• Re: alarum: Risch integrator fails to divide by zero

    From =?UTF-8?B?0JLQsNC70LXRgNC40Lkg0JfQs@21:1/5 to All on Wed Jun 15 06:39:35 2022
    Okay, why does the case u=i returns nonelementary
    result that has weierstrassPInverse(4, 0, x) on latest
    HEAD of master?

    Also I cannot get these results on latest HEAD of
    master I compiled today.
    http://www.math.uni.wroc.pl/~hebisch/fricas/p3
    not even talking about crazy
    http://www.math.uni.wroc.pl/~hebisch/fricas/p5 http://www.math.uni.wroc.pl/~hebisch/fricas/p6 http://www.math.uni.wroc.pl/~hebisch/fricas/p8

    This looks like a regression from 1.3.1!

    Also, Masser and Zannier published very nice one

    integrate(x/(x^2-1/5-2*%i/5)/(x^3-x)^(1/2), x)

    It does not work, timeouts after 8 hours and looks
    like even crashes because it exists (no warnings) as
    if )quit happened.

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  • From nobody@nowhere.invalid@21:1/5 to All on Thu Jun 16 08:15:58 2022
    ??????? ???????????? schrieb:

    Okay, why does the case u=i returns nonelementary
    result that has weierstrassPInverse(4, 0, x) on latest
    HEAD of master?

    Good grief! However:

    integrate(x/(x^2+1)/(x^3-x)^(1/2), x)

    still works on the web interface running version 1.3.7, the
    instantaneous result being:

    (log(((4*x^2+8*x+(-4))*(x^3+(-1)*x)^(1/2)+(x^4+8*x^3+2*x^2+(-8)*x+1))
    /(x^4+2*x^2+1))
    +2*atan(((x^2+(-2)*x+(-1))*(x^3+(-1)*x)^(1/2))/(2*x^3+(-2)*x)))/8

    which is reasonably compact. As mentioned earlier in this thread, it
    reduces to (in Derive notation):

    1/2*ATANH((x - 1)/SQRT(x^3 - x)) - 1/2*ATAN((x + 1)/SQRT(x^3 - x))


    Also I cannot get these results on latest HEAD of
    master I compiled today.
    http://www.math.uni.wroc.pl/~hebisch/fricas/p3
    not even talking about crazy
    http://www.math.uni.wroc.pl/~hebisch/fricas/p5 http://www.math.uni.wroc.pl/~hebisch/fricas/p6 http://www.math.uni.wroc.pl/~hebisch/fricas/p8

    This looks like a regression from 1.3.1!

    Also, Masser and Zannier published very nice one

    integrate(x/(x^2-1/5-2*%i/5)/(x^3-x)^(1/2), x)

    It does not work, timeouts after 8 hours and looks
    like even crashes because it exists (no warnings) as
    if )quit happened.

    I fear that the "master" branch you are using must be regarded a work
    in progress. One should perhaps better stick with version 1.3.7 until
    an official 1.3.8 arrives.

    Martin.

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  • From =?UTF-8?B?0JLQsNC70LXRgNC40Lkg0JfQs@21:1/5 to All on Thu Jun 16 04:59:25 2022
    You are right, I just checked HEAD of master again,
    and u=i is giving what you said. Strange.
    This still of course does not work: http://www.math.uni.wroc.pl/~hebisch/fricas/p3

    BTW, I cannot compile 1.3.2, compiler does no like this
    old code no longer. Do you maybe have it precompiled?

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  • From =?UTF-8?B?0JLQsNC70LXRgNC40Lkg0JfQs@21:1/5 to All on Thu Jun 16 05:21:21 2022
    Actually I was notified on a way to solve p3, p5, p8!

    Instead of integrate(x/(x^2-1/5-2*%i/5)/(x^3-x)^(1/2), x)

    use

    setSimplifyDenomsFlag(true)

    integrate(x/((x^2 - ((1 + 2*sqrt(-1))/5))*sqrt(x^3 - x)), x)

    See:
    https://github.com/fricas/fricas/pull/92

    Case closed!

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  • From nobody@nowhere.invalid@21:1/5 to All on Thu Jun 16 15:24:14 2022
    ??????? ???????????? schrieb:

    Actually I was notified on a way to solve p3, p5, p8!

    Instead of integrate(x/(x^2-1/5-2*%i/5)/(x^3-x)^(1/2), x)

    use

    setSimplifyDenomsFlag(true)

    integrate(x/((x^2 - ((1 + 2*sqrt(-1))/5))*sqrt(x^3 - x)), x)

    See:
    https://github.com/fricas/fricas/pull/92

    Case closed!

    I had no idea that you didn't know about setSimplifyDenomsFlag(true).
    In view of the potential consequences, the developers should make this
    the default setting.

    Martin.

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  • From nobody@nowhere.invalid@21:1/5 to All on Thu Jun 16 15:23:21 2022
    ??????? ???????????? schrieb:

    You are right, I just checked HEAD of master again,
    and u=i is giving what you said. Strange.
    This still of course does not work: http://www.math.uni.wroc.pl/~hebisch/fricas/p3

    For:

    integrate(x/((x^2 - (1 - 2*sqrt(3)/3))*sqrt(x^3 - x)), x)

    on the web interface running version 1.3.7 I get the instantaneous
    result (hopefully I didn't mess it up):

    (4*(6*3^(1/2)+9)^(1/4)*atan(((((27*x^6+(-171)*x^4+117*x^2+(-5))*3^(1/2) +((-81)*x^6+315*x^4+(-171)*x^2+9))*(x^3+(-1)*x)^(1/2)*((6*3^(1/2)+9)^(1 /4))^3+(((-216)*x^6+216*x^4)*3^(1/2)+(324*x^6+(-360)*x^4+36*x^2))*((6*3 ^(1/2)+9)^(1/4))^2+(((-270)*x^5+144*x^3+(-18)*x)*3^(1/2)+(324*x^5 +(-396)*x^3))*(x^3+(-1)*x)^(1/2)*(6*3^(1/2)+9)^(1/4)+((216*x^5+(-216)*x ^3)*3^(1/2)+(486*x^7+(-486)*x^5+18*x^3+(-18)*x)))*((((768*x^9+(-288)*x ^7+(-96)*x^5+(-96)*x^3+(-32)*x)*3^(1/2)+((-1296)*x^9+288*x^7+576*x^5 +(-32)*x^3+(-48)*x))*(x^3+(-1)*x)^(1/2)*((6*3^(1/2)+9)^(1/4))^3+ (((-432)*x^11+336*x^9+672*x^7+(-864)*x^5+272*x^3+16*x)*3^(1/2)+(864*x ^11+(-1440)*x^9+1152*x^7+(-1152)*x^5+544*x^3+32*x))*((6*3^(1/2)+9)^(1 /4))^2+((216*x^10+(-1080)*x^8+1104*x^6+(-1104)*x^4+600*x^2+8)*3^(1/2) +((-216)*x^10+648*x^8+1584*x^6+(-2448)*x^4+936*x^2+8))*(x^3+(-1)*x)^(1 /2)*(6*3^(1/2)+9)^(1/4)+((864*x^10+(-1728)*x^6+1536*x^4+(-672)*x^2)*3 ^(1/2)+(108*x^12+(-2376)*x^10+2916*x^8+(-2160)*x^6+2484*x^4+(-1224)*x^2 +(-4))))/(27*x^12+(-162)*x^10+297*x^8+(-108)*x^6+(-99)*x^4+(-18)*x^2 +(-1)))^(1/2)+((((-54)*x^6+(-198)*x^4+198*x^2+(-10))*3^(1/2)+(162*x^6 +342*x^4+(-378)*x^2+18))*(x^3+(-1)*x)^(1/2)*((6*3^(1/2)+9)^(1/4))^3 +(((-432)*x^5+144*x^3)*3^(1/2)+(324*x^5+(-504)*x^3+36*x))*(x^3+(-1)*x) ^(1/2)*(6*3^(1/2)+9)^(1/4)))/(972*x^7+(-324)*x^5+(-684)*x^3+36*x))+(4 *(6*3^(1/2)+9)^(1/4)*atan(((((27*x^6+(-171)*x^4+117*x^2+(-5))*3^(1/2) +((-81)*x^6+315*x^4+(-171)*x^2+9))*(x^3+(-1)*x)^(1/2)*((6*3^(1/2)+9)^(1 /4))^3+((216*x^6+(-216)*x^4)*3^(1/2)+((-324)*x^6+360*x^4+(-36)*x^2)) *((6*3^(1/2)+9)^(1/4))^2+(((-270)*x^5+144*x^3+(-18)*x)*3^(1/2)+(324*x^5 +(-396)*x^3))*(x^3+(-1)*x)^(1/2)*(6*3^(1/2)+9)^(1/4)+(((-216)*x^5+216 *x^3)*3^(1/2)+((-486)*x^7+486*x^5+(-18)*x^3+18*x)))*(((((-768)*x^9+288 *x^7+96*x^5+96*x^3+32*x)*3^(1/2)+(1296*x^9+(-288)*x^7+(-576)*x^5+32*x^3 +48*x))*(x^3+(-1)*x)^(1/2)*((6*3^(1/2)+9)^(1/4))^3+(((-432)*x^11+336*x ^9+672*x^7+(-864)*x^5+272*x^3+16*x)*3^(1/2)+(864*x^11+(-1440)*x^9+1152 *x^7+(-1152)*x^5+544*x^3+32*x))*((6*3^(1/2)+9)^(1/4))^2+(((-216)*x^10 +1080*x^8+(-1104)*x^6+1104*x^4+(-600)*x^2+(-8))*3^(1/2)+(216*x^10 +(-648)*x^8+(-1584)*x^6+2448*x^4+(-936)*x^2+(-8)))*(x^3+(-1)*x)^(1/2) *(6*3^(1/2)+9)^(1/4)+((864*x^10+(-1728)*x^6+1536*x^4+(-672)*x^2)*3^(1 /2)+(108*x^12+(-2376)*x^10+2916*x^8+(-2160)*x^6+2484*x^4+(-1224)*x^2 +(-4))))/(27*x^12+(-162)*x^10+297*x^8+(-108)*x^6+(-99)*x^4+(-18)*x^2 +(-1)))^(1/2)+((((-54)*x^6+(-198)*x^4+198*x^2+(-10))*3^(1/2)+(162*x^6 +342*x^4+(-378)*x^2+18))*(x^3+(-1)*x)^(1/2)*((6*3^(1/2)+9)^(1/4))^3 +(((-432)*x^5+144*x^3)*3^(1/2)+(324*x^5+(-504)*x^3+36*x))*(x^3+(-1)*x) ^(1/2)*(6*3^(1/2)+9)^(1/4)))/(972*x^7+(-324)*x^5+(-684)*x^3+36*x))+((6 *3^(1/2)+9)^(1/4)*log((((768*x^9+(-288)*x^7+(-96)*x^5+(-96)*x^3+(-32) *x)*3^(1/2)+((-1296)*x^9+288*x^7+576*x^5+(-32)*x^3+(-48)*x))*(x^3+(-1) *x)^(1/2)*((6*3^(1/2)+9)^(1/4))^3+(((-432)*x^11+336*x^9+672*x^7+(-864) *x^5+272*x^3+16*x)*3^(1/2)+(864*x^11+(-1440)*x^9+1152*x^7+(-1152)*x^5 +544*x^3+32*x))*((6*3^(1/2)+9)^(1/4))^2+((216*x^10+(-1080)*x^8+1104*x^6 +(-1104)*x^4+600*x^2+8)*3^(1/2)+((-216)*x^10+648*x^8+1584*x^6+(-2448) *x^4+936*x^2+8))*(x^3+(-1)*x)^(1/2)*(6*3^(1/2)+9)^(1/4)+((864*x^10 +(-1728)*x^6+1536*x^4+(-672)*x^2)*3^(1/2)+(108*x^12+(-2376)*x^10+2916 *x^8+(-2160)*x^6+2484*x^4+(-1224)*x^2+(-4))))/(27*x^12+(-162)*x^10+297 *x^8+(-108)*x^6+(-99)*x^4+(-18)*x^2+(-1)))+(-1)*(6*3^(1/2)+9)^(1/4) *log(((((-768)*x^9+288*x^7+96*x^5+96*x^3+32*x)*3^(1/2)+(1296*x^9+(-288) *x^7+(-576)*x^5+32*x^3+48*x))*(x^3+(-1)*x)^(1/2)*((6*3^(1/2)+9)^(1/4)) ^3+(((-432)*x^11+336*x^9+672*x^7+(-864)*x^5+272*x^3+16*x)*3^(1/2)+(864 *x^11+(-1440)*x^9+1152*x^7+(-1152)*x^5+544*x^3+32*x))*((6*3^(1/2)+9)^(1 /4))^2+(((-216)*x^10+1080*x^8+(-1104)*x^6+1104*x^4+(-600)*x^2+(-8))*3 ^(1/2)+(216*x^10+(-648)*x^8+(-1584)*x^6+2448*x^4+(-936)*x^2+(-8)))*(x^3 +(-1)*x)^(1/2)*(6*3^(1/2)+9)^(1/4)+((864*x^10+(-1728)*x^6+1536*x^4 +(-672)*x^2)*3^(1/2)+(108*x^12+(-2376)*x^10+2916*x^8+(-2160)*x^6+2484*x ^4+(-1224)*x^2+(-4))))/(27*x^12+(-162)*x^10+297*x^8+(-108)*x^6+(-99)*x^4 +(-18)*x^2+(-1))))))/24

