>> 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.
For consistency, resultant(p,q)=determinant sylvesterMatrix(p,q),
sylvesterMatrix should not be defined for zero argument.
And that's what Wikipedia and Bronstein's book says.
diff --git a/src/algebra/bezout.spad b/src/algebra/bezout.spad
index 16d3ed50..9f808600 100644
--- a/src/algebra/bezout.spad
+++ b/src/algebra/bezout.spad
@@ -32,7 +32,7 @@
Exports ==> with
sylvesterMatrix : (UP, UP) -> M
++ sylvesterMatrix(p, q) returns the Sylvester matrix for the two
- ++ polynomials p and q.
+ ++ nonzero polynomials p and q.
subSylvesterMatrix : (M, NNI) -> M
++ subSylvesterMatrix(S, j) returns the jth sub-Sylvester matrix
@@ -66,6 +66,7 @@
Implementation ==> add
sylvesterMatrix(p, q) ==
+ if p = 0 or q = 0 then error "sylvesterMatrix: argument is zero"
n1 := degree p; n2 := degree q; n := n1 + n2
sylmat : M := new(n, n, 0)
minR := minRowIndex sylmat; minC := minColIndex sylmat
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