def newtonRaphson(exp, x, error):
#PARSEO LA FUNCION
f = mathematica(exp)
print('f(x) ingresada = ' + str(f))
#CALCULO LA DERIVADA
df = diff(f)
print('f\'(x) = ' + str(df))
while (abs(f.subs('x', x)) > error):
xAnt = x
#IMPRIMO X y F(X) EN EL PUNTO
print('f(x) = ' + str(float(f.subs('x', xAnt))))
print('x = ' + str(float(xAnt)))
# EL X SIGUIENTE ES: X(n+1) = Xn - (f(Xn)/f'(Xn))
x = x - (f.subs('x', x) / df.subs('x', x))
# DEFINO LA RECTA TANGENTE
rect = str(float(df.subs('x', xAnt))) + '*x+' + str(
float(f.subs('x', xAnt) - df.subs('x', xAnt) * xAnt))
frect = mathematica(rect)
print('Recta: ', frect)
print('X(n+1) = ', float(x))
print('f(X(n+1)) = ', float(f.subs('x', x)))
#
if (f.subs('x', x) <= error):
print('El algoritmo ha convergido. f(X(n+1))<=error')
#GRAFICO DE LA FUNCION Y LA RECTA TANGENTE
plot(f, frect)
def test_mathematica():
d = {
'- 6x': '-6*x',
'Sin[x]^2': 'sin(x)**2',
'2(x-1)': '2*(x-1)',
'3y+8': '3*y+8',
'Arcsin[2x+9(4-x)^2]/x': 'asin(2*x+9*(4-x)**2)/x',
'x+y': 'x+y',
'355/113': '355/113',
'2.718281828': '2.718281828',
'Sin[12]': 'sin(12)',
'Exp[Log[4]]': 'exp(log(4))',
'(x+1)(x+3)': '(x+1)*(x+3)',
'Cos[Arccos[3.6]]': 'cos(acos(3.6))',
'Cos[x]==Sin[y]': 'cos(x)==sin(y)',
'2*Sin[x+y]': '2*sin(x+y)',
'Sin[x]+Cos[y]': 'sin(x)+cos(y)',
'Sin[Cos[x]]': 'sin(cos(x))',
'2*Sqrt[x+y]': '2*sqrt(x+y)', # Test case from the issue 4259
'+Sqrt[2]': 'sqrt(2)',
'-Sqrt[2]': '-sqrt(2)',
'-1/Sqrt[2]': '-1/sqrt(2)',
'-(1/Sqrt[3])': '-(1/sqrt(3))',
'1/(2*Sqrt[5])': '1/(2*sqrt(5))',
'Mod[5,3]': 'Mod(5,3)',
'-Mod[5,3]': '-Mod(5,3)',
'(x+1)y': '(x+1)*y',
'x(y+1)': 'x*(y+1)',
'Sin[x]Cos[y]': 'sin(x)*cos(y)',
'Sin[x]**2Cos[y]**2': 'sin(x)**2 * cos(y)**2',
'Cos[x]^2(1 - Cos[y]^2)': 'cos(x)**2*(1-cos(y)**2)',
}
for e in d:
assert mathematica(e) == sympify(d[e])
def test_mathematica():
d = {
'- 6x': '-6*x',
'Sin[x]^2': 'sin(x)**2',
'2(x-1)': '2*(x-1)',
'3y+8': '3*y+8',
'Arcsin[2x+9(4-x)^2]/x': 'asin(2*x+9*(4-x)**2)/x',
'x+y': 'x+y',
'355/113': '355/113',
'2.718281828': '2.718281828',
'Sin[12]': 'sin(12)',
'Exp[Log[4]]': 'exp(log(4))',
'(x+1)(x+3)': '(x+1)*(x+3)',
'Cos[Arccos[3.6]]': 'cos(acos(3.6))',
'Cos[x]==Sin[y]': 'cos(x)==sin(y)',
'2*Sin[x+y]': '2*sin(x+y)',
'Sin[x]+Cos[y]': 'sin(x)+cos(y)',
'Sin[Cos[x]]': 'sin(cos(x))',
'2*Sqrt[x+y]': '2*sqrt(x+y)', # Test case from the issue 4259
'+Sqrt[2]': 'sqrt(2)',
'-Sqrt[2]': '-sqrt(2)',
'-1/Sqrt[2]': '-1/sqrt(2)',
'-(1/Sqrt[3])': '-(1/sqrt(3))',
'1/(2*Sqrt[5])': '1/(2*sqrt(5))',
'Mod[5,3]': 'Mod(5,3)',
'-Mod[5,3]': '-Mod(5,3)',
'(x+1)y': '(x+1)*y',
'x(y+1)': 'x*(y+1)',
