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How to correct solve trigonometric functions equation by sympy?

I have an equation with trigonometric functions as below:
eq = Eq(cos(theta_3), a_2*a_3*(-a_2**2/2 - a_3**2/2 + b**2/2 + z_4**2/2))
Then I try solve θ by sympy and code as below:
solve([eq, theta_3 < pi ], theta_3)
But it raise a exception and part of the information as follows:
---------------------------------------------------------------------------
KeyError Traceback (most recent call last)
File E:\conda\lib\site-packages\sympy\polys\polyutils.py:211, in _parallel_dict_from_expr_if_gens(exprs, opt)
209 base, exp = decompose_power_rat(factor)
--> 211 monom[indices[base]] = exp
212 except KeyError:
KeyError: cos(_theta_3)
During handling of the above exception, another exception occurred:
PolynomialError Traceback (most recent call last)
File E:\conda\lib\site-packages\sympy\solvers\inequalities.py:809, in _solve_inequality(ie, s, linear)
808 try:
--> 809 p = Poly(expr, s)
810 if p.degree() == 0:
File E:\conda\lib\site-packages\sympy\polys\polytools.py:182, in Poly.__new__(cls, rep, *gens, **args)
181 else:
--> 182 return cls._from_expr(rep, opt)
File E:\conda\lib\site-packages\sympy\polys\polytools.py:311, in Poly._from_expr(cls, rep, opt)
310 """Construct a polynomial from an expression. """
--> 311 rep, opt = _dict_from_expr(rep, opt)
312 return cls._from_dict(rep, opt)
Why does such an exception raise?
How to correct solve trigonometric functions equation by sympy?

Error: _print_LambertW() got an unexpected keyword argument 'exp'

I am trying multiply the following equation with its derivative using Python, I made the following code
from sympy.abc import x, y, z, a,b
from sympy import *
a, b, n, t,N_0,x = symbols('a b n t N_0 x')
f=-LambertW(-N_0*b**(-a)*log(b)*log(t + 1))/((t + 1)*log(b)*log(t + 1))
f_a=diff(f,a)
d=f*f_a
d
When I try to run the code:
TypeError Traceback (most recent call last)
/usr/local/lib/python3.7/dist-packages/IPython/core/formatters.py in __call__(self, obj)
336 method = get_real_method(obj, self.print_method)
337 if method is not None:
--> 338 return method()
339 return None
340 else:
10 frames
/usr/local/lib/python3.7/dist-packages/sympy/printing/printer.py in _print(self, expr, **kwargs)
327 printmethod = '_print_' + cls.__name__
328 if hasattr(self, printmethod):
--> 329 return getattr(self, printmethod)(expr, **kwargs)
330 # Unknown object, fall back to the emptyPrinter.
331 return self.emptyPrinter(expr)
TypeError: _print_LambertW() got an unexpected keyword argument 'exp'

This error is no longer raised in the most recent version of SymPy (or at least the development version).

Python throws error when I call integrate( vector expression, t )

