def __add__(self, left):
if is_digit(self.contain) and is_digit(left.contain):
if left.coef == 1:
self.contain += left.contain
else:
self.contain -= left.contain
elif self.contain == left.contain:
if self.expo == left.expo:
self.coef += left.coef
if self.coef == 0:
self.coef = 1
self.contain = 0
self.expo = 1
else:
dic = {
(self.sign, self.contain, self.expo): self,
(left.sign, left.contain, left.expo): left
}
self.coef = 1
self.contain = deepcopy(dic)
self.expo = 1
else:
dic = {
(self.sign, self.contain, self.expo): self,
(left.sign, left.contain, left.expo): left
}
self.coef = 1
self.contain = deepcopy(dic)
self.expo = 1
return self
def get_range(self):
if is_digit(self.x_value1.text()) and is_digit(self.x_value2.text()):
self.ran_x[0] = float(self.x_value1.text())
self.ran_x[1] = float(self.x_value2.text())
self.interval_x = (self.ran_x[1] - self.ran_x[0]) / self.n_interval
else:
self.tt_label.setText(' Write ONLY digits')
return 0
if len(self.var_list) == 2:
if is_digit(self.y_value1.text()) and is_digit(
self.y_value2.text()):
self.ran_y[0] = float(self.y_value1.text())
self.ran_y[1] = float(self.y_value2.text())
self.interval_y = (self.ran_y[1] -
self.ran_y[0]) / self.n_interval
else:
self.tt_label.setText(' Write ONLY digits')
return 0
if self.ran_x[0] >= self.ran_x[1] or self.ran_y[0] >= self.ran_y[1]:
self.tt_label.setText(
' The Right value must be bigger than the Left value')
return 0
self.plot()
def calc(self, left):
factor = self.factor.eval()
if self.op == '^':
if is_digit(left.contain) and is_digit(factor.contain):
left.contain = left.contain**factor.contain
else:
left.expo = factor * left.expo
# left.expo *= factor
# left = left ** factor
if self.sequenceTail is None:
return left
else:
return self.sequenceTail.calc(left)
def plot_2D(eq, domain, in_domain, var_list, ran, interval):
var = var_list[0]
ipts = []
opts = []
ipt = []
opt = []
for n in range(int((ran[1]-ran[0])/interval)):
value = ran[0] + interval * n
if check_domain(domain, in_domain, var_list, var+'='+str(value)):
ans = change_x_to_num(eq, var_list, var + '=' + str(value))
if is_digit(ans):
ipt.append(value)
opt.append(float(ans))
else:
ipts.append(ipt)
opts.append(opt)
ipt = []
opt = []
else:
ipts.append(ipt)
opts.append(opt)
ipt = []
opt = []
ipts.append(ipt)
opts.append(opt)
return [ipts, opts]
def plot_3D(eq, domain, in_domain, var_list, ran1, ran2, interval_x, interval_y):
var1 = var_list[0]
var2 = var_list[1]
ipt1 = []
ipt2 = []
opt = []
for n in range(int((ran1[1]-ran1[0])/interval_x)):
value1 = ran1[0] + interval_x * n
for m in range(int((ran2[1]-ran2[0])/interval_y)):
value2 = ran2[0] + interval_y * m
if check_domain(domain, in_domain, var_list, var1+'='+str(value1) +','+ var2+'='+str(value2)):
ans = change_x_to_num(eq, var_list, var1+'='+str(value1) +','+ var2+'='+str(value2))
ipt1.append(value1)
ipt2.append(value2)
if is_digit(ans):
opt.append(float(ans))
else:
opt.append(nan)
else:
ipt1.append(value1)
ipt2.append(value2)
opt.append(nan)
return [ipt1, ipt2, opt]
def check_domain(domain, in_domain, var_list, input):
if domain:
