def evaluate_linear(self, expression):
if len(expression) == 0:
return "Enter valid expression"
try:
exp = expression.split("=")
sy_exp = kernS(exp[0])
if exp[1].isdigit():
req = int(exp[1])
else:
req = kernS(exp[1])
except SyntaxError:
return "Not a valid expression"
return sy.solveset(sy.Eq(sy_exp, req))
def test_kernS():
s = "-1 - 2*(-(-x + 1/x)/(x*(x - 1/x)**2) - 1/(x*(x - 1/x)))"
# when 1497 is fixed, this no longer should pass: the expression
# should be unchanged
assert -1 - 2 * (-(-x + 1 / x) / (x * (x - 1 / x) ** 2) - 1 / (x * (x - 1 / x))) == -1
# sympification should not allow the constant to enter a Mul
# or else the structure can change dramatically
ss = kernS(s)
assert ss != -1 and ss.simplify() == -1
s = "-1 - 2*(-(-x + 1/x)/(x*(x - 1/x)**2) - 1/(x*(x - 1/x)))".replace("x", "_kern")
ss = kernS(s)
assert ss != -1 and ss.simplify() == -1
# issue 3588
assert kernS("Interval(-1,-2 - 4*(-3))") == Interval(-1, 10)
assert kernS("_kern") == Symbol("_kern")
def test_kernS():
s = '-1 - 2*(-(-x + 1/x)/(x*(x - 1/x)**2) - 1/(x*(x - 1/x)))'
# when 1497 is fixed, this no longer should pass: the expression
# should be unchanged
assert -1 - 2 * (-(-x + 1 / x) / (x * (x - 1 / x)**2) - 1 /
(x * (x - 1 / x))) == -1
# sympification should not allow the constant to enter a Mul
# or else the structure can change dramatically
ss = kernS(s)
assert ss != -1 and ss.simplify() == -1
s = '-1 - 2*(-(-x + 1/x)/(x*(x - 1/x)**2) - 1/(x*(x - 1/x)))'.replace(
'x', '_kern')
ss = kernS(s)
assert ss != -1 and ss.simplify() == -1
# issue 3588
assert kernS('Interval(-1,-2 - 4*(-3))') == Interval(-1, 10)
assert kernS('_kern') == Symbol('_kern')
def test_kernS():
s = '-1 - 2*(-(-x + 1/x)/(x*(x - 1/x)**2) - 1/(x*(x - 1/x)))'
# when 1497 is fixed, this no longer should pass: the expression
# should be unchanged
assert -1 - 2*(-(-x + 1/x)/(x*(x - 1/x)**2) - 1/(x*(x - 1/x))) == -1
# sympification should not allow the constant to enter a Mul
# or else the structure can change dramatically
ss = kernS(s)
assert ss != -1 and ss.simplify() == -1
s = '-1 - 2*(-(-x + 1/x)/(x*(x - 1/x)**2) - 1/(x*(x - 1/x)))'.replace(
'x', '_kern')
ss = kernS(s)
assert ss != -1 and ss.simplify() == -1
# issue 6687
assert kernS('Interval(-1,-2 - 4*(-3))') == Interval(-1, 10)
assert kernS('_kern') == Symbol('_kern')
assert kernS('E**-(x)') == exp(-x)
e = 2*(x + y)*y
assert kernS(['2*(x + y)*y', ('2*(x + y)*y',)]) == [e, (e,)]
assert kernS('-(2*sin(x)**2 + 2*sin(x)*cos(x))*y/2') == \
-y*(2*sin(x)**2 + 2*sin(x)*cos(x))/2
def test_kernS():
s = '-1 - 2*(-(-x + 1/x)/(x*(x - 1/x)**2) - 1/(x*(x - 1/x)))'
# when 1497 is fixed, this no longer should pass: the expression
# should be unchanged
assert -1 - 2*(-(-x + 1/x)/(x*(x - 1/x)**2) - 1/(x*(x - 1/x))) == -1
# sympification should not allow the constant to enter a Mul
# or else the structure can change dramatically
ss = kernS(s)
assert ss != -1 and ss.simplify() == -1
s = '-1 - 2*(-(-x + 1/x)/(x*(x - 1/x)**2) - 1/(x*(x - 1/x)))'.replace(
'x', '_kern')
ss = kernS(s)
assert ss != -1 and ss.simplify() == -1
# issue 3588
assert kernS('Interval(-1,-2 - 4*(-3))') == Interval(-1, 10)
assert kernS('_kern') == Symbol('_kern')
assert kernS('E**-(x)') == exp(-x)
e = 2*(x + y)*y
assert kernS(['2*(x + y)*y', ('2*(x + y)*y',)]) == [e, (e,)]
assert kernS('-(2*sin(x)**2 + 2*sin(x)*cos(x))*y/2') == \
-y*(2*sin(x)**2 + 2*sin(x)*cos(x))/2
def test_kernS():
s = '-1 - 2*(-(-x + 1/x)/(x*(x - 1/x)**2) - 1/(x*(x - 1/x)))'
