def transform(self, st):
"""
>>> from sympy import *
>>> from symplus.strplus import init_mprinting
>>> init_mprinting()
>>> m = translation([2,3,5])
>>> m.transform((1,2,3))
(3, 5, 8)
>>> s = shearing(2*j,sqrt(3)*i)
>>> m.transform(s)
AffineTransformation([1 0 0; 2*sqrt(3) 1 0; 0 0 1], [0 -4*sqrt(3) 0]')
>>> import symplus.setplus
>>> x, y, z = symbols('x,y,z')
>>> m.transform(AbstractSet((x,y,z), x**2+y**2+z**2<1))
{(x + 2, y + 3, z + 5) | x**2 + y**2 + z**2 < 1}
"""
if is_Tuple(st) and len(st) == 3:
return self(*st)
elif is_Function(st):
return compose(self, st, inverse(self))
elif isinstance(st, Set):
return Image(self, st)
else:
raise ValueError
def __new__(cls, function, **kwargs):
evaluate = kwargs.pop('evaluate', global_evaluate[0])
if not is_Function(function):
raise TypeError('function is not a FunctionClass, Functor or Lambda: %s'%function)
if evaluate:
return FunctionInverse.eval(function)
return Functor.__new__(cls, function)
def __new__(cls, function, argument, **kwargs):
evaluate = kwargs.pop('evaluate', global_evaluate[0])
argument = repack_if_can(sympify(unpack_if_can(argument)))
if not is_Function(function):
raise TypeError('function is not a FunctionClass, Functor or Lambda: %s'%function)
if evaluate:
function, argument = Apply.reduce(function, argument)
if function == Id:
return argument
else:
return Expr.__new__(cls, function, argument, **kwargs)
def __new__(cls, function, zet, **kwargs):
evaluate = kwargs.pop("evaluate", global_evaluate[0])
if not is_Function(function):
raise TypeError("function is not a FunctionClass, Functor or Lambda: %s" % function)
if not isinstance(zet, Set):
raise TypeError("zet is not a Set: %s" % zet)
if evaluate:
function, zet = Image.reduce(function, zet)
if function == Id:
return zet
else:
return Set.__new__(cls, function, zet, **kwargs)
def __new__(cls, *functions, **kwargs):
evaluate = kwargs.pop('evaluate', global_evaluate[0])
for function in functions:
if not is_Function(function):
raise TypeError('function is not a FunctionClass, Functor or Lambda: %s'%function)
if evaluate:
functions = FunctionCompose.reduce(functions)
if len(functions) == 0:
return Id
elif len(functions) == 1:
return functions[0]
else:
return Functor.__new__(cls, *functions)
