Sage: Ticket #21873: (Maxima's) solve is unable to solve a linear system with complicated coefficients
https://trac.sagemath.org/ticket/21873
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Long story : see <a class="ext-link" href="https://groups.google.com/forum/#!topic/sage-support/8TB431izNDc"><span class="icon"></span>this</a> sage-support thread.
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Short story : Let M_x be the matrix representing a rotation of angle theta about the x axis (in <code></code><code>R^3</code><code></code>), and M_y the matrix representing a rotation of angle phi about the y axis. Trying to find by elementary methods the axis of the composition, i. e. solving M_y*M_x*V-V for V, the only solution found its the trivial null vector.
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This has been reproduced in Maxima and reported on their bug system as <a class="ext-link" href="https://sourceforge.net/p/maxima/bugs/3239/"><span class="icon"></span>bugs:3239</a>, with no answer at the time of the present filing.
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This can be worked around by using Sympy's solve, which involves some conversions using _sage_() (not <em>that</em> well documented).
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https://trac.sagemath.org/ticket/21873
Trac 1.1.6