Hi everyone,
I am Abhishek Verma and I will be applying for GSoC this year.
I'm having trouble computing a definite integral, as implemented below
integrate( ) Function in sympy to Integrate the Expr=X^log(X^log(X)) the
result is-
>>> integrate(x**log(x**log(x)),x)
⌠
⎮ 3
⎮ log (x)
⎮ ℯ dx
⌡
But For the Expr=X^log(X^log(X^log(X))) , sympy is unable to find the
result but as we know from Documentation If integrate is unable to compute
an integral, it returns an unevaluated Integral object.
But is shows like this.
>>> integrate(x**log(x**log(x**log(x))),x)
Traceback (most recent call last):
File "/usr/local/lib/python3.4/dist-packages/sympy/polys/rings.py", line
365, in from_expr
poly = self._rebuild_expr(expr, mapping)
File "/usr/local/lib/python3.4/dist-packages/sympy/polys/rings.py", line
359, in _rebuild_expr
return _rebuild(sympify(expr))
File "/usr/local/lib/python3.4/dist-packages/sympy/polys/rings.py", line
351, in _rebuild
return reduce(add, list(map(_rebuild, expr.args)))
File "/usr/local/lib/python3.4/dist-packages/sympy/polys/rings.py", line
353, in _rebuild
return reduce(mul, list(map(_rebuild, expr.args)))
File "/usr/local/lib/python3.4/dist-packages/sympy/polys/rings.py", line
351, in _rebuild
return reduce(add, list(map(_rebuild, expr.args)))
File "/usr/local/lib/python3.4/dist-packages/sympy/polys/rings.py", line
353, in _rebuild
return reduce(mul, list(map(_rebuild, expr.args)))
File "/usr/local/lib/python3.4/dist-packages/sympy/polys/rings.py", line
351, in _rebuild
return reduce(add, list(map(_rebuild, expr.args)))
File "/usr/local/lib/python3.4/dist-packages/sympy/polys/rings.py", line
353, in _rebuild
return reduce(mul, list(map(_rebuild, expr.args)))
File "/usr/local/lib/python3.4/dist-packages/sympy/polys/rings.py", line
357, in _rebuild
return domain.convert(expr)
File
"/usr/local/lib/python3.4/dist-packages/sympy/polys/domains/domain.py",
line 146, in convert
raise CoercionFailed("can't convert %s of type %s to %s" % (element,
type(element), self))
sympy.polys.polyerrors.CoercionFailed: can't convert _x0**_x1 of type
<class 'sympy.core.power.Pow'> to
QQ[_A0,_A1,_A2,_A3,_A4,_A5,_A6,_A7,_A8,_A9,_A10,_A11,_A12,_A13,_A14,_A15,_A16,_A17,_A18,_A19,_A20,_A21,_A22,_A23,_A24,_A25,_A26,_A27,_A28,_A29,_A30,_A31,_A32,_A33,_A34,_A35,_A36,_A37,_A38,_A39,_A40,_A41,_A42,_A43,_A44,_A45,_A46,_A47,_A48,_A49,_A50,_A51,_A52,_A53,_A54,_A55,_A56,_A57,_A58,_A59,_A60,_A61,_A62,_A63,_A64,_A65,_A66,_A67,_A68,_A69,_A70,_A71,_A72,_A73,_A74,_A75,_A76,_A77,_A78,_A79,_A80,_A81,_A82,_A83,_A84,_A85,_A86,_A87,_A88,_A89,_A90,_A91,_A92,_A93,_A94,_A95,_A96,_A97,_A98,_A99,_A100,_A101,_A102,_A103,_A104,_A105,_A106,_A107,_A108,_A109,_A110,_A111,_A112,_A113,_A114,_A115,_A116,_A117,_A118,_A119,_B0]
