7.3 Operations for Group Elements

g * h g / h

The operators * and / evaluate to the product and quotient of the two group elements g and h. The operands must of course lie in a common parent group, otherwise an error is signaled.

g ^ h

The operator ^ evaluates to the conjugate <h>^{-1}* <g>* <h> of g under h for two group elements elements g and h. The operands must of course lie in a common parent group, otherwise an error is signaled.

g ^ i

The powering operator ^ returns the i-th power of a group element g and an integer i. If i is zero the identity of a parent group of g is returned.

list * g g * list

In this form the operator * returns a new list where each entry is the product of g and the corresponding entry of list. Of course multiplication must be defined between g and each entry of list.

list / g

In this form the operator / returns a new list where each entry is the quotient of g and the corresponding entry of list. Of course division must be defined between g and each entry of list.

Comm( g, h )

Comm returns the commutator <g>^{-1}* <h>^{-1}* <g>* <h> of two group elements g and h. The operands must of course lie in a common parent group, otherwise an error is signaled.

LeftNormedComm( g1, ..., gn )

LeftNormedComm returns the left normed commutator Comm( LeftNormedComm( g1, ..., gn-1 ), gn ) of group elements g1, ..., gn. The operands must of course lie in a common parent group, otherwise an error is signaled.

RightNormedComm( g1, g2, ..., gn )

RightNormedComm returns the right normed commutator Comm( g1, RightNormedComm( g2, ..., gn ) ) of group elements g1, ..., gn. The operands must of course lie in a common parent group, otherwise an error is signaled.

LeftQuotient( g, h )

LeftQuotient returns the left quotient <g>^{-1}* <h> of two group elements g and h. The operands must of course lie in a common parent group, otherwise an error is signaled.

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