Ask Your Question

# Revision history [back]

The second example is the same as the first, since:

sage: +oo
+Infinity
sage: +2*oo
+Infinity


The problem seems that Sage (more precisely Maxima) knows that the sin function is odd, and learned how to use this to integrate fast if the endpoints are opposite to eachother:

sage: var("y")
y
sage: integrate(sin(x), x, -y, y)
0


Indeed, it is not able to compute half of it:

sage: integrate(sin(x), x, 0, y)
ValueError: Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(y>0)', see assume? for more details)
Is y positive, negative or zero?


While Maxima seems faulty:

sage: integrate(sin(x), x, -oo, oo, algorithm='maxima')
0


Sympy seems to know that there is a problem here:

sage: integrate(sin(x), x, -oo, oo, algorithm='sympy')
RuntimeError: cos_eval(): cos(infinity) encountered


Moreover:

sage: integrate(sin(x), x, 0, y, algorithm='sympy')
-cos(y) + 1


The second example is the same as the first, since:

sage: +oo
+Infinity
sage: +2*oo
+Infinity


The problem seems that Sage (more precisely Maxima) knows that the sin function is odd, and learned how to use this to integrate fast if the endpoints are opposite to eachother:

sage: var("y")
y
sage: integrate(sin(x), x, -y, y)
0
sage: integrate(tan(x), x, -oo, oo)
0


Indeed, it is not able to compute half of it:

sage: integrate(sin(x), x, 0, y)
ValueError: Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(y>0)', see assume? for more details)
Is y positive, negative or zero?


While Maxima seems faulty:

sage: integrate(sin(x), x, -oo, oo, algorithm='maxima')
0


Sympy seems to know that there is a problem here:

sage: integrate(sin(x), x, -oo, oo, algorithm='sympy')
RuntimeError: cos_eval(): cos(infinity) encountered


Moreover:

sage: integrate(sin(x), x, 0, y, algorithm='sympy')
-cos(y) + 1


The second example is the same as the first, since:

sage: +oo
+Infinity
sage: +2*oo
+Infinity


The problem seems that Sage (more precisely Maxima) knows that the sin function is odd, and learned how to use this to integrate fast if the endpoints are opposite to eachother:

sage: var("y")
y
sage: integrate(sin(x), x, -y, y)
0
sage: integrate(tan(x), x, -oo, oo)
0


Indeed, it is not able to compute half of it:

sage: integrate(sin(x), x, 0, y)
ValueError: Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(y>0)', see assume? for more details)
Is y positive, negative or zero?


While Maxima seems faulty:

sage: integrate(sin(x), x, -oo, oo, algorithm='maxima')
0


Sympy seems to know that there is a problem here:

sage: integrate(sin(x), x, -oo, oo, algorithm='sympy')
RuntimeError: cos_eval(): cos(infinity) encountered


Moreover:

sage: integrate(sin(x), x, 0, y, algorithm='sympy')
-cos(y) + 1


This is now reported at trac ticket 17109