how can I get first orthogonal(Gram–Schmidt process) and then orthonormal of basis vector list under integer mod.
l=[(1,2,3),(1,5,6)]
basis=[vector(GF(29),i) for i in l]
print(basis)
#[(1,2,3),(1,5,6)]
Here is a partial answer : instead of putting your "basis" in a list, you should put it in a matrix, so that you could benefit from the methods available there.
sage: M = matrix(basis)
sage: M
[1 2 3]
[1 5 6]
sage: M.parent()
Full MatrixSpace of 2 by 3 dense matrices over Finite Field of size 29
sage: M.gram_schmidt()
AttributeError: 'sage.rings.finite_rings.integer_mod.IntegerMod_int' object has no attribute 'conjugate'
Unfortunately, to compute the Gram-Schmidt orthogonalization of M, Sage needs to find the conjugate of elements GF(29), which seems not defined (if you replace GF(29) with ZZ, everythin seems fine).
You can perform Gram–Schmidt over QQ and then change ring to GF(29):
M = Matrix( QQ, [(1,2,3),(1,5,6)] )
[ t.change_ring(GF(29)) for t in M.gram_schmidt() ]
Asked: 2022-01-30 13:44:45 +0200
Seen: 408 times
Last updated: Jan 30 '22
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