>
> (1) -> determinant empty()$Matrix Integer
>
> >> Error detected within library code:
> elt: index out of range
>
> The determinant of 0x0 matrix should be 1.
Fixed now.
> The resultant of non-zero degree 0 polynomials is 1.
No. If degree(p1) = 0 and p2 ~= 0, then
resultant(p1, p2) = leadingCoefficient(p1)^degree(p2)
If p2 is nonzero, but p1 = 0, then resultant(p1, p2) = 0
by the formula above, which nicely agrees with basic
property that resultant is zero if and only if p1 and p2
have common factor. If p1 = 0 and p2 = 0 basic
property would give 0, but formula would give 1
(if one considers 0 polynomial to be of degree 0)
or undefined (if one considers 0 polynomial to
be of negative degree).
> Should sylvesterMatrix be defined for non-zero
> degree 0 polynomials? Should it give an error if
> one argument is zero?
I am not sure. Probably yes if second argument is
nonzero. However, there is also question of
usability. Empty matrices and vectors are convenient
as base case in various recursions, so it make
sense to support them. OTOH I am not sure how
useful are resultants of degree 0 polynomials.
--
Waldek Hebisch
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