At http://fricas.github.io/api/AlgebraicallyClosedField.html
I see listed the category "noZeroDivisors".
Obviously, one can create an algebraic number that proves this wrong.
(1) -> AN has noZeroDivisors
(1) true
(2) -> a := rootOf((x+1)*(x-1))
(2) x
Type: AlgebraicNumber
(3) -> (a-1)*(a+1)
(3) 0
Type: AlgebraicNumber
Clearly, one shouldn't create an element of AN via rootOf if the
argument is a non-irreducible polynomial. But the specification of
rootOf doesn't tell that explicitly.
In fact, it cannot say so, since then only linear polynomials would be
allowed.
As it is now, the use of elements created by rootOf must be restricted,
otherwise, AN loses the property noZeroDivisors.
Any ideas?
Ralf
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