I have a matrix "testmatrix" which lies in the following SAGE class:

Full MatrixSpace of 12 by 12 dense matrices over Real Field with 500
bits of precision

I would like to find the eigenvectors of this matrix using for example
PARI, with the command  mateigen.

There is documentation in the SAGE tutorial about how to save and load
PARI objects:

http://www.sagemath.org/doc/tutorial/interactive_shell.html#saving-and-loading-individual-objects

what I want to do is the converse of this: save a SAGE object (this
matrix "testmatrix") in a format that can easily be read by PARI and
understood as a matrix.  I am stuck because I don't see an easy way to
do this.

This may be more of a PARI, or general C-programming question, than a
SAGE question per se.   But maybe there's a better way of
accomplishing the task (finding the eigenvalues/vectors of a real
matrix generated in SAGE) than I have thought of, using the resources
in the SAGE distribution.

I also see that there is a GP interface in SAGE, but from the
reference manual, I was not able to figure out how to take a stored
variable in SAGE (such as a SAGE matrix) and get GP to recognize it as
a valid data type.

Thanks,
Eliot
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