from sage.structure.sage_object cimport SageObject
cdef class Matroid(SageObject):
cdef public __custom_name
cdef public _custom_name
cdef int _stored_full_rank
cdef int _stored_size
# virtual methods
cpdef groundset(self)
cpdef _rank(self, X)
# internal methods, assuming verified input
cpdef _max_independent(self, X)
cpdef _circuit(self, X)
cpdef _fundamental_circuit(self, B, e)
cpdef _closure(self, X)
cpdef _corank(self, X)
cpdef _max_coindependent(self, X)
cpdef _cocircuit(self, X)
cpdef _fundamental_cocircuit(self, B, e)
cpdef _coclosure(self, X)
cpdef _augment(self, X, Y)
cpdef _is_independent(self, X)
cpdef _is_basis(self, X)
cpdef _is_circuit(self, X)
cpdef _is_closed(self, X)
cpdef _is_coindependent(self, X)
cpdef _is_cobasis(self, X)
cpdef _is_cocircuit(self, X)
cpdef _is_coclosed(self, X)
cpdef _minor(self, contractions, deletions)
cpdef _has_minor(self, N)
cpdef _line_length(self, F)
cpdef _extension(self, element, hyperplanes)
# ** user-facing methods **
# cpdef _latex_(self) # Disabled, because not overridden by current subclasses
# cpdef show(self) # Disabled, because not implemented yet
cpdef size(self)
# matroid oracle
cpdef rank(self, X=*)
cpdef full_rank(self)
cpdef basis(self)
cpdef max_independent(self, X)
cpdef circuit(self, X=*)
cpdef fundamental_circuit(self, B, e)
cpdef closure(self, X)
cpdef augment(self, X, Y=*)
cpdef corank(self, X=*)
cpdef full_corank(self)
cpdef cobasis(self)
cpdef max_coindependent(self, X)
cpdef cocircuit(self, X=*)
cpdef fundamental_cocircuit(self, B, e)
cpdef coclosure(self, X)
cpdef loops(self)
cpdef is_independent(self, X)
cpdef is_dependent(self, X)
cpdef is_basis(self, X)
cpdef is_circuit(self, X)
cpdef is_closed(self, X)
cpdef coloops(self)
cpdef is_coindependent(self, X)
cpdef is_codependent(self, X)
cpdef is_cobasis(self, X)
cpdef is_cocircuit(self, X)
cpdef is_coclosed(self, X)
# verification
cpdef is_valid(self)
# enumeration
cpdef circuits(self)
cpdef nonspanning_circuits(self)
cpdef cocircuits(self)
cpdef noncospanning_cocircuits(self)
cpdef circuit_closures(self)
cpdef nonspanning_circuit_closures(self)
cpdef bases(self)
cpdef independent_r_sets(self, long r)
cpdef nonbases(self)
cpdef dependent_r_sets(self, long r)
cpdef _extend_flags(self, flags)
cpdef _flags(self, r)
cpdef flats(self, r)
cpdef coflats(self, r)
cpdef hyperplanes(self)
cpdef f_vector(self)
# isomorphism
cpdef is_isomorphic(self, other)
cpdef _is_isomorphic(self, other)
cpdef equals(self, other)
cpdef is_isomorphism(self, other, morphism)
cpdef _is_isomorphism(self, other, morphism)
# minors, dual, trucation
cpdef minor(self, contractions=*, deletions=*)
cpdef contract(self, X)
cpdef delete(self, X)
cpdef _backslash_(self, X)
cpdef dual(self)
cpdef truncation(self)
cpdef has_minor(self, N)
cpdef has_line_minor(self, k, hyperlines=*)
cpdef _has_line_minor(self, k, hyperlines)
# extension
cpdef extension(self, element=*, subsets=*)
cpdef coextension(self, element=*, subsets=*)
cpdef modular_cut(self, subsets)
cpdef linear_subclasses(self, line_length=*, subsets=*)
cpdef extensions(self, element=*, line_length=*, subsets=*)
# connectivity
cpdef simplify(self)
cpdef cosimplify(self)
cpdef is_simple(self)
cpdef is_cosimple(self)
cpdef components(self)
cpdef is_connected(self)
cpdef is_3connected(self)
# optimization
cpdef max_weight_independent(self, X=*, weights=*)
cpdef max_weight_coindependent(self, X=*, weights=*)
cpdef intersection(self, other, weights=*)
cpdef _intersection(self, other, weights)
cpdef _intersection_augmentation(self, other, weights, Y)
# invariants
cpdef _internal(self, B)
cpdef _external(self, B)
cpdef tutte_polynomial(self, x=*, y=*)
cpdef flat_cover(self)
