Test for constant expressions in Symbolics.jl

New to Julia
1

I am using Symbolics.jl and wish to test a symbolic expression to see if is a constant. The only way I can think of is to see if all the derivatives with respect to the independent symbolic variables are zero. I think there must be an simpler way. I have a two dimensional symbolic array and need to determine if all the entries are constants (not functions of a set of independent variables). I am taking the derivatives of the metric tensor if the tensor is not constant.

2

Yeah there probably is a quicker way using coeff.

3

I could probably convert the expression to a string and use regex to see if the string contains the names of any independent variables which I do know. For example if the string contains x, y, or z it is not constant even though it could contain a or b which are not independent variables or functions containing a or b.

4

Is there anyway to use the expression tree of a symbolics expression to see if it contains any in a list of independent variables?

5

I tried the following code -

#!/snap/bin/julia

using Pkg
Pkg.activate("symbolics", shared = true)
using Symbolics
using SymbolicUtils

@variables x,y,z

expr = x*sin(y)*z^2

println(SymbolicUtils.istree(expr))

and the answer was false. Am I doing something wrong here because if istree is true I can use the arguments function to see if a particular arg is in the tree.

6

You have to remove the Num wrapper to get at the BasicSymbolic inside:

julia> typeof(expr)
Num

julia> typeof(Symbolics.unwrap(expr))
SymbolicUtils.BasicSymbolic{Real}

julia> SymbolicUtils.istree(Symbolics.unwrap(expr))
true

julia> SymbolicUtils.arguments(Symbolics.unwrap(expr))
3-element Vector{Any}:
 x
 z^2
 sin(y)

Then I think you have to keep recursively applying arguments, and collecting the results until nothing istree