Dear Vincent,
you're exactly right. Here is a minimal example:
sage: M = Manifold(2, 'M', structure='top')
sage: X.<x,y> = M.chart()
sage: matrix = MatrixSpace(X.function_ring(), 2)([x,0,0,y]); matrix
[x 0]
[0 y]
sage: sage: matrix.adjugate()
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
<ipython-input-4-4d376cef30d0> in <module>()
----> 1 matrix.adjugate()
/home/michi/GitProjects/sage/local/lib/python2.7/site-packages/sage/matrix/matrix2.pyx
in sage.matrix.matrix2.Matrix.adjugate
(build/cythonized/sage/matrix/matrix2.c:66666)()
8948 return X
8949
-> 8950 X = self._adjugate()
8951 self.cache('adjugate', X)
8952 return X
/home/michi/GitProjects/sage/local/lib/python2.7/site-packages/sage/matrix/matrix2.pyx
in sage.matrix.matrix2.Matrix._adjugate
(build/cythonized/sage/matrix/matrix2.c:66896)()
9064 MS = self._parent
9065
-> 9066 f = self.charpoly()
9067
9068 # A will be the adjugate of M and N is used to store powers of M
/home/michi/GitProjects/sage/local/lib/python2.7/site-packages/sage/matrix/matrix2.pyx
in sage.matrix.matrix2.Matrix.charpoly
(build/cythonized/sage/matrix/matrix2.c:20041)()
2353 elif is_IntegerModRing(R):
2354 f = self.lift().charpoly(var).change_ring(R)
-> 2355 elif R.is_field(proof = False) and R.is_exact():
2356 f = self._charpoly_hessenberg(var)
2357 else:
TypeError: is_integral_domain() got an unexpected keyword argument 'proof'
It seems like huge parts of the code rely on is_field(). It'd be desireable
to make the code more flexible in this way and implement the adjugate
method as standard inversion algorithm for more general rings.
Regards,
Michael
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