Cartesian Product Constructor and Functions

The special constructor car< ... > is used for the creation of cartesian products of structures.

car< R₁, ..., R_k > : Str, ..., Str -> SetCart

Given a list of sets or algebraic structures R₁, ..., R_k, construct the cartesian product set R₁ x ... x R_k.

CartesianProduct(R, S) : Str, ..., Str -> SetCart

Given structures R and S, construct the cartesian product set R x S. This is the same as calling the car constructor with the two arguments R and S.

CartesianProduct(L) : [Str] -> SetCart

CartesianProduct(L) : <Str> -> SetCart

Given a sequence or tuple L of structures, construct the cartesian product of the elements of L.

CartesianPower(R, k) : Str, RngIntElt -> SetCart

Given a structure R and an integer k, construct the cartesian power set R^k.

Flat(C) : SetCart -> SetCart

Given a cartesian product C of structures which may themselves be cartesian products, return the cartesian product of the base structures, considered in depth-first order (see Flat for the element version).

NumberOfComponents(C) : SetCart -> RngIntElt

Given a cartesian product C, return the number of components of C.

Component(C, i) : SetCart, RngIntElt -> Str

C[i] : SetCart, RngIntElt -> Str

The i-th component of C.

Components(C) : SetCart -> List

The list of components of a cartesian product.

# C : SetCart -> RngIntElt

Given a cartesian product C, return the cardinality of C.

Rep(C) : SetCart -> Elt

Given a cartesian product C, return a representative of C.

Random(C) : SetCart -> Elt

Given a cartesian product C, return a random element of C.

> C := car< RationalField(), Integers() >;
> C;
Cartesian Product<Rational Field, Ring of Integers>