Well... the error message is pretty explicit: since
sage: SR.is_exact()
False
M.gram_schmidt() wont work if M.base_ring is SR.
Creating a second special case for SR may not be as simple as for RDF,
since a lot of other cases (beyond RDF) can happen in this case....
Le mardi 22 octobre 2019 17:03:52 UTC+2, Michael Jung a écrit :
>
> Hello everyone,
> I have a question regarding the implemented Gram-Schmidt procedure. Using
> a matrix in the symbolic ring leads to the following error message:
>
> m = matrix(SR, [[x,2*x],[x^2,1]])
> m.gram_schmidt()
>
> ---------------------------------------------------------------------------
> NotImplementedError Traceback (most recent call last)
> <ipython-input-21-6b8bbf989823> in <module>()
> 1 m = matrix(SR, [[x,Integer(2)*x],[x**Integer(2),Integer(1)]])
> ----> 2 m.gram_schmidt()
>
> /home/michi/GitProjects/sage/local/lib/python3.7/site-packages/sage/matrix/matrix2.pyx
> in sage.matrix.matrix2.Matrix.gram_schmidt
> (build/cythonized/sage/matrix/matrix2.c:70206)()
> 9871 Q, R = self.transpose()._gram_schmidt_noscale()
> 9872 else:
> -> 9873 raise NotImplementedError("Gram-Schmidt orthogonalization
> not implemented for matrices over inexact rings, except for RDF and CDF")
> 9874 return Q.transpose(), R.transpose()
> 9875
>
> NotImplementedError: Gram-Schmidt orthogonalization not implemented for
> matrices over inexact rings, except for RDF and CDF
>
>
> Why isn't it possible to compute an orthonormal basis from vectors with
> entries in the symbolic ring? I see no problem in that. What happens behind
> the scenes?
>
> Thanks in advance and best wishes
> Michael
>
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