I am trying to use the Gram Schmidt orthogonalization process on a
matrix over a number field. The following code works on Sage 4.7, but
not on 4.8. There doesn't appear to be any tickets registered about
this, so I thought I would try it here. Sorry if this is the wrong
place ! - Emil.
sage: x = polygen(QQ)
sage: K = sage_eval("NumberField(x^2+x-1/2, 'x', embedding=0.5)",
locals={'x': x})
sage: M = matrix(K, [[x,0],[1,1]])
sage: M.gram_schmidt()
---------------------------------------------------------------------------
NotImplementedError Traceback (most recent call last)
/Users/ev/Projects/flagmatic/flagmatic2/<ipython console> in <module>()
/usr/local/sage/local/lib/python2.6/site-packages/sage/matrix/matrix2.so
in sage.matrix.matrix2.Matrix.gram_schmidt
(sage/matrix/matrix2.c:40084)()
/usr/local/sage/local/lib/python2.6/site-packages/sage/matrix/matrix2.so
in sage.matrix.matrix2.Matrix._gram_schmidt_noscale
(sage/matrix/matrix2.c:39431)()
/usr/local/sage/local/lib/python2.6/site-packages/sage/modules/free_module_element.so
in sage.modules.free_module_element.FreeModuleElement.hermitian_inner_product
(sage/modules/free_module_element.c:14217)()
/usr/local/sage/local/lib/python2.6/site-packages/sage/modules/free_module_element.so
in sage.modules.free_module_element.FreeModuleElement.conjugate
(sage/modules/free_module_element.c:13674)()
/usr/local/sage/local/lib/python2.6/site-packages/sage/rings/number_field/number_field_element.so
in sage.rings.number_field.number_field_element.NumberFieldElement.conjugate
(sage/rings/number_field/number_field_element.cpp:15811)()
NotImplementedError: complex conjugation is not implemented (or
doesn't make sense).
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