On Thursday, January 9, 2014 2:33:54 PM UTC-8, David Roe wrote: > > Hm. I agree with you. What about having two methods, eigenvalues_exact > and eigenvalues_approx? Working in the splitting field seems like a great > choice when the degree is small, and a horrible choice when the degree is > large. Currently eigenvalues has "extend" as a keyword parameter, which > can be True or False. Perhaps allow it to also be something a string > "splitting_field" or a parent for the eigenvalues to live in? > David >
We are just talking about shorthands for M.characteristic_polynomial().roots(<FIELD>) here. By analogy M.eigenvalues(<FIELD>) would seem reasonable. In fact, for exact fields there doesn't seem to be a good rationale to use "eigenvalues" at all: just look at the characteristic polynomial if you have a serious application that goes beyond an introductory linear algebra class. Of course, for matrices over inexact fields, it would make a lot of sense to have a separate "eigenvalues" routine that tries to take care of numerical stability. -- You received this message because you are subscribed to the Google Groups "sage-nt" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send an email to [email protected]. Visit this group at http://groups.google.com/group/sage-nt. For more options, visit https://groups.google.com/d/optout.