'Sin[x]Cos[y]': 'sin(x)*cos(y)',
'Sin[x]**2Cos[y]**2': 'sin(x)**2 * cos(y)**2',
'Cos[x]^2(1 - Cos[y]^2)': 'cos(x)**2*(1-cos(y)**2)',
}
for e in d:
assert mathematica(e) == sympify(d[e])
def parse_equation(self, equation):
"""
:param equation: equation from string input, to be converted
:return: equation in form understand by Sympy library
"""
equation.replace("^", "**")
return mathematica(equation)
def __init__(self, exprStringOrObj, exprStringType="sympy"):
'''Initializes the object using string in a specific format or from an object'''
self.properties = {}
self.inRelation = {}
self.outRelation = {}
#jugaad for function overloading
if type(exprStringOrObj) is str:
flag = False
try:
if exprStringType == 'sympy':
self.symObj = parse_expr(exprStringOrObj)
#Note: Can use transformations as given in http://docs.sympy.org/dev/modules/parsing.html to improve the generality of possible expressions
elif exprStringType == 'mathematica':
self.symObj = mathematica(exprStringOrObj)
elif exprStringType == 'maxima':
self.symObj = parse_maxima(exprStringOrObj)
else:
flag = true
except:
raise Exception("Error in parsing \'"+exprStringType+"\' code: \'"+exprStringOrObj+"\'")
if flag:
raise Exception("Currently parsing strings of type \'"+exprStringType+"\' has not been implemented for the symPy backend. Please use \'sympy\', \'mathematica\' or \'maxima\' syntax")
else: #it is a sympy object directly
self.symObj = exprStringOrObj
def test_mathematica():
d = {
'- 6x': '-6*x',
'Sin[x]^2': 'sin(x)**2',
'2(x-1)': '2*(x-1)',
'3y+8': '3*y+8',
'Arcsin[2x+9(4-x)^2]/x': 'asin(2*x+9*(4-x)**2)/x',
'x+y': 'x+y',
'355/113': '355/113',
'2.718281828': '2.718281828',
'Sin[12]': 'sin(12)',
'Exp[Log[4]]': 'exp(log(4))',
'(x+1)(x+3)': '(x+1)*(x+3)',
'Cos[Arccos[3.6]]': 'cos(acos(3.6))',
'Cos[x]==Sin[y]': 'cos(x)==sin(y)',
'2*Sin[x+y]': '2*sin(x+y)',
'Sin[x]+Cos[y]': 'sin(x)+cos(y)',
'Sin[Cos[x]]': 'sin(cos(x))',
'2*Sqrt[x+y]': '2*sqrt(x+y)', # Test case from the issue 4259
'x y': 'x*y',
'x Sin[x]': 'x*sin(x)',
'x Sin[1/x]': 'x*sin(1/x)',
'Sin[1/x] x': 'x*sin(1/x)',
'x*Sin[1/x]': 'x*sin(1/x)', # Test case from the issue 8501
'Sin[1/x]*x': 'x*sin(1/x)'}
for e in d:
assert mathematica(e) == sympify(d[e])
def secante(exp, xAnt, x, error):
#PARSEO LA FUNCION
f = mathematica(exp)
print('f(x) ingresada = ' + str(f))
print('X1 = ' + str(xAnt) + ' X2 = ' + str(x))
while (abs(f.subs('x', x)) > error):
xAux = xAnt
xAnt = x
#IMPRIMO X y F(X) EN EL PUNTO
print('f(x) = ' + str(float(f.subs('x', xAnt))))
print('x = ' + str(float(xAnt)))
