w1 = w2
w1 < w2
The equality operator
= evaluates to
true if the two words w1 and
w2 are equal and to
false otherwise. The inequality operator
true if the two words w1 and w2 are not equal and to
You can compare words with objects of other types, but they are never equal of course.
gap> a := AbstractGenerator( "a" );; gap> b := AbstractGenerator( "b" );; gap> a = b; false gap> (a^2*b)^5*b^-1 = a^2*b*a^2*b*a^2*b*a^2*b*a^2; true
w1 < w2
w1 <= w2
w1 = w2
= evaluate to
true if the word
w1 is less than, less than or equal to, greater than, and greater than
or equal to the word w2.
Words are ordered as follows. One word w1 is considered smaller than
another word w2 it it is shorted, or, if they have the same length, if
it is first in the lexicographical ordering implied by the ordering of
the abstract generators. The ordering of abstract generators is as
follows. The abstract generators are ordered with respect to the strings
that were passed to
AbstractGenerator when creating these abstract
generators. Each abstract generator g is also smaller than its
inverse, but this inverse is smaller than any abstract generator that is
larger than g.
Words can also be compared with objects of other types. Integers, rationals, cyclotomics, finite field elements, and permutations are smaller than words, everything else is larger.
gap> IdWord<a; a<a^-1; a^-1<b; b<b^-1; b^-1<a^2; a^2<a*b; true true true true true true
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