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Macaulay2Doc :: getPrimeWithRootOfUnity

getPrimeWithRootOfUnity -- find a prime p with a primitive n-th root of unity r in ZZ/p

Synopsis

Description

We compute the prime p as a larger prime factor of r1n-1. If the largest p in the desired range does not work, we pass to r1+1 and repeat.

i1 : n = 12

o1 = 12
i2 : (p,r) = getPrimeWithRootOfUnity(n,5)

o2 = (20593, 12)

o2 : Sequence
i3 : factor(r^n-1)

o3 = 5*7*11*13*19*29*157*20593

o3 : Expression of class Product
i4 : r^12%p==1, r^6%p==1, r^4%p==1

o4 = (true, false, false)

o4 : Sequence
i5 : (p,r) = getPrimeWithRootOfUnity(12,11,Range=>(100,200))

o5 = (157, 22)

o5 : Sequence
i6 : factor(r^n-1)

      2      2
o6 = 3 5*7*13 23*97*157*463*1489

o6 : Expression of class Product
i7 : r^12%p==1, r^6%p==1, r^4%p==1

o7 = (true, false, false)

o7 : Sequence

See also

Ways to use getPrimeWithRootOfUnity :