(CCd to sage-devel) On 5/9/14, 13:32, David Guichard wrote:
Is there some deep reason I'm not seeing that G-S doesn't work for SR? It seems like everything should be fine. Is the problem in detecting dependent sets over SR? This keeps me from being able to do simple examples for a linear algebra class. I can do it over QQbar, but that's pretty ugly.
I ran into similar problems at one point with the LU decomposition, where it complained that the base ring was not exact. I think the problem ultimately is that if you are working in an 'inexact' ring, round-off error can be a bear (so you're right that detecting linear dependence is hard). The RDF and CDF matrices try to use numpy and stable algorithms for computing these sorts of things for real/complex floating point matrices.
Mike Hansen and I had a conversation about this at one point, and I think we concluded that instead of looking at the base ring in the case of SR, we should instead look at the specific matrix and decide if it was "exact" or an approximation. For example, an SR matrix with just integers and/or variables could be considered exact, while an SR matrix with floating point numbers wouldn't.
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