def argspec():
argspec = sage_getargspec(func)
args = ((argspec.args if not argspec.args is None else []) +
list(self.options))
defaults = (argspec.defaults or ()) + tuple(self.options.values())
# Note: argspec.defaults is not always a tuple for some reason
return ArgSpec(args, argspec.varargs, argspec.keywords, defaults)
def __init__(self, dep_var, indep_vars):
"""
INPUT:
- ``dep_var`` - The dependent variable (the function value will be
substituted for this).
- ``indep_vars`` - A list of independent variables (the parameters will be
substituted for these).
TESTS:
Because the base :class:`_Coordinates` class automatically checks the
initializing variables with the transform method, :class:`_Coordinates`
cannot be instantiated by itself. We test a subclass.
sage: from sage.plot.plot3d.plot3d import _ArbitraryCoordinates as arb
sage: x,y,z=var('x,y,z')
sage: arb((x+z,y*z,z), z, (x,y))
Arbitrary Coordinates coordinate transform (z in terms of x, y)
"""
all_vars = sage_getargspec(self.transform).args[1:]
if set(all_vars) != set(indep_vars + [dep_var]):
raise ValueError('variables were specified incorrectly for this coordinate system; incorrect variables were %s'%list(set(all_vars).symmetric_difference(set(indep_vars+[dep_var]))))
self.dep_var = dep_var
self.indep_vars = indep_vars
def argspec():
from sageinspect import sage_getargspec
argspec = sage_getargspec(func)
args = (argspec.args if not argspec.args is None else []) + self.options.keys()
defaults = tuple(argspec.defaults if not argspec.defaults is None else ()) \
+ tuple(self.options.values())
#Note: argspec.defaults is not always a tuple for some reason
return ArgSpec(args, argspec.varargs, argspec.keywords, defaults)
def argspec():
from sageinspect import sage_getargspec
argspec = sage_getargspec(func)
args = (argspec.args
if not argspec.args is None else []) + self.options.keys()
defaults = tuple(argspec.defaults if not argspec.defaults is None else ()) \
+ tuple(self.options.values())
#Note: argspec.defaults is not always a tuple for some reason
return ArgSpec(args, argspec.varargs, argspec.keywords, defaults)
def f(wrapper):
update_wrapper(wrapper, wrapped, assigned=assigned, updated=updated)
wrapper._sage_src_ = lambda: sage_getsource(wrapped)
wrapper._sage_src_lines_ = lambda: sage_getsourcelines(wrapped)
#Getting the signature right in documentation by Sphinx (Trac 9976)
#The attribute _sage_argspec_() is read by Sphinx if present and used
#as the argspec of the function instead of using reflection.
wrapper._sage_argspec_ = lambda: sage_getargspec(wrapped)
return wrapper
def f(wrapper):
update_wrapper(wrapper, wrapped, assigned=assigned, updated=updated)
wrapper._sage_src_ = lambda: sage_getsource(wrapped)
wrapper._sage_src_lines_ = lambda: sage_getsourcelines(wrapped)
#Getting the signature right in documentation by Sphinx (Trac 9976)
#The attribute _sage_argspec_() is read by Sphinx if present and used
#as the argspec of the function instead of using reflection.
wrapper._sage_argspec_ = lambda: sage_getargspec(wrapped)
return wrapper
def _explain_constructor(cl):
r"""
Internal function for use error messages when constructing encoders and decoders.
EXAMPLES::
sage: from sage.coding.linear_code import LinearCodeSyndromeDecoder
sage: from sage.coding.abstract_code import _explain_constructor
sage: cl = LinearCodeSyndromeDecoder
sage: _explain_constructor(cl)
"The constructor requires no arguments.\nIt takes the optional
arguments ['maximum_error_weight'].\nSee the documentation of
sage.coding.linear_code.LinearCodeSyndromeDecoder for more details."
sage: from sage.coding.information_set_decoder import LinearCodeInformationSetDecoder
sage: cl = LinearCodeInformationSetDecoder
sage: _explain_constructor(cl)
"The constructor requires the arguments ['number_errors'].\nIt takes the optional arguments ['algorithm'].\nIt accepts unspecified arguments as well.\nSee the documentation of sage.coding.information_set_decoder.LinearCodeInformationSetDecoder for more details."
