On Feb 11, 8:10 am, William Stein <[email protected]> wrote:
> By echelon form do you mean Hermite Normal Form over that base ring,
> or do you mean echelon form over the fraction field? If you just want
> the dimension, is their any chance you can specialize one of the variables and
> compute the rank there -- if you do this for enough values it's likely
> to give you the correct rank, and of course is very fast.
Yes, I meant Hermite Normal Form.
The code that I have now basically specializes the (lone) variable d.
I make 14x14 matrices e[0] through e[6] and then the last two lines of
the code are this:
L = gap.LieAlgebra('Rationals',e)
print 'Dimension:',gap.Dimension
(L)
What I really wanted to say in the paper is that L is the full 14x14
matrix algebra for all real values of d with |d| >= 2. I was already
90% sure that this is true. I wanted to use SAGE to provide a
computational proof, because if I worked out a human proof then I
would have to digress into a topic for a later paper. The problem, I
realized, is that with this code SAGE cannot provide a proof for all
relevant d, only for specific values of d. (Moreover there exist
algebraic values of d for which L is smaller.)
In truth, SAGE is missing two things for what I wanted. First, there
is no equivalent of gap.LieAlgebra. Second, the submodule method of
the FreeModule class is not implemented for Euclidean domains, even
though it is implemented for ZZ. Of course, if gap.LieAlgebra worked
over a Euclidean domain, that would also solve the problem, but I
don't think that it does.
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