Keys of a dictionary

edit

Please provide your code with a correct Sage/Python syntax, [[0 0 0 0 0]] is meaningless, also, it is not possible to have a list as a key for a dictionary since it is unhashable, so having a dictionary whose definition starts with {[0.0]: is meaningless too. As is, there is no hope we can reproduce anything.

Please give code producing a simple dictionary (with two keys) so that the values do not lead to errors - note that [0 0 0 0 0] immediately gives an error.

Why are the keys (displayed) above lists (and how did this dictionary come into sage)? Why not simple elements? Or tuples if we really need one element tuples? For instance:

sage: dic = {(0.0): [[0, 0, 0, 0, 0]], (1.27): [[0, 0, 0, 0, 1]], (2.63): [[1, 1, 1, 0, 0]], (5.619999999999999): [[1, 0, 1, 1, 1]]}
sage: dic[ (0.0) ]
[[0, 0, 0, 0, 0]]

Why do we use approximate values in the (tuples)? This may be a good reason to "miss the key", for instance the last one, if the precision does not match or if after computation an other value is delivered "not the expected one".

The code looks like this:

import itertools
W = itertools.product([0,1], repeat = n)
preimages = {}
for w in W:
     w = vector(w)
     w = w.row()
     v = w.transpose()
     u = w * K * v
     u.set_immutable()
     if u in preimages:
          preimages[u].append(w)
     else:
          preimages[u] = [w]

The problem is most likely because I have set u immutable, but I need to get preimages for my function u = w * K * v

if I change the last part of my code to:

...
u = w * K * v
for u in results:
     preimages[u] = [w]

(results are defines before as list or tuple of all u) the problem with keys seems to be solved, but I do not get appropriate vectors as preimages, instead I get (1, 1, 1, 1, 1) for all u

the best I can get, but the problem remains the same:

v = w.transpose()
for u in results:
     u = w * K * v
     u.set_immutable()
     preimages[u] = vector(w)

I think the problem is that u is a matrix, is there a way to convert it to a number ?

Please provide a code that we could repeat, for example n is not defined, K either.

Here it is:

v = random_vector(RR, 5)
K = diagonal_matrix(v)
import itertools
W = itertools.product([0,1], repeat = 5)
results = []
for w in W:
     w = vector(w)
     w = w.row()
     v = w.transpose()
     u = w * K * v
     results.append(u[0, 0])


W = itertools.product([0,1], repeat = 5)
for w in W:
     w = vector(w)
     w = w.row()
     v = w.transpose()
     for u in results:
          u = w * K * v
          u.set_immutable()
          preimages[u] = vector(w)
preimages