    A much shorter version appears earlier in this thread.


    BTW, I cannot compile 1.3.2, compiler does no like this
    old code no longer. Do you maybe have it precompiled?

    Sorry, I don't. You may also ask on fricas-devel.

    Martin.

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  • From =?UTF-8?B?0JLQsNC70LXRgNC40Lkg0JfQs@21:1/5 to All on Thu Jun 16 17:17:21 2022
    I did know about it (and did try it), but %i was the problem.

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  • From =?UTF-8?B?0JLQsNC70LXRgNC40Lkg0JfQs@21:1/5 to All on Sat Jun 18 23:57:29 2022
    No, you need both. Then it works.

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  • From nobody@nowhere.invalid@21:1/5 to All on Sun Jun 19 08:30:53 2022
    ??????? ???????????? schrieb:

    I did know about it (and did try it), but %i was the problem.

    I have no luck either when I submit the order-5 integrand with sqrt(-1)
    in place of %i to the FriCAS web interface currently running version
    1.3.7:

    unparse(integrate(x/(x^2 - 1/5 - 2*sqrt(-1)/5)/sqrt(x^3 - x),
    x)::InputForm)

    There are 9 exposed and 6 unexposed library operations named -
    having 2 argument(s) but none was determined to be applicable.
    Use HyperDoc Browse, or issue
    )display op -
    to learn more about the available operations. Perhaps
    package-calling the operation or using coercions on the arguments
    will allow you to apply the operation.

    Cannot find a definition or applicable library operation named -
    with argument type(s)
    Polynomial(Fraction(Integer))
    AlgebraicNumber

    Perhaps you should use "@" to indicate the required return type,
    or "$" to specify which version of the function you need.

    Grrrmbl. Will version 1.3.8 do better?

    Martin.

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  • From Nasser M. Abbasi@21:1/5 to clicliclic@freenet.de on Sun Jun 19 02:35:19 2022
    On 6/19/2022 1:30 AM, clicliclic@freenet.de wrote:

    ??????? ???????????? schrieb:

    I did know about it (and did try it), but %i was the problem.


    I have no luck either when I submit the order-5 integrand with sqrt(-1)
    in place of %i to the FriCAS web interface currently running version
    1.3.7:

    unparse(integrate(x/(x^2 - 1/5 - 2*sqrt(-1)/5)/sqrt(x^3 - x),
    x)::InputForm)

    There are 9 exposed and 6 unexposed library operations named -
    having 2 argument(s) but none was determined to be applicable.
    Use HyperDoc Browse, or issue
    )display op -
    to learn more about the available operations. Perhaps
    package-calling the operation or using coercions on the arguments
    will allow you to apply the operation.

    Cannot find a definition or applicable library operation named -
    with argument type(s)
    Polynomial(Fraction(Integer))
    AlgebraicNumber

    Perhaps you should use "@" to indicate the required return type,
    or "$" to specify which version of the function you need.

    Grrrmbl. Will version 1.3.8 do better?

    Martin.


    I just build the pre-release 1.3.8 from github on Linux and got this:

    setSimplifyDenomsFlag(true)
    r=integrate(x/((x^2 - ((1 + 2*sqrt(-1))/5))*sqrt(x^3 - x)), x); unparse(r::InputForm)