During handling of the above exception, another exception occurred:
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File
"/usr/local/lib/python3.4/dist-packages/sympy/utilities/decorator.py", line
35, in threaded_func
return func(expr, *args, **kwargs)
File
"/usr/local/lib/python3.4/dist-packages/sympy/integrals/integrals.py", line
1232, in integrate
risch=risch, manual=manual)
File
"/usr/local/lib/python3.4/dist-packages/sympy/integrals/integrals.py", line
487, in doit
conds=conds)
File
"/usr/local/lib/python3.4/dist-packages/sympy/integrals/integrals.py", line
862, in _eval_integral
h = heurisch_wrapper(g, x, hints=[])
File
"/usr/local/lib/python3.4/dist-packages/sympy/integrals/heurisch.py", line
128, in heurisch_wrapper
unnecessary_permutations)
File
"/usr/local/lib/python3.4/dist-packages/sympy/integrals/heurisch.py", line
566, in heurisch
solution = _integrate('Q')
File
"/usr/local/lib/python3.4/dist-packages/sympy/integrals/heurisch.py", line
555, in _integrate
numer = ring.from_expr(raw_numer)
File "/usr/local/lib/python3.4/dist-packages/sympy/polys/rings.py", line
367, in from_expr
raise ValueError("expected an expression convertible to a polynomial in
%s, got %s" % (self, expr))
ValueError: expected an expression convertible to a polynomial in
Polynomial ring in _x0, _x1, _x2, _x3, _x4, _x5, _x6 over
QQ[_A0,_A1,_A2,_A3,_A4,_A5,_A6,_A7,_A8,_A9,_A10,_A11,_A12,_A13,_A14,_A15,_A16,_A17,_A18,_A19,_A20,_A21,_A22,_A23,_A24,_A25,_A26,_A27,_A28,_A29,_A30,_A31,_A32,_A33,_A34,_A35,_A36,_A37,_A38,_A39,_A40,_A41,_A42,_A43,_A44,_A45,_A46,_A47,_A48,_A49,_A50,_A51,_A52,_A53,_A54,_A55,_A56,_A57,_A58,_A59,_A60,_A61,_A62,_A63,_A64,_A65,_A66,_A67,_A68,_A69,_A70,_A71,_A72,_A73,_A74,_A75,_A76,_A77,_A78,_A79,_A80,_A81,_A82,_A83,_A84,_A85,_A86,_A87,_A88,_A89,_A90,_A91,_A92,_A93,_A94,_A95,_A96,_A97,_A98,_A99,_A100,_A101,_A102,_A103,_A104,_A105,_A106,_A107,_A108,_A109,_A110,_A111,_A112,_A113,_A114,_A115,_A116,_A117,_A118,_A119,_B0]
with lex order, got _x0**5*_x5 - _x0**3*(2*_x0**_x2*_x2*(2*_A103*_x2*_x6 +
_A106*_x4*_x5 + _x4**2*_A107 + _A108*_x1*_x2 + _A110*_x4 + _A116*_x0*_x1 +
2*_A12*_x1*_x6 + 2*_A19*_x4*_x6 + _A2 + _A20*_x2*_x3 + _A21*_x1*_x3 +
_A23*_x3*_x4 + _A26*_x0*_x3 + _A3*_x2 + _x5**2*_A32 + _A35*_x0*_x2 +
_A39*_x1 + _x2**2*_A41 + _A50*_x3 + 3*_x6**2*_A52 + 2*_A58*_x6 +
_A6*_x0*_x4 + _A62*_x0*_x5 + _x1**2*_A69 + _A72*_x2*_x5 + _A74*_x2*_x4 +
2*_A77*_x0*_x6 + _x0**2*_A78 + _A8*_x5 + _x3**2*_A81 + 2*_A83*_x3*_x6 +
_A89*_x0 + 2*_A90*_x5*_x6 + _A95*_x1*_x4 + _A96*_x1*_x5 + _A99*_x3*_x5) +
_A101*_x0*_x1 + _A102*_x0*_x4 + _x6**2*_A103 + _A105*_x0*_x3 +
