a = b
For aut
For aut
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For aut
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For an aut group elements a and b, the operator
= evaluates to
true
if the aut
records correspond to the same aut, and
false otherwise.
Note that this may return
true even when the two records themselves are
different (one of them may have more information stored in it).
a * b
group elements a and b, the operator *
evaluates to the
product a b of the auts.
a / b
group elements a and b, the operator /
evaluates to the
quotient a b^{-1} of the auts.
a ^ i
group element a and an integer i, the operator ^
evaluates to the i-th power a^i of a.
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a ^ b
For aut
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The function group elements a and b, the operator
^ evaluates to the
conjugate b^{-1} a b of a by b.
Comm(a, b)
Comm returns the commutator a^{-1} b^{-1} a b
of the two aut
group elements a and b.
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g ^ a
For a sag group element g and an aut group element a, the operator
^ evaluates to the image g^a of the ag word g under the aut
a.
The sag group element g must be an element of a.group
.
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S ^ a
For a subgroup S of a sag group and an aut group element a, the
operator
^ evaluates to the image S^a of the subgroup S under the
aut
a. The subgroup S must be a subgroup of a.group
.
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list * a
a * list
For a list list and an aut
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For a list list and an aut group element a, the operator
*
evaluates to the list whose i-th entry is
list[i] * a or
a
* list[i] respectively.
list ^ a
group element a, the operator ^
evaluates to the list whose i-th entry is list[i] ^ a
.
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Note that the action of aut
inputOut.Orbit
group elements on the elements of the sag
group via the operator
^ corresponds to the default action
OnPoints
(see
Other Operations) so that the functions
Orbit and
Stabilizer can
be used in the natural way. For example:
April 1997