def expand(exprTree):
if not expr.isTree(exprTree):
return exprTree
left = expand(exprTree.node1)
right = expand(exprTree.node2)
if exprTree.oper == "+":
return expand(left) + expand(right)
if exprTree.oper == "*":
if expr.isTree(left):
if left.oper == "+":
return expand(leftFoil(right, left))
if expr.isTree(right):
if right.oper == "+":
return expand(leftFoil(left, right))
if exprTree.oper == "^":
if expr.isInt(right):
right = int(expr.numeric(right))
return expand(left * left**(right - 1))
return exprTree
def numeric(obj):
if not expr.isTree(obj):
try:
return obj.numeric()
except (AttributeError, NotImplementedError):
return obj
return expr.refresh(obj, numeric)
def evaluate(obj, var, repl):
if expr.isTree(obj):
return expr.refresh(obj, lambda x: evaluate(x, var, repl))
try:
if obj in var:
return repl[var.index(obj)]
else:
return obj
except TypeError:
if obj == var:
return repl
else:
return obj
def pow(base, exp):
if exp == 0:
return 1
if base == 0:
return 0
if exp == 1:
return base
if base == 1:
return 1
if expr.isTree(base):
if base.oper == "^":
return expr.ExprTree(base.node1, "^", (base.node2 * exp))
return expr.ExprTree(base, "^", exp)
def deriv(self, wrt):
if expr.isConstWrt(self, wrt):
return 0
if expr.isTree(self):
if self.oper == "+":
return add(self, wrt)
if self.oper == "*":
return mul(self, wrt)
if self.oper == "^":
return pow(self, wrt)
try:
# When it's a function
return self.deriv(wrt) * deriv(self.arg, wrt)
except AttributeError:
# When it's a variable
return self.deriv(wrt)