RATPOW

OUT = RATPOW(X,Y) computes X to the power of Y elementwisely. Both X and Y must be real and must have the same dimensions unless one is a scalar. Elements of Y should be rational numbers. If there is an irrational number, it will be approximated by a rational number with a pair of small numerator and denominator by means of function RAT. Element of Y is also reduced to the lowest terms fraction. The funtion return a single real solution OUT.

Specifically, suppose ABS(Y)=A./B where A and B are coprime (their corresponding elements have no common factor), then RATPOW performs X.^(1/B) first, and then raises it to the power of A. Hence, if an element of B is an odd number, the corresponding element of X must be non-negative. Otherwise, the error message is produced. Moreover, if an element of Y is negative, the function returns the inverse of the corresponding element of X^(A/B).