# DEFINO LA RECTA TANGENTE
m = float((f.subs('x', x) - f.subs('x', xAux)) / (x - xAux))
print('m', m)
b = float(f.subs('x', xAux) - (m * xAux))
print('b', b)
rect = '(' + str(m) + ') * x+ (' + str(b) + ')' # FORMATO STRING
print(rect)
frect = mathematica(rect) #PARSEO EL STRING
# CALCULO EL X SIGUIENTE:
# X(n+1) = Xn - (Xn - X(n-1)) / (f(Xn) - f(X(n-1)))*f(Xn)
x = x - ((x - xAux) /
(f.subs('x', x) - f.subs('x', xAux)) * f.subs('x', x))
print('Recta: ', frect)
print('X(n+1) = ', float(x))
print('f(X(n+1)) = ', float(f.subs('x', x)))
if (abs(f.subs('x', x)) <= error):
print('El algoritmo ha convergido. f(X(n+1))<=error')
#GRAFICO DE LA FUNCION Y LA RECTA TANGENTE
plot(f, frect)
def test_mathematica():
d = {
'- 6x': '-6*x',
'Sin[x]^2': 'sin(x)**2',
'2(x-1)': '2*(x-1)',
'3y+8': '3*y+8',
'ArcSin[2x+9(4-x)^2]/x': 'asin(2*x+9*(4-x)**2)/x',
'x+y': 'x+y',
'355/113': '355/113',
'2.718281828': '2.718281828',
'Sin[12]': 'sin(12)',
'Exp[Log[4]]': 'exp(log(4))',
'(x+1)(x+3)': '(x+1)*(x+3)',
'Cos[ArcCos[3.6]]': 'cos(acos(3.6))',
'Cos[x]==Sin[y]': 'cos(x)==sin(y)',
'2*Sin[x+y]': '2*sin(x+y)',
'Sin[x]+Cos[y]': 'sin(x)+cos(y)',
'Sin[Cos[x]]': 'sin(cos(x))',
'2*Sqrt[x+y]': '2*sqrt(x+y)', # Test case from the issue 4259
'+Sqrt[2]': 'sqrt(2)',
'-Sqrt[2]': '-sqrt(2)',
'-1/Sqrt[2]': '-1/sqrt(2)',
'-(1/Sqrt[3])': '-(1/sqrt(3))',
'1/(2*Sqrt[5])': '1/(2*sqrt(5))',
'Mod[5,3]': 'Mod(5,3)',
'-Mod[5,3]': '-Mod(5,3)',
'(x+1)y': '(x+1)*y',
'x(y+1)': 'x*(y+1)',
'Sin[x]Cos[y]': 'sin(x)*cos(y)',
'Sin[x]**2Cos[y]**2': 'sin(x)**2*cos(y)**2',
'Cos[x]^2(1 - Cos[y]^2)': 'cos(x)**2*(1-cos(y)**2)',
'x y': 'x*y',
'2 x': '2*x',
'x 8': 'x*8',
'2 8': '2*8',
'1 2 3': '1*2*3',
' - 2 * Sqrt[ 2 3 * ( 1 + 5 ) ] ': '-2*sqrt(2*3*(1+5))',
'Log[2,4]': 'log(4,2)',
'Log[Log[2,4],4]': 'log(4,log(4,2))',
'Exp[Sqrt[2]^2Log[2, 8]]': 'exp(sqrt(2)**2*log(8,2))',
'ArcSin[Cos[0]]': 'asin(cos(0))',
'Log2[16]': 'log(16,2)',
'Max[1,-2,3,-4]': 'Max(1,-2,3,-4)',
'Min[1,-2,3]': 'Min(1,-2,3)',
'Exp[I Pi/2]': 'exp(I*pi/2)',
'ArcTan[x,y]': 'atan2(y,x)',
'Pochhammer[x,y]': 'rf(x,y)'
}
for e in d:
assert mathematica(e) == sympify(d[e])
def readout(flag, tempdir, returnhash):
if (flag == 't') or (flag == 'n'):
with open(os.path.join(tempdir, returnhash), 'r') as f:
ret = f.read()
return ret
elif flag == 'p':
with open(os.path.join(tempdir, returnhash), 'r') as f:
ret = f.read()
return M.mathematica(ret)
elif flag == 'g':
ret = Image(os.path.join(tempdir, returnhash), format='png')
return ret
else:
raise Exception('Flag must be one of (\'t\', \'n\', \'p\', \'g\').')
