def get_problem():
# Initialize problem structure.
p_a = Point('A')
p_b = Point('B')
p_c = Point('C')
line_ab = Line('AB', end1=p_a, end2=p_b)
line_bc = Line('BC', end1=p_b, end2=p_c)
line_ac = Line('AC', end1=p_a, end2=p_c)
angle_a = Angle('BAC', side1=line_ab, side2=line_ac, vertex=p_a)
angle_b = Angle('ABC', side1=line_ab, side2=line_bc, vertex=p_b)
angle_c = Angle('ACB', side1=line_ac, side2=line_bc, vertex=p_c)
triangle = Triangle(
'ABC',
vertex1=p_c, vertex2=p_a, vertex3=p_b,
side1=line_ab, side2=line_bc, side3=line_ac,
angle1=angle_c, angle2=angle_a, angle3=angle_b)
entity = Entity('Basic test2')
entity.add_entity(triangle)
# Set target.
target = Target(angle_c, 'angle')
# Initialize conditions.
conditions = []
conditions.append(AttributeValue(angle_a, angle=60))
conditions.append(AttributeValue(angle_b, angle=30))
return entity, target, conditions
def get_problem():
# Initialize problem structure.
p_a = Point('A')
p_b = Point('B')
p_c = Point('C')
p_d = Point('D')
line_ab = Line('AB', end1=p_a, end2=p_b)
line_ac = Line('AC', end1=p_a, end2=p_c)
line_ad = Line('AD', end1=p_a, end2=p_d)
angle_bac = Angle('BAC', side1=line_ab, side2=line_ac, vertex=p_a)
angle_cad = Angle('CAD', side1=line_ac, side2=line_ad, vertex=p_a)
angle_bad = Angle('BAD', side1=line_ab, side2=line_ad, vertex=p_a)
entity = Entity('Basic test3')
entity.add_entity(p_a, p_b, p_c, p_d)
entity.add_entity(line_ab, line_ac, line_ad)
entity.add_entity(angle_bac, angle_bad, angle_cad)
# Initialize conditions.
conditions = []
conditions.append(AttributeValue(angle_bac, angle=60))
conditions.append(AttributeValue(angle_cad, angle=30))
cva = CommonVertexAngle('A_BCD', vertex=p_a, ends=[p_b, p_c, p_d])
r = RelationshipBased(cva)
conditions.append(r)
# Set target.
target = Target(angle_bad, 'angle')
return entity, target, conditions
def get_problem():
"""Test for line sum."""
# Initialize problem structure.
p_a = Point('A')
p_b = Point('B')
p_c = Point('C')
line_ab = Line('AB', end1=p_a, end2=p_b)
line_bc = Line('BC', end1=p_b, end2=p_c)
line_ac = Line('AC', end1=p_a, end2=p_c)
entity = Entity('Basic test1')
entity.add_entity(p_a, p_b, p_c)
entity.add_entity(line_ab, line_bc, line_ac)
# Set target.
target = Target(line_bc, 'length')
# Initialize conditions.
conditions = []
conditions.append(AttributeValue(line_ab, length=2))
conditions.append(AttributeValue(line_ac, length=5))
col = Collineation('ABC', [p_a, p_b, p_c])
r = RelationshipBased(col)
conditions.append(r)
return entity, target, conditions
def get_problem():
# Initialize problem structure.
p_a = Point('A')
p_b = Point('B')
p_c = Point('C')
p_d = Point('D')
line_ac = Line('AC', end1=p_a, end2=p_c)
line_bc = Line('BC', end1=p_b, end2=p_c)
line_bd = Line('BD', end1=p_b, end2=p_d)
line_cd = Line('CD', end1=p_c, end2=p_d)
angle_acb = Angle('ACB', side1=line_ac, side2=line_bc, vertex=p_c)
angle_acd = Angle('ACD', side1=line_ac, side2=line_cd, vertex=p_c)
entity = Entity('Basic test4')
entity.add_entity(p_a, p_b, p_c, p_d)
entity.add_entity(line_ac, line_bc, line_bd, line_cd)
entity.add_entity(angle_acb, angle_acd)
# Initialize conditions.
conditions = []
conditions.append(AttributeValue(angle_acb, angle=60))
sa = SupplementaryAngle('ACB_ACD', angle1=angle_acb, angle2=angle_acd)
col = Collineation('BCD', points=[p_b, p_c, p_d])
conditions.append(RelationshipBased(sa))
conditions.append(RelationshipBased(col))
# Set target.
target = Target(angle_acd, 'angle')
return entity, target, conditions
def get_problem():
