On 26 jan, 12:47, D. S. McNeil dsm...@gmail.com wrote:
(-6.66133814775094e-16, -1.00)
---???
Why isn't the first coordinate 0??? In theory it should be...
Such things are basically inevitable with floating point whenever any
number involved can't be perfectly represented-- and in this case
sqrt(2) is irrational to boot. Sometimes you luck out and sometimes
you don't. help(RR) gives a brief warning. Here I think you can
avoid the problem by working not in RR (2^(-53) ~ 1e-16) but the
symbolic ring SR.
I wasn't sure if it was the representation problem...
sage: V=VectorSpace(RR,2,inner_product_matrix=[[1, -sqrt(2)/2], [-
sqrt(2)/2, 1]])
sage: V.basis()
[
(1.00, 0.000),
(0.000, 1.00)
]
sage: V=VectorSpace(SR,2,inner_product_matrix=[[1, -sqrt(2)/2], [-
sqrt(2)/2, 1]])
sage: a,b = V.basis()
sage: a,b
((1, 0), (0, 1))
sage: r1=Sigma(a,b);r1
(sqrt(2), 1)
sage: r2=Sigma(r1,a);r2
(-1, -sqrt(2))
sage: r3=Sigma(r2,r1);r3
(0, -1)
This change does the thing!!! It is perfect for me!!
If you really want to work in floating point you're going to have to
loosen your definition of equality -- see,
e.g.,http://floating-point-gui.de/errors/comparison/-- possibly doing so
rigorously with interval arithmetic.
Doug
--
Department of Earth Sciences
University of Hong Kong
Thanks a lot!
J-P
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