_A108*_x1*_x6 + _A109*_x0*_x5 + _A11*_x3*_x5 + _A14*_x3 + 2*_A15*_x2*_x3 +
_A18*_x4 + _A20*_x3*_x6 + 2*_A24*_x1*_x2 + 2*_A27*_x2*_x5 + _A3*_x6 +
_A31*_x1*_x4 + _x5**2*_A33 + _A35*_x0*_x6 + 2*_A36*_x2 + 3*_x2**2*_A38 +
_A40*_x3*_x4 + 2*_A41*_x2*_x6 + _A42*_x1*_x5 + _A61*_x1 + _A70*_x0 +
_x0**2*_A71 + _A72*_x5*_x6 + _A74*_x4*_x6 + _A75*_x5 + 2*_A76*_x0*_x2 +
2*_A80*_x2*_x4 + _x1**2*_A82 + _A86*_x4*_x5 + _A87*_x1*_x3 + _x4**2*_A9 +
_x3**2*_A93 + _A94 + 2*_x2*(2*_A1*_x1*_x5 + _A10 + _A101*_x0*_x2 +
_A108*_x2*_x6 + _x5**2*_A112 + _A113*_x3*_x4 + _A116*_x0*_x6 +
2*_A117*_x0*_x1 + _x6**2*_A12 + 2*_A13*_x1 + _A21*_x3*_x6 + _x4**2*_A22 +
_x2**2*_A24 + _A31*_x2*_x4 + _A34*_x0*_x5 + _A37*_x3 + _A39*_x6 +
_A4*_x3*_x5 + _A42*_x2*_x5 + _A45*_x5 + _A47*_x0*_x4 + 3*_x1**2*_A5 +
_A51*_x0*_x3 + _x0**2*_A53 + _A56*_x0 + 2*_A59*_x1*_x4 + _A60*_x4*_x5 +
_A61*_x2 + _x3**2*_A64 + 2*_A66*_x1*_x3 + 2*_A69*_x1*_x6 + 2*_A82*_x1*_x2 +
_A87*_x2*_x3 + _A95*_x4*_x6 + _A96*_x5*_x6 + _A98*_x4) + (_x1 +
2*_x2**2)*(_A100*_x0*_x3 + _A102*_x0*_x2 + _A106*_x5*_x6 + 2*_A107*_x4*_x6
+ _A110*_x6 + _A113*_x1*_x3 + _x5**2*_A115 + _A16*_x0*_x5 + 2*_A17*_x3*_x4
+ _A18*_x2 + _x6**2*_A19 + 2*_A22*_x1*_x4 + _A23*_x3*_x6 + _A31*_x1*_x2 +
_A40*_x2*_x3 + 2*_A46*_x0*_x4 + _A47*_x0*_x1 + _x0**2*_A48 + _x3**2*_A55 +
_x1**2*_A59 + _A6*_x0*_x6 + _A60*_x1*_x5 + _A63 + _A65*_x0 + _A7*_x3*_x5 +
_A74*_x2*_x6 + 2*_A79*_x4*_x5 + _x2**2*_A80 + _A84*_x3 + _A85*_x5 +
_A86*_x2*_x5 + 2*_A88*_x4 + 2*_A9*_x2*_x4 + 3*_x4**2*_A91 + _A95*_x1*_x6 +
_A98*_x1) + (_x0**_x1*_x1 + 2*_x0**_x1*_x2**2)*(_A100*_x0*_x4 +
2*_A104*_x3*_x5 + _A105*_x0*_x2 + _A11*_x2*_x5 + _A113*_x1*_x4 +
2*_A118*_x0*_x3 + _A119*_x0*_x5 + _A14*_x2 + _x2**2*_A15 + _x4**2*_A17 +
_A20*_x2*_x6 + _A21*_x1*_x6 + _A23*_x4*_x6 + _A26*_x0*_x6 + _A29 + _A30*_x5
+ _A37*_x1 + _A4*_x1*_x5 + _A40*_x2*_x4 + _x0**2*_A43 + _A50*_x6 +
_A51*_x0*_x1 + _x5**2*_A54 + 2*_A55*_x3*_x4 + _A57*_x0 + 2*_A64*_x1*_x3 +
_x1**2*_A66 + _A7*_x4*_x5 + 2*_A81*_x3*_x6 + _x6**2*_A83 + _A84*_x4 +
_A87*_x1*_x2 + 2*_A92*_x3 + 2*_A93*_x2*_x3 + 3*_x3**2*_A97 + _A99*_x5*_x6)
+ (_x1*_x2*_x5 + 2*_x2**3*_x5 + _x4*_x5)*(_x1**2*_A1 + _x3**2*_A104 +
_A106*_x4*_x6 + _A109*_x0*_x2 + _A11*_x2*_x3 + _A111*_x0 + 2*_A112*_x1*_x5
+ _x0**2*_A114 + 2*_A115*_x4*_x5 + _A119*_x0*_x3 + _A16*_x0*_x4 +
_x2**2*_A27 + _A30*_x3 + 2*_A32*_x5*_x6 + 2*_A33*_x2*_x5 + _A34*_x0*_x1 +
_A4*_x1*_x3 + _A42*_x1*_x2 + 3*_x5**2*_A44 + _A45*_x1 + 2*_A49*_x5 +
2*_A54*_x3*_x5 + _A60*_x1*_x4 + _A62*_x0*_x6 + 2*_A68*_x0*_x5 + _A7*_x3*_x4
+ _A72*_x2*_x6 + _A73 + _A75*_x2 + _x4**2*_A79 + _A8*_x6 + _A85*_x4 +
_A86*_x2*_x4 + _x6**2*_A90 + _A96*_x1*_x6 + _A99*_x3*_x6)) -
_x0**2*(_x0**2*(_A100*_x3*_x4 + _A101*_x1*_x2 + _A102*_x2*_x4 +
