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I played with this a little, and I think I've been able to at least focus the problem a little more (using your f above):

sage: lambdas = [lambda x,y:f(x,y,t) for t in [0,1]]
sage: lambdas[0](.5,.5)
e^(-1)*sin(0.500000000000000*pi)^2
sage: lambdas[1](.5,.5)
e^(-1)*sin(0.500000000000000*pi)^2

So one aspect of the problem seems to be that the second lambda is overwriting the first

I played with this a little, and I think I've been able to at least focus the problem a little more (using your f above):

sage: lambdas = [lambda x,y:f(x,y,t) for t in [0,1]]
sage: lambdas[0](.5,.5)
e^(-1)*sin(0.500000000000000*pi)^2
sage: lambdas[1](.5,.5)
e^(-1)*sin(0.500000000000000*pi)^2

So one aspect of the problem seems to be that the second lambda is overwriting the firstfirst..

>>> lambdas = [lambda x,y: x*y*t for t in [1,2]]
>>> lambdas[0](2,3)
12
>>> lambdas[1](2,3)
12

I played with this a little, and I think I've been able to at least focus the problem a little more (using your f above):

sage: lambdas = [lambda x,y:f(x,y,t) for t in [0,1]]
sage: lambdas[0](.5,.5)
e^(-1)*sin(0.500000000000000*pi)^2
sage: lambdas[1](.5,.5)
e^(-1)*sin(0.500000000000000*pi)^2

So one aspect of the problem seems to be that the second lambda is overwriting the first..

UPDATE:

Oh wow -- this is a python bug!

>>> lambdas = [lambda x,y: x*y*t for t in [1,2]]
>>> lambdas[0](2,3)
12
>>> lambdas[1](2,3)
12

>>> f = lambda t: lambda x,y: x*y*t
>>> f(2)(2,3)
12
>>> f(1)(2,3)
6

def f(x,y,t): return(sin(pi*x)*sin(pi*y)*e^(-t)) 
base_frame = point3d((.5,.5,1), color='red', size=10)
L = lambda t: lambda x,y: f(x,y,t)
var('x,y')
(x, y)
frames = [plot3d(L(t)(x,y), (x, 0, 1), (y, 0, 1))+base_frame for t in [0,1]]

frames[0]

frames[1]

I played with this a little, and I think I've been able to at least focus the problem a little more (using your f above):

sage: lambdas = [lambda x,y:f(x,y,t) for t in [0,1]]
sage: lambdas[0](.5,.5)
e^(-1)*sin(0.500000000000000*pi)^2
sage: lambdas[1](.5,.5)
e^(-1)*sin(0.500000000000000*pi)^2

So one aspect of the problem seems to be that the second lambda is overwriting the first..

UPDATE:

Oh wow -- this is a python bug!bug! (Or is it a feature? PEP 227 seems to address something relevant; note especially the "Discussion" and "Examples" sections)

>>> lambdas = [lambda x,y: x*y*t for t in [1,2]]
>>> lambdas[0](2,3)
12
>>> lambdas[1](2,3)
12

UPDATE 2:

This morning I realized how to work around this problem: use nested lambda functions!

A python example:

>>> f = lambda t: lambda x,y: x*y*t
>>> f(2)(2,3)
12
>>> f(1)(2,3)
6

And a 3d plot example:

def f(x,y,t): return(sin(pi*x)*sin(pi*y)*e^(-t)) 
base_frame = point3d((.5,.5,1), color='red', size=10)
L = lambda t: lambda x,y: f(x,y,t)
var('x,y')
(x, y)
frames = [plot3d(L(t)(x,y), (x, 0, 1), (y, 0, 1))+base_frame for t in [0,1]]

frames[0]

frames[1]