def test_mathematica():
d = {
"- 6x": "-6*x",
"Sin[x]^2": "sin(x)**2",
"2(x-1)": "2*(x-1)",
"3y+8": "3*y+8",
"ArcSin[2x+9(4-x)^2]/x": "asin(2*x+9*(4-x)**2)/x",
"x+y": "x+y",
"355/113": "355/113",
"2.718281828": "2.718281828",
"Sin[12]": "sin(12)",
"Exp[Log[4]]": "exp(log(4))",
"(x+1)(x+3)": "(x+1)*(x+3)",
"Cos[ArcCos[3.6]]": "cos(acos(3.6))",
"Cos[x]==Sin[y]": "cos(x)==sin(y)",
"2*Sin[x+y]": "2*sin(x+y)",
"Sin[x]+Cos[y]": "sin(x)+cos(y)",
"Sin[Cos[x]]": "sin(cos(x))",
"2*Sqrt[x+y]": "2*sqrt(x+y)", # Test case from the issue 4259
"+Sqrt[2]": "sqrt(2)",
"-Sqrt[2]": "-sqrt(2)",
"-1/Sqrt[2]": "-1/sqrt(2)",
"-(1/Sqrt[3])": "-(1/sqrt(3))",
"1/(2*Sqrt[5])": "1/(2*sqrt(5))",
"Mod[5,3]": "Mod(5,3)",
"-Mod[5,3]": "-Mod(5,3)",
"(x+1)y": "(x+1)*y",
"x(y+1)": "x*(y+1)",
"Sin[x]Cos[y]": "sin(x)*cos(y)",
"Sin[x]**2Cos[y]**2": "sin(x)**2*cos(y)**2",
"Cos[x]^2(1 - Cos[y]^2)": "cos(x)**2*(1-cos(y)**2)",
"x y": "x*y",
"2 x": "2*x",
"x 8": "x*8",
"2 8": "2*8",
"1 2 3": "1*2*3",
" - 2 * Sqrt[ 2 3 * ( 1 + 5 ) ] ": "-2*sqrt(2*3*(1+5))",
"Log[2,4]": "log(4,2)",
"Log[Log[2,4],4]": "log(4,log(4,2))",
"Exp[Sqrt[2]^2Log[2, 8]]": "exp(sqrt(2)**2*log(8,2))",
"ArcSin[Cos[0]]": "asin(cos(0))",
"Log2[16]": "log(16,2)",
"Max[1,-2,3,-4]": "Max(1,-2,3,-4)",
"Min[1,-2,3]": "Min(1,-2,3)",
"Exp[I Pi/2]": "exp(I*pi/2)",
}
for e in d:
assert mathematica(e) == sympify(d[e])
def test_mathematica():
d = {
'- 6x': '-6*x',
'Sin[x]^2': 'sin(x)**2',
'2(x-1)': '2*(x-1)',
'3y+8': '3*y+8',
'ArcSin[2x+9(4-x)^2]/x': 'asin(2*x+9*(4-x)**2)/x',
'x+y': 'x+y',
'355/113': '355/113',
'2.718281828': '2.718281828',
'Sin[12]': 'sin(12)',
'Exp[Log[4]]': 'exp(log(4))',
'(x+1)(x+3)': '(x+1)*(x+3)',
'Cos[ArcCos[3.6]]': 'cos(acos(3.6))',
'Cos[x]==Sin[y]': 'cos(x)==sin(y)',
'2*Sin[x+y]': '2*sin(x+y)',
'Sin[x]+Cos[y]': 'sin(x)+cos(y)',
'Sin[Cos[x]]': 'sin(cos(x))',
'2*Sqrt[x+y]': '2*sqrt(x+y)', # Test case from the issue 4259
'+Sqrt[2]': 'sqrt(2)',
'-Sqrt[2]': '-sqrt(2)',
'-1/Sqrt[2]': '-1/sqrt(2)',
'-(1/Sqrt[3])': '-(1/sqrt(3))',
'1/(2*Sqrt[5])': '1/(2*sqrt(5))',
'Mod[5,3]': 'Mod(5,3)',
'-Mod[5,3]': '-Mod(5,3)',
'(x+1)y': '(x+1)*y',
