def Degree_1(self):
if self.a == 0:
self.result.append("No Solution.")
else:
self.eqn = Generate_EQN(self.a, self.b)
x = strfNumber(-self.b / self.a)
self.result.append(x)
def Generate_EQN(*num):
result = ''
for i in range(len(num) - 1, -1, -1):
if i == len(num) - 1:
if i != 1:
if num[0] == 1:
result += 'x^{' + str(i) + '}'
elif num[0] == -1:
result += '-x^{' + str(i) + '}'
else:
result += strfNumber(num[0]) + 'x^{' + str(i) + '}'
else:
if num[-2] == 1:
result += 'x'
elif num[-2] == -1:
result += '-x'
elif num[-2] > 0:
result += strfNumber(num[-2]) + 'x'
elif num[len(num) - 1 - i] < 0:
result += '-' + strfNumber(abs(num[-2])) + 'x'
elif i == 1 and i != len(num) - 1:
if num[-2] == 1:
result += ' + x'
elif num[-2] == -1:
result += ' - x'
elif num[-2] > 0:
result += ' + ' + strfNumber(num[-2]) + 'x'
elif num[len(num) - 1 - i] < 0:
result += ' - ' + strfNumber(abs(num[-2])) + 'x'
elif i == 0:
if num[-1] > 0:
result += ' + ' + strfNumber(num[-1])
elif num[-1] < 0:
result += ' - ' + strfNumber(abs(num[-1]))
else:
if num[len(num) - 1 - i] == 1:
result += ' + ' + 'x^{' + str(i) + '}'
elif num[len(num) - 1 - i] == -1:
result += ' - ' + 'x^{' + str(i) + '}'
elif num[len(num) - 1 - i] > 0:
result += ' + ' + strfNumber(
num[len(num) - 1 - i]) + 'x^{' + str(i) + '}'
elif num[len(num) - 1 - i] < 0:
result += ' - ' + strfNumber(abs(
num[len(num) - 1 - i])) + 'x^{' + str(i) + '}'
return result + ' = 0'
def Degree_5(self):
if self.a == 0:
Polynomial(self.b, self.c, self.d, self.e, self.f, 0).Degree_4()
else:
self.Generate_EQN(self.a, self.b, self.c, self.d, self.e, self.f)
self.eqn = f'{self.a}x^5 + {self.b}x^4 + {self.c}x^3 + {self.d}x^2 + {self.e}x + {self.f} = 0'
solve = Solve(self.eqn, 0)
solve.Solve()
self.result.append(strfNumber(solve.x))
factor = horner([self.a, self.b, self.c, self.d, self.e, self.f],
solve.x)
rest_x = Polynomial(factor[0], factor[1], factor[2], factor[3],
factor[4], 0)
rest_x.Degree_4()
for x in rest_x.result:
self.result.append(x)
def calc():
equation = ''
result = ''
show = ''
if request.method == 'POST':
equation = request.form.get('equation')
result = ReplaceSymbol(equation, 0)
if request.form.get('x') != None:
x = eval(request.form.get('x'))
result = ReplaceSymbol(equation, 0).replace('x', str(x))
if 'x' in result:
return render_template('calc.html', equation = equation, x = '', result = (show, ''))
show = ReplaceSymbol(equation, 1)
result = strfNumber(eval(result))
return render_template('calc.html', equation = equation, result = (show, result))
def Degree_4(self):
if self.a == 0:
Polynomial(self.b, self.c, self.d, self.e, 0, 0).Degree_3()
else:
self.eqn = Generate_EQN(self.a, self.b, self.c, self.d, self.e)
# t^4 + at^2 + bt + c = 0
a = (-3 * self.b**2 + 8 * self.a * self.c) / (8 * self.a**2)
b = (2 * self.b**3 - 8 * self.a * self.b * self.c +
16 * self.a**2 * self.d) / (16 * self.a**3)
c = (-3 * self.b**4 + 16 * self.a * self.b**2 * self.c -
64 * self.a**2 * self.b * self.d +
256 * self.a**3 * self.e) / (256 * self.a**4)
solve_m = Polynomial(8, -4 * a, -8 * c, 4 * a * c - b**2, 0,
0) #8m^3 - 4am^2 - 8cm + 4ac - b^2 = 0
solve_m.Degree_3()
m = eval(solve_m.result[0])
i = 1
while (2 * m - a) == 0 and i < len(solve_m.result):
m = eval(solve_m.result[i])
i += 1
list_t1 = Polynomial(1, -(2 * m - a)**0.5,
m + b / (2 * (2 * m - a)**0.5), 0, 0, 0)
list_t2 = Polynomial(1, (2 * m - a)**0.5,
m - b / (2 * (2 * m - a)**0.5), 0, 0, 0)
