I've discovered that the backslash operator produces a weird type error when used on matrices with Real Double Field entries:
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| Sage Version 5.6, Release Date: 2013-01-21 |
| Type "notebook()" for the browser-based notebook interface. |
| Type "help()" for help. |
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sage: A = matrix(QQ, 3, [1,2,4,2,3,1,0,1,2])
sage: B = matrix(QQ, 3, 2, [1,7,5,2,1,3])
sage: A\B
[ -1 1]
[13/5 -3/5]
[-4/5 9/5]
sage: A = matrix(RDF, 3, [1,2,4,2,3,1,0,1,2])
sage: B = matrix(RDF, 3, 2, [1,7,5,2,1,3])
sage: A\B
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
/home/gtmarks/<ipython console> in <module>()
/usr/local/sage-5.6/local/lib/python2.7/site-packages/sage/misc/preparser.pyc in __mul__(self, right)
1398 (0.0, 0.5, 1.0, 1.5, 2.0)
1399 """
-> 1400 return self.left._backslash_(right)
1401
1402
/usr/local/sage-5.6/local/lib/python2.7/site-packages/sage/matrix/matrix2.so in sage.matrix.matrix2.Matrix._backslash_ (sage/matrix/matrix2.c:3658)()
/usr/local/sage-5.6/local/lib/python2.7/site-packages/sage/matrix/matrix_double_dense.so in sage.matrix.matrix_double_dense.Matrix_double_dense.solve_right (sage/matrix/matrix_double_dense.c:11636)()
TypeError: vector of constants over Real Double Field incompatible with matrix over Real Double Field
I don't understand the final "imcompatibility" message: both the vector and the matrix are RDF type, so how could they be incompatible? This is a small version of a problem I encountered in the context of an attempt to demonstrate to a linear algebra class the computation time of solving systems of linear equations via LU factorization versus via matrix inversion by naive methods; to make the case for LU, I have to avoid various optimized algorithms built into SAGE. (Perhaps I should be using a call to LAPACK or something for this demonstration?)
