On 9/13/07, Justin C. Walker <[EMAIL PROTECTED]> wrote:
> A question about callable functions: I would like to create one, say
> "f(x,y)=x^2+y^2". There are several ways to do this:
Why. What problem are you trying to solve?
> - f = x^2+y^2
> This works but "f(a,b)" fails (it's not really "callable")
This is a symbolic expression. You can do:
f(x=a, y=b)
or
f.subs(x=a, y=b)
>
> - R.<x,y> = PolynomialRing(ZZ)
> g = x^2+y^2
> This works and "g(a,b)" does what I want. It seems kind
> of heavy-weight, though (I've now got a polynomial ring
> floating around when I don't really need it).
Actually polynomial rings aren't very big. They're just a few bites. :-)
> sage: h(x,y)=x^2+y^2
> sage: h
> (x, y) |--> y^2 + x^2
> sage: h(0,1)
> 1
> sage: print h(0,1)
> 1
> sage: type(h(0,1))
> <class 'sage.calculus.calculus.SymbolicArithmetic'>
>
> So, questions:
>
> - why is h(0,1) not an 'Integer'? Does that matter? I have some
> code (hacks, admittedly) that wants to be sure it's dealing with
> integers.
h(0,1) is a symbolic expression. If you want an integer, you would
have to write Integer(h(0,1)).
> - The fact that 'print h(0,1)' produces a bizarre result is really
> a bother, because I can't bank on formatting (unless I am missing
> something; it wouldn't be the first time, of course).
It's ascii art. If you just need a normal string without any
ascii art, do
print repr(h(0,1))
> - Is there some 4th alternative that I missed?
Yes, there are two more, which might be fine, depending on
your application:
def h(x,y):
return x^2 + y^2
and
h = lambda x,y: x^2 + y^2
Probably the very last one is exactly what you really want,
unless you want to do arithmetic with it (h^2 doesn't make
any sense).
> To complicate matters, I want to create these things in code, and
> return the result, to be used later, either directly or in other code.
The code analogue of "h(x,y) = x^2 + y^2" is:
sage: preparse('h(x,y) = x^2 + y^2')
'_=var("x,y");h=symbolic_expression(x**Integer(2) +
y**Integer(2)).function(x,y)'
I.e., make x and y symbolic, make the expression x^2 + y^2, and
finally make it into a function of x and y.
> Comments?
>
> Thanks for the help, in advance.
Please ask more questions.
-- William
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