To compare cyclotomics, the operators
< can be used, the result will be
true if the first operand is
smaller, smaller or equal, equal, larger or equal, larger, or inequal,
Cyclotomics are ordered as follows: The relation between rationals is as usual, and rationals are smaller than irrational cyclotomics. For two irrational cyclotomics z1, z2 which lie in different minimal cyclotomic fields, we have <z1> < <z2> if and only if 'NofCyc(<z1>)' < 'NofCyc(<z2>)'); if 'NofCyc(<z1>)' = 'NofCyc(<z2>)'), that one is smaller that has the smaller coefficient vector, i.e., <z1> leq <z2> if and only if 'COEFFSCYC(<z1>)' leq 'COEFFSCYC(<z2>)'.
You can compare cyclotomics with objects of other types; all objects which are not cyclotomics are larger than cyclotomics.
gap> E(5) < E(6); # the latter value lies in $Q_3$ false gap> E(3) < E(3)^2; # both lie in $Q_3$, so compare coefficients false gap> 3 < E(3); E(5) < E(7); true true gap> E(728) < (1,2); true
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