GA3165's profile - activity

How to list out the zero-divisors of this ring? Thank you.

The primes () method gives the list of all primes. Similarly, I need a list (Say PP) that consists of all $p^k-1$ where $p$ is a prime and $k \ge 1$. How to create this infinite list?

Also, I want all possible finite products of elements of PP. Using this I want to understand when two such products are equal.

How to do this? Kindly share your thoughts. Thank you.

@Max Alekseyev Thank you. How to list the elements less than 100 from PP?

Thank you. But I want for arbitrary k :)

list of all prime powers -1 The primes () method gives the list of all primes. Similarly, I need a list (Say PP) that co

list of all prime powers -1 The primes () method gives the list of all primes. Similarly, I need a list (Say PP) that co

list of all prime powers -1 The primes () method gives the list of all primes. Similarly, I need a list that consists of

list of all prime powers -1 The primes () method gives the list of all primes. Similarly, I need a list that consists of

Thank you :)

How to implement the cartesian product of finite commutative rings with 1 with pointwise multiplication in sage?

As far as I know, it is not there yet. So please help me with this. Thank you.

Product of finite rings in sage How to implement the cartesian product of finite commutative rings with 1 with pointwise

Thanks for the code. Someone, please explain to me how to use this code to construct the product of rings in jupiter? Th

In the given link, they are checking whether a list is a sublist of another list or not. I am unable to see how it can be used here. Can you please explain it to me? Thank you.

@John Palmieri No. The order doesn't matter. In your previous comment if you meant [[0,1],[2]] is a refinement of [[1,0,2]] then it is a refinement. Thank you.

Consider the following lists of lists L1 = [[0,1,2],[1,2],[2,2]] and L2 = [[0,1],[2],[1,2],[1,2]]. We say that L2 is a refinement of L1. How to check whether a list of lists is a refinement of another list of lists in Sage.

In the case of set partitions, we have the option refinement. But I need to work with the multisets and its multi partitions. So I am using lists and there is no refinement option for lists of lists.

Kindly help me with how to implement this.

Thank you.

@slelievre I have added the full code. Kindly check. Thank you. I directly feed M = [[0], [1, 2], [1, 2], [2, 2]] but it is throwing the same error message.

I have the following code to generate all multiset partitions of a given multiset (list).

k0 = 2
k1 = 1
k2 = 1
#k3 = 1
l = k0+k1+k2 #+k3 

L = [ ]
for i in range(k0) :
    L.append(0)
for i in range(k1) :
    L.append(1)
for i in range(k2) :
    L.append(2)
print L
#L = [0,1,2,3]
LL = list(range(len(L)))
print LL
P = SetPartitions(LL)
P = list(P)

J = []
for p in P :
    J.append([])
    aa = P.index(p)
    for i in p :
        J[aa].append(list(i))
#print J    


JJ =[]
for j in J :
    JJ.append([])
    bb = J.index(j)
    for i in j :
        JJ[bb].append([])
        aa = j.index(i)
        for k in i :
            #print aa
            JJ[bb][aa].append(L[k])
print JJ

The above code gives me the following output

[0, 0, 1, 2]
[0, 1, 2, 3]
[[[0, 0, 1, 2]], [[0], [0, 1, 2]], [[0, 1, 2], [0]], [[0, 0, 2], [1]], [[0, 0, 1], [2]], [[0, 0], [1, 2]], [[0, 1], [0, 2]], [[0, 2], [0, 1]], [[0], [0], [1, 2]], [[0], [0, 2], [1]], [[0], [0, 1], [2]], [[0, 2], [0], [1]], [[0, 1], [0], [2]], [[0, 0], [1], [2]], [[0], [0], [1], [2]]]

I have the following code to generate a poset out of JJ in which the order is given by the refinement.

sage: elms = JJ
sage: def fcn(A, B):
....:     if len(A) != len(B) + 1:
....:         return False
....:     for a in A:
....:         if not any(set(a).issubset(b) for b in B):
....:             return False
....:     return True
sage: Poset((elms, fcn), cover_relations=True)

I usually work with sets and my input JJ is usually a set partition and the program works well.

