def __call__(self, a, b, z, **kwargs):
"""
Return symbolic hypergeometric function expression.
INPUT:
- ``a`` -- a list or tuple of parameters
- ``b`` -- a list or tuple of parameters
- ``z`` -- a number or symbolic expression
EXAMPLES::
sage: hypergeometric([], [], 1)
hypergeometric((), (), 1)
sage: hypergeometric([], [1], 1)
hypergeometric((), (1,), 1)
sage: hypergeometric([2, 3], [1], 1)
hypergeometric((2, 3), (1,), 1)
sage: hypergeometric([], [], x)
hypergeometric((), (), x)
sage: hypergeometric([x], [], x^2)
hypergeometric((x,), (), x^2)
The only simplification that is done automatically is returning 1
if ``z`` is 0. For other simplifications use the
``simplify_hypergeometric`` method.
"""
return BuiltinFunction.__call__(self, SR._force_pyobject(a),
SR._force_pyobject(b), z, **kwargs)
def __call__(self, a, b, z, **kwargs):
"""
Return symbolic hypergeometric function expression.
INPUT:
- ``a`` -- a list or tuple of parameters
- ``b`` -- a list or tuple of parameters
- ``z`` -- a number or symbolic expression
EXAMPLES::
sage: hypergeometric([], [], 1)
hypergeometric((), (), 1)
sage: hypergeometric([], [1], 1)
hypergeometric((), (1,), 1)
sage: hypergeometric([2, 3], [1], 1)
hypergeometric((2, 3), (1,), 1)
sage: hypergeometric([], [], x)
hypergeometric((), (), x)
sage: hypergeometric([x], [], x^2)
hypergeometric((x,), (), x^2)
The only simplification that is done automatically is returning 1
if ``z`` is 0. For other simplifications use the
``simplify_hypergeometric`` method.
"""
return BuiltinFunction.__call__(self,
SR._force_pyobject(a),
SR._force_pyobject(b),
z, **kwargs)
def __call__(self, function_pieces, **kwds):
r"""
Piecewise functions
INPUT:
- ``function_pieces`` -- a list of pairs consisting of a
domain and a symbolic function.
- ``var=x`` -- a symbolic variable or ``None`` (default). The
real variable in which the function is piecewise in.
OUTPUT:
A piecewise-defined function. A ``ValueError`` will be raised
if the domains of the pieces are not pairwise disjoint.
EXAMPLES::
sage: my_abs = piecewise([((-1, 0), -x), ([0, 1], x)], var=x); my_abs
piecewise(x|-->-x on (-1, 0), x|-->x on [0, 1]; x)
sage: [ my_abs(i/5) for i in range(-4, 5)]
[4/5, 3/5, 2/5, 1/5, 0, 1/5, 2/5, 3/5, 4/5]
TESTS::
sage: piecewise([([-1, 0], -x), ([0, 1], x)], var=x)
Traceback (most recent call last):
...
ValueError: domains must be pairwise disjoint
sage: step = piecewise([((-1, 0), -1), ([0, 0], 0), ((0, 1), 1)], var=x); step
piecewise(x|-->-1 on (-1, 0), x|-->0 on {0}, x|-->1 on (0, 1); x)
sage: step(-1/2), step(0), step(1/2)
(-1, 0, 1)
"""
from types import FunctionType
var = kwds.pop('var', None)
parameters = []
domain_list = []
for piece in function_pieces:
domain, function = piece
if not isinstance(domain, RealSet):
domain = RealSet(domain)
if domain.is_empty():
continue
if isinstance(function, FunctionType):
if var is None:
var = SR.var('x')
if function.func_code.co_argcount == 0:
function = function()
else:
function = function(var)
function = SR(function)
if var is None and len(function.variables()) > 0:
var = function.variables()[0]
parameters.append((domain, function))
domain_list.append(domain)
if not RealSet.are_pairwise_disjoint(*domain_list):
raise ValueError('domains must be pairwise disjoint')
if var is None:
var = self.default_variable()
parameters = SR._force_pyobject(tuple(parameters), recursive=False)
return BuiltinFunction.__call__(self, parameters, var, **kwds)
def __call__(self, *args, **kwds):
"""
EXAMPLES::
sage: max_symbolic(3,5,x)
max(x, 5)
sage: max_symbolic(3,5,x, hold=True)
max(3, 5, x)
sage: max_symbolic([3,5,x])
max(x, 5)
::
sage: min_symbolic(3,5,x)
min(x, 3)
sage: min_symbolic(3,5,x, hold=True)
min(3, 5, x)
sage: min_symbolic([3,5,x])
min(x, 3)
TESTS:
We get an exception if no arguments are given::
sage: max_symbolic()
Traceback (most recent call last):
...
ValueError: number of arguments must be > 0
Check if we return None, when the builtin function would::
sage: max_symbolic([None]) is None
True
sage: max_symbolic([None, None]) is None
True
sage: min_symbolic([None]) is None
True
sage: min_symbolic([None, None]) is None
True
Check if a single argument which is not iterable works::
sage: max_symbolic(None)
Traceback (most recent call last):
...