"""
if inspect.isclass(cl):
argspec = sage_getargspec(cl.__init__)
skip = 2 # skip the self and code arguments
else:
# Not a class, assume it's a factory function posing as a class
argspec = sage_getargspec(cl)
skip = 1 # skip code argument
if argspec.defaults:
args = argspec.args[skip:-len(argspec.defaults)]
kwargs = argspec.args[-len(argspec.defaults):]
opts = "It takes the optional arguments {}.".format(kwargs)
else:
args = argspec.args[skip:]
opts = "It takes no optional arguments."
if args:
reqs = "The constructor requires the arguments {}.".format(args)
else:
reqs = "The constructor requires no arguments."
if argspec.varargs or argspec.keywords:
var = "It accepts unspecified arguments as well.\n"
else:
var = ""
return("{}\n{}\n{}See the documentation of {}.{} for more details."\
.format(reqs, opts, var, cl.__module__, cl.__name__))
def argspec():
argspec = sage_getargspec(func)
def listForNone(l):
return l if not l is None else []
newArgs = [self.name + opt for opt in self.options.keys()]
args = (argspec.args if not argspec.args is None else []) + newArgs
defaults = (argspec.defaults if not argspec.defaults is None else ()) \
+ tuple(self.options.values())
#Note: argspec.defaults is not always a tuple for some reason
return ArgSpec(args, argspec.varargs, argspec.keywords, defaults)
def argspec():
argspec = sage_getargspec(func)
def listForNone(l):
return l if not l is None else []
newArgs = [self.name + opt for opt in self.options.keys()]
args = (argspec.args if not argspec.args is None else []) + newArgs
defaults = (argspec.defaults if not argspec.defaults is None else ()) \
+ tuple(self.options.values())
#Note: argspec.defaults is not always a tuple for some reason
return ArgSpec(args, argspec.varargs, argspec.keywords, defaults)
def format_args(self):
# for classes, the relevant signature is the __init__ method's
initmeth = self.get_attr(self.object, '__init__', None)
# classes without __init__ method, default __init__ or
# __init__ written in C?
if initmeth is None or initmeth is object.__init__ or not \
(inspect.ismethod(initmeth) or inspect.isfunction(initmeth)):
return None
argspec = sage_getargspec(initmeth)
if argspec[0] and argspec[0][0] in ('cls', 'self'):
del argspec[0][0]
return inspect.formatargspec(*argspec)
def format_args(self):
# for classes, the relevant signature is the __init__ method's
initmeth = self.get_attr(self.object, '__init__', None)
# classes without __init__ method, default __init__ or
# __init__ written in C?
if initmeth is None or initmeth is object.__init__ or not \
(inspect.ismethod(initmeth) or inspect.isfunction(initmeth)):
return None
argspec = sage_getargspec(initmeth)
if argspec[0] and argspec[0][0] in ('cls', 'self'):
del argspec[0][0]
return inspect.formatargspec(*argspec)
def f(wrapper, assigned=assigned, updated=updated):
update_wrapper(wrapper, wrapped, assigned=assigned, updated=updated)
# For backwards-compatibility with old versions of sage_wraps
wrapper.f = wrapped
# For forwards-compatibility with functools.wraps on Python 3
wrapper.__wrapped__ = wrapped
wrapper._sage_src_ = lambda: sage_getsource(wrapped)
wrapper._sage_src_lines_ = lambda: sage_getsourcelines(wrapped)
#Getting the signature right in documentation by Sphinx (Trac 9976)
#The attribute _sage_argspec_() is read by Sphinx if present and used
#as the argspec of the function instead of using reflection.
wrapper._sage_argspec_ = lambda: sage_getargspec(wrapped)
return wrapper
def _sage_argspec_(self):
"""
Return the argument specification of the wrapped function or method.
TESTS::
sage: from sage.misc.sageinspect import sage_getargspec
sage: from sage.sets.set_from_iterator import Decorator
sage: d = Decorator()
sage: d.f = find_local_minimum
sage: sage_getargspec(d) # indirect doctest
ArgSpec(args=['f', 'a', 'b', 'tol', 'maxfun'], varargs=None, keywords=None, defaults=(1.48e-08, 500))
"""
from sage.misc.sageinspect import sage_getargspec
return sage_getargspec(self.f)
def _sage_argspec_(self):
"""
Return the argument specification of the wrapped function or method.
