2021-03-07 17:37:47 +0200 received badge ● Notable Question (source) 2021-01-29 16:18:57 +0200 asked a question Functions with operation (multiplication) as argument Suppose I have functions $f$, $g_1$, $g_2$, $h$ and an operation $*$, which is not necessarily multiplication, satisfying the following relations: $$f(X * Y) = g_1(X) g_2(Y) + g_1(Y) g_2(X) + f(X) * f(Y) + h(X * Y)$$ $$h(X * Y) = h^2(X) * g_1(Y)$$ How to find a symbolic expression for $f(X^7)$? 2021-01-21 16:26:34 +0200 asked a question Cluster transitivity The cluster transitivity (the fraction of closed triangles ) of g is equal to: C =(number of triangles) × 3/(number of connected triples) Formula (7.28) Networks Mark Newman (2018) I would like to ask you about the method cluster_transitivity() It gives 0.0853107962707866 for this network: http://snap.stanford.edu/data/email-E... , but a table from this page shows that Fraction of closed triangles is 0.03015. So, these two number are not equal. If I omit 3 in the formula (7.28) and I get 0.0284369320902622. Why? On this page: http://snap.stanford.edu/data/index.html (at the end), we have a definition of the fraction of closed triangles: Number of connected triples of nodes / number of (undirected) length 2 paths 2020-11-08 11:53:26 +0200 received badge ● Popular Question (source) 2020-05-21 16:29:39 +0200 answered a question Kronecker Power of sparse matrices problem Yes, I made many errors. Sorry! I took some unchecked codes and translated it. I had in my mind the following solution: def SparseMatrixPower(A,p): if p == 1: return(A) elif Mod(p,2): return(SparseMatrixProduct(A,SparseMatrixPower(SparseMatrixProduct(A,A), (p - 1) / 2))) else: return(SparseMatrixPower(SparseMatrixProduct(A,A), p / 2))  2020-05-12 13:10:38 +0200 commented answer Kronecker Power of sparse matrices problem Yes, this is typo, I repaired my code. It does not work as well. 2020-05-02 22:36:12 +0200 asked a question Kronecker Power of sparse matrices problem Why the following code does not work? I try it also in loops. import numpy from scipy import sparse from scipy.sparse import coo_matrix def SparseMatrixPower(A,p): if p == 1: return(A) elif Mod(p,2): return(SparseMatrixPower(A,SparseMatrixProduct(A,A)), (p - 1) / 2) else: return(SparseMatrixPower(SparseMatrixProduct(A,A), p / 2)) def SparseMatrixProduct(A,B): return(sparse.kron(A,B)+sparse.kronsum(A,B)) A=sparse.coo_matrix([[0,1,2],[1,1,2],[2,2,3]]) B=sparse.coo_matrix([[0,1,2],[1,1,2],[2,2,3]]) SparseMatrixProduct(A,B) SparseMatrixPower(A,3)  2020-05-02 22:20:19 +0200 received badge ● Scholar (source) 2020-05-02 22:20:15 +0200 received badge ● Supporter (source) 2020-05-02 17:28:01 +0200 answered a question Graph indexed from zero Maybe faster than that: def ChangeVertices(g,di): G=Graph() for v in di.values(): G.add_vertex(v) for e in g.edge_iterator(): G.add_edge(di[e] if e in di else e,di[e] if e in di else e) return(G) def GraphFromZero(g): return(ChangeVertices(g,{v:i for i,v in enumerate(g.vertices())}))  2020-05-02 17:01:38 +0200 asked a question Graph indexed from zero How to change vertices of a graph to that are indexed from 0? In Mathematica: ChangeVertices. We can change it to the adjacency matrix A and from A to the graph. A faster solution? Ho to get a permutation of vertices? 