list_t = []
for j in [list_t1, list_t2]:
j.Degree_2()
for i in j.result:
list_t.append(str(i))
for i in list_t:
if 'i' not in i:
x = round(eval(i) - self.b / (4 * self.a), 14)
self.result.append(x)
else:
classify = i.split(' ')
classify[0] = strfNumber(
round(eval(classify[0]) - self.b / (4 * self.a), 14))
x = ' '.join(classify)
self.result.append(x)
def Degree_2(self):
if self.a == 0:
self.eqn = Generate_EQN(self.b, self.c)
poly = Polynomial(self.b, self.c, 0, 0, 0, 0)
poly.Degree_1()
self.result = poly.result
else:
self.eqn = Generate_EQN(self.a, self.b, self.c)
common_deno = lcd(frac(self.a), frac(self.b), frac(self.c))
a, b, c = self.a * common_deno, self.b * common_deno, self.c * common_deno
if a < 0:
a, b, c = -a, -b, -c
delta = b**2 - 4 * a * c
self.hts = '$$ {' + self.eqn + '} $$'
if delta == 0:
x = strfNumber(-b / (2 * a))
self.result.append(x)
self.hts += r'$$ {\Leftrightarrow (x ' if (
self.a == 1) else r'$$ {\Leftrightarrow ' + strfNumber(
frac(self.a)) + '(x '
self.hts += '+' if b * a > 0 else ''
self.hts += strfNumber(b / (2 * a)) + ')^{2} = 0} $$'
self.hts += r'$$ {\Leftrightarrow x '
self.hts += '+' if b * a > 0 else ''
self.hts += strfNumber(b / (2 * a)) + ' = 0} $$'
self.hts += r'$$ {\Leftrightarrow x = ' + strfNumber(
-b / (2 * a)) + '} $$'
else:
if delta > 0:
if round(int(abs(delta)**0.5) - abs(delta)**0.5, 10) == 0:
x1 = strfNumber((-b + (delta)**(1 / 2)) / (2 * a))
x2 = strfNumber((-b - (delta)**(1 / 2)) / (2 * a))
self.hts += r'$$ {\Leftrightarrow (x ' if (
self.a
== 1) else r'$$ {\Leftrightarrow ' + strfNumber(
self.a) + '(x '
self.hts += '+' if '-' in x1 else '-'
self.hts += strfNumber(
abs((-b + (delta)**(1 / 2)) / (2 * a))) + ')(x '
self.hts += '+' if '-' in x2 else '-'
self.hts += strfNumber(
abs((-b - (delta)**(1 / 2)) /
(2 * a))) + ') = 0} $$'
self.hts += r'$$ {\Leftrightarrow \left[ \begin{array}{l} x_{1} = ' + x1 + r' \\ x_{2} =' + x2 + r' \end{array} \right.} $$'
else:
if common_deno != 1:
self.hts += r'$$ {\Leftrightarrow ' + strfNumber(
a / self.a) + '(' + self.eqn.split(
'=')[0] + ') = 0} $$'
self.hts += r'$$ {\Leftrightarrow ' + Generate_EQN(
a, b, c) + '} $$'
self.hts += r'$$ {\Delta = b^{2} - 4ac = ' + strfNumber(
delta) + ' > 0} $$'
self.hts += r'$$ {x_{1,2} = \frac{-b \pm \sqrt{\Delta}}{2a} = \frac{' + strfNumber(
-b) + r'\pm \sqrt{' + strfNumber(
delta) + r'}}{' + strfNumber(2 * a) + r'} = '
sgcd = int(SquaredGCD(delta)**0.5)
GCD = gcd(gcd(sgcd, 2 * a), b)
coefficient = ''
if abs(sgcd / GCD) != 1:
coefficient = strfNumber(abs(sgcd / GCD))
if GCD == 2 * a:
x1 = strfNumber(
-b / GCD
) + '+' + coefficient + r'\sqrt{' + strfNumber(
delta / (sgcd**2)) + '}'
x2 = strfNumber(
-b / GCD
) + '-' + coefficient + r'\sqrt{' + strfNumber(
delta / (sgcd**2)) + '}'
self.hts += strfNumber(
-b / GCD
) + r'\pm' + coefficient + r'\sqrt{' + strfNumber(
delta / (sgcd**2)) + '}'
else:
x1 = r'\frac{' + strfNumber(
-b / GCD
) + '+' + coefficient + r'\sqrt{' + strfNumber(
delta / (sgcd**2)) + '}}{' + strfNumber(
2 * a / GCD) + '}'
x2 = r'\frac{' + strfNumber(
-b / GCD
) + '-' + coefficient + r'\sqrt{' + strfNumber(
delta / (sgcd**2)) + '}}{' + strfNumber(
2 * a / GCD) + '}'
self.hts += r'\frac{' + strfNumber(
-b / GCD
) + r'\pm' + coefficient + r'\sqrt{' + strfNumber(
delta / (sgcd**2)) + '}}{' + strfNumber(
2 * a / GCD) + '}'
self.hts += '} $$'
else:
self.hts += r'$$ {\Delta = b^{2} - 4ac = ' + strfNumber(
