sonium wrote:
> Hi, I have problems calculating the eigenvectors of a symbolic matrix.
> I tried:
>
> a,b = var('a'),var('b')
> M = matrix(SR,4,4,((a, 0, 0, 0), (0,-a,0,0), (0,0,a,0), (0,0,0,-a)))
> M.eigenvectors_right()
>
> what results in:
> AttributeError: 'SymbolicArithmetic' object has no attribute 'degree'
>
This comes from us not having a special implementation of the eigen
functions for symbolic matrices (i.e., using maxima). For now, you can do:
sage: a,b = var('a'),var('b')
sage: M = matrix(SR,4,4,((a, 0, 0, 0), (0,-a,0,0), (0,0,a,0), (0,0,0,-a)))
sage: M._maxima_().eigenvectors().sage()
[[[-a, a], [2, 2]], [0, 1, 0, 0], [0, 0, 0, 1], [1, 0, 0, 0], [0, 0, 1, 0]]
See
http://maxima.sourceforge.net/docs/manual/en/maxima_25.html#Item_003a-eigenvectors
to understand the output of the command.
The specific error you received came from there not being a .degree()
method for a symbolic polynomial.
> and
>
> P.<a,b> = PolynomialRing(QQ)
> M = matrix(P,4,4,((a, 0, 0, 0), (0,-a,0,0), (0,0,a,0), (0,0,0,-a)))
> M.eigenvectros_right()
>
> what gives:
>
> Traceback (most recent call last):
> File "<stdin>", line 1, in <module>
> File "/home/sage/sagenb/sage_notebook/worksheets/sonium/1/code/
> 26.py", line 6, in <module>
> M.eigenvectors_right()
> File "/home/sage/sage_install/sage-a/local/lib/python2.5/site-
> packages/SQLAlchemy-0.4.6-py2.5.egg/", line 1, in <module>
>
> File "matrix2.pyx", line 3054, in
> sage.matrix.matrix2.Matrix.eigenvectors_right (sage/matrix/matrix2.c:
> 18020)
> File "matrix2.pyx", line 3000, in
> sage.matrix.matrix2.Matrix.eigenvectors_left (sage/matrix/matrix2.c:
> 17523)
> File "matrix2.pyx", line 2755, in
> sage.matrix.matrix2.Matrix.eigenspaces_left (sage/matrix/matrix2.c:
> 16250)
> File "matrix2.pyx", line 1058, in sage.matrix.matrix2.Matrix.fcp
> (sage/matrix/matrix2.c:7456)
> File "polynomial_element.pyx", line 2288, in
> sage.rings.polynomial.polynomial_element.Polynomial.factor (sage/rings/
> polynomial/polynomial_element.c:18681)
> NotImplementedError
I'm not sure what is going on here...
Thanks,
Jason
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