TESTS::
sage: from sage.misc.sageinspect import sage_getargspec
sage: from sage.sets.set_from_iterator import Decorator
sage: d = Decorator()
sage: d.f = find_local_minimum
sage: sage_getargspec(d) # indirect doctest
ArgSpec(args=['f', 'a', 'b', 'tol', 'maxfun'], varargs=None, keywords=None, defaults=(1.48e-08, 500))
"""
from sage.misc.sageinspect import sage_getargspec
return sage_getargspec(self.f)
def args_on_obj(self, obj):
if hasattr(obj, "_sage_argspec_"):
argspec = obj._sage_argspec_()
elif inspect.isbuiltin(obj) or inspect.ismethoddescriptor(obj):
# can never get arguments of a C function or method unless
# a function to do so is supplied
if self.env.config.autodoc_builtin_argspec:
argspec = self.env.config.autodoc_builtin_argspec(obj)
else:
return None
else:
# The check above misses ordinary Python methods in Cython
# files.
argspec = sage_getargspec(obj)
if argspec is not None and argspec[0] and argspec[0][0] in ('cls', 'self'):
del argspec[0][0]
return argspec
def args_on_obj(obj):
if hasattr(obj, "_sage_argspec_"):
argspec = obj._sage_argspec_()
elif inspect.isbuiltin(obj) or inspect.ismethoddescriptor(obj):
# can never get arguments of a C function or method unless
# a function to do so is supplied
if self.env.config.autodoc_builtin_argspec:
argspec = self.env.config.autodoc_builtin_argspec(obj)
else:
return None
else:
# The check above misses ordinary Python methods in Cython
# files.
argspec = sage_getargspec(obj) #inspect.getargspec(obj)
#if isclassinstance(obj) or inspect.isclass(obj):
if argspec is not None and argspec[0] and argspec[0][0] in ('cls', 'self'):
del argspec[0][0]
return argspec
def _find_arguments_for_callable(func):
"""
Find the names of arguments (that do not have default values) for
a callable function, taking care of several special cases in Sage.
If the parameters cannot be found, then return ``[]``.
EXAMPLES::
sage: from sage.plot.plot3d.plot3d import _find_arguments_for_callable
sage: _find_arguments_for_callable(lambda x,y: x+y)
['x', 'y']
sage: def f(a,b,c): return a+b+c
sage: _find_arguments_for_callable(f)
['a', 'b', 'c']
sage: _find_arguments_for_callable(lambda x,y,z=2: x+y+z)
['x', 'y']
sage: def f(a,b,c,d=2,e=1): return a+b+c+d+e
sage: _find_arguments_for_callable(f)
['a', 'b', 'c']
sage: g(w,r,t)=w+r+t
sage: _find_arguments_for_callable(g)
['w', 'r', 't']
sage: a,b = var('a,b')
sage: _find_arguments_for_callable(a+b)
['a', 'b']
sage: _find_arguments_for_callable(operator.add)
[]
"""
if inspect.isfunction(func):
pass
elif hasattr(func, 'arguments'):
# Might be a symbolic function with arguments
return [repr(s) for s in func.arguments()]
else:
func = func.__call__
f_args = sage_getargspec(func)
if f_args.defaults is None:
params = f_args.args
else:
params = f_args.args[:-len(f_args.defaults)]
return params
def _sage_argspec_(self):
"""
Returns the argument specification for this object, which is
just the argument specification for the underlying function.
See :module:`sage.misc.sageinspect` for more information on
this convention.
EXAMPLES::
sage: from sage.parallel.decorate import Parallel
sage: p = Parallel(2)
sage: def f(x, y):
....: return x + y
sage: from sage.misc.sageinspect import sage_getargspec
sage: sage_getargspec(p(f))
ArgSpec(args=['x', 'y'], varargs=None, keywords=None, defaults=None)
"""
from sage.misc.sageinspect import sage_getargspec
return sage_getargspec(self.func)
def _sage_argspec_(self):
"""
Returns the argument specification for this object, which is
just the argument specification for the underlying function.
See :module:`sage.misc.sageinspect` for more information on
this convention.
