On Wed, Dec 8, 2021 at 12:22 PM Fernando Q. Gouvea <fqgou...@colby.edu> wrote:
> Thank you, that works. What is strange is that this does not: > > sage: right=integrate(integrate(sin(x^2),y,0,x),x,0,1) > sage: wrong=integrate(integrate(sin(x^2),x,y,1),y,0,1) > sage: real(wrong)==right > -1/2*cos(1) + 1/2 == -1/2*cos(1) + 1/2 > > Is Sage seeing a difference there that I don't? > > I think I don't understand the difference between real(wrong)==right and > bool(real(wrong)==right). > In Sage "[symbol thing] == [symbolic thing]" is a constructor for a symbolic equation. sage: SR(2) == SR(2) 2 == 2 sage: parent(SR(2) == SR(2)) Symbolic Ring sage: bool(SR(2) == SR(2)) True # only because Sage can *prove* they are equal -- it's false if it can't prove they are equal, even if they are equal... https://cocalc.com/wstein/support/gouvea-equals > Fernando > On 12/8/2021 1:23 PM, William Stein wrote: > > 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 > <https://groups.google.com/d/msgid/sage-support/CACLE5GC6SNZuSsJ13iRFbO72Udn80Yy5OavR1SFwv03gjaQxvw%40mail.gmail.com?utm_medium=email&utm_source=footer> > . > > -- > ================================================================== > Fernando Q. Gouvea > Carter Professor of Mathematics > Colby College > Mayflower Hill 5836 > Waterville, ME 04901 fqgou...@colby.edu > http://www.colby.edu/~fqgouvea > > What is socialism? > > The painful transition from capitalism to capitalism. > > > -- > 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/5ea4d847-d5a5-1053-cc98-e071382cf49f%40colby.edu > <https://groups.google.com/d/msgid/sage-support/5ea4d847-d5a5-1053-cc98-e071382cf49f%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. 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