In many settings,
When working with the real numbers, - zero is its own unique square root - positive numbers have two square roots in the real numbers - negative numbers have no square root in the real numbers, but two square roots in the complex numbers
The two square roots of a positive number being opposite to each other, one is negative and one is positive. Since we find positive numbers more "natural", we often decide to give the positive root a special role and to call it "square root of y", which could be thought of as short for "the positive square root of y". The other root is then referred to as "minus square root of y".
In computer algebra systems, one has to decide what to do when the
user asks for square roots a command such as sqrt(y)
or y.sqrt()
:
I suppose the documentation you are referring to is the
SageMath documentation for sage.structure.element.CommutativeRingElement.sqrt
.
It explains that y.sqrt()
takes two optional parameters,
extend
to decide whether to look for square roots in a
larger ring if necessary, and all
to decide whether to
return all square roots or a preferred square root when
there is one. There's an additional optional parameter
name
to name the extra generator of the new ring if you
decide to extend.