I think you got it, but I'm just adding this below in case someone else is
also interested:
Here, this sequence defines a symbolic x, and that function f, and then
checks the types
x = var('x')
f=lambda x: x*sin(x)
type(f)
type(f(x))
and f(x) is still a symbolic expression.
Now we change x to be a floating point number
x = 9.81
type(f(x))
which gives us a *number* as a result.
And adding on top of your "conversion into symbolic expression", another
POV is that you can use python functions to construct
an
expression
programmatically. E.g. less trivial:
def builder(v1, n):
ex = 1 + v1
for i in range(n):
ex = (i + v1) * ex^2
return ex
x = var('x')
builder(x, 5)
gives (x + 4)*(x + 3)^2*(x + 2)^4*(x + 1)^40*x^16
-- harald
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