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Results tagged with sage
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user 34538
Sage is a mathematical software system, and this tag is intended for questions involving this software in a substantive way. This tag should hardly ever be the only tag of a question; typically there should be additional tags to indicate the mathematical content of the question. Please note that questions that are purely support-questions on Sage are not a good fit for this site.
4
votes
1
answer
378
views
Existence of a non-Eulerian atomistic lattice with this property on the Möbius function
No for $|L| \le 13$, as checked by the following Sage program (using these lists of Martin Malandro):
from itertools import product
def relationtest(L,n):
for l in L:
P=Poset((range(n),l)) …
25
votes
7
answers
2k
views
Number of collinear ways to fill a grid
Sage program
# %attach SAGE/grid.sage
from sage.all import *
import copy
def grid(m,n,j):
if [m,n,j]==[1,1,1]:
return 1
elif j < min(m,n) or m==0 or n==0:
return 0
else: … factorial(m+n-1)
def CheckFormula(M,N):
for m in range(1,M+1):
for n in range(M,N+1):
if not IsFormulaCorrect(m,n):
return False
return True
Computation
sage …
2
votes
0
answers
97
views
Is the bounded coset poset of a boolean interval of finite groups, Cohen-Macaulay?
It's also true (using the function is_cohen_macaulay on SAGE) for the three first rank $3$ boolean intervals $[H,G]$ with $G$ simple, listed here (my desktop isn't enough powerful for checking the fourth …
6
votes
0
answers
259
views
Is there an integral simple fusion ring rank<6, FPdim>60 and Frobenius type?
We checked by SAGE (by using this code) that the only integral simple fusion ring of Frobenius type, rank $\leq 5$ and FPdim $< 1000000$ (except $\mathcal{G}_p$) is the Grothendieck ring of the simple … The first non-group-like integral simple fusion ring found by SAGE is of rank $7$ and FPdim $210$ (see here). …
3
votes
0
answers
246
views
Is there an integral simple fusion ring of multiplicity one and Frobenius type? (obvious exc...
But by a SAGE computation (with this code), there is no integral simple fusion ring of Frobenius type, multiplicity one, rank $\le 10$ and FPdim $ \le 1000$ (except $\mathcal{G}_p$). …
12
votes
0
answers
1k
views
Euler's totient function and Riemann hypothesis
sage: champions(3,10000000000)
[7, 1.0081297159194946, 2 * 3 * 5 * 7^-1]
[11, 1.1900001764297485, 2 * 3 * 5 * 11^-1]
[13, 1.244431734085083, 2 * 3 * 5 * 13^-1]
[17, 1.3212575912475586, 2 * 3 * 5 * 17^- … See below $[n_r,\alpha(n_r)]$ for $r=11,12$:
[197325643515, 1.8032277291323942]
[7320457889745, 1.8197057337162745]
Code
# %attach SAGE/EulerRH.spyx
from sage.all import *
cpdef g(float x): …
3
votes
0
answers
698
views
Puzzle in 3D grid with black and white boxes, related to shelling
Brute-force search with SAGE
Computation:
sage: %attach SAGE/EulerianGrid.spyx
Compiling ./SAGE/EulerianGrid.spyx... … sage: S=[[1,1,1],[1,1,2],[1,2,1],[1,2,3],[1,3,2],[1,3,3],[2,1,1],[2,1,3],[2,2,2],[2,2,3],[2,3,1],[2,3,2],[3,1,2],[3,1,3],[3,2,1],[3,2,2],[3,3,1],[3,3,3]]
sage: %time PartialOrdering(S,[],8)
CPU times: …