Thank you all for the thoughtful responses, your comments helped me a lot.
One last bit of trouble that I've been having related to this topic. This
was is the code I was running:
Mz = matrix([[0,1],[1,0]])
Mx = matrix([[1,0],[0,-1]])
M1 = Matrix([[1,0],[0,1]])
import numpy as numpy
#R.<s> = QQ[]
_ = var('J,hx,alpha')
alphas = numpy.linspace(0,1,10)
Bp = Mz.tensor_product(M1).tensor_product(M1).tensor_product(M1) * M1.
tensor_product(Mz).tensor_product(M1).tensor_product(M1) * M1.tensor_product
(M1).tensor_product(Mz).tensor_product(M1) * M1.tensor_product(M1).
tensor_product(M1).tensor_product(Mz)
Plaqz = Mx.tensor_product(M1).tensor_product(M1).tensor_product(M1)
F = lambda s: -(1-s)*Bp - s*Plaqz
show(F(.1).eigenvalues())
If I run it, it gives me results with the error: "
UserWarning: Using generic algorithm for an inexact ring, which will probably
give incorrect results due to numerical precision issues."
I expected this error to be some minute difference in the far out decimal place
range, like I so often see with
complex numbers, but the answer I get is actually Quite a bit off from the
correct answer. Upon googling, i found that this can
be fixed by appending CDF to the beginning of every matrix definition, like
this:
Mz = matrix(CDF,[[0,1],[1,0]])
Mx = matrix(CDF,[[1,0],[0,-1]])
M1 = Matrix(CDF,[[1,0],[0,1]])
import numpy as numpy
#R.<s> = QQ[]
_ = var('J,hx,alpha')
alphas = numpy.linspace(0,1,10)
Bp = Mz.tensor_product(M1).tensor_product(M1).tensor_product(M1) *
M1.tensor_product(Mz).tensor_product(M1).tensor_product(M1) *
M1.tensor_product(M1).tensor_product(Mz).tensor_product(M1) *
M1.tensor_product(M1).tensor_product(M1).tensor_product(Mz)
Plaqz = Mx.tensor_product(M1).tensor_product(M1).tensor_product(M1)
F = lambda s: -(1-s)*Bp - s*Plaqz
show(F(.1).eigenvalues())
My question is, why is the default an alg that seems to give incorrect answers,
instead of just defaulting to CDF?
Also, is there a better way of doing this besides just appending CDF to the
beginning every time?
Thank you!
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