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1. ---------------------------------------------------------------------------
2. KeyboardInterrupt Traceback (most recent call last)
3. <ipython-input-114-fefb5a1b3c31> in <module>
4. ----> 1 integrand = sp.Integral(integrand,(x,-oo,oo)).doit()
5. 2 display(integrand)
6.
7. ~\.conda\envs\py37\lib\site-packages\sympy\integrals\integrals.py in doit(self, **hints)
8. 591 antideriv = None
9. 592 else:
10. --> 593 antideriv = self._eval_integral(
11. 594 function, xab[0], **eval_kwargs)
12. 595 if antideriv is None and meijerg is True:
13.
14. ~\.conda\envs\py37\lib\site-packages\sympy\integrals\integrals.py in _eval_integral(self, f, x, meijerg, risch, manual, heurisch, conds)
15. 1053 try:
16. 1054 if conds == 'piecewise':
17. -> 1055 h = heurisch_wrapper(g, x, hints=[])
18. 1056 else:
19. 1057 h = heurisch_(g, x, hints=[])
20.
21. ~\.conda\envs\py37\lib\site-packages\sympy\integrals\heurisch.py in heurisch_wrapper(f, x, rewrite, hints, mappings, retries, degree_offset, unnecessary_permutations, _try_heurisch)
22. 134 return f*x
23. 135
24. --> 136 res = heurisch(f, x, rewrite, hints, mappings, retries, degree_offset,
25. 137 unnecessary_permutations, _try_heurisch)
26. 138 if not isinstance(res, Basic):
27.
28. ~\.conda\envs\py37\lib\site-packages\sympy\integrals\heurisch.py in heurisch(f, x, rewrite, hints, mappings, retries, degree_offset, unnecessary_permutations, _try_heurisch)
29. 724 solution = _integrate()
30. 725 else:
31. --> 726 solution = _integrate()
32. 727
33. 728 if solution is not None:
34.
35. ~\.conda\envs\py37\lib\site-packages\sympy\integrals\heurisch.py in _integrate(field)
36. 710 except ValueError:
37. 711 raise PolynomialError
38. --> 712 solution = solve_lin_sys(numer.coeffs(), coeff_ring, _raw=False)
39. 713
40. 714 if solution is None:
41.
42. ~\.conda\envs\py37\lib\site-packages\sympy\polys\solvers.py in solve_lin_sys(eqs, ring, _raw)
43. 225 eqs_coeffs.append(eq_coeffs)
44. 226
45. --> 227 result = _solve_lin_sys(eqs_coeffs, eqs_rhs, ring)
46. 228
47. 229 if result is not None and as_expr:
48.
49. ~\.conda\envs\py37\lib\site-packages\sympy\polys\solvers.py in _solve_lin_sys(eqs_coeffs, eqs_rhs, ring)
50. 303 sol = {}
51. 304 for subsystem in subsystems:
52. --> 305 subsol = _solve_lin_sys_component(subsystem[0], subsystem[1], ring)
53. 306 if subsol is None:
54. 307 return None
55.
56. ~\.conda\envs\py37\lib\site-packages\sympy\polys\solvers.py in _solve_lin_sys_component(eqs_coeffs, eqs_rhs, ring)
57. 351
58. 352 # solve by row-reduction
59. --> 353 echelon, pivots = matrix.rref()
60. 354
61. 355 # construct the returnable form of the solutions
62.
63. ~\.conda\envs\py37\lib\site-packages\sympy\polys\domainmatrix.py in rref(self)
64. 607 if not self.domain.is_Field:
65. 608 raise ValueError('Not a field')
66. --> 609 rref_ddm, pivots = self.rep.rref()
67. 610 return self.from_ddm(rref_ddm), tuple(pivots)
68. 611
69.
70. ~\.conda\envs\py37\lib\site-packages\sympy\polys\domainmatrix.py in rref(a)
71. 139 """Reduced-row echelon form of a and list of pivots"""
72. 140 b = a.copy()
73. --> 141 pivots = ddm_irref(b)
74. 142 return b, pivots
75. 143
76.
77. ~\.conda\envs\py37\lib\site-packages\sympy\polys\domainmatrix.py in ddm_irref(a)
78. 264 ak[j] -= akj # ak[j] = zero
79. 265 for l in range(j+1, n):
80. --> 266 ak[l] -= akj * ai[l]
81. 267
82. 268 # next row
83.
84. ~\.conda\envs\py37\lib\site-packages\sympy\polys\fields.py in __sub__(f, g)
85. 440 return f.new(f.numer - g.numer, f.denom)
86. 441 else:
87. --> 442 return f.new(f.numer*g.denom - f.denom*g.numer, f.denom*g.denom)
88. 443 elif isinstance(g, field.ring.dtype):
89. 444 return f.new(f.numer - f.denom*g, f.denom)
90.