'x(y+1)': 'x*(y+1)',
'Sin[x]Cos[y]': 'sin(x)*cos(y)',
'Sin[x]**2Cos[y]**2': 'sin(x)**2*cos(y)**2',
'Cos[x]^2(1 - Cos[y]^2)': 'cos(x)**2*(1-cos(y)**2)',
'x y': 'x*y',
'2 x': '2*x',
'x 8': 'x*8',
'2 8': '2*8',
'1 2 3': '1*2*3',
' - 2 * Sqrt[ 2 3 * ( 1 + 5 ) ] ': '-2*sqrt(2*3*(1+5))',
'Log[2,4]': 'log(4,2)',
'Log[Log[2,4],4]': 'log(4,log(4,2))',
'Exp[Sqrt[2]^2Log[2, 8]]': 'exp(sqrt(2)**2*log(8,2))',
'ArcSin[Cos[0]]': 'asin(cos(0))',
'Log2[16]': 'log(16,2)',
'Max[1,-2,3,-4]': 'Max(1,-2,3,-4)',
'Min[1,-2,3]': 'Min(1,-2,3)',
'Exp[I Pi/2]': 'exp(I*pi/2)',
}
for e in d:
assert mathematica(e) == sympify(d[e])
def test_mathematica():
d = {'Sin[x]^2': 'sin(x)**2',
'2(x-1)': '2*(x-1)',
'3y+8': '3*y+8',
'Arcsin[2x+9(4-x)^2]/x': 'asin(2*x+9*(4-x)**2)/x',
'x+y': 'x+y',
'355/113': '355/113',
'2.718281828': '2.718281828',
'Sin[12]': 'sin(12)',
'Exp[Log[4]]': 'exp(log(4))',
'(x+1)(x+3)': '(x+1)*(x+3)',
'Cos[Arccos[3.6]]': 'cos(acos(3.6))',
'Cos[x]==Sin[y]': 'cos(x)==sin(y)'}
for e in d:
assert mathematica(e) == sympify(d[e])
def test_mathematica():
d = {
'- 6x': '-6*x',
'Sin[x]^2': 'sin(x)**2',
'2(x-1)': '2*(x-1)',
'3y+8': '3*y+8',
'Arcsin[2x+9(4-x)^2]/x': 'asin(2*x+9*(4-x)**2)/x',
'x+y': 'x+y',
'355/113': '355/113',
'2.718281828': '2.718281828',
'Sin[12]': 'sin(12)',
'Exp[Log[4]]': 'exp(log(4))',
'(x+1)(x+3)': '(x+1)*(x+3)',
'Cos[Arccos[3.6]]': 'cos(acos(3.6))',
'Cos[x]==Sin[y]': 'cos(x)==sin(y)',
'2*Sin[x+y]': '2*sin(x+y)',
'Sin[x]+Cos[y]': 'sin(x)+cos(y)',
'Sin[Cos[x]]': 'sin(cos(x))',
'2*Sqrt[x+y]': '2*sqrt(x+y)'} # Test case from the issue 4259
for e in d:
assert mathematica(e) == sympify(d[e])
sqrtand = (proall *
(9 * a * sumall + sqrt(81 * a**2 * sumall**2 + 48 * proall *
(a - 1)**3)))**(1 / 3)
D = (-2 * 6**(2 / 3) * proall *
(a - 1) + 6**(1 / 3) * sqrtand**2) / (3 * sqrtand)
return D.real
express2 = """
(-2 6^(2/3) (-1 + a) proall +
6^(1/3) (proall (9 a sumall + Sqrt[
48 (-1 + a)^3 proall + 81 a^2 sumall^2]))^(
2/3))/(3 (proall (9 a sumall + Sqrt[
48 (-1 + a)^3 proall + 81 a^2 sumall^2]))^(1/3))
"""
expr2 = M.mathematica(express2)
print(expr2)
express3 = """
