square root sign [closed]

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In a finite field, say

p = 0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab
F = GF(p)

does the square_root function always return the root r s.t. sign(r) = +1, assuming that a root exists, where sign is the function that return -1 iff r > (p-1)/2