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 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 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))
