You can compare the real and imaginary parts directly. https://cocalc.com/wstein/support/2021-12-08-gouvea
sage: bool(wrong.real() == right) True sage: wrong.imag() 0 On Wed, Dec 8, 2021 at 10:07 AM Fernando Q. Gouvea <fqgou...@colby.edu> wrote: > I was showing my students a famous calculus example of an integral that > can be computed in one order of the variables but not in the other. Knowing > that SageMath can compute anything, the students suggested trying the > integral the "wrong" way. > > The "right" way is > > sage: integrate(integrate(sin(x^2),y,0,x),x,0,1) > > -1/2*cos(1) + 1/2 > > The "wrong" way is > > sage: integrate(integrate(sin(x^2),x,y,1),y,0,1) > > -1/16*(-1)^(3/4)*((sqrt(2) + 4*(-1)^(1/4))*e^I - sqrt(-I)*((I + > 1)*sqrt(2)*(-1)^(1/4)*e^(2*I) - (I + 1)*sqrt(2)*(-1)^(1/4)*e^I) + > I*sqrt(2)*e^I - 2*(-1)^(1/4)*e^(2*I) - (I + 1)*sqrt(2) - > 2*(-1)^(1/4))*e^(-I) > > Is there any way to get Sage to check that these are equal? > > The obvious thing does not seem to work: > > sage: -1/16*(-1)^(3/4)*((sqrt(2) + 4*(-1)^(1/4))*e^I - sqrt(-I)*((I + > 1)*sqrt(2) > ....: *(-1)^(1/4)*e^(2*I) - (I + 1)*sqrt(2)*(-1)^(1/4)*e^I) + I*sqrt(2)*e^I - > 2* > ....: (-1)^(1/4)*e^(2*I) - (I + 1)*sqrt(2) - 2*(-1)^(1/4))*e^(-I) == > -1/2*cos(1) > ....: +1/2 > > -1/16*(-1)^(3/4)*((sqrt(2) + 4*(-1)^(1/4))*e^I - sqrt(-I)*((I + > 1)*sqrt(2)*(-1)^(1/4)*e^(2*I) > - (I + 1)*sqrt(2)*(-1)^(1/4)*e^I) + I*sqrt(2)*e^I - 2*(-1)^(1/4)*e^(2*I) - (I > + 1)*sqrt(2) > - 2*(-1)^(1/4))*e^(-I) == -1/2*cos(1) + 1/2 > > Thanks, > > Fernando > > -- > ================================================================== > Fernando Q. Gouvea > Carter Professor of Mathematics > Colby College > Mayflower Hill 5836 > Waterville, ME 04901 fqgou...@colby.edu > http://www.colby.edu/~fqgouvea > > I have had a perfectly wonderful evening, but this wasn't it. > --Groucho Marx > > > -- > You received this message because you are subscribed to the Google Groups > "sage-support" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sage-support+unsubscr...@googlegroups.com. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sage-support/9557c1a9-bd1c-69e1-358f-4ab02a058c3a%40colby.edu > <https://groups.google.com/d/msgid/sage-support/9557c1a9-bd1c-69e1-358f-4ab02a058c3a%40colby.edu?utm_medium=email&utm_source=footer> > . > -- William (http://wstein.org) -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-support/CACLE5GC6SNZuSsJ13iRFbO72Udn80Yy5OavR1SFwv03gjaQxvw%40mail.gmail.com.
