Subsections

• Parent and Category
• Arithmetic
• Equality and Membership
• Predicates on Elements

Parent(a) : FldFunElt -> FldFun

Parent(w) : RngFunOrdElt -> RngFunOrd

Category(a) : FldFunElt -> Cat

Category(w) : RngFunOrdElt -> Cat

The table below lists the generic arithmetic functions on function field and order elements. Note that automatic coercion ensures that the binary operations +, -, *, and / may be performed on an element of a function field and an element of one of its orders; the result will be a function field element. Since division of order elements does not generally result in an order element, / for two elements of an order returns an element of the field of fractions of the order; also, the exponent k in a^k must be non-negative. It is not possible to perform the binary operations on elements of different orders.

-a : FldFunElt -> FldFunElt

-w : RngFunOrdElt -> RngFunOrdElt

a + b : FldFunElt, FldFunElt -> FldFunElt

w + v : RngFunOrdElt, RngFunOrdElt -> RngFunOrdElt

a - b : FldFunElt, FldFunElt -> FldFunElt

w - v : RngFunOrdElt, RngFunOrdElt -> RngFunOrdElt

a * b : FldFunElt, FldFunElt -> FldFunElt

w * v : RngFunOrdElt, RngFunOrdElt -> RngFunOrdElt

a / b : FldFunElt, FldFunElt -> FldFunElt

w / v : RngFunOrdElt, RngFunOrdElt -> FldFunElt

a ^ k : FldFunElt, RngIntElt -> FldFunElt

w ^ k : RngFunOrdElt, RngIntElt -> RngFunOrdElt

ElementToSequence(a) : FldFunElt -> [ FldFunElt ]

Eltseq(a) : RngFunOrdElt -> [ RngElt ]

Eltseq(a) : FldFunElt -> [ FldFunElt ]

For an element a of a function field K, a sequence of coefficients (of length degree of K) with respect to the power basis is returned. For an element of an order O, the sequence of coefficients of the element with respect to the basis of O is returned.

a eq b : FldFunElt, FldFunElt -> BoolElt

w eq v : RngFunOrdElt, RngFunOrdElt -> RngFunOrdElt

a ne b : FldFunElt, FldFunElt -> BoolElt

w ne v : RngFunOrdElt, RngFunOrdElt -> FldFunElt

IsZero(a) : FldFunElt -> BoolElt

IsZero(w) : RngFunOrdElt -> BoolElt

IsOne(a) : FldFunElt -> BoolElt

IsOne(w) : RngFunOrdElt -> BoolElt

IsMinusOne(a) : FldFunElt -> BoolElt

IsMinusOne(w) : RngFunOrdElt -> BoolElt

IsUnit(w) : RngFunOrdElt -> BoolElt