14.1 Comparisons of Gaussians

x = y
x < y

The equality operator evaluates to true if the two Gaussians x and y are equal, and to false otherwise. The inequality operator < evaluates to true if the two Gaussians x and y are not equal, and to false otherwise. It is also possible to compare a Gaussian with an object of another type, of course they are never equal.

Two Gaussians a + b*E(4) and c + d*E(4) are considered equal if a = c and b = d.

    gap> 1 + E(4) = 2 / (1 - E(4));
    true
    gap> 1 + E(4) = 1 - E(4);
    false
    gap> 1 + E(4) = E(6);
    false 

x < y
x <= y
x y
x = y

The operators <, <=, , and = evaluate to true if the Gaussian x is less than, less than or equal to, greater than, and greater than or equal to the Gaussian y, and to false otherwise. Gaussians can also be compared to objects of other types, they are Comparisons of Cyclotomics).

A Gaussian a + b*E(4) is considered less than another Gaussian c + d*E(4) if a is less than c, or if a is equal to c and b is less than d.

    gap> 1 + E(4) < 2 + E(4);
    true
    gap> 1 + E(4) < 1 - E(4);
    false
    gap> 1 + E(4) < 1/2;
    false 

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