    "((4^(1/4))^3*((-2)*(-1)^(1/2)+11)^(1/4)*log(((((75669959187507629394531250*x
    ^18+(-669388100504875183105468750)*x^16+1261942088603973388671875000*x^14+959
    26225185394287109375000*x^12+(-1562852412462234497070312500)*x^10+86302682757
    3776245117187500*x^8+(-33326447010040283203125000)*x^6+(-41164457798004150390
    625000)*x^4+3458932042121887207031250*x^2+31664967536926269531250)*(-1)^(1/2)
    +((-52386894822120666503906250)*x^18+29103830456733703613281250*x^16+11501833
    79650115966796875000*x^14+(-2308748662471771240234375000)*x^12+10368414223194
    12231445312500*x^10+378187745809555053710937500*x^8+(-28655678033828735351562
    5000)*x^6+28498470783233642578125000*x^4+2047047019004821777343750*x^2+(-5774
    1999626159667968750)))*(4^(1/4))^2*(((-2)*(-1)^(1/2)+11)^(1/4))^2+((488944351
    673126220703125000*x^17+3352761268615722656250000000*x^15+(-13653188943862915
    039062500000)*x^13+12353062629699707031250000000*x^11+(-882893800735473632812
    50000)*x^9+(-3137230873107910156250000000)*x^7+748246908187866210937500000*x^
    5+7510185241699218750000000*x^3+(-5058944225311279296875000)*x)*(-1)^(1/2)+(1
    676380634307861328125000000*x^17+(-6798654794692993164062500000)*x^15+4079192
    876815795898437500000*x^13+8519738912582397460937500000*x^11+(-95494091510772
    70507812500000)*x^9+1992255449295043945312500000*x^7+412732362747192382812500
    000*x^5+(-104635953903198242187500000)*x^3+1281499862670898437500000*x)))*(x^
    3+(-1)*x)^(1/2)+(((128056854009628295898437500*x^19+(-50058588385581970214843
    7500)*x^17+9313225746154785156250000*x^15+1659616827964782714843750000*x^13+(
    -1897476613521575927734375000)*x^11+522278249263763427734375000*x^9+139370560
    646057128906250000*x^7+(-64030289649963378906250000)*x^5+33043324947357177734
    37500*x^3+152736902236938476562500*x)*(-1)^(1/2)+(23283064365386962890625000*
    x^19+(-535510480403900146484375000)*x^17+1732259988784790039062500000*x^15+(-
    1598149538040161132812500000)*x^13+(-192597508430480957031250000)*x^11+860676
    169395446777343750000*x^9+(-301808118820190429687500000)*x^7+6645917892456054
    687500000*x^5+5342066287994384765625000*x^3+(-141561031341552734375000)*x))*4
    ^(1/4)*(((-2)*(-1)^(1/2)+11)^(1/4))^3+((5820766091346740722656250*x^20+(-3492
    45965480804443359375000)*x^18+2005835995078086853027343750*x^16+(-32074749469
    75708007812500000)*x^14+960472971200942993164062500*x^12+14509409666061401367
    18750000*x^10+(-1016844063997268676757812500)*x^8+131219625473022460937500000
    *x^6+19775703549385070800781250*x^4+(-2406537532806396484375000)*x^2+(-186264
    5149230957031250))*(-1)^(1/2)+((-32014213502407073974609375)*x^20+46566128730
    7739257812500000*x^18+(-554719008505344390869140625)*x^16+(-16838312149047851
    56250000000)*x^14+3611529245972633361816406250*x^12+(-19629001617431640625000
    00000)*x^10+(-26958063244819641113281250)*x^8+226378440856933593750000000*x^6
    +(-32397918403148651123046875)*x^4+(-268220901489257812500000)*x^2+1024454832
    0770263671875))*(4^(1/4))^3*((-2)*(-1)^(1/2)+11)^(1/4)))/(1600000*x^20+(-3200
    000)*x^18+4160000*x^16+(-3584000)*x^14+2380800*x^12+(-1193984)*x^10+476160*x^
    8+(-143360)*x^6+33280*x^4+(-5120)*x^2+512))+((-1)*(4^(1/4))^3*((-2)*(-1)^(1/2
    )+11)^(1/4)*log(((((75669959187507629394531250*x^18+(-66938810050487518310546
    8750)*x^16+1261942088603973388671875000*x^14+95926225185394287109375000*x^12+
    (-1562852412462234497070312500)*x^10+863026827573776245117187500*x^8+(-333264
    47010040283203125000)*x^6+(-41164457798004150390625000)*x^4+34589320421218872
    07031250*x^2+31664967536926269531250)*(-1)^(1/2)+((-5238689482212066650390625
    0)*x^18+29103830456733703613281250*x^16+1150183379650115966796875000*x^14+(-2
    308748662471771240234375000)*x^12+1036841422319412231445312500*x^10+378187745
    809555053710937500*x^8+(-286556780338287353515625000)*x^6+2849847078323364257
    8125000*x^4+2047047019004821777343750*x^2+(-57741999626159667968750)))*(4^(1/
    4))^2*(((-2)*(-1)^(1/2)+11)^(1/4))^2+((488944351673126220703125000*x^17+33527
    61268615722656250000000*x^15+(-13653188943862915039062500000)*x^13+1235306262
    9699707031250000000*x^11+(-88289380073547363281250000)*x^9+(-3137230873107910
    156250000000)*x^7+748246908187866210937500000*x^5+7510185241699218750000000*x
    ^3+(-5058944225311279296875000)*x)*(-1)^(1/2)+(1676380634307861328125000000*x
    ^17+(-6798654794692993164062500000)*x^15+4079192876815795898437500000*x^13+85
    19738912582397460937500000*x^11+(-9549409151077270507812500000)*x^9+199225544
    9295043945312500000*x^7+412732362747192382812500000*x^5+(-1046359539031982421
    87500000)*x^3+1281499862670898437500000*x)))*(x^3+(-1)*x)^(1/2)+((((-12805685
    4009628295898437500)*x^19+500585883855819702148437500*x^17+(-9313225746154785
    156250000)*x^15+(-1659616827964782714843750000)*x^13+189747661352157592773437
    5000*x^11+(-522278249263763427734375000)*x^9+(-139370560646057128906250000)*x
    ^7+64030289649963378906250000*x^5+(-3304332494735717773437500)*x^3+(-15273690
    2236938476562500)*x)*(-1)^(1/2)+((-23283064365386962890625000)*x^19+535510480
    403900146484375000*x^17+(-1732259988784790039062500000)*x^15+1598149538040161
    132812500000*x^13+192597508430480957031250000*x^11+(-860676169395446777343750
    000)*x^9+301808118820190429687500000*x^7+(-6645917892456054687500000)*x^5+(-5
    342066287994384765625000)*x^3+141561031341552734375000*x))*4^(1/4)*(((-2)*(-1
    )^(1/2)+11)^(1/4))^3+(((-5820766091346740722656250)*x^20+34924596548080444335
    9375000*x^18+(-2005835995078086853027343750)*x^16+320747494697570800781250000
    0*x^14+(-960472971200942993164062500)*x^12+(-1450940966606140136718750000)*x^
    10+1016844063997268676757812500*x^8+(-131219625473022460937500000)*x^6+(-1977
    5703549385070800781250)*x^4+2406537532806396484375000*x^2+1862645149230957031
    250)*(-1)^(1/2)+(32014213502407073974609375*x^20+(-46566128730773925781250000
    0)*x^18+554719008505344390869140625*x^16+1683831214904785156250000000*x^14+(-
    3611529245972633361816406250)*x^12+1962900161743164062500000000*x^10+26958063
    244819641113281250*x^8+(-226378440856933593750000000)*x^6+3239791840314865112
    3046875*x^4+268220901489257812500000*x^2+(-10244548320770263671875)))*(4^(1/4
    ))^3*((-2)*(-1)^(1/2)+11)^(1/4)))/(1600000*x^20+(-3200000)*x^18+4160000*x^16+
    (-3584000)*x^14+2380800*x^12+(-1193984)*x^10+476160*x^8+(-143360)*x^6+33280*x
    ^4+(-5120)*x^2+512))+((-1)*(-1)^(1/2)*(4^(1/4))^3*((-2)*(-1)^(1/2)+11)^(1/4)*
    log((((((-75669959187507629394531250)*x^18+669388100504875183105468750*x^16+(
    -1261942088603973388671875000)*x^14+(-95926225185394287109375000)*x^12+156285
    2412462234497070312500*x^10+(-863026827573776245117187500)*x^8+33326447010040
    283203125000*x^6+41164457798004150390625000*x^4+(-3458932042121887207031250)*
    x^2+(-31664967536926269531250))*(-1)^(1/2)+(52386894822120666503906250*x^18+(
    -29103830456733703613281250)*x^16+(-1150183379650115966796875000)*x^14+230874
    8662471771240234375000*x^12+(-1036841422319412231445312500)*x^10+(-3781877458
    09555053710937500)*x^8+286556780338287353515625000*x^6+(-28498470783233642578
    125000)*x^4+(-2047047019004821777343750)*x^2+57741999626159667968750))*(4^(1/
    4))^2*(((-2)*(-1)^(1/2)+11)^(1/4))^2+((488944351673126220703125000*x^17+33527
    61268615722656250000000*x^15+(-13653188943862915039062500000)*x^13+1235306262
    9699707031250000000*x^11+(-88289380073547363281250000)*x^9+(-3137230873107910
    156250000000)*x^7+748246908187866210937500000*x^5+7510185241699218750000000*x
    ^3+(-5058944225311279296875000)*x)*(-1)^(1/2)+(1676380634307861328125000000*x
    ^17+(-6798654794692993164062500000)*x^15+4079192876815795898437500000*x^13+85
    19738912582397460937500000*x^11+(-9549409151077270507812500000)*x^9+199225544
    9295043945312500000*x^7+412732362747192382812500000*x^5+(-1046359539031982421
    87500000)*x^3+1281499862670898437500000*x)))*(x^3+(-1)*x)^(1/2)+(((2328306436
    5386962890625000*x^19+(-535510480403900146484375000)*x^17+1732259988784790039
    062500000*x^15+(-1598149538040161132812500000)*x^13+(-19259750843048095703125
    0000)*x^11+860676169395446777343750000*x^9+(-301808118820190429687500000)*x^7
    +6645917892456054687500000*x^5+5342066287994384765625000*x^3+(-14156103134155
    2734375000)*x)*(-1)^(1/2)+((-128056854009628295898437500)*x^19+50058588385581
    9702148437500*x^17+(-9313225746154785156250000)*x^15+(-1659616827964782714843
    750000)*x^13+1897476613521575927734375000*x^11+(-522278249263763427734375000)
    *x^9+(-139370560646057128906250000)*x^7+64030289649963378906250000*x^5+(-3304
    332494735717773437500)*x^3+(-152736902236938476562500)*x))*4^(1/4)*(((-2)*(-1
    )^(1/2)+11)^(1/4))^3+((32014213502407073974609375*x^20+(-46566128730773925781
    2500000)*x^18+554719008505344390869140625*x^16+1683831214904785156250000000*x
    ^14+(-3611529245972633361816406250)*x^12+1962900161743164062500000000*x^10+26
    958063244819641113281250*x^8+(-226378440856933593750000000)*x^6+3239791840314
    8651123046875*x^4+268220901489257812500000*x^2+(-10244548320770263671875))*(-
    1)^(1/2)+(5820766091346740722656250*x^20+(-349245965480804443359375000)*x^18+
    2005835995078086853027343750*x^16+(-3207474946975708007812500000)*x^14+960472
    971200942993164062500*x^12+1450940966606140136718750000*x^10+(-10168440639972
    68676757812500)*x^8+131219625473022460937500000*x^6+1977570354938507080078125
    0*x^4+(-2406537532806396484375000)*x^2+(-1862645149230957031250)))*(4^(1/4))^
    3*((-2)*(-1)^(1/2)+11)^(1/4)))/(1600000*x^20+(-3200000)*x^18+4160000*x^16+(-3
    584000)*x^14+2380800*x^12+(-1193984)*x^10+476160*x^8+(-143360)*x^6+33280*x^4+
    (-5120)*x^2+512))+(-1)^(1/2)*(4^(1/4))^3*((-2)*(-1)^(1/2)+11)^(1/4)*log((((((
    -75669959187507629394531250)*x^18+669388100504875183105468750*x^16+(-12619420
    88603973388671875000)*x^14+(-95926225185394287109375000)*x^12+156285241246223
    4497070312500*x^10+(-863026827573776245117187500)*x^8+33326447010040283203125
    000*x^6+41164457798004150390625000*x^4+(-3458932042121887207031250)*x^2+(-316
    64967536926269531250))*(-1)^(1/2)+(52386894822120666503906250*x^18+(-29103830
    456733703613281250)*x^16+(-1150183379650115966796875000)*x^14+230874866247177
    1240234375000*x^12+(-1036841422319412231445312500)*x^10+(-3781877458095550537
    10937500)*x^8+286556780338287353515625000*x^6+(-28498470783233642578125000)*x
    ^4+(-2047047019004821777343750)*x^2+57741999626159667968750))*(4^(1/4))^2*(((
    -2)*(-1)^(1/2)+11)^(1/4))^2+((488944351673126220703125000*x^17+33527612686157
    22656250000000*x^15+(-13653188943862915039062500000)*x^13+1235306262969970703
    1250000000*x^11+(-88289380073547363281250000)*x^9+(-3137230873107910156250000
    000)*x^7+748246908187866210937500000*x^5+7510185241699218750000000*x^3+(-5058
    944225311279296875000)*x)*(-1)^(1/2)+(1676380634307861328125000000*x^17+(-679
    8654794692993164062500000)*x^15+4079192876815795898437500000*x^13+85197389125
    82397460937500000*x^11+(-9549409151077270507812500000)*x^9+199225544929504394
    5312500000*x^7+412732362747192382812500000*x^5+(-104635953903198242187500000)
    *x^3+1281499862670898437500000*x)))*(x^3+(-1)*x)^(1/2)+((((-23283064365386962
    890625000)*x^19+535510480403900146484375000*x^17+(-17322599887847900390625000
    00)*x^15+1598149538040161132812500000*x^13+192597508430480957031250000*x^11+(
    -860676169395446777343750000)*x^9+301808118820190429687500000*x^7+(-664591789
    2456054687500000)*x^5+(-5342066287994384765625000)*x^3+1415610313415527343750
    00*x)*(-1)^(1/2)+(128056854009628295898437500*x^19+(-500585883855819702148437
    500)*x^17+9313225746154785156250000*x^15+1659616827964782714843750000*x^13+(-
    1897476613521575927734375000)*x^11+522278249263763427734375000*x^9+1393705606
    46057128906250000*x^7+(-64030289649963378906250000)*x^5+330433249473571777343
    7500*x^3+152736902236938476562500*x))*4^(1/4)*(((-2)*(-1)^(1/2)+11)^(1/4))^3+
    (((-32014213502407073974609375)*x^20+465661287307739257812500000*x^18+(-55471
    9008505344390869140625)*x^16+(-1683831214904785156250000000)*x^14+36115292459
    72633361816406250*x^12+(-1962900161743164062500000000)*x^10+(-269580632448196
    41113281250)*x^8+226378440856933593750000000*x^6+(-32397918403148651123046875
    )*x^4+(-268220901489257812500000)*x^2+10244548320770263671875)*(-1)^(1/2)+((-
    5820766091346740722656250)*x^20+349245965480804443359375000*x^18+(-2005835995
    078086853027343750)*x^16+3207474946975708007812500000*x^14+(-9604729712009429
    93164062500)*x^12+(-1450940966606140136718750000)*x^10+1016844063997268676757
    812500*x^8+(-131219625473022460937500000)*x^6+(-19775703549385070800781250)*x
    ^4+2406537532806396484375000*x^2+1862645149230957031250))*(4^(1/4))^3*((-2)*(
    -1)^(1/2)+11)^(1/4)))/(1600000*x^20+(-3200000)*x^18+4160000*x^16+(-3584000)*x
    ^14+2380800*x^12+(-1193984)*x^10+476160*x^8+(-143360)*x^6+33280*x^4+(-5120)*x
    ^2+512)))))/80"