EXAMPLES::
sage: from sage.parallel.decorate import Parallel
sage: p = Parallel(2)
sage: def f(x, y):
... return x + y
sage: from sage.misc.sageinspect import sage_getargspec
sage: sage_getargspec(p(f))
ArgSpec(args=['x', 'y'], varargs=None, keywords=None, defaults=None)
"""
from sage.misc.sageinspect import sage_getargspec
return sage_getargspec(self.func)
def args_on_obj(obj):
if hasattr(obj, "_sage_argspec_"):
return obj._sage_argspec_()
if inspect.isbuiltin(obj) or \
inspect.ismethoddescriptor(obj):
# can never get arguments of a C function or method unless
# a function to do so is supplied
if self.env.config.autodoc_builtin_argspec:
argspec = self.env.config.autodoc_builtin_argspec(obj)
return argspec
else:
return None
argspec = sage_getargspec(obj) #inspect.getargspec(obj)
if isclassinstance(obj) or inspect.isclass(obj):
# if a class should be documented as function, we try
# to use the constructor signature as function
# signature without the first argument.
if argspec is not None and argspec[0]:
del argspec[0][0]
return argspec
def args_on_obj(obj):
if hasattr(obj, "_sage_argspec_"):
return obj._sage_argspec_()
if inspect.isbuiltin(obj) or \
inspect.ismethoddescriptor(obj):
# can never get arguments of a C function or method unless
# a function to do so is supplied
if self.env.config.autodoc_builtin_argspec:
argspec = self.env.config.autodoc_builtin_argspec(obj)
return argspec
else:
return None
argspec = sage_getargspec(obj) #inspect.getargspec(obj)
if isclassinstance(obj) or inspect.isclass(obj):
# if a class should be documented as function, we try
# to use the constructor signature as function
# signature without the first argument.
if argspec is not None and argspec[0]:
del argspec[0][0]
return argspec
def harvest_function(self, method, semantic={}, store=True):
"""
Harvest metadata about a single function/method, including stuff in
`semantic`
INPUT:
- ``store`` -- a boolean (default: True): whether to store
the harvested information, or just return it
Storing is meant for global functions, non storing for methods
of classes whose data will be stored in the class
EXAMPLES::
sage: def f(x,y): pass
sage: Exporter().harvest_method(f, {"gap":"coucou"}, store=False)
{'__doc__': None,
'args': ['x', 'y'],
'argspec': ArgSpec(args=['x', 'y'], varargs=None, keywords=None, defaults=None),
'gap': 'coucou',
'name': 'f'}
"""
if isinstance(method, AbstractMethod):
method = method._f
try:
argspec = sage_getargspec(method)
result = {
"__doc__": method.__doc__,
"args": argspec.args,
"argspec": argspec # TODO: add code
}
except TypeError:
result = {}
result.update(semantic)
if store:
result['name'] = class_name(method)
self._database['functions'][result['name']] = result
return result
def __classcall__(cls,
constructor=None,
default_values=None,
names=None,
ignore_special_args=('cls', 'self'),
option_only_args=('conditioncheck', 'field', 'merge',
'condition_according_to_literature')):
# For classes, sage_getargspec uses the argspec of __call__, which is not useful for us.
if isinstance(constructor, ParametricFamily_base):
if default_values is None and names is None:
return constructor
arg_default_dict = copy(constructor.default_values())
args = constructor.names()
cls = constructor._reduction[0] # FIXME
else:
if constructor is None:
c = cls._construct_function
else:
c = constructor
args, varargs, keywords, defaults = sage_getargspec(c)
#import pdb; pdb.set_trace()
args = [
name for name in args if name not in ignore_special_args
] # cls and self do not appear in the default list, remove them first
if defaults:
arg_default_dict = OrderedDict(zip(args, defaults))
else:
arg_default_dict = OrderedDict.fromkeys(args)
if default_values is not None:
default_values = dict(default_values)
arg_default_dict.update(default_values)
if names is None:
names = [name for name in args if name not in option_only_args]
arg_default_dict = tuple(
(name, value) for name, value in arg_default_dict.items())
return super(ParametricFamily,
cls).__classcall__(cls, constructor, arg_default_dict,
tuple(names))
def test_finite_lattice(L):
"""
Test several functions on a given finite lattice.
The function contains tests of different kinds:
- Implications of Boolean properties. Examples: a distributive lattice is modular,
a dismantlable and distributive lattice is planar, a simple lattice can not be
constructible by Day's doublings.
- Dual and self-dual properties. Examples: Dual of a modular lattice is modular,
dual of an atomic lattice is co-atomic.
- Certificate tests. Example: certificate for a non-complemented lattice must be
an element without a complement.
- Verification of some property by known property or by a random test.
Examples: A lattice is distributive iff join-primes are exactly
join-irreducibles and an interval of a relatively complemented
lattice is complemented.