# when 1497 is fixed, this no longer should pass: the expression
# should be unchanged
assert -1 - 2*(-(-x + 1/x)/(x*(x - 1/x)**2) - 1/(x*(x - 1/x))) == -1
# sympification should not allow the constant to enter a Mul
# or else the structure can change dramatically
ss = kernS(s)
assert ss != -1 and ss.simplify() == -1
s = '-1 - 2*(-(-x + 1/x)/(x*(x - 1/x)**2) - 1/(x*(x - 1/x)))'.replace(
'x', '_kern')
ss = kernS(s)
assert ss != -1 and ss.simplify() == -1
# issue 6687
assert (kernS('Interval(-1,-2 - 4*(-3))')
== Interval(-1, Add(-2, Mul(12, 1, evaluate=False), evaluate=False)))
assert kernS('_kern') == Symbol('_kern')
assert kernS('E**-(x)') == exp(-x)
e = 2*(x + y)*y
assert kernS(['2*(x + y)*y', ('2*(x + y)*y',)]) == [e, (e,)]
assert kernS('-(2*sin(x)**2 + 2*sin(x)*cos(x))*y/2') == \
-y*(2*sin(x)**2 + 2*sin(x)*cos(x))/2
# issue 15132
assert kernS('(1 - x)/(1 - x*(1-y))') == kernS('(1-x)/(1-(1-y)*x)')
assert kernS('(1-2**-(4+1)*(1-y)*x)') == (1 - x*(1 - y)/32)
assert kernS('(1-2**(4+1)*(1-y)*x)') == (1 - 32*x*(1 - y))
assert kernS('(1-2.*(1-y)*x)') == 1 - 2.*x*(1 - y)
one = kernS('x - (x - 1)')
assert one != 1 and one.expand() == 1
assert kernS("(2*x)/(x-1)") == 2*x/(x-1)
# In[ ]:
eqn_str = '1 / (1 + x**2 + y**2)'
#x = Symbol('x')
#y = Symbol('y')
#i,j,k = symbols('i, j, k')
#kernS(eqn_str)
function = sympify(eqn_str)
symbols = list(function.free_symbols)
print(symbols)
sym_val_dict = {k: np.random.rand() for k in symbols}
print(sym_val_dict)
deriv = function.diff(x)
eqn_str2 = 'x+y+x+2*y-i-j*k+1'
function2 = kernS(eqn_str2)
deriv2 = function2.diff(x)
print(deriv)
print(deriv2)
print(function + function2)
print(2 * function2)
print(np.square(function2))
function.evalf(subs={x: 0, y: 1})
f = lambdify((x, y), function)
print(f(1, 1))
##inequality = 'x <= 2'
##ineq_func = sympify(inequality)
##ineq_func.evalf(subs = {x: 1})
zero = sympify('0')
zero.evalf() + 1
absolute = sympify(-x)
def optimize(self):
f1 = kernS(self.function1.get())
f2 = kernS(self.function2.get())
u1 = kernS(self.u1.get())
u2 = kernS(self.u2.get())
e = float(self.e.get())
# d lambda
dl = 0.5
f = (u1*f1 + u2*f2).expand()
print(f)
# let's begin
# preparations
x1, x2 = symbols("x1 x2")
# direction vector
ej = [0, 0]
# initial approximations for solution matrix and value
X = [1, 1]
F = f.subs({x1: X[0], x2: X[1]})
print("F " + str(F))
# optimal solution matrix and value, set as initial ones
opt_X = X
opt_F = F
while True:
# step 3
# checking if precision conditions met
j = 0
while j < len(X):
# step 2
# repeating this cycle for each direction toward each variable (x1, ..., xn)
# step 1
# optimizing initially approximated solution matrix toward current direction
# changing vector direction according to current argument
ej[j] = 1
print("ej " + str(ej))
# setting approximations for optimals
X = opt_X
F = opt_F
# forming 3 points for parabola approximation
# Y - points, lam - points for parabola, P - f(Yi)
Y = []
lam = []
P = []
# first point is current point
Y.append(X)
lam.append(0)
print("Y " + str(Y[0][0]) + " " + str(Y[0][1]))
P.append(f.subs({x1: Y[0][0], x2: Y[0][1]}))
# second point is current point + offset dl in ej direction
Y.append([X[0] + dl * ej[0], X[1] + dl * ej[1]])
lam.append(dl)
P.append(f.subs({x1: Y[1][0], x2: Y[1][1]}))
# third point is chosen according to first 2
if P[0] < P[1]:
Y.append([X[0] - dl * ej[0], X[1] - dl * ej[1]])
lam.append(-1 * dl)
P.append(f.subs({x1: Y[2][0], x2: Y[2][1]}))
else:
Y.append([X[0] + 2 * dl * ej[0], X[1] + 2 * dl * ej[1]])
