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.