    --Nasser

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Nasser M. Abbasi@21:1/5 to Nasser M. Abbasi on Sun Jun 19 02:41:29 2022
    On 6/19/2022 2:35 AM, Nasser M. Abbasi wrote:
    On 6/19/2022 1:30 AM, clicliclic@freenet.de wrote:

    ??????? ???????????? schrieb:

    I did know about it (and did try it), but %i was the problem.


    I have no luck either when I submit the order-5 integrand with sqrt(-1)
    in place of %i to the FriCAS web interface currently running version
    1.3.7:

    unparse(integrate(x/(x^2 - 1/5 - 2*sqrt(-1)/5)/sqrt(x^3 - x),
    x)::InputForm)

    There are 9 exposed and 6 unexposed library operations named -
    having 2 argument(s) but none was determined to be applicable.
    Use HyperDoc Browse, or issue
    )display op -
    to learn more about the available operations. Perhaps
    package-calling the operation or using coercions on the arguments
    will allow you to apply the operation.

    Cannot find a definition or applicable library operation named -
    with argument type(s)
    Polynomial(Fraction(Integer))
    AlgebraicNumber

    Perhaps you should use "@" to indicate the required return type,
    or "$" to specify which version of the function you need.

    Grrrmbl. Will version 1.3.8 do better?

    Martin.


    I just build the pre-release 1.3.8 from github on Linux and got this:

    setSimplifyDenomsFlag(true)
    r=integrate(x/((x^2 - ((1 + 2*sqrt(-1))/5))*sqrt(x^3 - x)), x); unparse(r::InputForm)