I wrote a Python program to calculate the Magnetic Field from a given time-varying Electric field. I used CoordSys3d from sympy.vector
I got it working this afternoon. It was giving correct answers. Then, I upgraded to the newest version of Anaconda (which updated the SymPy library), and now it throws an error when I call integrate().
Here is the error traceback:
>>> integrate( jimmy, t )
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "/opt/anaconda3/lib/python3.8/site-packages/sympy/integrals/integrals.py", line 1573, in integrate
new_args = [a.doit(**doit_flags) if isinstance(a, Integral) else a
File "/opt/anaconda3/lib/python3.8/site-packages/sympy/integrals/integrals.py", line 1573, in <listcomp>
new_args = [a.doit(**doit_flags) if isinstance(a, Integral) else a
File "/opt/anaconda3/lib/python3.8/site-packages/sympy/integrals/integrals.py", line 597, in doit
antideriv = self._eval_integral(
File "/opt/anaconda3/lib/python3.8/site-packages/sympy/integrals/integrals.py", line 941, in _eval_integral
result, i = risch_integrate(f, x, separate_integral=True,
File "/opt/anaconda3/lib/python3.8/site-packages/sympy/integrals/risch.py", line 1831, in risch_integrate
ans, i, b = integrate_hyperexponential(fa, fd, DE, conds=conds)
File "/opt/anaconda3/lib/python3.8/site-packages/sympy/integrals/risch.py", line 1564, in integrate_hyperexponential
qa, qd, b = integrate_hyperexponential_polynomial(pp, DE, z)
File "/opt/anaconda3/lib/python3.8/site-packages/sympy/integrals/risch.py", line 1516, in integrate_hyperexponential_polynomial
va, vd = rischDE(iDta, iDtd, Poly(aa, DE.t), Poly(ad, DE.t), DE)
File "/opt/anaconda3/lib/python3.8/site-packages/sympy/integrals/rde.py", line 774, in rischDE
_, (fa, fd) = weak_normalizer(fa, fd, DE)
File "/opt/anaconda3/lib/python3.8/site-packages/sympy/integrals/rde.py", line 126, in weak_normalizer
r = (a - Poly(z, DE.t)*derivation(d1, DE)).as_poly(DE.t).resultant(
File "/opt/anaconda3/lib/python3.8/site-packages/sympy/polys/polytools.py", line 65, in wrapper
return func(f, g)
File "/opt/anaconda3/lib/python3.8/site-packages/sympy/polys/polytools.py", line 4104, in __sub__
return f.sub(g)
File "/opt/anaconda3/lib/python3.8/site-packages/sympy/polys/polytools.py", line 1464, in sub
_, per, F, G = f._unify(g)
File "/opt/anaconda3/lib/python3.8/site-packages/sympy/polys/polytools.py", line 465, in _unify
dom, lev = f.rep.dom.unify(g.rep.dom, gens), len(gens) - 1
File "/opt/anaconda3/lib/python3.8/site-packages/sympy/polys/domains/domain.py", line 686, in unify
return K0.unify_with_symbols(K1, symbols)
File "/opt/anaconda3/lib/python3.8/site-packages/sympy/polys/domains/domain.py", line 666, in unify_with_symbols
return K0.unify(K1)
File "/opt/anaconda3/lib/python3.8/site-packages/sympy/polys/domains/domain.py", line 725, in unify
domain = domain.get_ring()
File "/opt/anaconda3/lib/python3.8/site-packages/sympy/polys/domains/complexfield.py", line 98, in get_ring
raise DomainError("there is no ring associated with %s" % self)
sympy.polys.polyerrors.DomainError: there is no ring associated with CC
Here is the code:
import numpy as np
import sympy as smp
import matplotlib.pyplot as plt
from sympy import *
from sympy import symbols
from sympy.vector import divergence
from sympy.vector import curl
from sympy import diff
from sympy import exp
from sympy import integrate
from sympy.vector import CoordSys3D
R = CoordSys3D('R')
# Variables
X, Y, Z = symbols('X Y Z')
X = R.x
Y = R.y
Z = R.z
# Basis Unit Vectors
i,j,k = symbols('i j k')
i = R.i
j = R.j
k = R.k
# Symbols
x,t = symbols('x t')
Ex = smp.Function('Ex')(x,t)
Ey = smp.Function('Ey')(x,t)
Ez = smp.Function('Ez')(x,t)
wavenumber = symbols('k')
E_0 = symbols('E_0') # Amplitude of E field
w = symbols('w' , real=True, positive=True)
# Define Ey(x,t)
Ey = E_0 * smp.exp( 1j * (wavenumber*X - w*t ))
# The Electric Field
E = Ex*i + Ey*j + Ez*k
init_printing(use_unicode=True, wrap_line=False)
# curl E = - dB/dt
# integrate( (curl E) , t ) = - B
jimmy = curl( E )
B = -integrate( jimmy, t )
pprint( B )
B = -integrate( jimmy, t ).doit()
pprint( B )