# Initialize problem structure.
p_a = Point('A')
p_b = Point('B')
p_c = Point('C')
p_d = Point('D')
line_ac = Line('AC', end1=p_a, end2=p_c)
line_bc = Line('BC', end1=p_b, end2=p_c)
line_bd = Line('BD', end1=p_b, end2=p_d)
line_cd = Line('CD', end1=p_c, end2=p_d)
angle_acb = Angle('ACB', side1=line_ac, side2=line_bc, vertex=p_c)
angle_acd = Angle('ACD', side1=line_ac, side2=line_cd, vertex=p_c)
entity = Entity('Basic test5')
entity.add_entity(p_a, p_b, p_c, p_d)
entity.add_entity(line_ac, line_bc, line_bd, line_cd)
entity.add_entity(angle_acb, angle_acd)
# Initialize conditions.
conditions = []
p = Perpendicular('AC_BD', line1=line_ac, line2=line_bd, foot_point=p_c)
conditions.append(RelationshipBased(p))
# Set target.
target = Target(angle_acd, 'angle')
return entity, target, conditions
def get_problem():
# Initialize problem structure.
p_a = Point('A')
p_b = Point('B')
p_c = Point('C')
p_d = Point('D')
line_ab = Line('AB', end1=p_a, end2=p_b)
line_ac = Line('AC', end1=p_a, end2=p_c)
line_ad = Line('AD', end1=p_a, end2=p_d)
angle_bac = Angle('BAC', side1=line_ab, side2=line_ac, vertex=p_a)
angle_bad = Angle('BAD', side1=line_ab, side2=line_ad, vertex=p_a)
angle_cad = Angle('CAD', side1=line_ac, side2=line_ad, vertex=p_a)
entity = Entity('Basic test20')
entity.add_entity(p_a, p_b, p_c, p_d)
entity.add_entity(line_ab, line_ac, line_ad)
entity.add_entity(angle_bac, angle_bad, angle_cad)
# Set target.
target = Target(angle_bad, 'angle')
# Initialize conditions.
conditions = []
conditions.append(AttributeValue(angle_bac, angle=30))
r = NAngleSector('BAD_AC',
angle=angle_bad,
split_line=line_ac,
near_line=line_ab)
conditions.append(RelationshipBased(r))
conditions.append(AttributeValue(r, ratio=0.25))
return entity, target, conditions
def get_problem():
"""Test for line sum."""
# Initialize problem structure.
p_a = Point('A')
p_b = Point('B')
p_c = Point('C')
p_d = Point('D')
p_e = Point('E')
p_f = Point('F')
p_g = Point('G')
p_h = Point('H')
line_ab = Line('AB', end1=p_a, end2=p_b)
line_af = Line('AF', end1=p_a, end2=p_f)
line_bf = Line('BF', end1=p_b, end2=p_f)
line_cd = Line('CD', end1=p_c, end2=p_d)
line_cg = Line('CG', end1=p_c, end2=p_g)
line_dg = Line('DG', end1=p_d, end2=p_g)
line_ef = Line('EF', end1=p_e, end2=p_f)
line_eg = Line('EG', end1=p_e, end2=p_g)
line_eh = Line('EH', end1=p_e, end2=p_h)
line_fg = Line('FG', end1=p_f, end2=p_g)
line_fh = Line('FH', end1=p_f, end2=p_h)
line_gh = Line('GH', end1=p_g, end2=p_h)
angle_afe = Angle('AFE', side1=line_af, side2=line_ef, vertex=p_f)
angle_bfe = Angle('BFE', side1=line_bf, side2=line_ef, vertex=p_f)
angle_afh = Angle('AFH', side1=line_af, side2=line_fh, vertex=p_f)
angle_bfh = Angle('BFH', side1=line_bf, side2=line_fh, vertex=p_f)
angle_cgh = Angle('CGH', side1=line_cg, side2=line_gh, vertex=p_g)
angle_dgh = Angle('DGH', side1=line_dg, side2=line_gh, vertex=p_g)
angle_cge = Angle('CGE', side1=line_cg, side2=line_eg, vertex=p_g)
angle_dge = Angle('DGE', side1=line_dg, side2=line_eg, vertex=p_g)
entity = Entity('Basic test14')
for name, obj in locals().items():
if name.startswith(tuple(['p_', 'line_', 'angle_'])):
entity.add_entity(obj)
# Initialize conditions.
conditions = []
conditions.append(AttributeValue(angle_afh, angle=60))
parallel = Parallel('AB_CD', line1=line_ab, line2=line_cd)
r = RelationshipBased(parallel)
conditions.append(r)
conditions.append(
RelationshipBased(Collineation('AFB', points=[p_a, p_f, p_b])))
conditions.append(
RelationshipBased(Collineation('CGD', points=[p_c, p_g, p_d])))
conditions.append(
RelationshipBased(Collineation('EFGH', points=[p_e, p_f, p_g, p_h])))
# Set target.
target = Target(angle_cge, 'angle')
return entity, target, conditions
def parse(self):
problem = self.get_problem()
solver = Solver(problem)
print('Create a triangle successfully!')
print(problem)
# Add targets.
for id_, type_, attr in self._target_dict:
target = Target(TargetType.EVALUATION,
entity=problem.entity.find_child(id_, type_),
attr=attr)
solver.add_target(target)
solver.solve()
return problem
def get_problem():
"""Test for equality of opposite vertical angle."""
