On 11/23/11 1:32 AM, Tom Boothby wrote:
This is a little on the terse side, but it works quite generally.
And it isn't quite the same as Callable symbolic expressions. I.e., if
you have two variables, you can't specify the order when you create the
matrix.
On the other hand, doing something like
sage: var('x,y')
(x, y)
sage:
M=matrix(CallableSymbolicExpressionRing((x,y)),[[x+2*y,sin(x),cos(y)],[x,y,x^2+y]])
sage: M(1,2)
[ 5 sin(1) cos(2)]
[ 1 2 3]
Really behaves like a callable expression. It prints sort of ugly, though:
sage: M
[(x, y) |--> x + 2*y (x, y) |--> sin(x) (x, y) |--> cos(y)]
[ (x, y) |--> x (x, y) |--> y (x, y) |--> x^2 + y]
That could be improved, e.g., see the printing for vectors over callable
symbolic rings, which print the arguments outside of the vector:
sage: M[0]
(x, y) |--> (x + 2*y, sin(x), cos(y))
Note that the syntax f(x,y)=... is preparsed as:
sage: preparse('f(x,y)=[[x^2,y],[x,y]]')
'__tmp__=var("x,y"); f =
symbolic_expression([[x**Integer(2),y],[x,y]]).function(x,y)'
so really all that is needed is changing the symbolic_expression
function to create a symbolic matrix if a list of lists (or tuples) is
given, and then adding a .function() method to a symbolic matrix to give
a matrix with base ring CallableSymbolicExpressionRing (as above).
Bonus points if you make those matrices print out with the arguments
first, instead of having the arguments inside of each element. I've
done this for vectors [1], so that could be a pattern for what to do here.
Thanks,
Jason
[1] See the symbolic_expression code, which has this case:
elif isinstance(x, (tuple,list)):
return vector(SR,x)
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