Looking at EigenPackage I noticed that in only handles
matrices of fractions of polynomials. I wonder what
good signature for functions should be:
- characteristic polynomial makes sense over any commutative
ring
- equation solvers work over fields, and via fractions can
work over integral domains
- we need a factorizer, but in general we can pass it as
a parameter. And several rings have now
PolynomialFactorizationExplicit, so we can use
'factorPolynomial'
So one natural setting is to require base ring to be a field,
pass factorizer as a parameter and use SparseUnivariatePolynomial
to represent algebraic eigenvalues and elements of eigenvectors.
One drawback of SparseUnivariatePolynomial is that unknown is
printed as '?', using named variables is nicer. So possible
approach would be to use Polynomial with a single named
variable to represent minimal polynomial of eigenvalue and
elements of eigenvector.
Opinions?
--
Waldek Hebisch
[email protected]
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