    "((4^(1/4))^3*((-2)*(-1)^(1/2)+11)^(1/4)*log(((((75669959187507629394531250*x
    ^18+(-669388100504875183105468750)*x^16+1261942088603973388671875000*x^14+959
    26225185394287109375000*x^12+(-1562852412462234497070312500)*x^10+86302682757
    3776245117187500*x^8+(-33326447010040283203125000)*x^6+(-41164457798004150390
    625000)*x^4+3458932042121887207031250*x^2+31664967536926269531250)*(-1)^(1/2)
    +((-52386894822120666503906250)*x^18+29103830456733703613281250*x^16+11501833
    79650115966796875000*x^14+(-2308748662471771240234375000)*x^12+10368414223194
    12231445312500*x^10+378187745809555053710937500*x^8+(-28655678033828735351562
    5000)*x^6+28498470783233642578125000*x^4+2047047019004821777343750*x^2+(-5774
    1999626159667968750)))*(4^(1/4))^2*(((-2)*(-1)^(1/2)+11)^(1/4))^2+((488944351
    673126220703125000*x^17+3352761268615722656250000000*x^15+(-13653188943862915
    039062500000)*x^13+12353062629699707031250000000*x^11+(-882893800735473632812
    50000)*x^9+(-3137230873107910156250000000)*x^7+748246908187866210937500000*x^
    5+7510185241699218750000000*x^3+(-5058944225311279296875000)*x)*(-1)^(1/2)+(1
    676380634307861328125000000*x^17+(-6798654794692993164062500000)*x^15+4079192
    876815795898437500000*x^13+8519738912582397460937500000*x^11+(-95494091510772
    70507812500000)*x^9+1992255449295043945312500000*x^7+412732362747192382812500
    000*x^5+(-104635953903198242187500000)*x^3+1281499862670898437500000*x)))*(x^
    3+(-1)*x)^(1/2)+(((128056854009628295898437500*x^19+(-50058588385581970214843
    7500)*x^17+9313225746154785156250000*x^15+1659616827964782714843750000*x^13+(
    -1897476613521575927734375000)*x^11+522278249263763427734375000*x^9+139370560
    646057128906250000*x^7+(-64030289649963378906250000)*x^5+33043324947357177734
    37500*x^3+152736902236938476562500*x)*(-1)^(1/2)+(23283064365386962890625000*
    x^19+(-535510480403900146484375000)*x^17+1732259988784790039062500000*x^15+(-
    1598149538040161132812500000)*x^13+(-192597508430480957031250000)*x^11+860676
    169395446777343750000*x^9+(-301808118820190429687500000)*x^7+6645917892456054
    687500000*x^5+5342066287994384765625000*x^3+(-141561031341552734375000)*x))*4
    ^(1/4)*(((-2)*(-1)^(1/2)+11)^(1/4))^3+((5820766091346740722656250*x^20+(-3492
    45965480804443359375000)*x^18+2005835995078086853027343750*x^16+(-32074749469
    75708007812500000)*x^14+960472971200942993164062500*x^12+14509409666061401367
    18750000*x^10+(-1016844063997268676757812500)*x^8+131219625473022460937500000
    *x^6+19775703549385070800781250*x^4+(-2406537532806396484375000)*x^2+(-186264
    5149230957031250))*(-1)^(1/2)+((-32014213502407073974609375)*x^20+46566128730
    7739257812500000*x^18+(-554719008505344390869140625)*x^16+(-16838312149047851
    56250000000)*x^14+3611529245972633361816406250*x^12+(-19629001617431640625000
    00000)*x^10+(-26958063244819641113281250)*x^8+226378440856933593750000000*x^6
    +(-32397918403148651123046875)*x^4+(-268220901489257812500000)*x^2+1024454832
    0770263671875))*(4^(1/4))^3*((-2)*(-1)^(1/2)+11)^(1/4)))/(1600000*x^20+(-3200
    000)*x^18+4160000*x^16+(-3584000)*x^14+2380800*x^12+(-1193984)*x^10+476160*x^
    8+(-143360)*x^6+33280*x^4+(-5120)*x^2+512))+((-1)*(4^(1/4))^3*((-2)*(-1)^(1/2
    )+11)^(1/4)*log(((((75669959187507629394531250*x^18+(-66938810050487518310546
    8750)*x^16+1261942088603973388671875000*x^14+95926225185394287109375000*x^12+
    (-1562852412462234497070312500)*x^10+863026827573776245117187500*x^8+(-333264
    47010040283203125000)*x^6+(-41164457798004150390625000)*x^4+34589320421218872
    07031250*x^2+31664967536926269531250)*(-1)^(1/2)+((-5238689482212066650390625
    0)*x^18+29103830456733703613281250*x^16+1150183379650115966796875000*x^14+(-2
    308748662471771240234375000)*x^12+1036841422319412231445312500*x^10+378187745
    809555053710937500*x^8+(-286556780338287353515625000)*x^6+2849847078323364257
    8125000*x^4+2047047019004821777343750*x^2+(-57741999626159667968750)))*(4^(1/
    4))^2*(((-2)*(-1)^(1/2)+11)^(1/4))^2+((488944351673126220703125000*x^17+33527
    61268615722656250000000*x^15+(-13653188943862915039062500000)*x^13+1235306262
    9699707031250000000*x^11+(-88289380073547363281250000)*x^9+(-3137230873107910
    156250000000)*x^7+748246908187866210937500000*x^5+7510185241699218750000000*x
    ^3+(-5058944225311279296875000)*x)*(-1)^(1/2)+(1676380634307861328125000000*x
    ^17+(-6798654794692993164062500000)*x^15+4079192876815795898437500000*x^13+85
    19738912582397460937500000*x^11+(-9549409151077270507812500000)*x^9+199225544
    9295043945312500000*x^7+412732362747192382812500000*x^5+(-1046359539031982421
    87500000)*x^3+1281499862670898437500000*x)))*(x^3+(-1)*x)^(1/2)+((((-12805685
    4009628295898437500)*x^19+500585883855819702148437500*x^17+(-9313225746154785
    156250000)*x^15+(-1659616827964782714843750000)*x^13+189747661352157592773437
    5000*x^11+(-522278249263763427734375000)*x^9+(-139370560646057128906250000)*x
    ^7+64030289649963378906250000*x^5+(-3304332494735717773437500)*x^3+(-15273690
    2236938476562500)*x)*(-1)^(1/2)+((-23283064365386962890625000)*x^19+535510480
    403900146484375000*x^17+(-1732259988784790039062500000)*x^15+1598149538040161
    132812500000*x^13+192597508430480957031250000*x^11+(-860676169395446777343750
    000)*x^9+301808118820190429687500000*x^7+(-6645917892456054687500000)*x^5+(-5
    342066287994384765625000)*x^3+141561031341552734375000*x))*4^(1/4)*(((-2)*(-1
    )^(1/2)+11)^(1/4))^3+(((-5820766091346740722656250)*x^20+34924596548080444335
    9375000*x^18+(-2005835995078086853027343750)*x^16+320747494697570800781250000
    0*x^14+(-960472971200942993164062500)*x^12+(-1450940966606140136718750000)*x^
    10+1016844063997268676757812500*x^8+(-131219625473022460937500000)*x^6+(-1977
    5703549385070800781250)*x^4+2406537532806396484375000*x^2+1862645149230957031
    250)*(-1)^(1/2)+(32014213502407073974609375*x^20+(-46566128730773925781250000
    0)*x^18+554719008505344390869140625*x^16+1683831214904785156250000000*x^14+(-
    3611529245972633361816406250)*x^12+1962900161743164062500000000*x^10+26958063
    244819641113281250*x^8+(-226378440856933593750000000)*x^6+3239791840314865112
    3046875*x^4+268220901489257812500000*x^2+(-10244548320770263671875)))*(4^(1/4
    ))^3*((-2)*(-1)^(1/2)+11)^(1/4)))/(1600000*x^20+(-3200000)*x^18+4160000*x^16+
    (-3584000)*x^14+2380800*x^12+(-1193984)*x^10+476160*x^8+(-143360)*x^6+33280*x
    ^4+(-5120)*x^2+512))+((-1)*(-1)^(1/2)*(4^(1/4))^3*((-2)*(-1)^(1/2)+11)^(1/4)*
    log((((((-75669959187507629394531250)*x^18+669388100504875183105468750*x^16+(
    -1261942088603973388671875000)*x^14+(-95926225185394287109375000)*x^12+156285
    2412462234497070312500*x^10+(-863026827573776245117187500)*x^8+33326447010040
    283203125000*x^6+41164457798004150390625000*x^4+(-3458932042121887207031250)*
    x^2+(-31664967536926269531250))*(-1)^(1/2)+(52386894822120666503906250*x^18+(
    -29103830456733703613281250)*x^16+(-1150183379650115966796875000)*x^14+230874
    8662471771240234375000*x^12+(-1036841422319412231445312500)*x^10+(-3781877458
    09555053710937500)*x^8+286556780338287353515625000*x^6+(-28498470783233642578
    125000)*x^4+(-2047047019004821777343750)*x^2+57741999626159667968750))*(4^(1/
    4))^2*(((-2)*(-1)^(1/2)+11)^(1/4))^2+((488944351673126220703125000*x^17+33527
    61268615722656250000000*x^15+(-13653188943862915039062500000)*x^13+1235306262
    9699707031250000000*x^11+(-88289380073547363281250000)*x^9+(-3137230873107910
    156250000000)*x^7+748246908187866210937500000*x^5+7510185241699218750000000*x
    ^3+(-5058944225311279296875000)*x)*(-1)^(1/2)+(1676380634307861328125000000*x
    ^17+(-6798654794692993164062500000)*x^15+4079192876815795898437500000*x^13+85
    19738912582397460937500000*x^11+(-9549409151077270507812500000)*x^9+199225544
    9295043945312500000*x^7+412732362747192382812500000*x^5+(-1046359539031982421
    87500000)*x^3+1281499862670898437500000*x)))*(x^3+(-1)*x)^(1/2)+(((2328306436
    5386962890625000*x^19+(-535510480403900146484375000)*x^17+1732259988784790039
    062500000*x^15+(-1598149538040161132812500000)*x^13+(-19259750843048095703125
    0000)*x^11+860676169395446777343750000*x^9+(-301808118820190429687500000)*x^7
    +6645917892456054687500000*x^5+5342066287994384765625000*x^3+(-14156103134155
    2734375000)*x)*(-1)^(1/2)+((-128056854009628295898437500)*x^19+50058588385581
    9702148437500*x^17+(-9313225746154785156250000)*x^15+(-1659616827964782714843
    750000)*x^13+1897476613521575927734375000*x^11+(-522278249263763427734375000)
    *x^9+(-139370560646057128906250000)*x^7+64030289649963378906250000*x^5+(-3304
    332494735717773437500)*x^3+(-152736902236938476562500)*x))*4^(1/4)*(((-2)*(-1
    )^(1/2)+11)^(1/4))^3+((32014213502407073974609375*x^20+(-46566128730773925781
    2500000)*x^18+554719008505344390869140625*x^16+1683831214904785156250000000*x
    ^14+(-3611529245972633361816406250)*x^12+1962900161743164062500000000*x^10+26
    958063244819641113281250*x^8+(-226378440856933593750000000)*x^6+3239791840314
    8651123046875*x^4+268220901489257812500000*x^2+(-10244548320770263671875))*(-
    1)^(1/2)+(5820766091346740722656250*x^20+(-349245965480804443359375000)*x^18+
    2005835995078086853027343750*x^16+(-3207474946975708007812500000)*x^14+960472
    971200942993164062500*x^12+1450940966606140136718750000*x^10+(-10168440639972
    68676757812500)*x^8+131219625473022460937500000*x^6+1977570354938507080078125
    0*x^4+(-2406537532806396484375000)*x^2+(-1862645149230957031250)))*(4^(1/4))^
    3*((-2)*(-1)^(1/2)+11)^(1/4)))/(1600000*x^20+(-3200000)*x^18+4160000*x^16+(-3
    584000)*x^14+2380800*x^12+(-1193984)*x^10+476160*x^8+(-143360)*x^6+33280*x^4+
    (-5120)*x^2+512))+(-1)^(1/2)*(4^(1/4))^3*((-2)*(-1)^(1/2)+11)^(1/4)*log((((((
    -75669959187507629394531250)*x^18+669388100504875183105468750*x^16+(-12619420
    88603973388671875000)*x^14+(-95926225185394287109375000)*x^12+156285241246223
    4497070312500*x^10+(-863026827573776245117187500)*x^8+33326447010040283203125
    000*x^6+41164457798004150390625000*x^4+(-3458932042121887207031250)*x^2+(-316
    64967536926269531250))*(-1)^(1/2)+(52386894822120666503906250*x^18+(-29103830
    456733703613281250)*x^16+(-1150183379650115966796875000)*x^14+230874866247177
    1240234375000*x^12+(-1036841422319412231445312500)*x^10+(-3781877458095550537
    10937500)*x^8+286556780338287353515625000*x^6+(-28498470783233642578125000)*x
    ^4+(-2047047019004821777343750)*x^2+57741999626159667968750))*(4^(1/4))^2*(((
    -2)*(-1)^(1/2)+11)^(1/4))^2+((488944351673126220703125000*x^17+33527612686157
    22656250000000*x^15+(-13653188943862915039062500000)*x^13+1235306262969970703
    1250000000*x^11+(-88289380073547363281250000)*x^9+(-3137230873107910156250000
    000)*x^7+748246908187866210937500000*x^5+7510185241699218750000000*x^3+(-5058
    944225311279296875000)*x)*(-1)^(1/2)+(1676380634307861328125000000*x^17+(-679
    8654794692993164062500000)*x^15+4079192876815795898437500000*x^13+85197389125
    82397460937500000*x^11+(-9549409151077270507812500000)*x^9+199225544929504394
    5312500000*x^7+412732362747192382812500000*x^5+(-104635953903198242187500000)
    *x^3+1281499862670898437500000*x)))*(x^3+(-1)*x)^(1/2)+((((-23283064365386962
    890625000)*x^19+535510480403900146484375000*x^17+(-17322599887847900390625000
    00)*x^15+1598149538040161132812500000*x^13+192597508430480957031250000*x^11+(
    -860676169395446777343750000)*x^9+301808118820190429687500000*x^7+(-664591789
    2456054687500000)*x^5+(-5342066287994384765625000)*x^3+1415610313415527343750
    00*x)*(-1)^(1/2)+(128056854009628295898437500*x^19+(-500585883855819702148437
    500)*x^17+9313225746154785156250000*x^15+1659616827964782714843750000*x^13+(-
    1897476613521575927734375000)*x^11+522278249263763427734375000*x^9+1393705606
    46057128906250000*x^7+(-64030289649963378906250000)*x^5+330433249473571777343
    7500*x^3+152736902236938476562500*x))*4^(1/4)*(((-2)*(-1)^(1/2)+11)^(1/4))^3+
    (((-32014213502407073974609375)*x^20+465661287307739257812500000*x^18+(-55471
    9008505344390869140625)*x^16+(-1683831214904785156250000000)*x^14+36115292459
    72633361816406250*x^12+(-1962900161743164062500000000)*x^10+(-269580632448196
    41113281250)*x^8+226378440856933593750000000*x^6+(-32397918403148651123046875
    )*x^4+(-268220901489257812500000)*x^2+10244548320770263671875)*(-1)^(1/2)+((-
    5820766091346740722656250)*x^20+349245965480804443359375000*x^18+(-2005835995
    078086853027343750)*x^16+3207474946975708007812500000*x^14+(-9604729712009429
    93164062500)*x^12+(-1450940966606140136718750000)*x^10+1016844063997268676757
    812500*x^8+(-131219625473022460937500000)*x^6+(-19775703549385070800781250)*x
    ^4+2406537532806396484375000*x^2+1862645149230957031250))*(4^(1/4))^3*((-2)*(
    -1)^(1/2)+11)^(1/4)))/(1600000*x^20+(-3200000)*x^18+4160000*x^16+(-3584000)*x
    ^14+2380800*x^12+(-1193984)*x^10+476160*x^8+(-143360)*x^6+33280*x^4+(-5120)*x
    ^2+512)))))/80"

    --Nasser

    Opps, sorry, it looks I used the wrong integral from another listing.

    Let me try again

    setSimplifyDenomsFlag(true)
    r=integrate(x/(x^2 - 1/5 - 2*sqrt(-1)/5)/sqrt(x^3 - x),x);
    There are 9 exposed and 6 unexposed library operations named -
    having 2 argument(s) but none was determined to be applicable.
    Use HyperDoc Browse, or issue
    )display op -
    to learn more about the available operations. Perhaps
    package-calling the operation or using coercions on the arguments
    will allow you to apply the operation.

    Cannot find a definition or applicable library operation named -
    with argument type(s)
    Polynomial(Fraction(Integer))
    AlgebraicNumber

    Perhaps you should use "@" to indicate the required return type,
    or "$" to specify which version of the function you need.


    So I get same error as you do on the pre-release 1.3.8 Fricas

    --Nasser

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  • From =?UTF-8?B?0JLQsNC70LXRgNC40Lkg0JfQs@21:1/5 to All on Sun Jun 19 06:15:41 2022
    But that is the same integral, Nasser.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From antispam@math.uni.wroc.pl@21:1/5 to val.zapod.vz@gmail.com on Sun Jun 19 13:56:28 2022
    ??????? ???????????? <val.zapod.vz@gmail.com> wrote:
    You are right, I just checked HEAD of master again,
    and u=i is giving what you said. Strange.
    This still of course does not work: http://www.math.uni.wroc.pl/~hebisch/fricas/p3

    BTW, I cannot compile 1.3.2, compiler does no like this
    old code no longer. Do you maybe have it precompiled?

    For Linux there are binaries at SourceForge.

    --
    Waldek Hebisch

    --- SoupGate-Win32 v1.05
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  • From Nasser M. Abbasi@21:1/5 to All on Sun Jun 19 15:49:40 2022
    On 6/19/2022 8:15 AM, Валерий Заподовников wrote:
    But that is the same integral, Nasser.

