q1 + q2
q1 - q2
q1 * q2
q1 / q2
/ evaluate to the sum, difference,
product, and quotient of the two rationals q1 and q2. For the
/ q2 must of course be nonzero, otherwise an error is
signalled. Either operand may also be an integer i, which is
interpreted as a rational with denominator 1. The result of those
operations is always reduced. If, after the reduction, the denominator
is 1, the rational is in fact an integer, and is represented as such.
gap> 2/3 + 4/5; 22/15 gap> 7/6 * 2/3; 7/9 # note how the result is cancelled gap> 67/6 - 1/6; 11 # the result is an integer
q ^ i
The powering operator
^ returns the i-th power of the rational q.
i must be an integer. If the exponent i is zero,
defined as 1; if i is positive,
q^i is defined as the i-fold
q*q*..*q; finally, if i is negative,
(1/q)^-i. In this case q must of course be nonzero.
gap> (2/3) ^ 3; 8/27 gap> (-17/13) ^ -1; -13/17 # note how the sign switched gap> (1/2) ^ -2; 4
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