TypeError: 'NoneType' object is not iterable
sage: max_symbolic(5)
Traceback (most recent call last):
...
TypeError: 'sage.rings.integer.Integer' object is not iterable
sage: max_symbolic(x)
Traceback (most recent call last):
...
TypeError: 'sage.symbolic.expression.Expression' object is not iterable
sage: min_symbolic(5)
Traceback (most recent call last):
...
TypeError: 'sage.rings.integer.Integer' object is not iterable
sage: min_symbolic(x)
Traceback (most recent call last):
...
TypeError: 'sage.symbolic.expression.Expression' object is not iterable
"""
if len(args) == 0:
raise ValueError("number of arguments must be > 0")
if len(args) == 1:
try:
args=(SR._force_pyobject(iter(args[0])),)
except TypeError as e:
raise e
try:
return BuiltinFunction.__call__(self, *args, **kwds)
except ValueError as e:
if e.args[0] == "return None":
return None
def __call__(self, *args, **kwds):
"""
EXAMPLES::
sage: max_symbolic(3,5,x)
max(x, 5)
sage: max_symbolic(3,5,x, hold=True)
max(3, 5, x)
sage: max_symbolic([3,5,x])
max(x, 5)
::
sage: min_symbolic(3,5,x)
min(x, 3)
sage: min_symbolic(3,5,x, hold=True)
min(3, 5, x)
sage: min_symbolic([3,5,x])
min(x, 3)
TESTS:
We get an exception if no arguments are given::
sage: max_symbolic()
Traceback (most recent call last):
...
ValueError: number of arguments must be > 0
Check if we return None, when the builtin function would::
sage: max_symbolic([None]) is None
True
sage: max_symbolic([None, None]) is None
True
sage: min_symbolic([None]) is None
True
sage: min_symbolic([None, None]) is None
True
Check if a single argument which is not iterable works::
sage: max_symbolic(None)
Traceback (most recent call last):
...
TypeError: 'NoneType' object is not iterable
sage: max_symbolic(5)
Traceback (most recent call last):
...
TypeError: 'sage.rings.integer.Integer' object is not iterable
sage: max_symbolic(x)
Traceback (most recent call last):
...
TypeError: 'sage.symbolic.expression.Expression' object is not iterable
sage: min_symbolic(5)
Traceback (most recent call last):
...
TypeError: 'sage.rings.integer.Integer' object is not iterable
sage: min_symbolic(x)
Traceback (most recent call last):
...
TypeError: 'sage.symbolic.expression.Expression' object is not iterable
"""
if len(args) == 0:
raise ValueError("number of arguments must be > 0")
if len(args) == 1:
try:
args=(SR._force_pyobject(iter(args[0])),)
except TypeError as e:
raise e
try:
return BuiltinFunction.__call__(self, *args, **kwds)
except ValueError as e:
if e.args[0] == "return None":
return None
def __call__(self, function_pieces, **kwds):
r"""
Piecewise functions
INPUT:
- ``function_pieces`` -- a list of pairs consisting of a
domain and a symbolic function.
- ``var=x`` -- a symbolic variable or ``None`` (default). The
real variable in which the function is piecewise in.
OUTPUT:
A piecewise-defined function. A ``ValueError`` will be raised
if the domains of the pieces are not pairwise disjoint.
EXAMPLES::
sage: my_abs = piecewise([((-1, 0), -x), ([0, 1], x)], var=x); my_abs
piecewise(x|-->-x on (-1, 0), x|-->x on [0, 1]; x)
sage: [ my_abs(i/5) for i in range(-4, 5)]
[4/5, 3/5, 2/5, 1/5, 0, 1/5, 2/5, 3/5, 4/5]
TESTS::
sage: piecewise([([-1, 0], -x), ([0, 1], x)], var=x)
Traceback (most recent call last):
...
ValueError: domains must be pairwise disjoint
sage: step = piecewise([((-1, 0), -1), ([0, 0], 0), ((0, 1), 1)], var=x); step
piecewise(x|-->-1 on (-1, 0), x|-->0 on {0}, x|-->1 on (0, 1); x)
sage: step(-1/2), step(0), step(1/2)
(-1, 0, 1)
"""
from types import FunctionType
var = kwds.pop('var', None)
parameters = []
domain_list = []
for piece in function_pieces:
domain, function = piece
if not isinstance(domain, RealSet):
domain = RealSet(domain)
if domain.is_empty():
continue
if isinstance(function, FunctionType):
if var is None:
var = SR.var('x')
if function.func_code.co_argcount == 0:
function = function()
else:
function = function(var)
function = SR(function)
if var is None and len(function.variables()) > 0:
var = function.variables()[0]
parameters.append((domain, function))
domain_list.append(domain)
if not RealSet.are_pairwise_disjoint(*domain_list):
raise ValueError('domains must be pairwise disjoint')
if var is None:
var = self.default_variable()
parameters = SR._force_pyobject(tuple(parameters), recursive=False)
return BuiltinFunction.__call__(self, parameters, var, **kwds)
