#18935: Finite field linear function to polynomial
-------------------------------------+-------------------------------------
Reporter: tgagne | Owner:
Type: enhancement | Status: needs_work
Priority: minor | Milestone: sage-6.10
Component: finite rings | Resolution:
Keywords: finite field, | Merged in:
polynomial | Reviewers: Vincent Delecroix
Authors: Thomas Gagne | Work issues:
Report Upstream: N/A | Commit:
Branch: | 1608ecbe6702539fdbcbfef4f6b27dbe39d275dc
u/tgagne/finite_field_matrix_to_polynomial| Stopgaps:
Dependencies: #18714 |
-------------------------------------+-------------------------------------
Changes (by vdelecroix):
* status: needs_review => needs_work
* reviewer: => Vincent Delecroix
* milestone: sage-6.8 => sage-6.10
Comment:
Why `base_matrix_to_polynomial` and not simply `matrix_to_polynomial`?
`poly(el)` is simpler than `poly.subs(x=el)`
This test is really bad
{{{
not all([matrix[i,j] in self.base_ring() for i in range(n) for j in
range(n)])
}}}
You have several better options
- {{{matrix.base_ring() == self}}}
- {{{matrix = matrix.change_ring(self)}}} (this might make an unneeded
copy)
If `var` is already an element of a polynomial ring then you should not
recreate another one. In particular, I might want to work over QQ[x,y] and
obtain a polynomial in the variable x in this specific ring. I would
simply do
{{{
if isinstance(var, str):
from sage.rings.polynomial.polynomial_ring import polygen
var = polygen(self)
}}}
If the matrix is sparse you are doing a lot of unwanted computations. I
would actually separate
{{{
if matrix.is_sparse():
entries = matrix.nonzero_positions()
else:
entries = ((i,j) for i in range(n) for j in range(n))
for i,j in entries:
# do the looping
}}}
And add a test with a huge matrix with very few coefficients like
{{{
sage: M = matrix(GF(3,4), 1000, sparse=True)
sage: M[0,3] = 1
}}}
The operation `gen**i` is actually very fast. So I would avoid computing
the list `basis` and replace `basis[i]` with `gen**i`
You should not compute a list and then make a sum of elements. Do
everything at once
{{{
s = 0
for i in range(10):
s += 1
}}}
is much better than
{{{
l = []
for i in range(10):
l.append(i)
s = sum(l)
}}}
--
Ticket URL: <http://trac.sagemath.org/ticket/18935#comment:5>
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