Now, I am working with multisets (like [0,1,1,2,2,2,2]) and multi partitions (like [[0],[1,2],[1,2],[2,2]). By a multi-partition, I mean a partition in which each part is a multiset and parts can be repeated in a partition. So basically it is a list of lists. We cannot implement this using sets. I have codes given above to generate all such partitions in sage using lists.

Now, the set of all multi partitions JJ (which is implements as a list) of a multiset (which is also implemented as a list) has to be fed as an input to the above code to generate the poset. But the above code throws the error

 ---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-42-993ec557f50c> in <module>()
      7             return False
      8     return True
----> 9 Poset((elms, fcn), cover_relations=True)

/Applications/SageMath-8.1.app/Contents/Resources/sage/local/lib/python2.7/site-packages/sage/combinat/posets/posets.pyc in Poset(data, element_labels, cover_relations, linear_extension, category, facade, key)
    674                         raise TypeError("not a list of relations")
    675             D = DiGraph()
--> 676             D.add_vertices(elements)
    677             D.add_edges(relations, loops=False)
    678         elif len(data) > 2:

/Applications/SageMath-8.1.app/Contents/Resources/sage/local/lib/python2.7/site-packages/sage/graphs/generic_graph.pyc in add_vertices(self, vertices)
   9602 
   9603         """
-> 9604         return self._backend.add_vertices(vertices)
   9605 
   9606     def delete_vertex(self, vertex, in_order=False):

/Applications/SageMath-8.1.app/Contents/Resources/sage/src/sage/graphs/base/c_graph.pyx in sage.graphs.base.c_graph.CGraphBackend.add_vertices (build/cythonized/sage/graphs/base/c_graph.c:14020)()
   1504         for v in vertices:
   1505             if v is not None:
-> 1506                 self.add_vertex(v)
   1507             else:
   1508                 nones += 1

/Applications/SageMath-8.1.app/Contents/Resources/sage/src/sage/graphs/base/c_graph.pyx in sage.graphs.base.c_graph.CGraphBackend.add_vertex (build/cythonized/sage/graphs/base/c_graph.c:13856)()
   1454             retval = name
   1455 
-> 1456         self.check_labelled_vertex(name,
   1457                      (self._directed and
   1458                       self._cg_rev is not None)) # this will add the vertex

/Applications/SageMath-8.1.app/Contents/Resources/sage/src/sage/graphs/base/c_graph.pyx in sage.graphs.base.c_graph.CGraphBackend.check_labelled_vertex (build/cythonized/sage/graphs/base/c_graph.c:12310)()
   1153         cdef CGraph G_rev = self._cg_rev
   1154 
-> 1155         cdef int u_int = self.get_vertex(u)
   1156         if u_int != -1:
   1157             if not bitset_in(G.active_vertices, u_int):

/Applications/SageMath-8.1.app/Contents/Resources/sage/src/sage/graphs/base/c_graph.pyx in sage.graphs.base.c_graph.CGraphBackend.get_vertex (build/cythonized/sage/graphs/base/c_graph.c:11902)()
   1120         cdef CGraph G = self._cg
   1121         cdef long u_long
-> 1122         if u in vertex_ints:
   1123             return vertex_ints[u]
   1124         try:

TypeError: unhashable type: 'list'

How to overcome this issue? Kindly help me with this. Thank you.

@rburing. Thank you. It works. Cute idea.

Let L = [0,1,1,2,2,2,2,]. I want to generate all the multi-partitions of L in which each part can have repeated entries and the parts themselves can repeat in the partition.

For example, [[0],[1,2],[1,2],[2,2]] is one such partition of L.

Kindly help me with this. Thank you.

Let L be equal to the list [0,1,1,2,2,2,2]. I want to generate all the multiset partitions of L in which each part is a multiset (or a list with repeated entries) and parts are allowed to repeat. For example, [[0],[1,2],[1,2],[2,2]] is one such multi partitions. Kindly help me with this. Thank you.