(Sqrt[-8 a proall sumall +
2^(1/3) (27 (-1 + a)^2 proall^2 + Sqrt[
proall^3 (729 (-1 + a)^4 proall + 256 a^3 sumall^3)])^(
2/3)] - \[Sqrt](8 a proall sumall -
2^(1/3) (27 (-1 + a)^2 proall^2 + Sqrt[
proall^3 (729 (-1 + a)^4 proall + 256 a^3 sumall^3)])^(
2/3) - (12 Sqrt[3] (-1 + a) proall)/
Sqrt[(-8 a proall sumall +
2^(1/3) (27 (-1 + a)^2 proall^2 + Sqrt[
proall^3 (729 (-1 + a)^4 proall + 256 a^3 sumall^3)])^(
2/3))/(27 (-1 + a)^2 proall^2 + Sqrt[
proall^3 (729 (-1 + a)^4 proall +
import sympy
import tensorflow as tf
import sympy.parsing.mathematica as symath
math_expr = '(t^3+10t^2*a*Sin[x]+b*32t+32)/(t^2+2t-15)'
parsed_expr = symath.mathematica(s=math_expr)
print("parsed sympy expression", parsed_expr)
tf_expr = sympy.lambdify(parsed_expr.free_symbols, parsed_expr, 'tensorflow')
data = tf.linspace(0., 10., num=10)
print(tf_expr)
a = tf.Variable(15.)
b = tf.Variable(13.)
tensor = tf_expr(a=a, b=b, x=data, t=data)
print(tensor)
def test_mathematica():
d = {
'- 6x': '-6*x',
'Sin[x]^2': 'sin(x)**2',
'2(x-1)': '2*(x-1)',
'3y+8': '3*y+8',
'ArcSin[2x+9(4-x)^2]/x': 'asin(2*x+9*(4-x)**2)/x',
'x+y': 'x+y',
'355/113': '355/113',
'2.718281828': '2.718281828',
'Sin[12]': 'sin(12)',
'Exp[Log[4]]': 'exp(log(4))',
'(x+1)(x+3)': '(x+1)*(x+3)',
'Cos[ArcCos[3.6]]': 'cos(acos(3.6))',
'Cos[x]==Sin[y]': 'Eq(cos(x), sin(y))',
'2*Sin[x+y]': '2*sin(x+y)',
'Sin[x]+Cos[y]': 'sin(x)+cos(y)',
'Sin[Cos[x]]': 'sin(cos(x))',
'2*Sqrt[x+y]': '2*sqrt(x+y)', # Test case from the issue 4259
'+Sqrt[2]': 'sqrt(2)',
'-Sqrt[2]': '-sqrt(2)',
'-1/Sqrt[2]': '-1/sqrt(2)',
'-(1/Sqrt[3])': '-(1/sqrt(3))',
'1/(2*Sqrt[5])': '1/(2*sqrt(5))',
'Mod[5,3]': 'Mod(5,3)',
'-Mod[5,3]': '-Mod(5,3)',
'(x+1)y': '(x+1)*y',
'x(y+1)': 'x*(y+1)',
'Sin[x]Cos[y]': 'sin(x)*cos(y)',
'Sin[x]^2Cos[y]^2': 'sin(x)**2*cos(y)**2',
'Cos[x]^2(1 - Cos[y]^2)': 'cos(x)**2*(1-cos(y)**2)',
'x y': 'x*y',
'x y': 'x*y',
'2 x': '2*x',
'x 8': 'x*8',
'2 8': '2*8',
'4.x': '4.*x',
'4. 3': '4.*3',
'4. 3.': '4.*3.',
'1 2 3': '1*2*3',
' - 2 * Sqrt[ 2 3 * ( 1 + 5 ) ] ': '-2*sqrt(2*3*(1+5))',
'Log[2,4]': 'log(4,2)',
'Log[Log[2,4],4]': 'log(4,log(4,2))',
