On 04/16/2013 09:57 PM, GaryMak wrote:
Hi
I am trying to use plot functions for the first time in sage - apologies
if this is a dumb question for a change.
I have a square matrix M of fixed complex numbers which are then all
multiplied by a different phase depending on which column they are in.
(In the 2x2 example below M=[a,b;c,d] and column 1 is multiplied by
exp(i*theta) and column 2 is multiplied by exp(i*phi) ). I then take
another fixed matrix A away from M and take f=det(M-A).abs() as my
output. I have explicitly written this formula for A = [1,1;0,0] below.
So the function I would like to plot is f as a function of theta and phi
(in this case).
a = 1/2
b = - i/3
c = 1/4
d = i/5
theta, phi = var('theta,phi')
f(theta,phi) = ( (a*exp(i*theta)-1)*d*exp(i*phi) -
(b*exp(i*phi)-1)*c*exp(i*theta) ) . abs()
plot3d(f, (theta,0,pi), (phi,0,pi))
No matter how I try to do this, even if I explicitly write out the
complex conjugates of each element, I get what for me is a record-length
screed of error stuff ending in 'TypeError: unable to coerce to a real
number', originating in the command 'plot3d(...etc...)'. I have attached
a text file with the full output of one of my attempts.
I can see that in a way I am asking a lot of the interpreter; but then
again I feel I have explicitly made the thing real by the time it gets
to be an input for the plot3d function.
Is there any way around this, or do I have to start writing complexes as
a+bi etc and do it the hard way?
Many thanks
Gary
The problem is actually in the conversion of your function to a
fast_float() version of the function. Apparently, it fails for symbolic
"complex" functions (which are not really complex) even in this trivial
example:
f(theta, phi) = (theta + i * phi).abs()
ff = fast_float(f, 'theta', 'phi')
One trivial workaround is to define your function to be a python
function. Somehow, it works. :)
def f(theta,phi): return ( (a*exp(i*theta)-1)*d*exp(i*phi) -
(b*exp(i*phi)-1)*c*exp(i*theta) ) . abs()
plot3d(f, (theta, 0, pi), (phi, 0, phi))
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