domain = domain_to_string(domain, var_list)
if in_domain:
in_domain = domain_to_string(in_domain, var_list)
for n in range(len(domain)):
opt = change_x_to_num(domain[n], var_list, input)
if is_digit(opt):
if float(opt) == 0:
return 0
else:
return 0
for n in range(len(in_domain)):
opt = change_x_to_num(in_domain[n], var_list, input)
if is_digit(opt):
if float(opt) < 0:
return 0
else:
return 0
return 1
def differentiable_1D(eq, eq_diff, domain, in_domain, string, var_list):
try:
epsilon = 10 ** -10
var = []
value = []
string1 = string.replace(" ", "")
string1 = string1.split(',')
for n in range(len(string1)):
temp = string1[n].split('=')
if temp[0] not in var_list:
raise Exception('%s is not in current variable list' % (temp[0]))
if len(temp) != 2 or not is_digit(temp[1]):
raise Exception('Wrong input')
var.append(temp[0])
value.append(temp[1])
if len(var) != 1:
raise Exception('Expected 1 variable but got %d' % (len(var)))
else:
var = var[0]
value = value[0]
if check_domain(domain, in_domain, [var], var+'='+str(float(value)+epsilon)):
ans_l_p = change_x_to_num(eq, [var], var+'='+str(float(value)+epsilon))
ans_d_l_p = change_x_to_num(eq_diff[0], [var], var+'='+str(float(value)+epsilon))
else:
return 0
if check_domain(domain, in_domain, [var], var+'='+str(float(value)-epsilon)):
ans_l_m = change_x_to_num(eq, [var], var+'='+str(float(value)-epsilon))
ans_d_l_m = change_x_to_num(eq_diff[0], [var], var+'='+str(float(value)-epsilon))
else:
return 0
if check_domain(domain, in_domain, [var], var+'='+str(value)):
ans = change_x_to_num(eq, [var], var+'='+value)
ans_d = change_x_to_num(eq_diff[0], [var], var+'='+value)
else:
return 0
if is_same([ans_l_p, ans_l_m, ans], epsilon) and is_same([ans_d_l_p, ans_d_l_m, ans_d], epsilon):
return 1
else:
return 0
except Exception as e:
return '*Error* ' + str(e)
def change_x_to_num(eq, var_list, string):
try:
eq = eq.replace(" ", "")
eq_list = tokenize(eq, var_list)
variable = []
value = []
string = string.replace(" ", "")
string = string.split(',')
for n in range(len(string)):
temp = string[n].split('=')
if temp[0] not in var_list:
raise Exception('%s is not in current variable list' % (temp[0]))
if len(temp) != 2 or not is_digit(temp[1]):
raise Exception('Wrong input')
variable.append(temp[0])
value.append(temp[1])
for n in range(len(variable)):
eq_temp = []
for m in range(len(eq_list)):
if eq_list[m] == variable[n]:
eq_temp.append(float(value[n]))
else:
eq_temp.append(eq_list[m])
eq_list = eq_temp
if eq_list[0] == 'sig':
sig_eq = ''
for n in range(4, len(eq_list)-6):
sig_eq += str(eq_list[n])
ans, _, _ = sigma(eq_list[2], sig_eq, eq_list[-5], eq_list[-3], var_list)
return ans[0]
E = Parser(eq_list, var_list)
ans = E.eval()
return from_list_to_str('', ans)
except Exception as e:
return '*Error* ' + str(e)
def calc(self, left):
factor = self.factor.eval()
if self.op == '^':
if factor == [2]:
left = many_mul([], left, left, var_list)
else:
if is_digit(factor[0]) and len(factor) == 1:
if 0 < factor[0] < 1:
if left not in in_eq:
in_eq.append(left)
left = power(left, factor, var_list)
left = double_bracket(left)
if self.sequenceTail is None:
