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 get_vertex(self):
"""Returns this quadratic's vertex (point intersected by
axis of symmetry)."""
a, b, c = self.getabc()
x = eval('-' + b + '/(2*' + a + ')')
y = self.evaluate(x)
return num(str(x)), num(str(y))
def __init__(self, equation):
Equation.__init__(self, equation)
self.form = self.get_form()
self.x_coefficient = self.get_x_coefficient()
self.y_coefficient = self.get_y_coefficient()
self.slope = self.get_slope()
self.y_intercept = num(self.solve_for("x", 0))
def getpower(a):
"""Returns exponent of term a."""
if TermOperations.ispowered(a):
return num(a[a.find('**') + 2:])
elif isanumber(a):
return 0
return 1
def solve(self):
"""Returns the solution to this system of equation."""
if self.is_compatible() is False:
return None
if self.get_number_of_solutions() == 'Infinitely many solutions':
raise InfinitelySolutionsError
x_coefficient = str(
num(self.linear_2.x_coefficient) -
num(self.linear_1.x_coefficient))
x_coefficient = '' if x_coefficient == '1' else x_coefficient
equation = x_coefficient + 'x' + '=' + str(
self.linear_1.y_intercept) + '-' + str(self.linear_2.y_intercept)
x_value = Equation(equation).solve()
return self.linear_1.get_point(x_value)
def solve(self, debug=False):
"""Returns the solution of the equation as integer or float, depending on what
the solution is."""
rhs_no_var_terms = [
num(term) for term in Expression(
self.rhs, no_vars_intended=True).get_terms() if isanumber(term)
]
lhs_no_var_terms = [
num(term) for term in Expression(
self.lhs, no_vars_intended=True).get_terms() if isanumber(term)
]
rhs_var_terms = [
term for term in Expression(self.rhs,
no_vars_intended=True).get_terms()
if any(var in term for var in self.variables)
]
lhs_var_terms = [
term for term in Expression(self.lhs,
no_vars_intended=True).get_terms()
if any(var in term for var in self.variables)
]
polynomial = '+'.join(lhs_var_terms) + '-' + '+'.join(rhs_var_terms)
polynomial = if_assign(polynomial.endswith('-'), polynomial[:-1],
polynomial)
lhs = Polynomial(polynomial)
coefficient = self.get_number(0, lhs.polynomial)
result = sum(rhs_no_var_terms) - sum(lhs_no_var_terms)
if debug:
print(lhs, '=', result, '-->',
str(result) + '/(' + coefficient + ')')
if coefficient is '0':
if result == 0:
return "All real numbers are solutions."
return "No solutions."
return num(str((eval(str(result) + '/(' + coefficient + ')'))))
def get_roots(self):
"""Returns a list containing the roots of this quadratic."""
if self._roots_type == RootTypes.ComplexConjugateRoots:
return [self.bhaskarize()]
bhask = self.bhaskarize().replace('½', '0.5')
if self._roots_type == RootTypes.IdenticRealRoots:
return [num(str(eval(bhask.replace('+/-', '+'))))]
roots = [
eval(bhask.replace('+/-', '+')),
eval(bhask.replace('+/-', '-'))
]
return roots
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 solve_for(self, variable, value, show=False):
"""Solves the equation after changing variable into value.
Keyword Arguments:
variable (str): the variable to be replaced by a value.
value (int): the value to replace the variable by.
(optional) show (bool) : print the sorted equation."""
eqtn, value = self.equation, str(value)
sol_side = self.sort(variable)
if eqtn[eqtn.find(variable) -
1] == "(" and self.form is not LinearForms.PointSlope:
eqtn = eqtn.replace("(" + variable, "*(" + variable)
sol_side = eqtn[eqtn.find("=") + 1:]
if show is True:
self.show_sorted(variable, value, sol_side)
return num(eval(sol_side.replace(variable, value)))
def get_slope(self):
"""Returns the slope of this linear equation."""
a_points, b_points = self.get_point(1), self.get_point(2)
return num((a_points[1] - b_points[1]) / (a_points[0] - b_points[0]))