def __new__(cls, variables, expr):
if not is_Tuple(variables) or len(variables) != 3:
raise TypeError('variables is not a 3-Tuple: %s'%variables)
if not is_Tuple(expr) or len(expr) != 3:
raise TypeError('expr is not a 3-Tuple: %s'%expr)
return Functor.__new__(cls, variables, expr)
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 _contains(self, other):
if not is_Tuple(other) or len(other) != 3:
return false
v = Mat(other)
if self.closed:
return dot(v, self.direction) >= self.offset
else:
return dot(v, self.direction) > self.offset
def _contains(self, other):
if not is_Tuple(other) or len(other) != 3:
return false
v = Mat(other)
p = v - self.center
if self.closed:
return norm(cross(p, self.direction)) <= self.slope*dot(p, self.direction)
else:
return norm(cross(p, self.direction)) < self.slope*dot(p, self.direction)
def _contains(self, other):
if not is_Tuple(other) or len(other) != 3:
return false
v = Mat(other)
p = v - self.center
if self.closed:
return norm(cross(p, self.direction))**2 <= self.radius**2
else:
return norm(cross(p, self.direction))**2 < self.radius**2
def _contains(self, other):
if not is_Tuple(other) or len(other) != 3:
return false
v = Mat(other)
if self.closed:
return norm(v-self.center)**2 <= self.radius**2
else:
return norm(v-self.center)**2 < self.radius**2
def rename_variables_in(variables, varspace):
if not is_Tuple(variables):
return rename_variables_in((variables,), varspace)[0]
names = [v.name for v in variables]
namespace = {v.name for v in varspace}
for i in range(len(names)):
while names[i] in namespace:
names[i] += '_'
namespace.add(names[i])
return list(Symbol(n, **v.assumptions0)
if isinstance(v, Symbol) else MatrixSymbol(n, v.rows, v.cols)
for n, v in zip(names, variables))
def _contains(self, other):
return is_Tuple(other) and len(other) == 3
def _contains(self, other):
if not is_Tuple(other) or len(other) != 3:
return false
v = Mat(other)
p = v - self.center
return self.func(dot(p, self.direction), norm(cross(p, self.direction)))