    You are right. But they are written differently. Since one gave an error
    and not the second, I assumed they are different and I thought I copied
    the wrong one from somewhere else.

    This looks like bug in Fricas parser in this case?

    (1) -> setSimplifyDenomsFlag(true)
    (2) -> r=integrate(x/((x^2 - ((1 + 2*sqrt(-1))/5))*sqrt(x^3 - x)), x);
    Type: Equation(Expression(Integer))

    (3) -> r2=integrate(x/(x^2 - 1/5 - 2*sqrt(-1)/5)/sqrt(x^3 - x),x);
    There are 9 exposed and 6 unexposed library operations named -
    having 2 argument(s) but none was determined to be applicable.
    Use HyperDoc Browse, or issue
    )display op -
    to learn more about the available operations. Perhaps
    package-calling the operation or using coercions on the arguments
    will allow you to apply the operation.

    Cannot find a definition or applicable library operation named -
    with argument type(s)
    Polynomial(Fraction(Integer))
    AlgebraicNumber

    Perhaps you should use "@" to indicate the required return type,
    or "$" to specify which version of the function you need.


    --Nasser

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From nobody@nowhere.invalid@21:1/5 to Nasser M. Abbasi on Mon Jun 20 09:10:28 2022
    "Nasser M. Abbasi" schrieb:

    On 6/19/2022 8:15 AM, Валерий Заподовников wrote:
    But that is the same integral, Nasser.

    You are right. But they are written differently. Since one gave an
    error and not the second, I assumed they are different and I thought
    I copied the wrong one from somewhere else.

    This looks like bug in Fricas parser in this case?

    (1) -> setSimplifyDenomsFlag(true)
    (2) -> r=integrate(x/((x^2 - ((1 + 2*sqrt(-1))/5))*sqrt(x^3 - x)), x);
    Type: Equation(Expression(Integer))

    (3) -> r2=integrate(x/(x^2 - 1/5 - 2*sqrt(-1)/5)/sqrt(x^3 - x),x);
    There are 9 exposed and 6 unexposed library operations named -
    having 2 argument(s) but none was determined to be applicable.
    Use HyperDoc Browse, or issue
    )display op -
    to learn more about the available operations. Perhaps
    package-calling the operation or using coercions on the arguments
    will allow you to apply the operation.

    Cannot find a definition or applicable library operation named -
    with argument type(s)
    Polynomial(Fraction(Integer))
    AlgebraicNumber

    Perhaps you should use "@" to indicate the required return type,
    or "$" to specify which version of the function you need.


    I would consider it a natural behaviour for the FriCAS parser to
    resolve:

    Polynomial(Fraction(Integer)) - AlgebraicNumber

    by automatically downgrading to Polynomial(AlgebraicNumber), assuming
    that is a valid FriCAS type. Presumably, the integrand would then again
    end up as Expression(Integer) and thus be palatable to the integrator.

    Martin.

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  • From =?UTF-8?B?0JLQsNC70LXRgNC40Lkg0JfQs@21:1/5 to All on Tue Jun 21 10:17:19 2022
    Yep, it is a second minus that is the problem.

    I also does not like removal of 1/5

    integrate(x/(x^2 - 2*sqrt(-1)/5)/sqrt(x^3 - x),x);

    That again causes catdef: division by zero if
    you do it 2 times very fast (and I mean VERY).
    That still requires setSimplifyDenomsFlag(true).

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From nobody@nowhere.invalid@21:1/5 to All on Wed Jun 22 08:25:13 2022
    ??????? ???????????? schrieb:

    Yep, it is a second minus that is the problem.

    I also does not like removal of 1/5

    integrate(x/(x^2 - 2*sqrt(-1)/5)/sqrt(x^3 - x),x);

    That again causes catdef: division by zero if
    you do it 2 times very fast (and I mean VERY).
    That still requires setSimplifyDenomsFlag(true).

    On the FriCAS web interface, which runs version 1.3.7, your modified
    integral:

    integrate(x/(x^2 - 2*sqrt(-1)/5)/sqrt(x^3 - x), x)

    is immediately returned unevaluated. Indeed, Masser and Zannier predict
    the absence of an elementary evaluation when the modified denominator
    is no longer a factor of a division polynomial for the elliptic curve
    involved.

    An example of a non-elementary algebraic integral whose evaluation systematically stops with the "catdef: division by zero" message is:

    integrate((5*x - 9*sqrt(6) + 26)
    /((x^2 - 4*x - 50)*sqrt(x^3 - 30*x - 56)), x)

    And an elementary specimen due to Sam Blake is:

    integrate((x^4 - 1)*(x^4 + x^2 + 1)*sqrt(-x^4 + x^2 - 1)
    /(x^4 + 1)^3, x)

    where the radicand is negative everywhere on the real axis.

    So a minor "uninteresting programming problem" described at the start
    of this thread continues to harm the reputation of algebraic Risch-
    Trager integration in FriCAS.

    Martin.

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  • From Nasser M. Abbasi@21:1/5 to clicliclic@freenet.de on Wed Jun 22 02:15:56 2022
    On 6/22/2022 1:25 AM, clicliclic@freenet.de wrote:

    ??????? ???????????? schrieb:

    Yep, it is a second minus that is the problem.

    I also does not like removal of 1/5

    integrate(x/(x^2 - 2*sqrt(-1)/5)/sqrt(x^3 - x),x);

    That again causes catdef: division by zero if
    you do it 2 times very fast (and I mean VERY).
    That still requires setSimplifyDenomsFlag(true).

    On the FriCAS web interface, which runs version 1.3.7, your modified integral:

    integrate(x/(x^2 - 2*sqrt(-1)/5)/sqrt(x^3 - x), x)

    is immediately returned unevaluated.

    When calling it first time the catdef happens, but it also must load some
    code into memory or causes something internall to change, because the
    second time same call is made, it now hangs and no longer gives catdef.

    This is strange.

    But if one uses setSimplifyDenomsFlag(true) first, then it returns unevaluated and no catdef happens. I always use setSimplifyDenomsFlag(true) anyway:


    fricas
    FriCAS Computer Algebra System
    Version: FriCAS 1.3.8
    Timestamp: Tue Jun 21 15:11:38 CDT 2022 ----------------------------------------------------------------------------- (1) -> integrate(x/(x^2 - 2*sqrt(-1)/5)/sqrt(x^3 - x),x)

    >> Error detected within library code:
    catdef: division by zero

    (1) -> integrate(x/(x^2 - 2*sqrt(-1)/5)/sqrt(x^3 - x),x)
    *** HANGS or takes long time to wait but no catdef ****

    (1) -> setSimplifyDenomsFlag(true)
    (2) -> integrate(x/(x^2 - 2*sqrt(-1)/5)/sqrt(x^3 - x),x)

    +--------+
    x +---+ 2 | 3
    ++ (10 \|- 1 + 25 %B )\|%B - %B
    (2) | ------------------------------- d%B
    ++ 6 4 2
    25 %B - 25 %B + 4 %B - 4
    Type: Union(Expression(Integer),...) (3) ->

    --Nasser

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  • From nobody@nowhere.invalid@21:1/5 to Nasser M. Abbasi on Wed Jun 22 11:00:50 2022
    "Nasser M. Abbasi" schrieb:

    [...] I always use setSimplifyDenomsFlag(true) anyway:


    So do I, Martin.

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  • From nobody@nowhere.invalid@21:1/5 to clicliclic@freenet.de on Sat Jun 25 10:58:35 2022
    "clicliclic@freenet.de" schrieb:

    For:

    integrate(x/((x^2 - (1 - 2*sqrt(3)/3))*sqrt(x^3 - x)), x)

    on the web interface running version 1.3.7 I get the instantaneous
    result (hopefully I didn't mess it up):

