For integers, Pari also has an ispower function.  I think that
it is useful to have an n.is_power(k) member function
for integers (or more general for ring elements which admit
unique factorization of polynomials), and prefer the syntax
n.root(k) rather than n.nth_root(k)

--David

P.S. Back in 1998, when some of my elliptic curve functions
were incorporated into Magma, I naively introduced, or accepted,
the syntax nTorsionSubgroup, after which mTorsionSubgroup, and
pTorsionSubgroup were introduced to cover all of the "natural"
spellings that users were missing.   It took years to drop the
nonsensical leading letters and settle on TorsionSubgroup(E,p)
rather than the Trinity of [nmp]TorsionSubgroup(E,p).



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