return left
else:
return self.sequenceTail.calc(left)
def eval(self):
if isinstance(self.expr, Expr):
a = self.expr.eval()
self.contain = a
else:
self.contain = self.expr
if self.sign is '-':
self.coef *= -1
return self
elif self.sign in self.funcs_list:
func = self.funcs[self.sign]
if is_digit(self.contain):
self.contain = func(self.contain)
self.sign = None
# elif self.sign == 'log':
# elif self.sign == 'sig':
return self
def __mul__(self, left):
if is_digit(left):
self.contain *= left
elif is_digit(self.contain) and is_digit(left.contain):
expo = left.expo if is_digit(left.expo) else left.expo.contain
if expo == 1:
self.contain *= left.contain
else:
self.contain /= left.contain
elif is_digit(self.contain):
if self.expo == 1:
left.coef *= (self.coef * self.contain)
else:
left.coef /= (self.coef * self.contain)
return left
elif is_digit(left.contain):
if left.expo == 1:
self.coef *= (left.coef * left.contain)
else:
self.coef /= (left.coef * left.contain)
else:
if self.contain == left.contain:
self.coef *= left.coef
self.expo += left.expo
if self.expo == 0:
if self.coef > 0:
self.contain = self.coef
self.coef = 1
else:
self.contain = self.coef * -1
self.coef = -1
self.expo = 1
return self
def differentiable_2D(eq, eq_diff, domain, in_domain, string, var_list):
try:
epsilon = 10**(-10)
var = []
value = []
string1 = string.replace(" ", "")
string1 = string1.split(',')
for n in range(len(string1)):
temp = string1[n].split('=')
if temp[0] not in var_list:
raise Exception('%s is not in current variable list' % (temp[0]))
if len(temp) != 2 or not is_digit(temp[1]):
raise Exception('Wrong input')
var.append(temp[0])
value.append(temp[1])
if len(var) != 2:
raise Exception('Expected 2 variable but got %d' % (len(var)))
PlusMinus_epsilon = [+epsilon, -epsilon]
ans_l_x = []
ans_l_dx = []
ans_l_y = []
ans_l_dy = []
for n in range(len(PlusMinus_epsilon)):
temp_string = var[0] + '=' + str(float(value[0])+PlusMinus_epsilon[n]) + ',' + var[1] + '=' + value[1]
if check_domain(domain, in_domain, var, temp_string):
ans_l_x.append(change_x_to_num(eq, var, temp_string))
ans_l_dx.append(change_x_to_num(eq_diff[0], var, temp_string))
else:
return [0, 0]
for n in range(len(PlusMinus_epsilon)):
temp_string = var[0] + '=' + value[0] + ',' + var[1] + '=' + str(float(value[1])+PlusMinus_epsilon[n])
if check_domain(domain, in_domain, var, temp_string):
ans_l_y.append(change_x_to_num(eq, var, temp_string))
ans_l_dy.append(change_x_to_num(eq_diff[0], var, temp_string))
else:
return [0, 0]
if check_domain(domain, in_domain, var, string):
ans = change_x_to_num(eq, var, string)
ans_dx = change_x_to_num(eq_diff[0], var, string)
ans_dy = change_x_to_num(eq_diff[1], var, string)
else:
return [0, 0]
epsilon = epsilon * 10
if is_same([ans_l_x[0], ans_l_x[1], ans], epsilon):
if is_same([ans_l_dx[0], ans_l_dx[1], ans_dx], epsilon):
dx = 1
else:
return [0, 0]
else:
return [0, 0]
if is_same([ans_l_y[0], ans_l_y[1], ans], epsilon):
if is_same([ans_l_dy[0], ans_l_dy[1], ans_dy], epsilon):
dy = 1
else:
return [0, 0]
else:
return [0, 0]
return [dx, dy]
except Exception as e:
return '*Error* ', str(e)
def on_click_eq(self):
temp = self.variable.text()
self.eq = self.equation.text()
self.domain_title_label.setText('')
self.domain_label.setText('')
self.dt_label.setText('')
if not self.eq:
self.a_label.setText('Enter Equation')
self.d_label.setText('')
self.da_label.setText('')
return 0
self.var_list = []
temp = temp.replace(" ", "")
temp = temp.split(',')
if temp[0] != '':
for n in range(len(temp)):
if temp[n] in ['e', 'pi']:
self.a_label.setText(temp[n] + ' is not available')
return 0
self.var_list.append(temp[n])
self.var_list.sort()
ans, self.domain, self.in_domain = calcul(self.eq, self.var_list)
if ans == 'Error':
self.a_label.setText('*Error* ' + self.domain.args[0])
self.d_label.setText('')
return 0
if self.eq[0:3] == 'sig':
self.eq = ans[0]
self.diff = []
for n in range(len(self.var_list)):
differential = ans[1]
if differential[0] == 'Error':
self.diff = 'Error' + differential[1].args[0]
break
else:
self.diff.append(differential[0])
else:
self.eq = from_list_to_str('', ans)
self.diff = []
for n in range(len(self.var_list)):
differential = diff(ans, self.var_list[n], self.var_list)
if differential[0] == 'Error':
self.diff = 'Error' + differential[1].args[0]
break
else:
self.diff.append(from_list_to_str('', differential[0]))
self.a_label.setText('Equation is: ' + str(self.eq))
self.d_label.setText('Differential')
if not self.domain and not self.in_domain:
str_domain = 'Domain: R'
if len(self.var_list) > 1:
str_domain = str_domain + '^' + str(len(self.var_list))
self.domain_title_label.setText(str_domain)
else:
str_domain = ''
for n in range(len(self.domain)):
str_domain = str_domain + from_list_to_str(
'', self.domain[n]) + ' ≠ 0' + '\n'
for n in range(len(self.in_domain)):
str_domain = str_domain + from_list_to_str(
'', self.in_domain[n]) + ' ≥ 0' + '\n'
self.domain_title_label.setText('Domain')
self.domain_label.setText(str_domain)
if not is_digit(self.eq):
if len(self.var_list) < 3 and self.eq[0:3] != 'sig':
self.open_new_dialog(self.eq, self.diff, self.domain,
self.in_domain, self.var_list)
if not self.diff:
self.a_label.setText('Answer is: ' + str(self.eq))
self.d_label.setText('')
self.da_label.setText('')
return 0
diff_ans = ''
if isinstance(self.diff, str):
diff_ans = self.diff
else:
for n in range(len(self.diff)):
diff_ans = diff_ans + 'Differentiated by ' + self.var_list[
n] + ': ' + self.diff[n] + '\n'
self.da_label.setText(diff_ans)
return 0
def eval(self):
temp = self.expr.eval() if isinstance(self.expr, Expr) else self.expr
if temp in var_list:
temp = [1, temp, 1]
elif is_digit(temp):
temp = [temp]
elif temp in ['e', 'pi']:
temp = [self.funcs[temp]]
elif is_gathered(temp) and len(temp) == 1:
temp = temp[0]
if self.sign is '-':
temp = many_mul([], [-1], temp, var_list)
return temp
elif self.sign in self.funcs_list:
func = self.funcs[self.sign]
if not is_digit(temp[0]) or len(temp) > 1 and self.sign == 'tan':
if temp not in eq:
temp_pi = plus(deepcopy(temp), [pi / 2], var_list)
if temp_pi not in eq:
eq.append(temp_pi)
if is_digit(temp[0]) and len(temp) == 1:
if self.sign == 'tan' and temp[0] == (pi / 2):
