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Nemocas / Nemo.jl

Julia bindings for the FLINT number theory C library
http://nemocas.github.io/Nemo.jl/
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isunit is wrong for polynomials over a non-integral domain #323

Open wbhart opened 7 years ago

wbhart commented 7 years ago

Polynomials can be units in more cases than currently being tested, over a non-integral domain.

wbhart commented 7 years ago

We have the following theorems:

Thm: If R is of finite characteristic (and commutative) then f in R[x] is a unit iff f = u + r(x)*x for u a unit in R and all coefficients of r(x) are nilpotent in R.

Thm: a in Z/nZ is nilpotent iff rad(a) = rad(n).