'Exp[Sqrt[2]^2Log[2, 8]]': 'exp(sqrt(2)**2*log(8,2))',
'ArcSin[Cos[0]]': 'asin(cos(0))',
'Log2[16]': 'log(16,2)',
'Max[1,-2,3,-4]': 'Max(1,-2,3,-4)',
'Min[1,-2,3]': 'Min(1,-2,3)',
'Exp[I Pi/2]': 'exp(I*pi/2)',
'ArcTan[x,y]': 'atan2(y,x)',
'Pochhammer[x,y]': 'rf(x,y)',
'ExpIntegralEi[x]': 'Ei(x)',
'SinIntegral[x]': 'Si(x)',
'CosIntegral[x]': 'Ci(x)',
'AiryAi[x]': 'airyai(x)',
'AiryAiPrime[5]': 'airyaiprime(5)',
'AiryBi[x]': 'airybi(x)',
'AiryBiPrime[7]': 'airybiprime(7)',
'LogIntegral[4]': ' li(4)',
'PrimePi[7]': 'primepi(7)',
'Prime[5]': 'prime(5)',
'PrimeQ[5]': 'isprime(5)'
}
for e in d:
assert mathematica(e) == sympify(d[e])
# The parsed form of this expression should not evaluate the Lambda object:
assert mathematica("Sin[#]^2 + Cos[#]^2 &[x]") == sin(x)**2 + cos(x)**2
d1, d2, d3 = symbols("d1:4", cls=Dummy)
assert mathematica("Sin[#] + Cos[#3] &").dummy_eq(
Lambda((d1, d2, d3),
sin(d1) + cos(d3)))
assert mathematica("Sin[#^2] &").dummy_eq(Lambda(d1, sin(d1**2)))
assert mathematica("Function[x, x^3]") == Lambda(x, x**3)
assert mathematica("Function[{x, y}, x^2 + y^2]") == Lambda((x, y),
x**2 + y**2)
from sympy.parsing.mathematica import mathematica
from sympy import *
from mpmath import *
mp.dps = 32
mp.pretty = True
nu1 = var('nu1')
nu2 = var('nu2')
with open("matter.txt", "r") as file:
expr = file.read()
mathexpr = mathematica(expr)
M12temp = lambdify([nu1, nu2], mathexpr, "mpmath")
def J(nu1, nu2):
return (gamma(1.5 - nu1) * gamma(1.5 - nu2) * gamma(nu1 + nu2 - 1.5) /
(gamma(nu1) * gamma(nu2) * gamma(3. - nu2 - nu1))) / (8. *
pi**(1.5))
def M12(nu1, nu2):
return J(nu1, nu2) * M12temp(nu1, nu2)
b = -0.8
def convert(s):
s = s.replace(b'(', b'').replace(b')', b'')
s = s.replace(b'^', b'10^')
s = s.replace(b'e', b'*10^')
return complex(mathematica(s.decode('utf-8')))
from sympy.parsing.mathematica import mathematica
from clipboard import copy, paste
additional_translations = {
'Pochhammer[x,y]': 'rf(x,y)',
'ArcTan[x,y]': 'atan2(y,x)'
}
copy(str(mathematica(paste(),
additional_translations=additional_translations)))
atan2(y, x)
"""
Sin[x]
ArcTan[x,y]
"""