In Sage, this can be written wrong.maxima_methods().trigrat().expand().
HTH, Le jeudi 9 décembre 2021 à 10:37:11 UTC+1, Daniel Volinski a écrit : > Hi All, > > In Maxima (embedded in SageMath) you can use: > > expand(trigrat(integrate(integrate(sin(x^2),x,y,1),y,0,1))); > > in order to get exactly the same result in both cases. > > Daniel > > > > En miércoles, 8 de diciembre de 2021 23:02:00 GMT+2, Fernando Q. Gouvea < > fqgo...@colby.edu> escribió: > > > I see. So the difference between this and, say, 1+1==2 (which returns > True) is that 1+1 and 2 are numbers, not symbolic things. > > Fernando > On 12/8/2021 3:37 PM, William Stein wrote: > > > > On Wed, Dec 8, 2021 at 12:22 PM Fernando Q. Gouvea <fqgo...@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 <fqgo...@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 fqgo...@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...@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...@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 fqgo...@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...@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. > To unsubscribe from this group and stop receiving emails from it, send an > email to sage-support...@googlegroups.com. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sage-support/CACLE5GCjm_qE-ufEiOWQ%3DxLsFVsV_Nm6hKdygv121Ss2Tf_iGg%40mail.gmail.com > > <https://groups.google.com/d/msgid/sage-support/CACLE5GCjm_qE-ufEiOWQ%3DxLsFVsV_Nm6hKdygv121Ss2Tf_iGg%40mail.gmail.com?utm_medium=email&utm_source=footer> > . > > -- > ================================================================== > Fernando Q. Gouvea > Carter Professor of Mathematics > Colby College > Mayflower Hill 5836 > Waterville, ME 04901 fqgo...@colby.edu > http://www.colby.edu/~fqgouvea > > Being powerful is like being a lady. If you have to tell people you > are, you aren't. > -- Margaret Thatcher > > > -- > 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...@googlegroups.com. > To view this discussion on the web visit > > https://groups.google.com/d/msgid/sage-support/b79f24fb-bc12-894b-bfe7-10c95edc81a2%40colby.edu > > <https://groups.google.com/d/msgid/sage-support/b79f24fb-bc12-894b-bfe7-10c95edc81a2%40colby.edu?utm_medium=email&utm_source=footer> > . > -- You received this message because you are subscribed to the Google Groups "sage-support" group. 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