sqrtqq

Sqrtqq is not a standard mathematical operator in common textbooks, but it is sometimes encountered as a shorthand notation for the square root of the product q times q, i.e., sqrt(q q) or sqrt(q^2). In this use, sqrtqq(q) is typically interpreted as the nonnegative magnitude associated with q.

For real numbers, sqrt(q^2) equals the absolute value of q, written as |q|. Therefore, when sqrtqq is read as sqrt(q^2) for real q, it discards the sign of q and returns a nonnegative result that represents the magnitude of q. This interpretation makes sqrtqq equivalent to the absolute value function in real analysis.

In the context of complex numbers, the situation is more subtle. The expression sqrt(q^2) does not, in general, simplify to q or to |q| in a straightforward way because the complex square root is multivalued and depends on branch choices. Consequently, sqrt(q^2) may differ from q by a sign or branch choice, and care must be taken when using sqrtqq with complex operands.

In programming and symbolic algebra, sqrtqq might appear as sqrt(q*q) or as an alias for Abs(q) when the variable is known to be real. Some algebra systems may also simplify sqrt(q^2) to Abs(q) or leave it unevaluated depending on context and assumptions about q.

Examples: sqrtqq(3) = 3, sqrtqq(-5) = 5, sqrtqq(0) = 0. Overall, sqrtqq commonly conveys the idea of a nonnegative magnitude derived from q, aligning with the absolute value in the real case, but it is not a universal, formally defined operator.