def express_as(self, form):
"""Expresses the equation in the form passed as an argument
and returns an instance of that form's class as the new expression.
Valid forms are , Standard and .
Keyword arguments:
form (str): the form the equation will be converted to"""
slope = str(self.slope)
if not isinstance(form, LinearForms):
raise InvalidFormError(form)
if form is self.form:
raise RedundantConversionError(self.form, form)
if form is LinearForms.PointSlope:
points = self.get_point(2)
x_point, y_point = str(points[0]), str(points[1])
rewritten = "y-" + y_point + "=" + slope + "(x-" + x_point + ")"
rewritten = Expression.beautify(rewritten)
return PointSlope(rewritten)
if form == LinearForms.SlopeIntercept:
operator = "+" if self.y_intercept > 0 else ""
rewritten = "y=" + slope + "x" + operator + str(self.y_intercept)
rewritten = Expression.beautify(rewritten)
return SlopeIntercept(rewritten)
raise InvalidFormError(form)
def substract(a, b):
"""Returns the expression resultant of substracting terms a and b."""
a = Expression(a, no_vars_intended=True)
b = Expression(b, no_vars_intended=True)
if isanumber(a.expression) or isanumber(b.expression):
raise NonAlgebraicOperationError
if len(a.terms) > 1 or len(b.terms) > 1:
raise InvalidOperationError(a, b)
if TermOperations.getpower(
a.expression) is not TermOperations.getpower(
b.expression) or a.variables != b.variables:
result = a.expression + '-' + b.expression
return Expression.beautify(result)
a_coefficient = a.get_number(0, frac_to_number=True)
b_coefficient = b.get_number(0, frac_to_number=True)
result = str(num(a_coefficient) - num(b_coefficient))
result = if_assign(result == '1', "", result)
result = if_assign(result == '-1', "-", result)
result += "".join(a.variables) + '**' + str(
TermOperations.getpower(a.expression))
return Expression.beautify(result)
def add(a, b, non_algebraic=False):
"""Returns the expression resultant of adding terms a and b."""
a = Expression(a, no_vars_intended=True)
b = Expression(b, no_vars_intended=True)
if isanumber(a.expression) or isanumber(b.expression):
if non_algebraic is True:
return num(num(a.expression) + num(b.expression))
raise NonAlgebraicOperationError
if len(a.terms) > 1 or len(b.terms) > 1:
raise InvalidOperationError(a, b)
if TermOperations.getpower(
a.expression) is not TermOperations.getpower(
b.expression) or a.variables != b.variables:
operator = if_assign(b.expression.startswith('-'), '', '+')
return Expression.beautify(a.expression + operator + b.expression)
a_coefficient = a.get_number(0)
b_coefficient = b.get_number(0)
result = str(num(a_coefficient) + num(b_coefficient))
result = if_assign(result == '1', "", result)
result = if_assign(result == '-1', "-", result)
result += "".join(a.variables) + '**' + str(
TermOperations.getpower(a.expression))
if result.endswith('**1'):
result = result.replace('**1', '')
return Expression.beautify(result)
def sort(self, for_variable):
"""Sorts a Standard Form linear equation
to be solved for a given variable.
Keyword arguments:
variable (str): the variable this equation will be sorted to solve for."""
# Required and convenient variables definition.
eqtn = self.equation
c_pos, a, b = eqtn.find(
"=") + 1, self.x_coefficient, self.y_coefficient
c = self.get_number(c_pos, eqtn)
den = if_assign(for_variable == 'y', a, b)
mult = if_assign(for_variable == 'y', b, a)
if eqtn[eqtn.index(for_variable) - len(str(mult)) - 1] == "-":
operator = "+"
else:
operator = "-"
# Expressing
sol_side = "(" + c + operator + mult + "*" + for_variable + ")" + "/" + den
sol_side = Expression.beautify(sol_side)
return sol_side
def addition(p, q, name=None):
"""Performs addition between polynomials p and q."""
