18.3 Comparisons of Cyclotomics

To compare cyclotomics, the operators <, <=, =, >=, > and <> can be used, the result will be true if the first operand is smaller, smaller or equal, equal, larger or equal, larger, or inequal, respectively, and false otherwise.

Cyclotomics are ordered as follows: The relation between rationals is the natural one, rationals are smaller than irrational cyclotomics, and infinity is the largest cyclotomic. For two irrational cyclotomics with different conductors, the one with smaller conductor is regarded as smaller. Two irrational cyclotomics with same conductor are compared via their external representation.

For comparisons of cyclotomics and other GAP objects, see Section Comparisons.

gap> E(5) < E(6);      # the latter value has conductor 3
false
gap> E(3) < E(3)^2;    # both have conductor 3, compare the ext. repr.
false
gap> 3 < E(3); E(5) < E(7);
true
true

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