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1.00000000000001
[0.503313896311354, -0.483558115311354]
0.453877992191000
0.723098492199436
[-0.0780117001638897, -0.493362685936110]
Traceback (most recent call last): norm=integral_numerical(phi1s(p)*phi2s(p)*dv(p),0,1.5,max-points=500)[0]
File "", line 1, in <module>
File "/tmp/tmpVI6ZIf/___code___.py", line 8
norm=integral_numerical(phi1s(p)*phi2s(p)*dv(p),_sage_const_0 ,_sage_const_1p5 ,max-points=_sage_const_500 )[_sage_const_0 ]
SyntaxError: keyword can't be an expression
0.864664716763387
__main__:1: UserWarning: Using generic algorithm for an inexact ring, which will probably give incorrect results due to numerical precision issues.
[-0.0645188106435643, -0.497523440956436]
32*(4*p^3*z - p*z^3)*sqrt(pi)*sqrt(2)*z^(3/2)/((64*p^6 + 48*p^4*z^2 + 12*p^2*z^4 + z^6)*p)
32*(4*p^3*z - p*z^3)*sqrt(pi)*sqrt(2)*z^(3/2)/((64*p^6 + 48*p^4*z^2 + 12*p^2*z^4 + z^6)*p)
1
arctan(sqrt(a)*x)/sqrt(a)
-1/2*pi
[9.02842160392669e7, 0.568518377317205]
-18778.2965035507
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "_sage_input_5.py", line 9, in <module>
exec compile(ur'open("___code___.py","w").write("# -*- coding: utf-8 -*-\n" + _support_.preparse_worksheet_cell(base64.b64decode("QT1tYXRyaXgoW1sgLTAuODUzNDhFKzAzICwtMC4xNTA2MEUrMDIgIF0sWyAtMC4xNTA2MEUrMDIgLCAgLTAuMjMxMjlFKzAzIF1dKQpBLmVpZ2VudmVjdG9ycygp"),globals())+"\n"); execfile(os.path.abspath("___code___.py"))' + '\n', '', 'single')
File "", line 1, in <module>
File "/tmp/tmpsooe2n/___code___.py", line 4, in <module>
exec compile(ur'A.eigenvectors()' + '\n', '', 'single')
File "", line 1, in <module>
File "element.pyx", line 305, in sage.structure.element.Element.__getattr__ (sage/structure/element.c:2743)
File "parent.pyx", line 237, in sage.structure.parent.getattr_from_other_class (sage/structure/parent.c:2844)
File "parent.pyx", line 169, in sage.structure.parent.raise_attribute_error (sage/structure/parent.c:2611)
AttributeError: 'sage.matrix.matrix_generic_dense.Matrix_generic_dense' object has no attribute 'eigenvectors'
Traceback (most recent call last): sage: A.eigenvalues()
File "", line 1, in <module>
File "/tmp/tmppubkUF/___code___.py", line 3
http://sagemath.org/doc/constructions/linear_algebra.html
^
SyntaxError: invalid syntax
[(-0.8541019662496845?, [(1, -0.618033988749895?)], 1), (5.854101966249684?, [(1, 1.618033988749895?)], 1)]
[(-875.3628205804243?, [(1, -0.04130088754805030?)], 1), (1.292790580424279?, [(1, 24.21255472625327?)], 1)]
1.00058518805631
8*(pi*b1^3 - 3*pi*b1^2*b2 + 3*pi*b1*b2^2 - pi*b2^3)*b1^(3/2)*b2^(3/2)/((b1^6 - 3*b1^4*b2^2 + 3*b1^2*b2^4 - b2^6)*pi)