) => 1 * cos(~x))

julia> simplify(cos(a) - cos(-a),rewriter = r)
cos(a) - cos(-a)

julia> r = @rule cos(-(~x))  => cos(~x)
cos(-(~x)) => cos(~x)

julia> simplify(cos(a) - cos(-a),rewriter = r)
cos(a) - cos(-a)

arguably, these properties should be included in the standard rules, or at least there should be some mention in the docs if it is not possible to make them work.

[yewalenikhil65]

@NilsNiggemann I was told by Symbolics code maintainer to close it since it was answered to me on slack.. I will post details how i did it as soon as possible next week and try to make a PR out of this

[karlwessel]

I had the same issue and solved it with the following rule for cosine:

isnegative(x) = x < 0
cosrule = @rule cos(*(~a::isnegative, ~~x)) => cos(*(-(~a), (~~x)...))

and similar for sine.