GaussRoot(R, xi, xiord)

qetasqrt.spad line 203 [edit on github]

• R: Ring

• xi: R

• xiord: PositiveInteger

GaussRoot(R, r, n) provides functions to express a square root of a positive radical integer in terms of r (a n-th root of unity). A radical integer is an integer that is not divisible by a square of a prime.

squareRoot: Fraction Integer -> R

squareRoot(x) returns an element z in R such that z^2=x. It returns 0, if such an element z cannot be found in R. The function assumes that x is different from zero.

squareRootOfRadicalInteger: Integer -> R

squareRootOfRadicalInteger(x) returns an element z in R such that z^2=x. It returns 0, if such an element z cannot be found in R. The function assumes that x is a radical integer and different from zero, i.e. x does not contain a square of a prime as a factor.