    (4*(6*3^(1/2)+9)^(1/4)*atan(((((27*x^6+(-171)*x^4+117*x^2+(-5))*3^(1/2) +((-81)*x^6+315*x^4+(-171)*x^2+9))*(x^3+(-1)*x)^(1/2)*((6*3^(1/2)+9)^(1 /4))^3+(((-216)*x^6+216*x^4)*3^(1/2)+(324*x^6+(-360)*x^4+36*x^2))*((6*3 ^(1/2)+9)^(1/4))^2+(((-270)*x^5+144*x^3+(-18)*x)*3^(1/2)+(324*x^5 +(-396)*x^3))*(x^3+(-1)*x)^(1/2)*(6*3^(1/2)+9)^(1/4)+((216*x^5+(-216)*x ^3)*3^(1/2)+(486*x^7+(-486)*x^5+18*x^3+(-18)*x)))*((((768*x^9+(-288)*x ^7+(-96)*x^5+(-96)*x^3+(-32)*x)*3^(1/2)+((-1296)*x^9+288*x^7+576*x^5 +(-32)*x^3+(-48)*x))*(x^3+(-1)*x)^(1/2)*((6*3^(1/2)+9)^(1/4))^3+ (((-432)*x^11+336*x^9+672*x^7+(-864)*x^5+272*x^3+16*x)*3^(1/2)+(864*x ^11+(-1440)*x^9+1152*x^7+(-1152)*x^5+544*x^3+32*x))*((6*3^(1/2)+9)^(1 /4))^2+((216*x^10+(-1080)*x^8+1104*x^6+(-1104)*x^4+600*x^2+8)*3^(1/2) +((-216)*x^10+648*x^8+1584*x^6+(-2448)*x^4+936*x^2+8))*(x^3+(-1)*x)^(1 /2)*(6*3^(1/2)+9)^(1/4)+((864*x^10+(-1728)*x^6+1536*x^4+(-672)*x^2)*3 ^(1/2)+(108*x^12+(-2376)*x^10+2916*x^8+(-2160)*x^6+2484*x^4+(-1224)*x^2 +(-4))))/(27*x^12+(-162)*x^10+297*x^8+(-108)*x^6+(-99)*x^4+(-18)*x^2 +(-1)))^(1/2)+((((-54)*x^6+(-198)*x^4+198*x^2+(-10))*3^(1/2)+(162*x^6 +342*x^4+(-378)*x^2+18))*(x^3+(-1)*x)^(1/2)*((6*3^(1/2)+9)^(1/4))^3 +(((-432)*x^5+144*x^3)*3^(1/2)+(324*x^5+(-504)*x^3+36*x))*(x^3+(-1)*x) ^(1/2)*(6*3^(1/2)+9)^(1/4)))/(972*x^7+(-324)*x^5+(-684)*x^3+36*x))+(4 *(6*3^(1/2)+9)^(1/4)*atan(((((27*x^6+(-171)*x^4+117*x^2+(-5))*3^(1/2) +((-81)*x^6+315*x^4+(-171)*x^2+9))*(x^3+(-1)*x)^(1/2)*((6*3^(1/2)+9)^(1 /4))^3+((216*x^6+(-216)*x^4)*3^(1/2)+((-324)*x^6+360*x^4+(-36)*x^2)) *((6*3^(1/2)+9)^(1/4))^2+(((-270)*x^5+144*x^3+(-18)*x)*3^(1/2)+(324*x^5 +(-396)*x^3))*(x^3+(-1)*x)^(1/2)*(6*3^(1/2)+9)^(1/4)+(((-216)*x^5+216 *x^3)*3^(1/2)+((-486)*x^7+486*x^5+(-18)*x^3+18*x)))*(((((-768)*x^9+288 *x^7+96*x^5+96*x^3+32*x)*3^(1/2)+(1296*x^9+(-288)*x^7+(-576)*x^5+32*x^3 +48*x))*(x^3+(-1)*x)^(1/2)*((6*3^(1/2)+9)^(1/4))^3+(((-432)*x^11+336*x ^9+672*x^7+(-864)*x^5+272*x^3+16*x)*3^(1/2)+(864*x^11+(-1440)*x^9+1152 *x^7+(-1152)*x^5+544*x^3+32*x))*((6*3^(1/2)+9)^(1/4))^2+(((-216)*x^10 +1080*x^8+(-1104)*x^6+1104*x^4+(-600)*x^2+(-8))*3^(1/2)+(216*x^10 +(-648)*x^8+(-1584)*x^6+2448*x^4+(-936)*x^2+(-8)))*(x^3+(-1)*x)^(1/2) *(6*3^(1/2)+9)^(1/4)+((864*x^10+(-1728)*x^6+1536*x^4+(-672)*x^2)*3^(1 /2)+(108*x^12+(-2376)*x^10+2916*x^8+(-2160)*x^6+2484*x^4+(-1224)*x^2 +(-4))))/(27*x^12+(-162)*x^10+297*x^8+(-108)*x^6+(-99)*x^4+(-18)*x^2 +(-1)))^(1/2)+((((-54)*x^6+(-198)*x^4+198*x^2+(-10))*3^(1/2)+(162*x^6 +342*x^4+(-378)*x^2+18))*(x^3+(-1)*x)^(1/2)*((6*3^(1/2)+9)^(1/4))^3 +(((-432)*x^5+144*x^3)*3^(1/2)+(324*x^5+(-504)*x^3+36*x))*(x^3+(-1)*x) ^(1/2)*(6*3^(1/2)+9)^(1/4)))/(972*x^7+(-324)*x^5+(-684)*x^3+36*x))+((6 *3^(1/2)+9)^(1/4)*log((((768*x^9+(-288)*x^7+(-96)*x^5+(-96)*x^3+(-32) *x)*3^(1/2)+((-1296)*x^9+288*x^7+576*x^5+(-32)*x^3+(-48)*x))*(x^3+(-1) *x)^(1/2)*((6*3^(1/2)+9)^(1/4))^3+(((-432)*x^11+336*x^9+672*x^7+(-864) *x^5+272*x^3+16*x)*3^(1/2)+(864*x^11+(-1440)*x^9+1152*x^7+(-1152)*x^5 +544*x^3+32*x))*((6*3^(1/2)+9)^(1/4))^2+((216*x^10+(-1080)*x^8+1104*x^6 +(-1104)*x^4+600*x^2+8)*3^(1/2)+((-216)*x^10+648*x^8+1584*x^6+(-2448) *x^4+936*x^2+8))*(x^3+(-1)*x)^(1/2)*(6*3^(1/2)+9)^(1/4)+((864*x^10 +(-1728)*x^6+1536*x^4+(-672)*x^2)*3^(1/2)+(108*x^12+(-2376)*x^10+2916 *x^8+(-2160)*x^6+2484*x^4+(-1224)*x^2+(-4))))/(27*x^12+(-162)*x^10+297 *x^8+(-108)*x^6+(-99)*x^4+(-18)*x^2+(-1)))+(-1)*(6*3^(1/2)+9)^(1/4) *log(((((-768)*x^9+288*x^7+96*x^5+96*x^3+32*x)*3^(1/2)+(1296*x^9+(-288) *x^7+(-576)*x^5+32*x^3+48*x))*(x^3+(-1)*x)^(1/2)*((6*3^(1/2)+9)^(1/4)) ^3+(((-432)*x^11+336*x^9+672*x^7+(-864)*x^5+272*x^3+16*x)*3^(1/2)+(864 *x^11+(-1440)*x^9+1152*x^7+(-1152)*x^5+544*x^3+32*x))*((6*3^(1/2)+9)^(1 /4))^2+(((-216)*x^10+1080*x^8+(-1104)*x^6+1104*x^4+(-600)*x^2+(-8))*3 ^(1/2)+(216*x^10+(-648)*x^8+(-1584)*x^6+2448*x^4+(-936)*x^2+(-8)))*(x^3 +(-1)*x)^(1/2)*(6*3^(1/2)+9)^(1/4)+((864*x^10+(-1728)*x^6+1536*x^4 +(-672)*x^2)*3^(1/2)+(108*x^12+(-2376)*x^10+2916*x^8+(-2160)*x^6+2484*x ^4+(-1224)*x^2+(-4))))/(27*x^12+(-162)*x^10+297*x^8+(-108)*x^6+(-99)*x^4 +(-18)*x^2+(-1))))))/24

    A much shorter version appears earlier in this thread.


    One more question on the Masser-Zannier integrals. Can Maple do this
    one and the other cases from

    <https://www.math.uni.wroc.pl/~hebisch/fricas/p3>
    <https://www.math.uni.wroc.pl/~hebisch/fricas/p5>
    <https://www.math.uni.wroc.pl/~hebisch/fricas/p6>
    <https://www.math.uni.wroc.pl/~hebisch/fricas/p8>

    too? Especially newer versions of Maple in which the Risch-Trager
    algorithm is applied even to integrands not converted to root objects.

    Martin.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Nasser M. Abbasi@21:1/5 to clicliclic@freenet.de on Sat Jun 25 05:31:36 2022
    On 6/25/2022 3:58 AM, clicliclic@freenet.de wrote:

    "clicliclic@freenet.de" schrieb:

    For:

    integrate(x/((x^2 - (1 - 2*sqrt(3)/3))*sqrt(x^3 - x)), x)

    on the web interface running version 1.3.7 I get the instantaneous
    result (hopefully I didn't mess it up):