- Set inclusions. Example: Every co-atom must be meet-irreducible.
- And several other tests. Example: The skeleton of a pseudocomplemented
lattice must be Boolean.
EXAMPLES::
sage: from sage.tests.finite_poset import test_finite_lattice
sage: L = posets.RandomLattice(10, 0.98)
sage: test_finite_lattice(L) is None # Long time
True
"""
from sage.combinat.posets.lattices import LatticePoset
from sage.sets.set import Set
from sage.combinat.subset import Subsets
from sage.misc.prandom import randint
from sage.misc.flatten import flatten
from sage.misc.misc import attrcall
from sage.misc.sageinspect import sage_getargspec
if L.cardinality() < 4:
# Special cases should be tested in specific TESTS-sections.
return None
all_props = set(list(implications) + flatten(implications.values()))
P = {x: test_attrcall('is_' + x, L) for x in all_props}
### Relations between boolean-valued properties ###
# Direct one-property implications
for prop1 in implications:
if P[prop1]:
for prop2 in implications[prop1]:
if not P[prop2]:
raise ValueError("error: %s should implicate %s" %
(prop1, prop2))
# Impossible combinations
for p1, p2 in mutually_exclusive:
if P[p1] and P[p2]:
raise ValueError(
"error: %s and %s should be impossible combination" % (p1, p2))
# Two-property implications
for p1, p2, p3 in two_to_one:
if P[p1] and P[p2] and not P[p3]:
raise ValueError("error: %s and %s, so should be %s" %
(p1, p2, p3))
Ldual = L.dual()
# Selfdual properties
for p in selfdual_properties:
if P[p] != test_attrcall('is_' + p, Ldual):
raise ValueError("selfdual property %s error" % p)
# Dual properties and elements
for p1, p2 in dual_properties:
if P[p1] != test_attrcall('is_' + p2, Ldual):
raise ValueError("dual properties error %s" % p1)
for e1, e2 in dual_elements:
if set(attrcall(e1)(L)) != set(attrcall(e2)(Ldual)):
raise ValueError("dual elements error %s" % e1)
### Certificates ###
# Return value must be a pair with correct result as first element.
for p_ in all_props:
# Dirty fix first
if p_[:9] == 'doubling_' or p_[:5] == 'uniq_': continue
p = "is_" + p_
if 'certificate' in sage_getargspec(getattr(L, p)).args:
res = attrcall(p, certificate=True)(L)
if type(res) != type((1, 2)) or len(res) != 2:
raise ValueError(
"certificate-option does not return a pair in %s" % p)
if P[p_] != res[0]:
raise ValueError("certificate-option changes result in %s" % p)
# Test for "yes"-certificates
if P['supersolvable']:
a = L.is_supersolvable(certificate=True)[1]
S = Subsets(L).random_element()
if L.is_chain_of_poset(S):
if not L.sublattice(a + list(S)).is_distributive():
raise ValueError("certificate error in is_supersolvable")
if P['dismantlable']:
elms = L.is_dismantlable(certificate=True)[1]
if len(elms) != L.cardinality():
raise ValueError("certificate error 1 in is_dismantlable")
elms = elms[:randint(0, len(elms) - 1)]
L_ = L.sublattice([x for x in L if x not in elms])
if L_.cardinality() != L.cardinality() - len(elms):
raise ValueError("certificate error 2 in is_dismantlable")
if P['vertically_decomposable']:
c = L.is_vertically_decomposable(certificate=True)[1]
if c == L.bottom() or c == L.top():
raise ValueError(
"certificate error 1 in is_vertically_decomposable")
e = L.random_element()
if L.compare_elements(c, e) is None:
raise ValueError(
"certificate error 2 in is_vertically_decomposable")
# Test for "no"-certificates
if not P['atomic']:
a = L.is_atomic(certificate=True)[1]
if a in L.atoms() or a not in L.join_irreducibles():
raise ValueError("certificate error in is_atomic")
if not P['coatomic']:
a = L.is_coatomic(certificate=True)[1]
if a in L.coatoms() or a not in L.meet_irreducibles():
raise ValueError("certificate error in is_coatomic")
if not P['complemented']:
a = L.is_complemented(certificate=True)[1]
if L.complements(a) != []:
raise ValueError("compl. error 1")
if not P['sectionally_complemented']:
