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. > > -- > 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.
