How can I get Sage to go over all possible maps between two sets?

phoenix
15 ●5 ●5 ●10

What I want to do is this : Say I take a graph $K_{n,n}$ and choose an ordering for each edge arbitrarily - say denote each edge as $(i,j)$ where $i$ is in the left partition and $j$ is in the right partition. I have a set of matrices $A = { A_1, A_2,...,A_k }$ . I want to iterate over all possible ways in which one could have assigned an A matrix to an edge of this graph.

How does one do that? (..apart from writing a massive sequence of nested loops!..)

answered 9 years ago

Nathann
1615 ●2 ●15 ●36

To list all functions from A to B you must iterate on all points of B^|A|. This can be achieved with itertools' 'product' function:

def all_functions(A,B):
    from itertools import product
    B_to_the_A = product(B,repeat=len(A))
    for p in B_to_the_A:
        yield dict(zip(A,p))

sage: for f in all_functions("abc",[0,1]):
....:     print f
{'a': 0, 'c': 0, 'b': 0}
{'a': 0, 'c': 1, 'b': 0}
{'a': 0, 'c': 0, 'b': 1}
{'a': 0, 'c': 1, 'b': 1}
{'a': 1, 'c': 0, 'b': 0}
{'a': 1, 'c': 1, 'b': 0}
{'a': 1, 'c': 0, 'b': 1}
{'a': 1, 'c': 1, 'b': 1}

Nathann

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Is that "repeat" a command?

phoenix ( 9 years ago )

Why is this slightly modified thing not working? def All_Maps(A,B): from itertools import product k = len (A) return product(B,repeat = k)

for f in All_Maps ([a,b],[0,1]): print f

phoenix ( 9 years ago )

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