Derivative of `sinpi(2x)` evaluates pi numerically when differentiating

[Joel-Dahne]

With Symbolics v4.2.3 we get

julia> @variables x
1-element Vector{Num}:
 x
julia> sinpi(2x)
sinpi(2x)
julia> Symbolics.derivative(sinpi(2x), x)
6.283185307179586cospi(2x)

Whereas we would expect the result 2πcospi(2x). Somehow the π gets mixed up with the 2, for example we also have

julia> Symbolics.derivative(sinpi(big(2)x), x)
6.283185307179586476925286766559005768394338798750211641949889184615632812572396cospi(2x)

The same happens to cospi as well.

┆Issue is synchronized with this Trello card by Unito

[Joel-Dahne]

After looking a bit more at this I realize that the issue seems to be that Symbolics.jl doesn't have a symbolic representation of π at all. So the issue is not related to sinpi or cospi at all. Feel free to close it if you don't think it is relevant.

I can maybe note that I'm even more confused about Symbolics.derivative(sin(π * x), x) = 3.141592653589793cos(πx), here the π is converter to Float64 outside the cos but not inside.

[kbarros]

Having a symbolic representation of π would be very valuable and (I think) an eventually planned feature. Is there already an issue for that?

[Joel-Dahne]

Actually I don't find one when searching for pi or irrational in the open issues. I got to that conclusion from this post. It is related to #497 but not quite the same. A symbolic representation of general irrational numbers would be very convenient to have indeed!

[edljk]

With Symbolics v6.51.0 I still get the same result regarding the differentiation of sinpi function.
Is there a workaround to preserve the precision of x when evaluating pi?

[ChrisRackauckas]

not yet