Hi, The issue is that .roots() now returns tuples with the root and its multiplicity. You can see this if you look at v. You need to select the 0th entry of the tuple to raise to a power.
sage: RDF = RealDoubleField() sage: R.<y> = PolynomialRing(RDF) sage: # Let y be x^(1/9). sage: f = y + RDF(2^(8/9) - 2^(1/9))*(y^9-1) - y^8 sage: v = f.roots(); v [(0.925874712287, 1), (1.0, 1), (1.08005973889, 1)] sage: [a[0]^9 for a in v] [0.5, 1.0, 2.0] --Mike On Mon, Apr 7, 2008 at 2:06 PM, John P. Burkett <[EMAIL PROTECTED]> wrote: > > Last September I asked how to use SAGE to find the roots of > f = x^(1/9) + (2^(8/9) - 2^(1/9))*(x - 1) - x^(8/9). > William Stein then kindly offered the following code: > sage: RDF = RealDoubleField() > sage: R.<y> = PolynomialRing(RDF) > sage: # Let y be x^(1/9). > sage: f = y + RDF(2^(8/9) - 2^(1/9))*(y^9-1) - y^8 > sage: v = f.roots(); v > sage: [a^9 for a in v] > > This code worked well on my machines when I first tried it. However, > today in SAGE 2.11 the same code running on the same machines produces > the following error message: > > <type 'exceptions.TypeError'> Traceback (most recent call last) > > /home/john/<ipython console> in <module>() > > /home/john/integer.pyx in sage.rings.integer.Integer.__pow__() > > <type 'exceptions.TypeError'>: unsupported operand type(s) for ** or > pow(): 'tuple' and 'int' > > I would be very grateful for ideas about what has gone wrong and how to > fix it. > > Best regards, > John > -- > John P. Burkett > Department of Environmental and Natural Resource Economics > and Department of Economics > University of Rhode Island > Kingston, RI 02881-0808 > USA > > phone (401) 874-9195 > > > > --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