Usually we ask users to include the full traceback when asking about errors.
In a sympy context I expect to see "won't integrate" description when result is an expression containing the integral sign. Similarly for "can't solve" results, where the result is the original expression, or a barely simplified one.
Your case is an actual error.
In [6]: jimmy = curl( E, R )
In [7]: jimmy
Out[7]:
1.0⋅ⅈ⋅(Rₓ⋅k - t⋅w)
1.0⋅ⅈ⋅E₀⋅k⋅ℯ r_z
In [8]: smp.integrate( jimmy, t )
/usr/local/lib/python3.8/dist-packages/sympy/core/sympify.py:456: SymPyDeprecationWarning:
String fallback in sympify has been deprecated since SymPy 1.6. Use
sympify(str(obj)) or sympy.core.sympify.converter or obj._sympy_
instead. See https://github.com/sympy/sympy/issues/18066 for more
info.
SymPyDeprecationWarning(
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
ValueError: Error from parse_expr with transformed code: "Float ('1.0' )*I *Symbol ('E_0' )*Symbol ('k' )*exp (Float ('1.0' )*I *(Symbol ('R_x' )*Symbol ('k' )-Symbol ('t' )*Symbol ('w' )))*Symbol ('R' ).z "
The above exception was the direct cause of the following exception:
AttributeError Traceback (most recent call last)
<ipython-input-8-8d40c4ce949f> in <module>
----> 1 smp.integrate( jimmy, t )
/usr/local/lib/python3.8/dist-packages/sympy/integrals/integrals.py in integrate(meijerg, conds, risch, heurisch, manual, *args, **kwargs)
1566 'manual': manual
1567 }
-> 1568 integral = Integral(*args, **kwargs)
1569
1570 if isinstance(integral, Integral):
/usr/local/lib/python3.8/dist-packages/sympy/integrals/integrals.py in __new__(cls, function, *symbols, **assumptions)
89 useinstead="the as_expr or integrate methods of Poly").warn()
90
---> 91 obj = AddWithLimits.__new__(cls, function, *symbols, **assumptions)
92 return obj
93
/usr/local/lib/python3.8/dist-packages/sympy/concrete/expr_with_limits.py in __new__(cls, function, *symbols, **assumptions)
496
497 def __new__(cls, function, *symbols, **assumptions):
--> 498 pre = _common_new(cls, function, *symbols, **assumptions)
499 if type(pre) is tuple:
500 function, limits, orientation = pre
/usr/local/lib/python3.8/dist-packages/sympy/concrete/expr_with_limits.py in _common_new(cls, function, *symbols, **assumptions)
23 (function, limits, orientation). This code is common to
24 both ExprWithLimits and AddWithLimits."""
---> 25 function = sympify(function)
26
27 if isinstance(function, Equality):
/usr/local/lib/python3.8/dist-packages/sympy/core/sympify.py in sympify(a, locals, convert_xor, strict, rational, evaluate)
477 try:
478 a = a.replace('\n', '')
--> 479 expr = parse_expr(a, local_dict=locals, transformations=transformations, evaluate=evaluate)
480 except (TokenError, SyntaxError) as exc:
481 raise SympifyError('could not parse %r' % a, exc)
....
AttributeError: 'Symbol' object has no attribute 'z'
So while:
In [9]: R.z
Out[9]: r_z
it has replaced that with:
In [10]: parse_expr(Symbol ('R' ).z)
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
<ipython-input-10-60a85cf12db4> in <module>
----> 1 parse_expr(Symbol ('R' ).z)
AttributeError: 'Symbol' object has no attribute 'z'
I don't know enough sympy to understand the issue, but it is more informative than "won't integrate".