# Initialize problem structure.
p_a = Point('A')
p_b = Point('B')
p_c = Point('C')
p_d = Point('D')
p_o = Point('O')
line_ao = Line('AO', end1=p_a, end2=p_o)
line_ad = Line('AD', end1=p_a, end2=p_d)
line_do = Line('DO', end1=p_d, end2=p_o)
line_bo = Line('BO', end1=p_b, end2=p_o)
line_bc = Line('BC', end1=p_b, end2=p_c)
line_co = Line('CO', end1=p_c, end2=p_o)
angle_aob = Angle('AOB', side1=line_ao, side2=line_bo, vertex=p_o)
angle_aoc = Angle('AOC', side1=line_ao, side2=line_co, vertex=p_o)
angle_cod = Angle('COD', side1=line_co, side2=line_do, vertex=p_o)
angle_bod = Angle('BOD', side1=line_bo, side2=line_do, vertex=p_o)
entity = Entity('Basic test6')
entity.add_entity(p_a, p_b, p_c, p_d, p_o)
entity.add_entity(line_ao, line_ad, line_do, line_bo, line_bc, line_co)
entity.add_entity(angle_aob, angle_aoc, angle_cod, angle_bod)
# Initialize conditions.
conditions = []
ova1 = OppositeVerticalAngle('AOB_COD',
angle1=angle_aob,
angle2=angle_cod,
vertex=p_o)
ova2 = OppositeVerticalAngle('AOC_BOD',
angle1=angle_aoc,
angle2=angle_bod,
vertex=p_o)
conditions.append(RelationshipBased(ova1))
conditions.append(RelationshipBased(ova2))
conditions.append(AttributeValue(angle_aob, angle=60))
# Set target.
target = Target(angle_cod, 'angle')
return entity, target, conditions
def get_problem():
# Initialize problem structure.
p_a = Point('A')
p_b = Point('B')
p_c = Point('C')
line_ab = Line('AB', end1=p_a, end2=p_b)
line_bc = Line('BC', end1=p_b, end2=p_c)
line_ac = Line('AC', end1=p_a, end2=p_c)
angle_a = Angle('BAC', side1=line_ab, side2=line_ac, vertex=p_a)
angle_b = Angle('ABC', side1=line_ab, side2=line_bc, vertex=p_b)
angle_c = Angle('ACB', side1=line_ac, side2=line_bc, vertex=p_c)
triangle = Triangle('ABC',
vertex1=p_c,
vertex2=p_a,
vertex3=p_b,
side1=line_ab,
side2=line_bc,
side3=line_ac,
angle1=angle_c,
angle2=angle_a,
angle3=angle_b)
entity = Entity('Basic test23')
entity.add_entity(triangle)
# Set target.
target = Target(angle_c, 'angle')
# Initialize conditions.
conditions = []
conditions.append(AttributeValue(angle_b, angle=30))
r = ValueEquivalence('AB_AC',
obj_list=[line_ab, line_ac],
attr_list=['length', 'length'])
conditions.append(RelationshipBased(r))
return entity, target, conditions
def get_problem():
# Initialize problem structure.
p_a = Point('A')
p_b = Point('B')
p_c = Point('C')
line_ab = Line('AB', end1=p_a, end2=p_b)
line_ac = Line('AC', end1=p_a, end2=p_c)
line_bc = Line('BC', end1=p_b, end2=p_c)
entity = Entity('Basic test21')
entity.add_entity(line_ab, line_ac, line_bc)
# Set target.
target = Target(line_ac, 'length')
# Initialize conditions.
conditions = []
conditions.append(AttributeValue(line_ab, length=1))
r = NLineSector('AC_B', line=line_ac, split_point=p_b, nearer_point=p_a)
conditions.append(RelationshipBased(r))
conditions.append(AttributeValue(r, ratio=0.5))
return entity, target, conditions
def create_target(problem):
target = Target(TargetType.EVALUATION,
entity=problem.entity.find_child('DE', type_=Line),
attr='length')
return target
def create_target2(problem):
target = Target(TargetType.EVALUATION,
entity=problem.entity.find_child('BDC', type_=Angle),
attr='angle')
return target
def get_problem():