if not isinstance(p, Polynomial) or not isinstance(q, Polynomial):
raise InvalidOperationError(p, q)
result = ""
alr_added = []
for term in p.terms:
if term in alr_added:
continue
match = PolynomialOperation.find_term_by_degree(term, q)
if match is not None and match not in alr_added:
result += str(
TermOperations.add(term, match, non_algebraic=True)) + '+'
alr_added.extend([term, match])
continue
result += term + '+'
alr_added.append(term)
for term in q.terms:
if PolynomialOperation.find_term_by_degree(term, p) is None:
result += term + '+'
return Polynomial(Expression.beautify(result), name)
def multiply(a, b):
"""Multiplies terms a and b."""
a = Expression(a, no_vars_intended=True)
b = Expression(b, no_vars_intended=True)
power = str(
if_assign(
TermOperations.getpower(a.expression) >=
TermOperations.getpower(b.expression),
TermOperations.getpower(a.expression),
TermOperations.getpower(b.expression)))
variables = set(a.variables + b.variables)
if len(TermOperations.commonvars(a.expression, b.expression)) > 0:
power = str(
int(TermOperations.getpower(a.expression)) +
int(TermOperations.getpower(b.expression)))
power = if_assign(power == '1', '', power)
if power == '1':
return "".join(variables)
a_coefficient = a.get_number(0)
b_coefficient = b.get_number(0)
result = str(int(a_coefficient) *
int(b_coefficient)) + "".join(variables) + '**' + power
return Expression.beautify(result)
def simplify(self):
"""Simplify terms of same degree into single term."""
polynomial = ""
for k, v in self.terms_by_degree.items():
polynomial += v + "+"
return Expression.beautify(polynomial)
def express_as(self, form):
"""Expresses the equation in the form passed as an argument
and returns an instance of that form's class as the new expression.
Valid forms are , Standard and .
Keyword arguments:
form (str): the form the equation will be converted to"""
# Required and convenient variables definition.
slope, y_intercept = str(self.slope), str(self.y_intercept)
if not isinstance(form, LinearForms):
raise InvalidFormError(self.equation.form, form)
if form == self.form:
raise RedundantConversionError(self.form, form)
# Express in Standard Form.
if form is LinearForms.Standard:
slope = slope.replace('-', '')
x_op = if_assign(self.slope < 0, '', '-')
# 'y' will always be positive, for negative multipliers of it will
# be distributed. Hence why '+' is the operator before 'y'.
rewritten = x_op + slope + "x" + '+' + "y" + "=" + y_intercept
rewritten = Expression.beautify(rewritten)
return Standard(rewritten)
# Express in form.
if form is LinearForms.PointSlope:
points = self.get_point(2)
x_point, y_point = str(points[0]), str(points[1])
rewritten = "y-" + y_point + "=" + slope + "(x-" + x_point + ")"
rewritten = Expression.beautify(rewritten)
return PointSlope(rewritten)
raise InvalidFormError(form)
def reorder_terms(self):
"""Reorders the terms of the polynomial; higher degrees first."""
ordered_terms = []
for degree in self.degrees:
ordered_terms.append(self.terms_by_degree[degree])
expression = "+".join(ordered_terms)
return Expression.beautify(expression)
def sort_for_y(self):
"""Sorts equation for y."""
eqtn, sol_side = self.equation, self.rhs
x_index = eqtn.index('x')
operator = if_assign(eqtn[x_index + 1] == '-', '+', '-')
slope_sign = if_assign(eqtn[0] == '-', '-', '')
sol_side = "(" + self.y_coefficient + "*y" + operator + \
str(self.y_intercept).replace('-', '') + ")/" + slope_sign + str(self.slope)
sol_side = Expression.beautify(sol_side)
return sol_side
def product(p, q, name=None):
"""Takes the product of polynomials p and q."""
if not isinstance(p, Polynomial) or not isinstance(q, Polynomial):
raise InvalidOperationError(p, q)
result = []
for term_of_p in p.terms:
for term_of_q in q.terms:
result.append(TermOperations.multiply(term_of_p, term_of_q))
result = '+'.join(result)
return Polynomial(Expression.beautify(result), name)
def sort_for_x(self):
"""Sorts equation for x."""
eqtn, sol_side, y_coefficient = self.equation, self.rhs, self.y_coefficient
x_index = eqtn.index('x')
# Set the solution side
sol_side = "(" + sol_side + ")/" + y_coefficient
# Add a * symbol before the x if there's a number before it.
sol_side = if_assign(eqtn[x_index - 1].isdigit(),
sol_side.replace('x', '*x'), sol_side)
# Beautify the solution side.
sol_side = Expression.beautify(sol_side)
return sol_side
def sort_for_y(self):
"""Sorts equation for y."""