I discovered the problem was being caused by me using "1j" for "i". I changed it to "I" and now it works.
Causes error:
Ey = E_0 * smp.exp( 1j * (wavenumber*X - w*t ))
Works fine:
Ey = E_0 * smp.exp( I * (wavenumber*X - w*t ))

Problem with sending argument using dblquad integrator

from scipy import integrate
def g(y,x,a):
return x*y**2 + a
a= 13
integrate.dblquad(g, 0, 2, lambda x: 0, lambda x: x, args=(a))
TypeError Traceback (most recent call last)
in
5 a= 13
6
----> 7 integrate.dblquad(g, 0, 2, lambda x: 0, lambda x: x, args=(a))
~\anaconda3\lib\site-packages\scipy\integrate\quadpack.py in dblquad(func, a, b, gfun, hfun, args, epsabs, epsrel)
599 hfun(args[0]) if callable(hfun) else hfun]
600
--> 601 return nquad(func, [temp_ranges, [a, b]], args=args,
602 opts={"epsabs": epsabs, "epsrel": epsrel})
603
~\anaconda3\lib\site-packages\scipy\integrate\quadpack.py in nquad(func, ranges, args, opts, full_output)
824 else:
825 opts = [opt if callable(opt) else _OptFunc(opt) for opt in opts]
--> 826 return _NQuad(func, ranges, opts, full_output).integrate(*args)
827
828
TypeError: integrate() argument after * must be an iterable, not int

You could just define a inside (or even outside) of g:
from scipy import integrate
a = 13
def g(y, x):
return x * y ** 2 + a
integrate.dblquad(g, 0, 2, lambda x: 0, lambda x: x)
(I was never a big of the args argument.)

PyMC3 & Theano - Theano code that works stop working after pymc3 import

Some simple theano code that works perfectly, stop working when I import pymc3
Here some snipets in order to reproduce the error:
#Initial Theano Code (this works)
import theano.tensor as tsr
x = tsr.dscalar('x')
y = tsr.dscalar('y')
z = x + y
#Snippet 1
import pymc3 as pm
import theano.tensor as tsr
x = tsr.dscalar('x')
y = tsr.dscalar('y')
z = x + y
#Snippet 2
import theano.tensor as tsr
import pymc3 as pm
x = tsr.dscalar('x')
y = tsr.dscalar('y')
z = x + y
#Snippet 3
import pymc3 as pm
x = pm.theano.tensor.dscalar('x')
y = pm.theano.tensor.dscalar('y')
z = x + y
And I get the following error for each of the previous snippets:
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
/Users/tom/anaconda/lib/python3.4/site-packages/theano/gof/op.py in __call__(self, *inputs, **kwargs)
516 try:
--> 517 storage_map[ins] = [self._get_test_value(ins)]
518 compute_map[ins] = [True]
/Users/tom/anaconda/lib/python3.4/site-packages/theano/gof/op.py in _get_test_value(cls, v)
478
--> 479 raise AttributeError('%s has no test value' % v)
480
AttributeError: x has no test value
During handling of the above exception, another exception occurred:
ValueError Traceback (most recent call last)
<ipython-input-2-ef8582b040f8> in <module>()
3 x = pm.theano.tensor.dscalar('x')
4 y = pm.theano.tensor.dscalar('y')
----> 5 z = x + y
/Users/tom/anaconda/lib/python3.4/site-packages/theano/tensor/var.py in __add__(self, other)
126 def __add__(self, other):
127 try:
--> 128 return theano.tensor.basic.add(self, other)
129 # We should catch the minimum number of exception here.
130 # Otherwise this will convert error when Theano flags
/Users/tom/anaconda/lib/python3.4/site-packages/theano/gof/op.py in __call__(self, *inputs, **kwargs)
523 run_perform = False
524 elif config.compute_test_value == 'raise':
--> 525 raise ValueError('Cannot compute test value: input %i (%s) of Op %s missing default value' % (i, ins, node))
526 elif config.compute_test_value == 'ignore':
527 # silently skip test
ValueError: Cannot compute test value: input 0 (x) of Op Elemwise{add,no_inplace}(x, y) missing default value
Any Ideas ?
Thanks in advance

I think this is related to pymc3 setting theano.config.compute_test_value = 'raise': https://github.com/pymc-devs/pymc3/blob/master/pymc3/model.py#L395
You can explicitly set theano.config.compute_test_value back to 'ignore' to get rid of the error.

Solution proposed here lasts a bit longer than setting the flag. In your shell type:
theano-cache purge