raise Exception('Cannot define tan(pi/2)')
else:
return [func(temp[0])]
else:
return [1, [self.sign, temp], 1]
elif self.sign == 'log':
if not is_digit(temp[0]) or len(temp) > 1:
if temp not in in_eq:
in_eq.append(temp)
if temp not in eq:
eq.append(temp)
if self.base == None:
base = [e]
else:
base = self.base.eval() if isinstance(self.base,
Expr) else self.base
if not is_digit(base[0]) or len(base) > 1:
if base not in in_eq:
in_eq.append(base)
if base not in eq:
eq.append(base)
base_1 = plus(deepcopy(base), [-1], var_list)
if base_1 not in eq:
if not is_digit(base[0]) or len(base) > 1:
eq.append(base_1)
if is_digit(temp[0]) and len(temp) == 1 and is_digit(
base[0]) and len(base) == 1:
return [log(temp[0], base[0])]
else:
if not is_gathered(temp) and len(temp) == 3:
if is_digit(base[0]) and len(base) == 1:
if [temp[0], temp[1], 1] == [1, base, 1]:
return many_mul([], [1], [temp[2]], var_list)
else:
return [1, ['log', temp, base], 1]
# return many_mul([], [1, ['log', [temp[0], temp[1], 1], base], 1], [temp[2]], var_list)
else:
if [temp[0], temp[1], 1] == base:
return many_mul([], [1], [temp[2]], var_list)
else:
return [1, ['log', temp, base], 1]
# return many_mul([], [1, ['log', [temp[0], temp[1], 1], base], 1], [temp[2]], var_list)
else:
return [1, ['log', temp, base], 1]
elif self.sign == 'sig':
var_list.append(self.k)
temp = self.expr.eval() if isinstance(self.expr,
Expr) else self.expr
var_list.pop()
# sigma(self.k, temp, self.base[0], self.base[1], var_list)
return [0, 'sig']
return temp
def tokenize(eq, var_list):
eq_list = []
funcs_list = ['log', 'sin', 'cos', 'tan', 'pow', 'sig']
op_list = ['+', '-', '*', '/', '^', '(', ')', ',']
temp = '0'
for n in range(len(eq)):
if n == len(eq) - 1:
if is_digit(eq[n]) or eq[n] == '.':
temp += str(eq[n])
eq_list.append(float(temp))
elif eq[n] in var_list:
if temp != '0':
eq_list.append(float(temp))
eq_list.append(eq[n])
elif eq[n - 1:n + 1] == 'pi':
eq_list.pop()
eq_list.append(eq[n - 1:n + 1])
elif eq[n] in op_list:
if temp != '0':
eq_list.append(float(temp))
eq_list.append(eq[n])
else:
eq_list.append(eq[n])
elif n == 0:
if is_digit(eq[n]) or eq[n] == '.':
temp += str(eq[n])
if n == len(eq) - 1:
eq_list.append(float(temp))
elif eq[n] in var_list or eq[n] in op_list:
eq_list.append(eq[n])
else:
eq_list.append(eq[n])
elif n == (1 or 2):
if is_digit(eq[n]) or eq[n] == '.':
temp += str(eq[n])
elif eq[n - 1:n + 1] == 'pi':
eq_list.pop()
eq_list.append(eq[n - 1:n + 1])
elif eq[n] in var_list or eq[n] in op_list:
if is_digit(eq[n - 1]) or eq[n - 1] == '.':
eq_list.append(float(temp))
temp = '0'
eq_list.append(eq[n])
else:
eq_list.append(eq[n])
else:
if is_digit(eq[n]) or eq[n] == '.':
temp += str(eq[n])
elif eq[n - 1:n + 1] == 'pi':
eq_list.pop()
eq_list.append(eq[n - 1:n + 1])
elif eq[n - 2:n + 1] in funcs_list:
eq_list.pop()
eq_list.pop()
eq_list.append(eq[n - 2:n + 1])
elif eq[n] in var_list or eq[n] in op_list:
if is_digit(eq[n - 1]) or eq[n - 1] == '.':
eq_list.append(float(temp))
temp = '0'
eq_list.append(eq[n])
else:
eq_list.append(eq[n])
eq_list.append('$')
return eq_list
