Hi all:
This looks like a bug in Sage 4.5.3 regarding solving linear systems.
Alex
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| Sage Version 4.5.3, Release Date: 2010-09-04 |
| Type notebook() for the GUI, and license() for information. |
----------------------------------------------------------------------
sage: var('a')
a
sage: M= matrix([[a,0,a+1],[2*a,2*a+1,4*a+2]])
sage: v= vector([3*a,2*a+1,5*a+3])
sage: s= M.solve_left(v)
sage: print s
(1, 1)
sage: print ((s/a)*M == v/a)
True
sage: print M.solve_left(v/a)
---------------------------------------------------------------------------
ValueError Traceback (most recent call
last)
/Users/arai021/<ipython console> in <module>()
/Applications/sage/local/lib/python2.6/site-packages/sage/matrix/
matrix2.so in sage.matrix.matrix2.Matrix.solve_left (sage/matrix/
matrix2.c:2959)()
/Applications/sage/local/lib/python2.6/site-packages/sage/matrix/
matrix2.so in sage.matrix.matrix2.Matrix.solve_right (sage/matrix/
matrix2.c:3461)()
/Applications/sage/local/lib/python2.6/site-packages/sage/matrix/
matrix2.so in sage.matrix.matrix2.Matrix._solve_right_general (sage/
matrix/matrix2.c:4363)()
ValueError: matrix equation has no solutions
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