code
stringlengths
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return (False, (0,0,0,0)
v (includes v=0)
return (True, (t,v,k,b)
return (True, (0,0,0,0)
binomial(v-t',t-t')
binomial(k-t',t-t')
in (range(1,k+1)
if (b*binomial(k,tt)
binomial(v,tt)
combinations(block,tt)
s.get(i,0)
len(set(s.values()
binomial(k,tt)
binomial(v,tt)
if ((t is not None and t!=tt)
or (l is not None and l!=ll)
return (False, (0,0,0,0)
return (True, (tt,v,k,ll)
is_generalized_quadrangle(self, verbose=False, parameters=False)
references (e.g. [PT09]_ or [GQwiki]_)
designs.CremonaRichmondConfiguration()
h.is_generalized_quadrangle()
h.is_generalized_quadrangle(parameters=True)
IncidenceStructure((2*graphs.CompleteGraph(3)
edges(labels=False)
H.is_generalized_quadrangle(verbose=True)
graphs.CycleGraph(5)
list(G.subgraph_search_iterator(graphs.PathGraph(3)
IncidenceStructure(B)
H.is_generalized_quadrangle(verbose=True)
hypergraphs.CompleteUniform(4,2)
is_generalized_quadrangle(verbose=1)
self.incidence_graph()
g.diameter()
print("Some point is at distance >3 from some block.")
g.girth()
print("Two blocks intersect on >1 points.")
print("Some point has two projections on some line.")
self.is_uniform()
self.is_regular()
if (s is not False and s>=2)
if (t is not False and t>=2)
return (s,t)
dual(self, algorithm=None)
implementation (``algorithm=None``, default)
s (``algorithm="gap"``)
package (included in the gap_packages Sage spkg)
designs.DesarguesianProjectivePlaneDesign(4)
PP.dual()
is_t_design(return_parameters=True)
IncidenceStructure(4, [[0,2],[1,2,3],[2,3]])
D.dual()
print(D.dual(algorithm="gap")
IncidenceStructure(7, blocks, name="FanoPlane")
print(BD.dual(algorithm="gap")
BD.dual()
gap.load_package("design")
self._gap_()
gap.eval("DD:=DualBlockDesign("+gD+")
eval(gap.eval("DD.v")
eval(gap.eval("DD.blocks")
gB.append([x-1 for x in b])
IncidenceStructure(list(range(v)
self.incidence_matrix()
transpose()
automorphism_group(self)
is (isomorphic to)
designs.DesarguesianProjectivePlaneDesign(2)
P (7,3,1)
P.automorphism_group()
G.is_isomorphic(PGL(3,2)
G.cardinality()
IncidenceStructure(list(range(4)
IS.automorphism_group()
cardinality()
IS.dual()
automorphism_group()
cardinality()
IncidenceStructure('abc', ('ab','ac','bc')
I.automorphism_group()
IncidenceStructure([[(1,2)
automorphism_group()
Graph()
self.num_points()
g.add_edges((i+n,x)
enumerate(self._blocks)
g.automorphism_group(partition=[list(range(n)
list(range(n,n+self.num_blocks()
tuple([self._points[i] for i in cycle if (not cycle or cycle[0]<n)
g.cycle_tuples()
ag.gens()
tuple(cycle)
g.cycle_tuples()
if (not cycle or cycle[0]<n)
ag.gens()
PermutationGroup(gens, domain=self._points)
is_resolvable(self, certificate=False, solver=None, verbose=0, check=True)
GLPK (the default LP solver)
solver (CPLEX, Gurobi, ...)
answer (see examples below)