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import sympy
import math
class Expression:
def __init__(self):
pass
def __add__(self, other):
return Sum([self, other])
def __radd__(self, other):
return Sum([other, self])
def __mul__(self, other):
return Product([self, other])
def __rmul__(self, other):
return Product([other, self])
class Variable(Expression):
def __init__(self, id, name, integer=True):
Expression.__init__(self)
self.id = id
self.name = name
self.integer = integer
def __iter__(self):
yield self
def __eq__(self, other):
return isinstance(other, Variable) and self.id == other.id
def __hash__(self):
return hash(self.id)
def __str__(self):
return f"{self.name}"
def sympy(self):
return sympy.Symbol(self.id, integer=self.integer)
class Constant(Expression):
def __init__(self, value):
Expression.__init__(self)
self.value = value
def __iter__(self):
yield self
def __eq__(self, other):
return isinstance(other, Constant) and self.value == other.value
def __hash__(self):
return hash(self.value)
def __str__(self):
return str(self.value)
def sympy(self):
return self.value
class Sum(Expression):
@staticmethod
def maybe(children):
if len(children) == 0:
return Constant(0)
elif len(children) == 1:
return children[0]
elif all(isinstance(c, Constant) for c in children):
return Constant(sum(c.value for c in children))
else:
return Sum(children)
def __init__(self, children):
Expression.__init__(self)
self.children = [to_term(c) for c in children]
def __iter__(self):
yield self
for child in self.children:
yield from child
def __eq__(self, other):
return isinstance(other, Sum) and self.children == other.children
def __hash__(self):
return hash(tuple(self.children))
def __str__(self):
return " + ".join(str(c) for c in self.children)
def sympy(self):
return sum([c.sympy() for c in self.children])
class Product(Expression):
@staticmethod
def maybe(children):
if len(children) == 0:
return Constant(1)
elif len(children) == 1:
return children[0]
elif all(isinstance(c, Constant) for c in children):
return Constant(math.prod(c.value for c in children))
else:
return Product(children)
def __init__(self, children):
Expression.__init__(self)
self.children = [to_term(c) for c in children]
def __iter__(self):
yield self
for child in self.children:
yield from child
def __eq__(self, other):
return isinstance(other, Product) and self.children == other.children
def __hash__(self):
return hash(tuple(self.children))
def __str__(self):
return " * ".join(str(c) for c in self.children)
def sympy(self):
return math.prod([c.sympy() for c in self.children])
def to_term(x):
if isinstance(x, int):
return Constant(x)
else:
if not isinstance(x, Expression):
raise TypeError(f"Expected Expression, got {type(x)}")
return x
class SolveException(Exception):
def __init__(self, message):
super().__init__(message)
def solve(equations):
equations = [(to_term(t1), to_term(t2)) for t1, t2 in equations]
equations = [(t1, t2) for t1, t2 in equations if t1 != t2]
equations = list(set(equations))
variables = {
v.id: v for terms in equations for term in terms for v in term if isinstance(v, Variable)
}
# Find equivalence classes of variables to speed up sympy solver #####
# Find constant definitions
constants = {} # id: constant value
for t1, t2 in equations:
if isinstance(t1, Variable) and isinstance(t2, Constant):
if constants.get(t1.id, t2.value) != t2.value:
raise SolveException(
f"Found contradictory values { {constants[t1.id], t2.value} } for "
f"expression '{t1.name}'"
)
constants[t1.id] = t2.value
elif isinstance(t1, Constant) and isinstance(t2, Variable):
if constants.get(t2.id, t1.value) != t1.value:
raise SolveException(
f"Found contradictory values { {constants[t2.id], t1.value} } for "
f"expression '{t2.name}'"
)
constants[t2.id] = t1.value
elif isinstance(t1, Constant) and isinstance(t2, Constant):
if t1.value != t2.value:
raise SolveException(
f"Found contradictory values {t1.value} != {t2.value} in input equation"
)
# Find equivalence classes of variables
classes = {v: {v} for v in variables} # id: set of equivalent ids
for t1, t2 in equations:
if isinstance(t1, Variable) and isinstance(t2, Variable):
assert t1.id in classes and t2.id in classes
set1 = classes[t1.id]
set2 = classes[t2.id]
for t_id in set2:
classes[t_id] = set1
set1.add(t_id)
# For every class: Use constant if it exists, or create single class variable
origvar_to_solvevar = {} # id: Variable or Constant
for eclass in {id(s): s for s in classes.values()}.values():
if any(n in constants for n in eclass):
# Use constant
class_constants = {constants[n] for n in eclass if n in constants}
if len(class_constants) != 1:
names = {variables[a].name for a in eclass}
if len(names) == 1:
raise SolveException(
f"Found contradictory values {class_constants} for expression "
f"'{next(iter(names))}'"
)
else:
raise SolveException(
f"Found contradictory values {class_constants} for equivalent "
f"expressions {names}"
)
v = Constant(next(iter(class_constants)))
else:
# Create new variable for class
v = Variable(
f"Class-{id(eclass)}",
f"Equivalent expressions { {variables[a].name for a in eclass} }",
)
for n in eclass:
assert n not in origvar_to_solvevar
origvar_to_solvevar[n] = v
# Apply to equations
def replace(t):
if isinstance(t, Variable) and t.id in origvar_to_solvevar:
return origvar_to_solvevar[t.id]
elif isinstance(t, Constant):
return t
elif isinstance(t, Sum):
return Sum.maybe([replace(c) for c in t.children])
elif isinstance(t, Product):
return Product.maybe([replace(c) for c in t.children])
else:
raise AssertionError()
equations2 = []
for t1o, t2o in equations:
t1 = replace(t1o)
t2 = replace(t2o)
if isinstance(t1, Constant) and isinstance(t2, Constant):
if t1.value != t2.value:
raise SolveException(
f"Found contradictory values {t1.value} != {t2.value} "
"for same equivalence class"
)
elif t1 != t2:
equations2.append((t1, t2))
equations = equations2
# Solve remaining equations using sympy #####
solutions = {}
if len(equations) > 0:
sympy_equations = [sympy.Eq(t1.sympy(), t2.sympy()) for t1, t2 in equations]
if all(eq.is_Boolean and bool(eq) for eq in sympy_equations):
solutions = {}
else:
solutions = sympy.solve(sympy_equations, set=True, manual=True)
if solutions == []:
solutions = {}
elif isinstance(solutions, tuple) and len(solutions) == 2:
variables, solutions = solutions
if len(solutions) == 0:
raise SolveException("Sympy returned no solutions")
elif len(solutions) > 1:
raise SolveException("Sympy returned multiple possible solutions")
else:
solutions = next(iter(solutions))
solutions = {
str(k): int(v) for k, v in zip(variables, solutions) if v.is_number
}
else:
raise SolveException("Sympy returned unexpected result")
# Determine values for original variables in equivalence classes
orig_solutions = {}
for k, v in origvar_to_solvevar.items():
if isinstance(v, Constant):
orig_solutions[k] = v.value
elif isinstance(v, Variable):
if v.id in solutions:
orig_solutions[k] = solutions[v.id]
else:
raise AssertionError()
return orig_solutions
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