a, b = L.is_sectionally_complemented(certificate=True)[1]
L_ = L.sublattice(L.interval(L.bottom(), a))
if L_.is_complemented():
raise ValueError("sec. compl. error 1")
if len(L_.complements(b)) > 0:
raise ValueError("sec. compl. error 2")
if not P['cosectionally_complemented']:
a, b = L.is_cosectionally_complemented(certificate=True)[1]
L_ = L.sublattice(L.interval(a, L.top()))
if L_.is_complemented():
raise ValueError("cosec. compl. error 1")
if len(L_.complements(b)) > 0:
raise ValueError("cosec. compl. error 2")
if not P['relatively_complemented']:
a, b, c = L.is_relatively_complemented(certificate=True)[1]
I = L.interval(a, c)
if len(I) != 3 or b not in I:
raise ValueError("rel. compl. error 1")
if not P['upper_semimodular']:
a, b = L.is_upper_semimodular(certificate=True)[1]
if not set(L.lower_covers(a)).intersection(set(
L.lower_covers(b))) or set(L.upper_covers(a)).intersection(
set(L.upper_covers(b))):
raise ValueError("certificate error in is_upper_semimodular")
if not P['lower_semimodular']:
a, b = L.is_lower_semimodular(certificate=True)[1]
if set(L.lower_covers(a)).intersection(set(
L.lower_covers(b))) or not set(L.upper_covers(a)).intersection(
set(L.upper_covers(b))):
raise ValueError("certificate error in is_lower_semimodular")
if not P['distributive']:
x, y, z = L.is_distributive(certificate=True)[1]
if L.meet(x, L.join(y, z)) == L.join(L.meet(x, y), L.meet(x, z)):
raise ValueError("certificate error in is_distributive")
if not P['modular']:
x, a, b = L.is_modular(certificate=True)[1]
if not L.is_less_than(x, b) or L.join(x, L.meet(a, b)) == L.meet(
L.join(x, a), b):
raise ValueError("certificate error in is_modular")
if not P['pseudocomplemented']:
a = L.is_pseudocomplemented(certificate=True)[1]
L_ = L.subposet([e for e in L if L.meet(e, a) == L.bottom()])
if L_.has_top():
raise ValueError("certificate error in is_pseudocomplemented")
if not P['join_pseudocomplemented']:
a = L.is_join_pseudocomplemented(certificate=True)[1]
L_ = L.subposet([e for e in L if L.join(e, a) == L.top()])
if L_.has_bottom():
raise ValueError("certificate error in is_join_pseudocomplemented")
if not P['join_semidistributive']:
e, x, y = L.is_join_semidistributive(certificate=True)[1]
if L.join(e, x) != L.join(e, y) or L.join(e, x) == L.join(
e, L.meet(x, y)):
raise ValueError("certificate error in is_join_semidistributive")
if not P['meet_semidistributive']:
e, x, y = L.is_meet_semidistributive(certificate=True)[1]
if L.meet(e, x) != L.meet(e, y) or L.meet(e, x) == L.meet(
e, L.join(x, y)):
raise ValueError("certificate error in is_meet_semidistributive")
if not P['simple']:
c = L.is_simple(certificate=True)[1]
if len(L.congruence([c[randint(0, len(c) - 1)]])) == 1:
raise ValueError("certificate error in is_simple")
if not P['isoform']:
c = L.is_isoform(certificate=True)[1]
if len(c) == 1:
raise ValueError("certificate error in is_isoform")
if all(
L.subposet(c[i]).is_isomorphic(L.subposet(c[i + 1]))
for i in range(len(c) - 1)):
raise ValueError("certificate error in is_isoform")
if not P['uniform']:
c = L.is_uniform(certificate=True)[1]
if len(c) == 1:
raise ValueError("certificate error in is_uniform")
if all(len(c[i]) == len(c[i + 1]) for i in range(len(c) - 1)):
raise ValueError("certificate error in is_uniform")
if not P['regular']:
c = L.is_regular(certificate=True)[1]
if len(c[0]) == 1:
raise ValueError("certificate error 1 in is_regular")
if Set(c[1]) not in c[0]:
raise ValueError("certificate error 2 in is_regular")
if L.congruence([c[1]]) == c[0]:
raise ValueError("certificate error 3 in is_regular")
if not P['subdirectly_reducible']:
x, y = L.is_subdirectly_reducible(certificate=True)[1]
a = L.random_element()
b = L.random_element()
c = L.congruence([[a, b]])
if len(c) != L.cardinality():
for c_ in c:
if x in c_:
if y not in c_:
raise ValueError(
"certificate error 1 in is_subdirectly_reducible")
