Filed Maxima's [bugs:3243] <https://sourceforge.net/p/maxima/bugs/3243/> about eigenvalue()'s bug.
HTH, - Emmanuel Charpentier Le dimanche 13 novembre 2016 20:06:57 UTC+1, Emmanuel Charpentier a écrit : > > > > Le dimanche 13 novembre 2016 15:38:57 UTC+1, Dima Pasechnik a écrit : >> >> >> >> On Sunday, November 13, 2016 at 2:14:07 PM UTC, Dima Pasechnik wrote: >>> >>> >>> >>> On Sunday, November 13, 2016 at 1:05:48 PM UTC, Emmanuel Charpentier >>> wrote: >>>> >>>> Note that Sage's Maxima is still at 5.35.1... Hence my questions : >>>> tickets or not tickets ? >>>> >>> >>> well, your report on Maxima site talks about 5.38.1. >>> So it's not impossible that the bug you report is fixed by the patch on >>> Sage's #18920. >>> Let me check. >>> >>> it's another bug, indeed. (I mentioned this on >> https://sourceforge.net/p/maxima/bugs/3239/ too) >> Open a ticket, please... >> > > Done in Trac#21873 <https://trac.sagemath.org/ticket/21873>. Care for a > ticket for the eigenvector's bug ? > > HTH, > > -- > Emmanuel Charpentier > >> >> >> >>> >>> >>>> >>>> -- >>>> Emanuel Charpentier >>>> >>>> Le dimanche 13 novembre 2016 13:57:13 UTC+1, Dima Pasechnik a écrit : >>>>> >>>>> this looks like bug in 5.38.1 that we patch on >>>>> https://trac.sagemath.org/ticket/18920 >>>>> by importing their fix which is not in a release yet: >>>>> >>>>> >>>>> https://git.sagemath.org/sage.git/diff/build/pkgs/maxima/patches/0001-In-eigenvectors-iterate-over-all-eigenvalues.patch?id=3afa33ba089b4b13e80ec9fbf41d7f83b7c00645 >>>>> >>>>> >>>>> >>>>> On Sunday, November 13, 2016 at 12:38:04 PM UTC, Emmanuel Charpentier >>>>> wrote: >>>>>> >>>>>> Problem : exhibit a concrete example of non-commutative operations to >>>>>> students stuck (at best) at high-school level in mathematics. >>>>>> Idea of solution : use rotations in R^3 : they can been (literally) >>>>>> shown. >>>>>> >>>>>> But I stumbled on the (apparently) simple step of computing the >>>>>> invariant vector (= axis) of the rotation, which fails, except in >>>>>> trivial >>>>>> cases. Let's setup an example (editer transcript of a session with cut'n >>>>>> aste from an editor) : >>>>>> >>>>>> sage: var("x,y,z,theta,phi", domain="real") >>>>>> ## Rotation of angle theta about the X axis : >>>>>> ....: >>>>>> M_x=matrix([[1,0,0],[0,cos(theta),-sin(theta)],[0,sin(theta),cos(theta)]]) >>>>>> ## Ditto, angle phi about the Y axis : >>>>>> ....: >>>>>> M_y=Matrix([[cos(phi),0,-sin(phi)],[0,1,0],[sin(phi),0,cos(phi)]]) >>>>>> ## A vector >>>>>> ....: V=vector([x,y,z]) >>>>>> ....: >>>>>> (x, y, z, theta, phi) >>>>>> >>>>>> Try to find the axis of (the rotation whose matrix is )M_x : >>>>>> >>>>>> sage: S_x=solve((M_x*V-V).list(),V.list());S_x >>>>>> [[x == r1, y == 0, z == 0]] >>>>>> >>>>>> So far, so good : one solution, easy to check : >>>>>> >>>>>> sage: V_x=vector(map(lambda e:e.rhs(), S_x[0])) >>>>>> ....: (M_x*V_x-V_x).simplify_trig() >>>>>> ....: >>>>>> (0, 0, 0) >>>>>> >>>>>> Things go pear-shaped when we try to find the axis of the composition >>>>>> of the rotations about X and Y axes : >>>>>> >>>>>> sage: S_yx_bad=solve((M_y*M_x*V-V).list(),V.list());S_yx_bad >>>>>> [[x == 0, y == 0, z == 0]] >>>>>> >>>>>> A rotation with no axis ? Now, now... >>>>>> >>>>>> I have explored a bit this (Maxima) problem, which led me to file >>>>>> Maxima's >>>>>> ticket 3239 <https://sourceforge.net/p/maxima/bugs/3239/>. It turns >>>>>> out that this is a Maxima error solving a simple linear equarion with >>>>>> complicated coefficients. >>>>>> >>>>>> Now, there is a workaround in sage : use Sympy's solvers : >>>>>> >>>>>> sage: import sympy >>>>>> ....: D_yx=sympy.solve((M_y*M_x*V-V).list(),V.list());D_yx >>>>>> ....: >>>>>> {x: -z*sin(phi)/(cos(phi) - 1), y: z*sin(theta)/(cos(theta) - 1)} >>>>>> >>>>>> Checking it is a bit more intricate, since this solution is expressed >>>>>> as Sympy's objects. But it can be done : >>>>>> >>>>>> sage: SD_yx={k._sage_():D_yx.get(k)._sage_() for k in D_yx.keys()} >>>>>> ....: V_yx=vector([SD_yx.get(x),SD_yx.get(y),z]) >>>>>> ....: (M_y*M_x*V_yx-V_yx).simplify_trig() >>>>>> ....: >>>>>> (0, 0, 0) >>>>>> >>>>>> This one doesn't seem to be covered in the "Solve tickets'" section >>>>>> of the Track symbolics <https://trac.sagemath.org/wiki/symbolics> >>>>>> page. Does this problem deserve a specific ticket ? >>>>>> >>>>>> And, by the way, (M_y*M_x).eigenvectors_right() : >>>>>> >>>>>> 1. needs about 10 minutes to >>>>>> 2. return an absolutely unusable solution (a few tens pages...). >>>>>> >>>>>> >>>>>> Is this one known ? Does it deserve a ticket ? >>>>>> >>>>>> Now for the suggestion : could we emulate what has been done with >>>>>> integrate(), and add an option "algorithm=" to Sage's solve ? >>>>>> >>>>>> HTH, >>>>>> >>>>>> -- >>>>>> Emmanuel Charpentier >>>>>> >>>>> -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
