def example_2():
"""
AB is tangent to circle O, AO = BO = 1 and AB = sqrt(2). What is the radius of circle O?
:return:
"""
vh = VariableHandler()
O = vh.point('O')
A = vh.point('A')
B = vh.point('B')
AO = vh.line(A, O)
BO = vh.line(B, O)
AB = vh.line(A, B)
# vh.circle() with one argument assumes the radius is an unknown value (i.e. variable).
# if you want to define radius, just give it two arguments, e.g. vh.circle(O, r)
cO = vh.circle(O)
a = vh.apply('LengthOf', AO)
b = vh.apply('LengthOf', BO)
o = vh.apply('LengthOf', AB)
p1 = a == 1
p2 = b == 1
p3 = o == np.sqrt(2)
p4 = vh.apply('Tangent', AB, cO)
ns = NumericSolver([p1, p2, p3, p4], vh)
ans = vh.apply('RadiusOf', cO)
if ns.is_sat():
print ns.evaluate(ans), 1/np.sqrt(2) # the latter is the true answer
else:
print("Given information is not satisfiable.")
def example_1():
"""
AB perpendicular to BC, AB = x, and BC = 4. Is CA = sqrt(x^2+16) a correct answer?
:return:
"""
vh = VariableHandler()
x = vh.number('x')
A = vh.point('A')
B = vh.point('B')
C = vh.point('C')
AB = vh.line(A, B)
BC = vh.line(B, C)
CA = vh.line(C, A)
c = vh.apply('LengthOf', AB)
a = vh.apply('LengthOf', BC)
b = vh.apply('LengthOf', CA)
p1 = a == 4
p2 = c == x
p3 = vh.apply('Perpendicular', AB, BC)
q1 = b == (16 + x**2)**0.5
q2 = b == x**2
ns = NumericSolver([p1, p2, p3], vh)
print(
ns.find_assignment(q1)
) # find_assignment simply analyzes whether the query relation can be satisfied
print(ns.query_invar(q1)
) # query_invar analyzes whether the query relation must hold true
print(ns.find_assignment(q2)
) # this is satisfiable; there exists x that satisfies q2.
print(ns.query_invar(q2)
) # this is False because q2 is not true for all possible x.
def __init__(self, prior_atoms, variable_handler=None, max_num_resets=10, tol=10**-3):
if variable_handler is None:
variable_handler = VariableHandler()
self.variable_handler = variable_handler
self.atoms = [variable_handler.add(prior_atom) for prior_atom in prior_atoms]
self.max_num_resets = max_num_resets
self.tol = tol
self.assignment = None
self.assigned = False
def example_1():
"""
AB perpendicular to BC, AB = x, and BC = 4. Is CA = sqrt(x^2+16) a correct answer?
:return:
"""
vh = VariableHandler()
x = vh.number('x')
A = vh.point('A')
B = vh.point('B')
C = vh.point('C')
AB = vh.line(A, B)
BC = vh.line(B, C)
CA = vh.line(C, A)
c = vh.apply('LengthOf', AB)
a = vh.apply('LengthOf', BC)
b = vh.apply('LengthOf', CA)
p1 = a == 4
p2 = c == x
p3 = vh.apply('Perpendicular', AB, BC)
q1 = b == (16 + x**2)**0.5
q2 = b == x**2
ns = NumericSolver([p1, p2, p3], vh)
print(ns.find_assignment(q1)) # find_assignment simply analyzes whether the query relation can be satisfied
print(ns.query_invar(q1)) # query_invar analyzes whether the query relation must hold true
print(ns.find_assignment(q2)) # this is satisfiable; there exists x that satisfies q2.
print(ns.query_invar(q2)) # this is False because q2 is not true for all possible x.
def __init__(self,
prior_atoms,
variable_handler=None,
max_num_resets=10,
tol=10**-3):
if variable_handler is None:
variable_handler = VariableHandler()
self.variable_handler = variable_handler
self.atoms = [
variable_handler.add(prior_atom) for prior_atom in prior_atoms
]
self.max_num_resets = max_num_resets
self.tol = tol
self.assignment = None
self.assigned = False
def example_0():
"""
AB = x, BC = 3, CA = 4. Is an answer x=5, x=8 possible?
:return:
"""
vh = VariableHandler()
x = vh.number('x')
A = vh.point('A')
B = vh.point('B')
C = vh.point('C')
AB = vh.line(A, B)
BC = vh.line(B, C)
CA = vh.line(C, A)
c = vh.apply('LengthOf', AB)
a = vh.apply('LengthOf', BC)
b = vh.apply('LengthOf', CA)
p1 = a == 3
p2 = b == 4
p3 = c == x
q1 = x == 8
q2 = x == 5
ns = NumericSolver([p1, p2, p3], vh)
print(ns.find_assignment(q1))
print(ns.find_assignment(q2))
def example_0():
"""
AB = x, BC = 3, CA = 4. Is an answer x=5, x=8 possible?