2020-04-29 15:58:57 +0200 asked a question How to create url/file link in jupyter/sage? I have file/url: load("/home/***/MJRun.sage")  I would like to open (fast) this file/url in Jupyter in another card of Firefox. For example by one click. I use this file very often. How to do that? 2020-04-29 11:39:31 +0200 commented answer Problem: Jupyter (Sage) with Numba and pypy What's about PyPy? 2020-04-29 11:38:26 +0200 commented answer Problem: Jupyter (Sage) with Numba and pypy I now have (after the substitution): TypingError: Failed in nopython mode pipeline (step: nopython frontend) Cannot unify array(int64, 2d, C) and array(float64, 2d, C) for '$56binary_add.2', defined at (12) File "", line 12: def go_fast(a): # Function is compiled and runs in machine code trace += np.tanh(a[i, i]) return a + trace ^  During: typing of intrinsic-call at (12) File "", line 12: def go_fast(a): # Function is compiled and runs in machine code trace += np.tanh(a[i, i]) return a + trace ^  2020-04-28 22:21:46 +0200 commented answer Problem: Jupyter (Sage) with Numba and pypy Does not work. 2020-04-28 18:43:44 +0200 received badge ● Student (source) 2020-04-28 16:40:16 +0200 commented answer Problem: Jupyter (Sage) with Numba and pypy Now I get: TypingError: Failed in nopython mode pipeline (step: nopython frontend) Untyped global name 'Integer': cannot determine Numba type of File "", line 9: def go_fast(a): # Function is compiled and runs in machine code trace = Integer(0) ^  2020-04-28 12:48:10 +0200 received badge ● Editor (source) 2020-04-28 12:42:46 +0200 commented answer Problems with AMS symbols in Sage, Jupyter Great! Thank you. 2020-04-28 12:39:37 +0200 asked a question Problem: Jupyter (Sage) with Numba and pypy I install it by: pip3 install numba  How to use and import numba, pypy in sage. I get: ModuleNotFoundError: No module named 'numba'  when I run the following code (from https://numba.pydata.org/numba-doc/la... ) from numba import jit import numpy as np import time x = np.arange(100).reshape(10, 10) @jit(nopython=True) def go_fast(a): # Function is compiled and runs in machine code trace = 0 for i in range(a.shape): trace += np.tanh(a[i, i]) return a + trace start = time.time() go_fast(x) end = time.time() print("Elapsed (with compilation) = %s" % (end - start)) start = time.time() go_fast(x) end = time.time() print("Elapsed (after compilation) = %s" % (end - start))  2020-04-28 12:38:12 +0200 asked a question Problem Jupyter (Sage) with numba and pypy How to use and import numba, pypy in sage. I get: ModuleNotFoundError: No module named 'numba' when I run the following code: from numba import jit import numpy as np import time x = np.arange(100).reshape(10, 10) @jit(nopython=True) def go_fast(a): # Function is compiled and runs in machine code trace = 0 for i in range(a.shape): trace += np.tanh(a[i, i]) return a + trace start = time.time() go_fast(x) end = time.time() print("Elapsed (with compilation) = %s" % (end - start)) start = time.time() go_fast(x) end = time.time() print("Elapsed (after compilation) = %s" % (end - start))  2019-10-12 16:45:27 +0200 asked a question Problems with AMS symbols in Sage, Jupyter How to display the square (\square) symbol in a graph (Jupyter, maybe not only). Why \boxtimes is too large? plot(x, (x,-1,10), axes_labels=[r'$F(G\,\square\,H)$',r'$F(G\,\times\,H)$']).show() plot(x, (x,-1,10), axes_labels=[r'$F(G\,\square\,H)$',r'$F(G\,\times\,H)$']).show()  I tried \box \square \emptybox etc. and from sage.misc.latex import latex_extra_preamble latex.add_to_preamble('\\usepackage{amssymb}')  I get: ValueError: F(G\,\square\,H) ^ Unknown symbol: \square (at char 5), (line:1, col:6) 2019-10-12 16:45:27 +0200 asked a question Problems with AMS symbols in Sage, Jupyter How to display the square (\square) symbol in a graph (Jupyter, maybe not only). Why \boxtimes is too large? plot(x, (x,-1,10), axes_labels=[r'$F(G\,\square\,H)$',r'$F(G\,\times\,H)$']).show() plot(x, (x,-1,10), axes_labels=[r'$F(G\,\square\,H)$',r'$F(G\,\times\,H)\$']).show()  I tried \box \square \emptybox etc. and from sage.misc.latex import latex_extra_preamble latex.add_to_preamble('\\usepackage{amssymb}')  I get: ValueError: F(G\,\square\,H) ^ Unknown symbol: \square (at char 5), (line:1, col:6)