On Thu, Sep 16, 2010 at 5:32 PM, Aaron S. Meurer <asmeu...@gmail.com> wrote: > I get 8.94, 0.01, 0.00 on the first run and 1.31, 0.01, 0.00 on subsequent > runs (cache enabled). > > But more importantly, I get this: > > In [69]: a = sin(40*x).expand(trig=True) > > In [70]: b = chebyshevt(40, cos(x)) > > In [71]: c = chebyshevt_poly(40, cos(x)) > > In [72]: a == b > Out[72]: False > > In [73]: a == c > Out[73]: False > > In [74]: b == c > Out[74]: True > > In [75]: print a > -149387552489472*cos(x)**29*sin(x) - 112939386273792*cos(x)**25*sin(x) - > 61332132986880*cos(x)**33*sin(x) - 30004268236800*cos(x)**21*sin(x) - > 5222680231936*cos(x)**37*sin(x) - 2814663720960*cos(x)**17*sin(x) - > 85201715200*cos(x)**13*sin(x) - 669442048*cos(x)**9*sin(x) - > 842688*cos(x)**5*sin(x) - 40*cos(x)*sin(x) + 10640*cos(x)**3*sin(x) + > 31380096*cos(x)**7*sin(x) + 9128755200*cos(x)**11*sin(x) + > 549755813888*cos(x)**39*sin(x) + 569634324480*cos(x)**15*sin(x) + > 10501493882880*cos(x)**19*sin(x) + 22883585753088*cos(x)**35*sin(x) + > 66175421644800*cos(x)**23*sin(x) + 112442243809280*cos(x)**31*sin(x) + > 148655260565504*cos(x)**27*sin(x) > > In [76]: print b > 1 - 800*cos(x)**2 + 106400*cos(x)**4 - 5617920*cos(x)**6 + > 156900480*cos(x)**8 - 2677768192*cos(x)**10 + 30429184000*cos(x)**12 - > 243433472000*cos(x)**14 + 1424085811200*cos(x)**16 - 6254808268800*cos(x)**18 > + 21002987765760*cos(x)**20 - 54553214976000*cos(x)**22 + > 110292369408000*cos(x)**24 - 173752901959680*cos(x)**26 + > 212364657950720*cos(x)**28 - 199183403319296*cos(x)**30 + > 140552804761600*cos(x)**32 - 72155450572800*cos(x)**34 + > 25426206392320*cos(x)**36 - 5497558138880*cos(x)**38 + 549755813888*cos(x)**40 > > So are you sure that that identity is true? If I plot a - b in Maple, it > doesn't appear to be 0.
Yes, it works: In [1]: n = 40 In [2]: sin(n*x).expand(trig=True) == (chebyshevu(n-1, cos(x))*sin(x)).expand() Out[2]: True My link in my first post is correct, only my benchmarks are wrong. Ondrej -- You received this message because you are subscribed to the Google Groups "sympy" group. To post to this group, send email to sy...@googlegroups.com. To unsubscribe from this group, send email to sympy+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/sympy?hl=en.