_A105*_x2*_x3 + _A109*_x2*_x5 + _A111*_x5 + 2*_A114*_x0*_x5 + _A116*_x1*_x6
+ _x1**2*_A117 + _x3**2*_A118 + _A119*_x3*_x5 + _A16*_x4*_x5 +
3*_x0**2*_A25 + _A26*_x3*_x6 + 2*_A28*_x0 + _A34*_x1*_x5 + _A35*_x2*_x6 +
2*_A43*_x0*_x3 + _x4**2*_A46 + _A47*_x1*_x4 + 2*_A48*_x0*_x4 + _A51*_x1*_x3
+ 2*_A53*_x0*_x1 + _A56*_x1 + _A57*_x3 + _A6*_x4*_x6 + _A62*_x5*_x6 +
_A65*_x4 + _A67 + _x5**2*_A68 + _A70*_x2 + 2*_A71*_x0*_x2 + _x2**2*_A76 +
_x6**2*_A77 + 2*_A78*_x0*_x6 + _A89*_x6 + _B0) + _x0*(-_A0 - _x1**2*_A1*_x5
- _A10*_x1 - _A100*_x0*_x3*_x4 - _A101*_x0*_x1*_x2 - _A102*_x0*_x2*_x4 -
_x6**2*_A103*_x2 - _x3**2*_A104*_x5 - _A105*_x0*_x2*_x3 - _A106*_x4*_x5*_x6
- _x4**2*_A107*_x6 - _A108*_x1*_x2*_x6 - _A109*_x0*_x2*_x5 -
_A11*_x2*_x3*_x5 - _A110*_x4*_x6 - _A111*_x0*_x5 - _x5**2*_A112*_x1 -
_A113*_x1*_x3*_x4 - _x0**2*_A114*_x5 - _x5**2*_A115*_x4 - _A116*_x0*_x1*_x6
- _x1**2*_A117*_x0 - _x3**2*_A118*_x0 - _A119*_x0*_x3*_x5 - _x6**2*_A12*_x1
- _x1**2*_A13 - _A14*_x2*_x3 - _x2**2*_A15*_x3 - _A16*_x0*_x4*_x5 -
_x4**2*_A17*_x3 - _A18*_x2*_x4 - _x6**2*_A19*_x4 - _A2*_x6 -
_A20*_x2*_x3*_x6 - _A21*_x1*_x3*_x6 - _x4**2*_A22*_x1 - _A23*_x3*_x4*_x6 -
_x2**2*_A24*_x1 - _x0**3*_A25 - _A26*_x0*_x3*_x6 - _x2**2*_A27*_x5 -
_x0**2*_A28 - _A29*_x3 - _A3*_x2*_x6 - _A30*_x3*_x5 - _A31*_x1*_x2*_x4 -
_x5**2*_A32*_x6 - _x5**2*_A33*_x2 - _A34*_x0*_x1*_x5 - _A35*_x0*_x2*_x6 -
_x2**2*_A36 - _A37*_x1*_x3 - _x2**3*_A38 - _A39*_x1*_x6 - _A4*_x1*_x3*_x5 -
_A40*_x2*_x3*_x4 - _x2**2*_A41*_x6 - _A42*_x1*_x2*_x5 - _x0**2*_A43*_x3 -
_x5**3*_A44 - _A45*_x1*_x5 - _x4**2*_A46*_x0 - _A47*_x0*_x1*_x4 -
_x0**2*_A48*_x4 - _x5**2*_A49 - _x1**3*_A5 - _A50*_x3*_x6 -
_A51*_x0*_x1*_x3 - _x6**3*_A52 - _x0**2*_A53*_x1 - _x5**2*_A54*_x3 -
_x3**2*_A55*_x4 - _A56*_x0*_x1 - _A57*_x0*_x3 - _x6**2*_A58 -
_x1**2*_A59*_x4 - _A6*_x0*_x4*_x6 - _A60*_x1*_x4*_x5 - _A61*_x1*_x2 -
_A62*_x0*_x5*_x6 - _A63*_x4 - _x3**2*_A64*_x1 - _A65*_x0*_x4 -
_x1**2*_A66*_x3 - _A67*_x0 - _x5**2*_A68*_x0 - _x1**2*_A69*_x6 -
_A7*_x3*_x4*_x5 - _A70*_x0*_x2 - _x0**2*_A71*_x2 - _A72*_x2*_x5*_x6 -
_A73*_x5 - _A74*_x2*_x4*_x6 - _A75*_x2*_x5 - _x2**2*_A76*_x0 -
_x6**2*_A77*_x0 - _x0**2*_A78*_x6 - _x4**2*_A79*_x5 - _A8*_x5*_x6 -
_x2**2*_A80*_x4 - _x3**2*_A81*_x6 - _x1**2*_A82*_x2 - _x6**2*_A83*_x3 -
_A84*_x3*_x4 - _A85*_x4*_x5 - _A86*_x2*_x4*_x5 - _A87*_x1*_x2*_x3 -
_x4**2*_A88 - _A89*_x0*_x6 - _x4**2*_A9*_x2 - _x6**2*_A90*_x5 - _x4**3*_A91
- _x3**2*_A92 - _x3**2*_A93*_x2 - _A94*_x2 - _A95*_x1*_x4*_x6 -
_A96*_x1*_x5*_x6 - _x3**3*_A97 - _A98*_x1*_x4 - _A99*_x3*_x5*_x6))
what's happening ,unable to figure out, can anyone tell me????
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