It would be interesting to be able to create an array of subscripted symbolic variables automatically

[mvainstein]

It would be nice to automatically create an array of subscripted variables given n with Symbolics:

For the case n=6, I would like to do what the code below does without having to type out the variables explicitly.

using Polynomials, Symbolics

@variables a₂ a₃ a₄ a₅ a₆
a = [0, 0, a₂, a₃, a₄, a₅, a₆]
p = Polynomial(a)

From the Symbolics docs, it is possible to do something like

@variables a[1:3]

but then I cannot start the array from index 0 or from another arbitrary value, which is what I want so that the index of the array matches the exponent of the monomial. I have managed to do this with Sympy, but would like to have the same kind of array with Symbolics.

[bowenszhu]

Try this

Symbolics.jl/src/variable.jl

Lines 450 to 452 in da72404

	function variables(name, indices...; T=Real)
	[variable(name, ij...; T=T) for ij in Iterators.product(indices...)]
	end

Symbolics.jl/src/variable.jl

Lines 470 to 477 in da72404

	function variable(name, idx...; T=Real)
	name_ij = Symbol(name, join(map_subscripts.(idx), "ˏ"))
	if T <: FnType
	first(@variables $name_ij(..))
	else
	first(@variables $name_ij::T)
	end
	end

using Symbolics
as = Symbolics.variables(:a, 0:3)

gives

4-element Vector{Num}:
 a₀
 a₁
 a₂
 a₃

And

using Symbolics
@variables t
as = Symbolics.variables(:a, 0:3, -1:2; T = Symbolics.FnType)
as = map(a -> a(t), as)

result:

4×4 Matrix{Num}:
 a₀ˏ₋₁(t)  a₀ˏ₀(t)  a₀ˏ₁(t)  a₀ˏ₂(t)
 a₁ˏ₋₁(t)  a₁ˏ₀(t)  a₁ˏ₁(t)  a₁ˏ₂(t)
 a₂ˏ₋₁(t)  a₂ˏ₀(t)  a₂ˏ₁(t)  a₂ˏ₂(t)
 a₃ˏ₋₁(t)  a₃ˏ₀(t)  a₃ˏ₁(t)  a₃ˏ₂(t)

[mvainstein]

Thanks! It worked.

[ChrisRackauckas]

No the suggested form is just to interpolate into the macro. I.e. @variables $x with some symbol for the name. This looks like in full:

x = :somesymbol
y = only(@variables($x))

where y is now the Julia name to a variable that is programmatically generated to have a name matching the symbol from the value of x.

The above post does not instantiate the metadata.

It would be nice for a simpler function to exist but it does not right now.