# Required and convenient variables definition.
eqtn, y_index = self.equation, self.equation.index('y')
x_index = eqtn.index('x')
y_point = self.get_number(y_index + 2, eqtn)
x_point = self.get_number(x_index + 2, eqtn)
x_point_op = if_assign(eqtn[x_index + 1] == '-', '-', '+')
# Expression
sol_side = "(y" + eqtn[y_index + 1] + y_point + "-" + str(self.slope) + \
"*" + x_point_op + x_point + ")/" + str(self.slope)
sol_side = Expression.beautify(sol_side)
return sol_side
def divide(a, b):
a = Expression(a)
b = Expression(b)
variables = set(a.variables + b.variables)
power = '**' + str(
int(TermOperations.getpower(a.expression)) -
int(TermOperations.getpower(b.expression)))
power = if_assign(power == '**1', '', power)
if power == '**0':
return "/".join(variables)
a_coefficient = a.get_number(0)
b_coefficient = b.get_number(0)
result = str(num(
int(a_coefficient) / int(b_coefficient))) + "/".join(variables)
result = if_assign(power != '', '(' + result + ')' + power, result)
return Expression.beautify(result)
def _complete(self):
if not any('**2' in term for term in self.terms):
raise NoSquareError(self.expression)
term_count = len(self.terms)
if term_count is 3:
return
if term_count is 2:
if any(self.variables[0] not in term for term in self.terms):
self.terms.insert(1, '0' + self.variables[0])
else:
self.terms.insert(2, '0')
if term_count is 1:
self.terms.insert(1, '0' + self.variables[0])
self.terms.insert(2, '0')
self.expression = Expression.beautify('+'.join(self.terms))
def express_as(self, form):
"""Expresses the equation in the form passed as an argument
and returns an instance of that form's class as the new expression.
Valid forms are , Standard and .
Keyword arguments:
form (str): the form the equation will be converted to"""
eqtn, slope = self.equation, str(self.slope)
if not isinstance(form, LinearForms):
raise InvalidFormError(form)
if form is self.form:
raise RedundantConversionError(self.form, form)
if form is LinearForms.SlopeIntercept:
operator = if_assign(self.y_intercept < 0, '', '+')
rewritten = 'y=' + slope + "x" + operator + str(self.y_intercept)
if '--' in rewritten:
rewritten = rewritten.replace('--', '+')
return SlopeIntercept(rewritten)
if form is LinearForms.Standard:
operator = if_assign(eqtn[0] == '-', '-', '+')
y_coefficient = if_assign(self.y_coefficient == '1', '',
self.y_coefficient)
rewritten = '-' + self.x_coefficient + 'x' + operator + \
y_coefficient + 'y' + '=' + str(self.y_intercept)
rewritten = Expression.beautify(rewritten)
return Standard(rewritten)
raise InvalidFormError(form)
def sort_for_x(self):
"""Sorts equation for x."""
eqtn, y_index = self.equation, self.equation.index('y')
x_index = eqtn.index('x')
y_point = self.get_number(y_index + 2, eqtn)
x_point = self.get_number(x_index + 2, eqtn)
slope_pos = self.equal_index + 1
# Gets the slope instead of using self.slope because this method is called
# before defining (and to define) the slope attribute.
slope = self.get_number(slope_pos, eqtn)
first_op = if_assign(eqtn[y_index + 1] == '-', '+', '-')
second_op = eqtn[x_index + 1]
sol_side = slope + "*(x" + second_op + x_point + ")" + first_op + y_point
sol_side = Expression.beautify(sol_side)
return sol_side