:return:
"""
vh = VariableHandler()
x = vh.number('x')
A = vh.point('A')
B = vh.point('B')
C = vh.point('C')
AB = vh.line(A, B)
BC = vh.line(B, C)
CA = vh.line(C, A)
c = vh.apply('LengthOf', AB)
a = vh.apply('LengthOf', BC)
b = vh.apply('LengthOf', CA)
p1 = a == 3
p2 = b == 4
p3 = c == x
q1 = x == 8
q2 = x == 5
ns = NumericSolver([p1, p2, p3], vh)
print(ns.find_assignment(q1))
print(ns.find_assignment(q2))
def example_3():
"""
Question ID: 1
In the diagram at the right, circle O has a radius of 5, and CE = 2.
Diameter AC is perpendicular to chord BD at E.
What is the length of BD?
:return:
"""
vh = VariableHandler()
A = vh.point('A')
B = vh.point('B')
C = vh.point('C')
D = vh.point('D')
E = vh.point('E')
O = vh.point('O')
CE = vh.line(C, E)
AC = vh.line(A, C)
BD = vh.line(B, D)
cO = vh.circle(O)
p1 = vh.apply('RadiusOf', cO) == 5 # Equals(RadiusOf(cO), 5))
p2 = vh.apply('LengthOf', CE) == 2 # Equals(LengthOf(CE), 2)
p3 = vh.apply('IsDiameterLineOf', AC, cO)
p4 = vh.apply('IsChordOf', BD, cO)
p5 = vh.apply('Perpendicular', AC, BD)
p6 = vh.apply('PointLiesOnLine', E,
AC) # AC intersects BD at E is broken down into two atoms
p7 = vh.apply('PointLiesOnLine', E, BD)
ps = [p1, p2, p3, p4, p5, p6, p7]
ns = NumericSolver(ps, vh)
ans = vh.apply('LengthOf', BD)
if ns.is_sat():
print ns.evaluate(ans), 8 # 8 is the answer
else:
print "Given information is not satisfiable."
def example_2():
"""
AB is tangent to circle O, AO = BO = 1 and AB = sqrt(2). What is the radius of circle O?
:return:
"""
vh = VariableHandler()
O = vh.point('O')
A = vh.point('A')
B = vh.point('B')
AO = vh.line(A, O)
BO = vh.line(B, O)
AB = vh.line(A, B)
# vh.circle() with one argument assumes the radius is an unknown value (i.e. variable).
# if you want to define radius, just give it two arguments, e.g. vh.circle(O, r)
cO = vh.circle(O)
a = vh.apply('LengthOf', AO)
b = vh.apply('LengthOf', BO)
o = vh.apply('LengthOf', AB)
p1 = a == 1
p2 = b == 1
p3 = o == np.sqrt(2)
p4 = vh.apply('Tangent', AB, cO)
ns = NumericSolver([p1, p2, p3, p4], vh)
ans = vh.apply('RadiusOf', cO)
if ns.is_sat():
print ns.evaluate(ans), 1 / np.sqrt(2) # the latter is the true answer
else:
print("Given information is not satisfiable.")
def example_3():
"""
Question ID: 1
In the diagram at the right, circle O has a radius of 5, and CE = 2.
Diameter AC is perpendicular to chord BD at E.
What is the length of BD?
:return:
"""
vh = VariableHandler()
A = vh.point('A')
B = vh.point('B')
C = vh.point('C')
D = vh.point('D')
E = vh.point('E')
O = vh.point('O')
CE = vh.line(C, E)
AC = vh.line(A, C)
BD = vh.line(B, D)
cO = vh.circle(O)
p1 = vh.apply('RadiusOf', cO) == 5 # Equals(RadiusOf(cO), 5))
p2 = vh.apply('LengthOf', CE) == 2 # Equals(LengthOf(CE), 2)
p3 = vh.apply('IsDiameterLineOf', AC, cO)
p4 = vh.apply('IsChordOf', BD, cO)
p5 = vh.apply('Perpendicular', AC, BD)
p6 = vh.apply('PointLiesOnLine', E, AC) # AC intersects BD at E is broken down into two atoms
p7 = vh.apply('PointLiesOnLine', E, BD)
ps = [p1, p2, p3, p4, p5, p6, p7]
ns = NumericSolver(ps, vh)
ans = vh.apply('LengthOf', BD)
if ns.is_sat():
print ns.evaluate(ans), 8 # 8 is the answer
else:
print "Given information is not satisfiable."
