Note that Sage's Maxima is still at 5.35.1... Hence my questions : tickets or not tickets ?
-- 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.
