John Cremona wrote: > 2008/9/23 pong <[EMAIL PROTECTED]>: >> >> I tried >> >> sage: A=matrix([[1,1],[2,3]]) >> sage: A.eigenvalues() >> [0.2679491924311228?, 3.732050807568878?] >> >> My question is why the last digit before ? in 0.2679491924311228? is >> '8'? Shouldn't it be "7" according to >> >> sage: ch=characteristic_polynomial(A) >> sage: solve(ch(x)==0,x) >> [x == 2 - sqrt(3), x == sqrt(3) + 2] >> sage: N(2-sqrt(3), digits=18) >> 0.267949192431122706 >> >> >> >> > > Alternatively: > > sage: e1,e2= A.eigenvalues() > sage: e1 > 0.2679491924311228? > sage: e1.interval(ComplexIntervalField(53)) # the default is 53 bits precision > 0.2679491924311228? > sage: e1.interval(ComplexIntervalField(100)) > 0.267949192431122706472553658494? > sage: e1.interval(ComplexIntervalField(200)) > 0.267949192431122706472553658494127633057194746189619371944193? > > i.e. e1 is a number of a type which is essentially infinite precision, > and you can ask for it to any desired precision later. > > However I'm still not sure why the original display ends 8? and not > 7?. The ? notatation was introduced quite recently, so I am not sure > whether this is a feature or a bug.
To me, it looks like it may be a bug: sage: A=matrix([[1,1],[2,3]]) sage: e1,e2=A.eigenvalues() sage: e1.interval(ComplexIntervalField(53)) 0.2679491924311228? sage: b=e1.interval(ComplexIntervalField(53)) sage: b 0.2679491924311228? sage: b.str(style='brackets') '[0.26794919243112269 .. 0.26794919243112276]' The question mark notation indicates that this last interval (the "real" interval) should lie inside of [0.2679491924311227 .. 0.2679491924311229] But it doesn't seem to lie in that range. Carl, what do you think? Thanks, Jason > > John Cremona > > > > --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-support@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-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
