Zero(O) : AlgAssVOrd -> AlgAssVOrdElt
The zero element of the associative order O.
One(O) : AlgAssVOrd -> AlgAssVOrdElt
The identity element of the associative order O.
Given an associative order O and an integer i,
returns the ith basis element as an order over the base ring.
Note that the element 1 may or may not be the first element of a basis.
These basis elements are returned as elements of the algebra of O not as
elements of O itself.
Return an element of the associative order O described by x, where x
may be a sequence, an element of an associative order, an element coercible
into the coefficient ring of O or into the algebra of O.
The sum of elements x and y of an order of an associative algebra.
The difference of elements x and y of an order of an associative algebra.
The negation of element x of an order of an associative algebra.
The product of elements x and y of an associative algebra.
c * u : RngElt, AlgAssVOrdElt -> AlgAssVOrdElt
The product of the element u of an associative order by the scalar c.
The quotient of x by the unit y in the parent algebra.
The exact division of x by y in the order containing them.
The product of the element x of an associative order with itself n times.
Returns true if and only if the elements x and y are equal.
Returns true if and only if the elements x and y are not equal.
Return true if the element x of an associative order is the zero element.
Return true if the element x of an associative order is a unit in that
order.
Returns true if and only if x is an element of the base ring
of the order containing it, and if so returns the coerced element.
Eltseq(x) : AlgAssVOrdElt -> SeqEnum
Given an element x of an associative order O, returns
the sequence of coordinates of x in terms of the basis of O.
The norm of the element x of an order as an element of its parent algebra.
The trace of the element x of an order as an element of its parent algebra.
RightRepresentationMatrix(e) : AlgAssVOrdElt -> AlgMatElt
The representation matrix describing left (right) multiplication by the element
e of an associative order.
Side: MonStgElt Default: em "Left"
The representation matrix of the element a of an associative order. This
describes left multiplication unless the parameter Side is set to
"Right".
The characteristic polynomial of the element x of an order
as an element of its parent algebra.
The minimal polynomial of the element x of an order
as an element of its parent algebra.
V2.28, 13 July 2023