break
else:
raise ValueError(
"certificate error 2 in is_subdirectly_reducible")
if not P['join_distributive']:
a = L.is_join_distributive(certificate=True)[1]
L_ = L.sublattice(L.interval(a, L.join(L.upper_covers(a))))
if L_.is_distributive():
raise ValueError("certificate error in is_join_distributive")
if not P['meet_distributive']:
a = L.is_meet_distributive(certificate=True)[1]
L_ = L.sublattice(L.interval(L.meet(L.lower_covers(a)), a))
if L_.is_distributive():
raise ValueError("certificate error in is_meet_distributive")
### Other ###
# Other ways to recognize some boolean property
if P['distributive'] != (set(L.join_primes()) == set(
L.join_irreducibles())):
raise ValueError(
"every join-irreducible of a distributive lattice should be join-prime"
)
if P['distributive'] != (set(L.meet_primes()) == set(
L.meet_irreducibles())):
raise ValueError(
"every meet-irreducible of a distributive lattice should be meet-prime"
)
if P['join_semidistributive'] != all(
L.canonical_joinands(e) is not None for e in L):
raise ValueError(
"every element of join-semidistributive lattice should have canonical joinands"
)
if P['meet_semidistributive'] != all(
L.canonical_meetands(e) is not None for e in L):
raise ValueError(
"every element of meet-semidistributive lattice should have canonical meetands"
)
# Random verification of a Boolean property
if P['relatively_complemented']:
a = L.random_element()
b = L.random_element()
if not L.sublattice(L.interval(a, b)).is_complemented():
raise ValueError("rel. compl. error 3")
if P['sectionally_complemented']:
a = L.random_element()
if not L.sublattice(L.interval(L.bottom(), a)).is_complemented():
raise ValueError("sec. compl. error 3")
if P['cosectionally_complemented']:
a = L.random_element()
if not L.sublattice(L.interval(a, L.top())).is_complemented():
raise ValueError("cosec. compl. error 2")
# Element set inclusions
for s1, s2 in set_inclusions:
if not set(attrcall(s1)(L)).issubset(set(attrcall(s2)(L))):
raise ValueError("%s should be a subset of %s" % (s1, s2))
# Sublattice-closed properties
L_ = L.sublattice(Subsets(L).random_element())
for p in sublattice_closed:
if P[p] and not test_attrcall('is_' + p, L_):
raise ValueError("property %s should apply to sublattices" % p)
# Some sublattices
L_ = L.center() # Center is a Boolean lattice
if not L_.is_atomic() or not L_.is_distributive():
raise ValueError("error in center")
if P['pseudocomplemented']:
L_ = L.skeleton() # Skeleton is a Boolean lattice
if not L_.is_atomic() or not L_.is_distributive():
raise ValueError("error in skeleton")
L_ = L.frattini_sublattice()
S = Subsets(L).random_element()
if L.sublattice(S) == L and L.sublattice([e
for e in S if e not in L_]) != L:
raise ValueError("error in Frattini sublattice")
L_ = L.maximal_sublattices()
L_ = L_[randint(0, len(L_) - 1)]
e = L.random_element()
if e not in L_ and L.sublattice(list(L_) + [e]) != L:
raise ValueError("error in maximal_sublattices")
# Reverse functions: vertical composition and decomposition
L_ = reduce(lambda a, b: a.vertical_composition(b),
L.vertical_decomposition(), LatticePoset())
if not L.is_isomorphic(L_):
raise ValueError("error in vertical [de]composition")
# Meet and join
a = L.random_element()
b = L.random_element()
m = L.meet(a, b)
j = L.join(a, b)
m_ = L.subposet([
e for e in L.principal_lower_set(a) if e in L.principal_lower_set(b)
]).top()
j_ = L.subposet([
e for e in L.principal_upper_set(a) if e in L.principal_upper_set(b)
]).bottom()
if m != m_ or m != Ldual.join(a, b):
raise ValueError("error in meet")
if j != j_ or j != Ldual.meet(a, b):
raise ValueError("error in join")
# Misc misc
e = L.neutral_elements()
e = e[randint(0, len(e) - 1)]
a = L.random_element()
b = L.random_element()
if not L.sublattice([e, a, b]).is_distributive():
raise ValueError("error in neutral_elements")