91. ~\.conda\envs\py37\lib\site-packages\sympy\polys\fields.py in new(f, numer, denom)
92. 290 return f.__class__(numer, denom)
93. 291 def new(f, numer, denom):
94. --> 292 return f.raw_new(*numer.cancel(denom))
95. 293
96. 294 def to_poly(f):
97.
98. ~\.conda\envs\py37\lib\site-packages\sympy\polys\rings.py in cancel(self, g)
99. 2215
100. 2216 if not (domain.is_Field and domain.has_assoc_Ring):
101. -> 2217 _, p, q = f.cofactors(g)
102. 2218
103. 2219 if q.is_negative:
104.
105. ~\.conda\envs\py37\lib\site-packages\sympy\polys\rings.py in cofactors(f, g)
106. 2131
107. 2132 J, (f, g) = f.deflate(g)
108. -> 2133 h, cff, cfg = f._gcd(g)
109. 2134
110. 2135 return (h.inflate(J), cff.inflate(J), cfg.inflate(J))
111.
112. ~\.conda\envs\py37\lib\site-packages\sympy\polys\rings.py in _gcd(f, g)
113. 2164 return f._gcd_QQ(g)
114. 2165 elif ring.domain.is_ZZ:
115. -> 2166 return f._gcd_ZZ(g)
116. 2167 else: # TODO: don't use dense representation (port PRS algorithms)
117. 2168 return ring.dmp_inner_gcd(f, g)
118.
119. ~\.conda\envs\py37\lib\site-packages\sympy\polys\rings.py in _gcd_ZZ(f, g)
120. 2169
121. 2170 def _gcd_ZZ(f, g):
122. -> 2171 return heugcd(f, g)
123. 2172
124. 2173 def _gcd_QQ(self, g):
125.
126. ~\.conda\envs\py37\lib\site-packages\sympy\polys\heuristicgcd.py in heugcd(f, g)
127. 78 h, cff, cfg = domain.cofactors(ff, gg)
128. 79 else:
129. ---> 80 h, cff, cfg = heugcd(ff, gg)
130. 81
131. 82 h = _gcd_interpolate(h, x, ring)
132.
133. ~\.conda\envs\py37\lib\site-packages\sympy\polys\heuristicgcd.py in heugcd(f, g)
134. 78 h, cff, cfg = domain.cofactors(ff, gg)
135. 79 else:
136. ---> 80 h, cff, cfg = heugcd(ff, gg)
137. 81
138. 82 h = _gcd_interpolate(h, x, ring)
139.
140. ~\.conda\envs\py37\lib\site-packages\sympy\polys\heuristicgcd.py in heugcd(f, g)
141. 78 h, cff, cfg = domain.cofactors(ff, gg)
142. 79 else:
143. ---> 80 h, cff, cfg = heugcd(ff, gg)
144. 81
145. 82 h = _gcd_interpolate(h, x, ring)
146.
147. ~\.conda\envs\py37\lib\site-packages\sympy\polys\heuristicgcd.py in heugcd(f, g)
148. 78 h, cff, cfg = domain.cofactors(ff, gg)
149. 79 else:
150. ---> 80 h, cff, cfg = heugcd(ff, gg)
151. 81
152. 82 h = _gcd_interpolate(h, x, ring)
153.
154. ~\.conda\envs\py37\lib\site-packages\sympy\polys\heuristicgcd.py in heugcd(f, g)
155. 59 domain = ring.domain
156. 60
157. ---> 61 gcd, f, g = f.extract_ground(g)
158. 62
159. 63 f_norm = f.max_norm()
160.
161. ~\.conda\envs\py37\lib\site-packages\sympy\polys\rings.py in extract_ground(self, g)
162. 2034 gcd = f.ring.domain.gcd(fc, gc)
163. 2035
164. -> 2036 f = f.quo_ground(gcd)
165. 2037 g = g.quo_ground(gcd)
166. 2038
167.
168. ~\.conda\envs\py37\lib\site-packages\sympy\polys\rings.py in quo_ground(f, x)
169. 1988 terms = [ (monom, quo(coeff, x)) for monom, coeff in f.iterterms() ]
170. 1989 else:
171. -> 1990 terms = [ (monom, coeff // x) for monom, coeff in f.iterterms() if not (coeff % x) ]
172. 1991
173. 1992 return f.new(terms)
174.
175. ~\.conda\envs\py37\lib\site-packages\sympy\polys\rings.py in <listcomp>(.0)
176. 1988 terms = [ (monom, quo(coeff, x)) for monom, coeff in f.iterterms() ]
177. 1989 else:
178. -> 1990 terms = [ (monom, coeff // x) for monom, coeff in f.iterterms() if not (coeff % x) ]
179. 1991
180. 1992 return f.new(terms)
181.
182. KeyboardInterrupt: