2023-01-05 05:51:17 +0100 received badge ● Notable Question (source) 2022-07-23 09:51:23 +0100 received badge ● Popular Question (source) 2021-05-18 07:32:16 +0100 received badge ● Popular Question (source) 2021-04-12 06:39:43 +0100 commented answer Product of finite rings in sage How to list out the zero-divisors of this ring? Thank you. 2021-04-12 06:28:02 +0100 marked best answer list of all prime powers -1 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. 2021-04-12 06:27:50 +0100 commented answer list of all prime powers -1 @Max Alekseyev Thank you. How to list the elements less than 100 from PP? 2021-04-12 06:25:44 +0100 commented answer list of all prime powers -1 Thank you. But I want for arbitrary k :) 2021-04-10 03:53:12 +0100 edited question list of all prime powers -1 list of all prime powers -1 The primes () method gives the list of all primes. Similarly, I need a list (Say PP) that co 2021-04-10 03:53:11 +0100 edited question list of all prime powers -1 list of all prime powers -1 The primes () method gives the list of all primes. Similarly, I need a list (Say PP) that co 2021-04-10 03:40:31 +0100 edited question list of all prime powers -1 list of all prime powers -1 The primes () method gives the list of all primes. Similarly, I need a list that consists of 2021-04-10 03:40:02 +0100 asked a question list of all prime powers -1 list of all prime powers -1 The primes () method gives the list of all primes. Similarly, I need a list that consists of 2021-04-10 02:32:28 +0100 commented answer Product of finite rings in sage Thank you :) 2021-04-10 02:32:14 +0100 marked best answer Product of finite rings in sage 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. 2021-03-31 04:24:31 +0100 asked a question Product of finite rings in sage Product of finite rings in sage How to implement the cartesian product of finite commutative rings with 1 with pointwise 2021-03-31 04:08:07 +0100 received badge ● Scholar (source) 2021-03-30 16:22:32 +0100 commented answer construction of product rings Z/nZ x Z/mZ Thanks for the code. Someone, please explain to me how to use this code to construct the product of rings in jupiter? Th 2020-10-10 13:04:59 +0100 received badge ● Nice Question (source) 2020-10-09 07:57:33 +0100 commented question Refinement between Lists of lists 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. 2020-10-09 07:55:29 +0100 commented question Refinement between Lists of lists @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. 2020-10-09 05:46:28 +0100 received badge ● Supporter (source) 2020-10-09 05:38:52 +0100 asked a question Refinement between Lists of lists 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. 2020-10-09 02:49:00 +0100 commented question TypeError: unhashable type: 'list' in constructing poset @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. 2020-10-08 08:21:47 +0100 received badge ● Editor (source) 2020-10-08 08:21:09 +0100 asked a question TypeError: unhashable type: 'list' in constructing poset 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) in () 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. 2020-10-08 05:23:09 +0100 commented question Multipartitions of a multiset in Sage @rburing. Thank you. It works. Cute idea. 2020-10-07 20:38:04 +0100 received badge ● Student (source) 2020-10-07 16:53:56 +0100 asked a question Multipartitions of a multiset in Sage 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. 2020-10-07 16:53:56 +0100 asked a question multipartitions of multisets in sage 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.