delta) + ' < 0} $$'
self.hts += r'$$ {x_{1,2} = \frac{-b \pm \sqrt{\Delta}}{2a} = \frac{' + strfNumber(
-b) + r'\pm \sqrt{' + strfNumber(
delta) + r'}}{' + strfNumber(2 * a) + r'} = '
if round(int(abs(delta)**0.5) - abs(delta)**0.5, 10) == 0:
imagine = strfNumber(((-delta)**(1 / 2)) / (2 * a))
imagine = '' if imagine == '1' else imagine
else:
sgcd = int(SquaredGCD(-delta)**0.5)
GCD = gcd(sgcd, 2 * a)
coefficient = ''
if abs(sgcd / GCD) != 1:
coefficient = strfNumber(abs(sgcd / GCD))
if GCD == 2 * a:
imagine = coefficient + r'\sqrt{' + strfNumber(
-delta / (sgcd**2)) + '}'
else:
imagine = r'\frac{' + coefficient + r'\sqrt{' + strfNumber(
-delta / (sgcd**2)) + '}}{' + strfNumber(
2 * a / GCD) + '}'
if b != 0:
real = strfNumber(-b / (2 * a))
x1 = f"{real} + {imagine}i"
x2 = f"{real} - {imagine}i"
self.hts += real + r' \pm ' + imagine + 'i} $$ <br><div class="row justify-content-center" style="border:1px solid; margin: 0 60px; border-radius: 10px;"><div style="margin-top:15px;">Assuming </div> <div>$$ i $$</div><div style="margin-top:15px"> is the imaginary unit</div></div>'
else:
x1 = f"{imagine}i"
x2 = f"-{imagine}i"
self.hts += r' \pm ' + imagine + 'i} $$ <br><div class="row justify-content-center" style="border:1px solid; margin: 0 60px; border-radius: 10px;"><div style="margin-top:15px;">Assuming </div> <div>$$ i $$</div><div style="margin-top:15px"> is the imaginary unit</div></div>'
self.result.append(x1)
self.result.append(x2)
def Degree_3(self):
if self.a == 0:
Polynomial(self.b, self.c, self.d, 0, 0, 0).Degree_2()
else:
self.eqn = Generate_EQN(self.a, self.b, self.c, self.d)
delta = self.b**2 - 3 * self.a * self.c
if delta == 0:
x = round(
(-self.b + cbrt(self.b**3 - 27 * self.a**2 * self.d)) /
(3 * self.a), 14)
self.result.append(strfNumber(x))
if x != 0:
factor = horner([self.a, self.b, self.c, self.d], x)
rest_x = Polynomial(factor[0], factor[1], factor[2], 0, 0,
0)
rest_x.Degree_2()
for x in rest_x.result:
self.result.append(x)
else:
k = (9 * self.a * self.b * self.c - 2 * self.b**3 -
27 * self.a**2 * self.d) / (2 * (abs(delta**3))**0.5)
if delta > 0:
if abs(k) < 1:
x1 = round(
(2 * delta**0.5 * cos(acos(k) / 3) - self.b) /
(3 * self.a), 14)
x2 = round((2 * delta**0.5 * cos(
(acos(k) - 2 * self.pi) / 3) - self.b) /
(3 * self.a), 14)
x3 = round((2 * delta**0.5 * cos(
(acos(k) + 2 * self.pi) / 3) - self.b) /
(3 * self.a), 14)
self.result.append(strfNumber(x1))
self.result.append(strfNumber(x2))
self.result.append(strfNumber(x3))
elif abs(k) == 1:
x1 = round((2 * delta**0.5 - self.b) / (3 * self.a),
14)
x2 = round((-delta**0.5 - self.b) / (3 * self.a), 14)
self.result.append(strfNumber(x1))
self.result.append(strfNumber(x2))
else:
x = round((delta**0.5 * abs(k) / (3 * self.a * k)) *
(cbrt(abs(k) + (k * k - 1)**0.5) +
cbrt(abs(k) - (k * k - 1)**0.5)) - self.b /
(3 * self.a), 14)
self.result.append(strfNumber(x))
factor = horner([self.a, self.b, self.c, self.d], x)
rest_x = Polynomial(factor[0], factor[1], factor[2], 0,
0, 0)
rest_x.Degree_2()
for x in rest_x.result:
self.result.append(x)
else:
x = round(
(abs(delta)**0.5 / (3 * self.a)) *
(cbrt(k +
(k * k + 1)**0.5) - cbrt((k * k + 1)**0.5 - k)) -
self.b / (3 * self.a), 14)
self.result.append(strfNumber(x))
factor = horner([self.a, self.b, self.c, self.d], x)
rest_x = Polynomial(factor[0], factor[1], factor[2], 0, 0,
0)
rest_x.Degree_2()
for x in rest_x.result:
self.result.append(x)