lam.append(2 * dl)
P.append(f.subs({x1: Y[2][0], x2: Y[2][1]}))
# setting new lambda
print("lam " + str(lam))
print("P " + str(P))
opt_l = parabolic_interpolation(lam, P)
print("dl " + str(dl))
# getting new optimal solution matrix and value
opt_X = [X[0] + opt_l * ej[0], X[1] + opt_l * ej[1]]
opt_F = f.subs({x1: opt_X[0], x2: opt_X[1]})
print("opt_F " + str(opt_F))
# resetting direction
ej[j] = 0
j += 1
if (sqrt((opt_X[0]-X[0])**2+(opt_X[1]-X[1])**2) <= e) or (abs(opt_F - F) <= e):
# if precision conditions are met, then optimals are found
break
else:
continue
# rounding to one-thousandth for output
for i in range(0, len(opt_X)):
opt_X[i] = round(opt_X[i], 3)
opt_F = round(opt_F, 3)
answer_string = "Оптимальное значение достигнуто \nв точке " + str(opt_X) + " и равно " + str(opt_F)
self.answer.configure(text=answer_string)
self.answer.grid(row=self.current_row, column=self.current_col, columnspan=4)
# sympy solution (autosimplification alters the order and the brackets)
from sympy import Symbol, sympify
scale_f = Symbol("scale_f")
Vmax_bA = Symbol("Vmax_bA")
Km_A = Symbol("Km_A")
e__A = Symbol("e__A")
c__A = Symbol("c__A")
from sympy.core.sympify import kernS
s = 'scale_f * (Vmax_bA / Km_A) * ((e__A - c__A) / (1 + e__A / Km_A + c__A / Km_A))'
expr = sympify(s)
print(expr)
expr = kernS(s)
print(expr)
expr = sympify("(e__A - c__A)")
latex_str = latex(expr,
order=None,
mode='equation',
itex=True,
mul_symbol='dot',
symbol_names={
e__A: 'A_{(e)}',
c__A: 'A_{(c)}',
})
print(latex_str)
# Equation solution, necessary to make replacements
def test_kernS():
s = "-1 - 2*(-(-x + 1/x)/(x*(x - 1/x)**2) - 1/(x*(x - 1/x)))"
# when 1497 is fixed, this no longer should pass: the expression
# should be unchanged
assert (-1 - 2 * (-(-x + 1 / x) / (x * (x - 1 / x)**2) - 1 /
(x * (x - 1 / x))) == -1)
# sympification should not allow the constant to enter a Mul
# or else the structure can change dramatically
ss = kernS(s)
assert ss != -1 and ss.simplify() == -1
s = "-1 - 2*(-(-x + 1/x)/(x*(x - 1/x)**2) - 1/(x*(x - 1/x)))".replace(
"x", "_kern")
ss = kernS(s)
assert ss != -1 and ss.simplify() == -1
# issue 6687
assert kernS("Interval(-1,-2 - 4*(-3))") == Interval(-1, 10)
assert kernS("_kern") == Symbol("_kern")
assert kernS("E**-(x)") == exp(-x)
e = 2 * (x + y) * y
assert kernS(["2*(x + y)*y", ("2*(x + y)*y", )]) == [e, (e, )]
assert (kernS("-(2*sin(x)**2 + 2*sin(x)*cos(x))*y/2") == -y *
(2 * sin(x)**2 + 2 * sin(x) * cos(x)) / 2)
# issue 15132
assert kernS("(1 - x)/(1 - x*(1-y))") == kernS("(1-x)/(1-(1-y)*x)")
assert kernS("(1-2**-(4+1)*(1-y)*x)") == (1 - x * (1 - y) / 32)
assert kernS("(1-2**(4+1)*(1-y)*x)") == (1 - 32 * x * (1 - y))
assert kernS("(1-2.*(1-y)*x)") == 1 - 2.0 * x * (1 - y)
one = kernS("x - (x - 1)")
assert one != 1 and one.expand() == 1
# sympy solution (autosimplification alters the order and the brackets)
from sympy import Symbol, sympify
scale_f = Symbol("scale_f")
Vmax_bA = Symbol("Vmax_bA")
Km_A = Symbol("Km_A")
e__A = Symbol("e__A")
c__A = Symbol("c__A")
from sympy.core.sympify import kernS
s = 'scale_f * (Vmax_bA / Km_A) * ((e__A - c__A) / (1 + e__A / Km_A + c__A / Km_A))'
expr = sympify(s)
print(expr)
expr = kernS(s)
print(expr)
expr = sympify("(e__A - c__A)")
latex_str = latex(expr, order=None, mode='equation', itex=True,
mul_symbol='dot',
symbol_names={
e__A: 'A_{(e)}',
c__A: 'A_{(c)}',
})
print(latex_str)
# Equation solution, necessary to make replacements
import Equation
from Equation import Expression
