-----BEGIN PGP SIGNED MESSAGE----- Hash: SHA1 Hi,
There are some inconsistencies in linear algebra over fields like CDF. Some trouble was already reported in #2256. The following is another issue: sage: M = matrix(CDF, 2, 2, [(-1 - 2*I, 5 - 6*I), (-2 - 4*I, 10 - 12*I)]) sage: M.is_invertible() True sage: M.determinant() 5.3290705182e-15 + 1.7763568394e-15*I sage: M.inverse() [ 1.01330991616e+15 - 2.58956978574e+15*I -5.06654958079e+14 + 1.29478489287e+15*I] [ 5.62949953421e+14 + 5.62949953421e+14*I -2.81474976711e+14 - 2.81474976711e+14*I] So because of roundoff errors, Sage thinks that we have an invertible matrix. But the code for echelon_form knows that it's not invertible: sage: M.echelon_form() [ 1.0 1.4 + 3.2*I] [-2.22044604925e-16 - 4.4408920985e-16*I ~ 0] sage: M.rank() 1 This behavior is inconsistent. Either there is enough precision to decide that the matrix is invertible, or there isn't. Doing this in two different ways should not yield two mutually exclusive answers. Similar problems occur over CC. I hope it's clear by now that I have no idea how CDF and friends actually work, so I don't know what would be a good solution or even whether such a solution should exist. My initial guess would be that finding the determinant requires more computations so there is more precision loss than in computing the echelon form; in that case, maybe over such fields we should not base is_invertible() and inverse() on determinant() but rather on echelon_form(). Note also that this problem does not seem to occur over RR or RDF. Best, Alex - -- Alexandru Ghitza Assistant Professor Department of Mathematics Colby College Waterville, ME 04901 http://bayes.colby.edu/~ghitza/ -----BEGIN PGP SIGNATURE----- Version: GnuPG v2.0.7 (GNU/Linux) Comment: Using GnuPG with Mozilla - http://enigmail.mozdev.org iD8DBQFH//uydZTaNFFPILgRArYKAJ4r9QOJNYSSCgVzSutUW7gEfcv3uQCfd3aj nYV2EFH6znwShoGL7q2BjRY= =74HR -----END PGP SIGNATURE----- --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
