Cartesian products

To create the set

$$\{(a^2,b)\ \vert\ 1\leq a\leq 10,\ -2\leq b\leq 6\},$$

type

> L:=[];
> for i in [1..10] do
for> L:=Append(L,i^2);
for> end for;
> M:=[];
> for i in [-2..6] do
for> M:=Append(M,i);  
for> end for;
> LxM:=[<x,y>:x in L,y in M];

Now > LxM; will return

[ <1, -2>, <4, -2>, <9, -2>, <16, -2>, <25, -2>, <36, -2>, <49, -2>, <64, -2>, 
<81, -2>, <100, -2>, <1, -1>, <4, -1>, <9, -1>, <16, -1>, <25, -1>, <36, -1>, 
<49, -1>, <64, -1>, <81, -1>, <100, -1>, <1, 0>, <4, 0>, <9, 0>, <16, 0>, <25, 
0>, <36, 0>, <49, 0>, <64, 0>, <81, 0>, <100, 0>, <1, 1>, <4, 1>, <9, 1>, <16, 
1>, <25, 1>, <36, 1>, <49, 1>, <64, 1>, <81, 1>, <100, 1>, <1, 2>, <4, 2>, <9, 
2>, <16, 2>, <25, 2>, <36, 2>, <49, 2>, <64, 2>, <81, 2>, <100, 2>, <1, 3>, <4, 
3>, <9, 3>, <16, 3>, <25, 3>, <36, 3>, <49, 3>, <64, 3>, <81, 3>, <100, 3>, <1, 
4>, <4, 4>, <9, 4>, <16, 4>, <25, 4>, <36, 4>, <49, 4>, <64, 4>, <81, 4>, <100, 
4>, <1, 5>, <4, 5>, <9, 5>, <16, 5>, <25, 5>, <36, 5>, <49, 5>, <64, 5>, <81, 
5>, <100, 5>, <1, 6>, <4, 6>, <9, 6>, <16, 6>, <25, 6>, <36, 6>, <49, 6>, <64, 
6>, <81, 6>, <100, 6> ]

Exercise 8   Create the list of all pairs of integers of the form $(n,n^2+1)$, $1\leq n\leq 20$.

There are also commands CartesianProduct and CartesianPower in MAGMA. However, they do not return a list or sequence structure, even if you are taking the cartesian product of lists.