Multiplying NumberSymbols turns them into their numerical approximation

[mkualquiera]

When a NumberSymbol such as pi is multiplied by a number or negated, it is converted to a Float64:

julia> typeof(pi)
Irrational{:π}

julia> typeof(pi*2)
Float64

For comparison, this is the result in python:

>>> type(pi)
<class 'sympy.core.numbers.Pi'>
>>> type(2*pi)
<class 'sympy.core.mul.Mul'>

This breaks any symbolic computation that involves such constants and their properties, for instance:

julia> i = symbols(:i, integer=True)
i

julia> sin(i*pi)
0

julia> sin(i*-pi)
-sin(3.14159265358979⋅i)

[jverzani]

Yes, this is true. You have to be wary of eager conversion to floating point before a value is converted to a symbolic value. In this case you can use PI (which is the same as PI=Sym(pi)) and the symbolic value will force others numbers to promote to symbolic values.

(As an example. Even this 1/2*PI will be an issue as 1/2 will be a floating point number. To avoid this you can use rationals, as in 1//2 * pi, or reexpress, as in PI/2.

Hope that clarifies.