# Initialize problem structure.
p_a = Point('A')
p_b = Point('B')
p_c = Point('C')
line_ab = Line('AB', end1=p_a, end2=p_b)
line_bc = Line('BC', end1=p_b, end2=p_c)
line_ac = Line('AC', end1=p_a, end2=p_c)
angle_a = Angle('BAC', side1=line_ab, side2=line_ac, vertex=p_a)
angle_b = Angle('ABC', side1=line_ab, side2=line_bc, vertex=p_b)
angle_c = Angle('ACB', side1=line_ac, side2=line_bc, vertex=p_c)
triangle_abc = Triangle('ABC',
vertex1=p_c,
vertex2=p_a,
vertex3=p_b,
side1=line_ab,
side2=line_bc,
side3=line_ac,
angle1=angle_c,
angle2=angle_a,
angle3=angle_b)
p_d = Point('D')
p_e = Point('E')
p_f = Point('F')
line_de = Line('DE', end1=p_d, end2=p_e)
line_ef = Line('EF', end1=p_e, end2=p_f)
line_df = Line('DF', end1=p_d, end2=p_f)
angle_d = Angle('EDF', side1=line_de, side2=line_df, vertex=p_d)
angle_e = Angle('DEF', side1=line_de, side2=line_ef, vertex=p_e)
angle_f = Angle('DFE', side1=line_df, side2=line_ef, vertex=p_f)
triangle_def = Triangle('DEF',
vertex1=p_f,
vertex2=p_d,
vertex3=p_e,
side1=line_de,
side2=line_ef,
side3=line_df,
angle1=angle_f,
angle2=angle_d,
angle3=angle_e)
entity = Entity('Basic test19')
entity.add_entity(triangle_abc)
entity.add_entity(triangle_def)
# Set target.
target = Target(line_df, 'length')
# Initialize conditions.
conditions = []
conditions.append(AttributeValue(angle_a, angle=60))
conditions.append(AttributeValue(angle_b, angle=90))
conditions.append(AttributeValue(angle_c, angle=30))
conditions.append(AttributeValue(angle_d, angle=60))
conditions.append(AttributeValue(angle_e, angle=90))
conditions.append(AttributeValue(angle_f, angle=30))
conditions.append(AttributeValue(line_ab, length=1))
conditions.append(AttributeValue(line_ac, length=2))
conditions.append(AttributeValue(line_de, length=1))
return Problem(entity, conditions, target)
def create_target(problem):
target = Target(TargetType.PROOF,
entity=problem.entity.find_child('ABC', type_=Triangle).state,
attr='rt_state',
value=TriangleState.RT.rt)
return target
def create_target(problem):
target = Target(TargetType.EVALUATION,
entity=problem.entity.find_child('COD'),
attr='angle')
return target
def get_problem():
# Initialize problem structure.
p_a = Point('A')
p_b = Point('B')
p_c = Point('C')
line_ab = Line('AB', end1=p_a, end2=p_b)
line_bc = Line('BC', end1=p_b, end2=p_c)
line_ac = Line('AC', end1=p_a, end2=p_c)
angle_a = Angle('BAC', side1=line_ab, side2=line_ac, vertex=p_a)
angle_b = Angle('ABC', side1=line_ab, side2=line_bc, vertex=p_b)
angle_c = Angle('ACB', side1=line_ac, side2=line_bc, vertex=p_c)
triangle_abc = Triangle('ABC',
vertex1=p_c,
vertex2=p_a,
vertex3=p_b,
side1=line_ab,
side2=line_bc,
side3=line_ac,
angle1=angle_c,
angle2=angle_a,
angle3=angle_b)
p_d = Point('D')
p_e = Point('E')
p_f = Point('F')
line_de = Line('DE', end1=p_d, end2=p_e)
line_ef = Line('EF', end1=p_e, end2=p_f)
line_df = Line('DF', end1=p_d, end2=p_f)
angle_d = Angle('EDF', side1=line_de, side2=line_df, vertex=p_d)
angle_e = Angle('DEF', side1=line_de, side2=line_ef, vertex=p_e)
angle_f = Angle('DFE', side1=line_df, side2=line_ef, vertex=p_f)
triangle_def = Triangle('DEF',
vertex1=p_f,
vertex2=p_d,
vertex3=p_e,
side1=line_de,
side2=line_ef,
side3=line_df,
angle1=angle_f,
angle2=angle_d,
angle3=angle_e)
entity = Entity('Basic test17')
entity.add_entity(triangle_abc)
entity.add_entity(triangle_def)
# Set target.
target = Target(angle_f, 'angle')
# Initialize conditions.
conditions = []
conditions.append(AttributeValue(angle_a, angle=60))
conditions.append(AttributeValue(angle_b, angle=90))
st = SimilarTriangle('ABC_DEF',
triangle_abc,
triangle_def,
cor_angle=[(angle_a, angle_d), (angle_b, angle_e),
(angle_c, angle_f)])
conditions.append(RelationshipBased(st))
return entity, target, conditions