On 12/10/10 2:36 PM, Joris Vankerschaver wrote:
Dear all,
Is there a reason why Sage doesn't allow you to define vector
functions using the following short hand:
sage: Q = var('x, y, z')
sage: f(Q) = [x - z, y - z]
sage: f
Q |--> (x - z, y - z)
I would have expected/liked the last line to be
sage: f
(x, y, z) |--> (x - z, y - z)
We recently implemented what you want, but it's slightly different
syntax (and for good reason).
1. When using the f(...)=... syntax, the preparser first does some magic
to auto-declare the variables:
sage: preparse('f(Q)=[x-z,y-z]')
'__tmp__=var("Q"); f = symbolic_expression([x-z,y-z]).function(Q)'
Notice that it declares the variable "Q" there.
2. To get what you want, just name the variables (of course, order
matters here):
sage: f(x,y,z)=[x-z,y-z]
sage: f
(x, y, z) |--> (x - z, y - z)
Note that you don't have to do var('x,y,z') since the variables are
auto-declared:
sage: preparse('f(x,y,z)=[x-z,y-z]')
'__tmp__=var("x,y,z"); f = symbolic_expression([x-z,y-z]).function(x,y,z)'
Personally, I like to use parentheses around the function on the right,
since then it looks more like a vector, but the code takes either a list
or tuple (parentheses or square brackets):
sage: f(x,y,z)=(x-z,y-z)
sage: f
(x, y, z) |--> (x - z, y - z)
3. If you *really* want to use Q like you did above, you could do this:
sage: Q=var('x,y,z')
sage: f(*Q)=(x-z,y-z)
sage: f
(x, y, z) |--> (x - z, y - z)
Thanks,
Jason
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