    (4*(6*3^(1/2)+9)^(1/4)*atan(((((27*x^6+(-171)*x^4+117*x^2+(-5))*3^(1/2)
    +((-81)*x^6+315*x^4+(-171)*x^2+9))*(x^3+(-1)*x)^(1/2)*((6*3^(1/2)+9)^(1
    /4))^3+(((-216)*x^6+216*x^4)*3^(1/2)+(324*x^6+(-360)*x^4+36*x^2))*((6*3
    ^(1/2)+9)^(1/4))^2+(((-270)*x^5+144*x^3+(-18)*x)*3^(1/2)+(324*x^5
    +(-396)*x^3))*(x^3+(-1)*x)^(1/2)*(6*3^(1/2)+9)^(1/4)+((216*x^5+(-216)*x
    ^3)*3^(1/2)+(486*x^7+(-486)*x^5+18*x^3+(-18)*x)))*((((768*x^9+(-288)*x
    ^7+(-96)*x^5+(-96)*x^3+(-32)*x)*3^(1/2)+((-1296)*x^9+288*x^7+576*x^5
    +(-32)*x^3+(-48)*x))*(x^3+(-1)*x)^(1/2)*((6*3^(1/2)+9)^(1/4))^3+
    (((-432)*x^11+336*x^9+672*x^7+(-864)*x^5+272*x^3+16*x)*3^(1/2)+(864*x
    ^11+(-1440)*x^9+1152*x^7+(-1152)*x^5+544*x^3+32*x))*((6*3^(1/2)+9)^(1
    /4))^2+((216*x^10+(-1080)*x^8+1104*x^6+(-1104)*x^4+600*x^2+8)*3^(1/2)
    +((-216)*x^10+648*x^8+1584*x^6+(-2448)*x^4+936*x^2+8))*(x^3+(-1)*x)^(1
    /2)*(6*3^(1/2)+9)^(1/4)+((864*x^10+(-1728)*x^6+1536*x^4+(-672)*x^2)*3
    ^(1/2)+(108*x^12+(-2376)*x^10+2916*x^8+(-2160)*x^6+2484*x^4+(-1224)*x^2
    +(-4))))/(27*x^12+(-162)*x^10+297*x^8+(-108)*x^6+(-99)*x^4+(-18)*x^2
    +(-1)))^(1/2)+((((-54)*x^6+(-198)*x^4+198*x^2+(-10))*3^(1/2)+(162*x^6
    +342*x^4+(-378)*x^2+18))*(x^3+(-1)*x)^(1/2)*((6*3^(1/2)+9)^(1/4))^3
    +(((-432)*x^5+144*x^3)*3^(1/2)+(324*x^5+(-504)*x^3+36*x))*(x^3+(-1)*x)
    ^(1/2)*(6*3^(1/2)+9)^(1/4)))/(972*x^7+(-324)*x^5+(-684)*x^3+36*x))+(4
    *(6*3^(1/2)+9)^(1/4)*atan(((((27*x^6+(-171)*x^4+117*x^2+(-5))*3^(1/2)
    +((-81)*x^6+315*x^4+(-171)*x^2+9))*(x^3+(-1)*x)^(1/2)*((6*3^(1/2)+9)^(1
    /4))^3+((216*x^6+(-216)*x^4)*3^(1/2)+((-324)*x^6+360*x^4+(-36)*x^2))
    *((6*3^(1/2)+9)^(1/4))^2+(((-270)*x^5+144*x^3+(-18)*x)*3^(1/2)+(324*x^5
    +(-396)*x^3))*(x^3+(-1)*x)^(1/2)*(6*3^(1/2)+9)^(1/4)+(((-216)*x^5+216
    *x^3)*3^(1/2)+((-486)*x^7+486*x^5+(-18)*x^3+18*x)))*(((((-768)*x^9+288
    *x^7+96*x^5+96*x^3+32*x)*3^(1/2)+(1296*x^9+(-288)*x^7+(-576)*x^5+32*x^3
    +48*x))*(x^3+(-1)*x)^(1/2)*((6*3^(1/2)+9)^(1/4))^3+(((-432)*x^11+336*x
    ^9+672*x^7+(-864)*x^5+272*x^3+16*x)*3^(1/2)+(864*x^11+(-1440)*x^9+1152
    *x^7+(-1152)*x^5+544*x^3+32*x))*((6*3^(1/2)+9)^(1/4))^2+(((-216)*x^10
    +1080*x^8+(-1104)*x^6+1104*x^4+(-600)*x^2+(-8))*3^(1/2)+(216*x^10
    +(-648)*x^8+(-1584)*x^6+2448*x^4+(-936)*x^2+(-8)))*(x^3+(-1)*x)^(1/2)
    *(6*3^(1/2)+9)^(1/4)+((864*x^10+(-1728)*x^6+1536*x^4+(-672)*x^2)*3^(1
    /2)+(108*x^12+(-2376)*x^10+2916*x^8+(-2160)*x^6+2484*x^4+(-1224)*x^2
    +(-4))))/(27*x^12+(-162)*x^10+297*x^8+(-108)*x^6+(-99)*x^4+(-18)*x^2
    +(-1)))^(1/2)+((((-54)*x^6+(-198)*x^4+198*x^2+(-10))*3^(1/2)+(162*x^6
    +342*x^4+(-378)*x^2+18))*(x^3+(-1)*x)^(1/2)*((6*3^(1/2)+9)^(1/4))^3
    +(((-432)*x^5+144*x^3)*3^(1/2)+(324*x^5+(-504)*x^3+36*x))*(x^3+(-1)*x)
    ^(1/2)*(6*3^(1/2)+9)^(1/4)))/(972*x^7+(-324)*x^5+(-684)*x^3+36*x))+((6
    *3^(1/2)+9)^(1/4)*log((((768*x^9+(-288)*x^7+(-96)*x^5+(-96)*x^3+(-32)
    *x)*3^(1/2)+((-1296)*x^9+288*x^7+576*x^5+(-32)*x^3+(-48)*x))*(x^3+(-1)
    *x)^(1/2)*((6*3^(1/2)+9)^(1/4))^3+(((-432)*x^11+336*x^9+672*x^7+(-864)
    *x^5+272*x^3+16*x)*3^(1/2)+(864*x^11+(-1440)*x^9+1152*x^7+(-1152)*x^5
    +544*x^3+32*x))*((6*3^(1/2)+9)^(1/4))^2+((216*x^10+(-1080)*x^8+1104*x^6
    +(-1104)*x^4+600*x^2+8)*3^(1/2)+((-216)*x^10+648*x^8+1584*x^6+(-2448)
    *x^4+936*x^2+8))*(x^3+(-1)*x)^(1/2)*(6*3^(1/2)+9)^(1/4)+((864*x^10
    +(-1728)*x^6+1536*x^4+(-672)*x^2)*3^(1/2)+(108*x^12+(-2376)*x^10+2916
    *x^8+(-2160)*x^6+2484*x^4+(-1224)*x^2+(-4))))/(27*x^12+(-162)*x^10+297
    *x^8+(-108)*x^6+(-99)*x^4+(-18)*x^2+(-1)))+(-1)*(6*3^(1/2)+9)^(1/4)
    *log(((((-768)*x^9+288*x^7+96*x^5+96*x^3+32*x)*3^(1/2)+(1296*x^9+(-288)
    *x^7+(-576)*x^5+32*x^3+48*x))*(x^3+(-1)*x)^(1/2)*((6*3^(1/2)+9)^(1/4))
    ^3+(((-432)*x^11+336*x^9+672*x^7+(-864)*x^5+272*x^3+16*x)*3^(1/2)+(864
    *x^11+(-1440)*x^9+1152*x^7+(-1152)*x^5+544*x^3+32*x))*((6*3^(1/2)+9)^(1
    /4))^2+(((-216)*x^10+1080*x^8+(-1104)*x^6+1104*x^4+(-600)*x^2+(-8))*3
    ^(1/2)+(216*x^10+(-648)*x^8+(-1584)*x^6+2448*x^4+(-936)*x^2+(-8)))*(x^3
    +(-1)*x)^(1/2)*(6*3^(1/2)+9)^(1/4)+((864*x^10+(-1728)*x^6+1536*x^4
    +(-672)*x^2)*3^(1/2)+(108*x^12+(-2376)*x^10+2916*x^8+(-2160)*x^6+2484*x
    ^4+(-1224)*x^2+(-4))))/(27*x^12+(-162)*x^10+297*x^8+(-108)*x^6+(-99)*x^4
    +(-18)*x^2+(-1))))))/24

    A much shorter version appears earlier in this thread.


    One more question on the Masser-Zannier integrals. Can Maple do this
    one and the other cases from

    <https://www.math.uni.wroc.pl/~hebisch/fricas/p3>
    <https://www.math.uni.wroc.pl/~hebisch/fricas/p5>
    <https://www.math.uni.wroc.pl/~hebisch/fricas/p6>
    <https://www.math.uni.wroc.pl/~hebisch/fricas/p8>

    too? Especially newer versions of Maple in which the Risch-Trager
    algorithm is applied even to integrands not converted to root objects.

    Martin.

    The first 3 all give result using Elliptic functions. It says all
    these failed

    "gosper", "lookup", "derivativedivides", "norman", "trager", "meijerg", "risch"

    I used integrate(...., x,method=_RETURNVERBOSE) on all of them.

    Only last one "trager" gave answer but it also had
    Elliptic function in its output

    Here is the result in same order

    ---- 1 ----
    integrate(x/((x^2 - (1 - 2*sqrt(3)/3))*sqrt(x^3 - x)), x,method=_RETURNVERBOSE)

    ["default" = 1/2*(x+1)^(1/2)*(-2*x+2)^(1/2)*(-x)^(1/2)/(x^3-x)^(1/2)/(-1-1/3*I* (6*3^(1/2)-9)^(1/2))*EllipticPi((x+1)^(1/2),-1/(-1-1/3*I*(6*3^(1/2)-9)^(1/2)),1 /2*2^(1/2))+1/2*(x+1)^(1/2)*(-2*x+2)^(1/2)*(-x)^(1/2)/(x^3-x)^(1/2)/(1/3*I*(6*3 ^(1/2)-9)^(1/2)-1)*EllipticPi((x+1)^(1/2),-1/(1/3*I*(6*3^(1/2)-9)^(1/2)-1),1/2* 2^(1/2)), "elliptic" = 1/2*(x+1)^(1/2)*(-2*x+2)^(1/2)*(-x)^(1/2)/(x^3-x)^(1/2)/ (-1-1/3*I*(6*3^(1/2)-9)^(1/2))*EllipticPi((x+1)^(1/2),-1/(-1-1/3*I*(6*3^(1/2)-9 )^(1/2)),1/2*2^(1/2))+1/2*(x+1)^(1/2)*(-2*x+2)^(1/2)*(-x)^(1/2)/(x^3-x)^(1/2)/( 1/3*I*(6*3^(1/2)-9)^(1/2)-1)*EllipticPi((x+1)^(1/2),-1/(1/3*I*(6*3^(1/2)-9)^(1/ 2)-1),1/2*2^(1/2)), FAILS = ("gosper", "lookup", "derivativedivides", "norman", "trager", "meijerg", "risch")]


    ---- 2 -----
    integrate(x/((x^2 - ((1 + 2*sqrt(-1))/5))*sqrt(x^3 - x)), x,method=_RETURNVERBOSE)

    ["default" = 1/2*(x+1)^(1/2)*(-2*x+2)^(1/2)*(-x)^(1/2)/(x^3-x)^(1/2)/(1/5*(5+10 *I)^(1/2)-1)*EllipticPi((x+1)^(1/2),-1/(1/5*(5+10*I)^(1/2)-1),1/2*2^(1/2))+1/2* (x+1)^(1/2)*(-2*x+2)^(1/2)*(-x)^(1/2)/(x^3-x)^(1/2)/(-1-1/5*(5+10*I)^(1/2))* EllipticPi((x+1)^(1/2),-1/(-1-1/5*(5+10*I)^(1/2)),1/2*2^(1/2)), "elliptic" = 1/ 2*(x+1)^(1/2)*(-2*x+2)^(1/2)*(-x)^(1/2)/(x^3-x)^(1/2)/(1/5*(5+10*I)^(1/2)-1)* EllipticPi((x+1)^(1/2),-1/(1/5*(5+10*I)^(1/2)-1),1/2*2^(1/2))+1/2*(x+1)^(1/2)*( -2*x+2)^(1/2)*(-x)^(1/2)/(x^3-x)^(1/2)/(-1-1/5*(5+10*I)^(1/2))*EllipticPi((x+1) ^(1/2),-1/(-1-1/5*(5+10*I)^(1/2)),1/2*2^(1/2)), FAILS = ("gosper", "lookup", "derivativedivides", "norman", "trager", "meijerg", "risch")]

    ---- 3 ------
    integrate(x/((x^2 + 2*sqrt(3) + 3)*sqrt(x^3 - x)), x,method=_RETURNVERBOSE)

    ["default" = 1/2*(x+1)^(1/2)*(-2*x+2)^(1/2)*(-x)^(1/2)/(x^3-x)^(1/2)/(-1-I*(2*3 ^(1/2)+3)^(1/2))*EllipticPi((x+1)^(1/2),-1/(-1-I*(2*3^(1/2)+3)^(1/2)),1/2*2^(1/ 2))+1/2*(x+1)^(1/2)*(-2*x+2)^(1/2)*(-x)^(1/2)/(x^3-x)^(1/2)/(I*(2*3^(1/2)+3)^(1 /2)-1)*EllipticPi((x+1)^(1/2),-1/(I*(2*3^(1/2)+3)^(1/2)-1),1/2*2^(1/2)), "elliptic" = 1/2*(x+1)^(1/2)*(-2*x+2)^(1/2)*(-x)^(1/2)/(x^3-x)^(1/2)/(-1-I*(2*3 ^(1/2)+3)^(1/2))*EllipticPi((x+1)^(1/2),-1/(-1-I*(2*3^(1/2)+3)^(1/2)),1/2*2^(1/ 2))+1/2*(x+1)^(1/2)*(-2*x+2)^(1/2)*(-x)^(1/2)/(x^3-x)^(1/2)/(I*(2*3^(1/2)+3)^(1 /2)-1)*EllipticPi((x+1)^(1/2),-1/(I*(2*3^(1/2)+3)^(1/2)-1),1/2*2^(1/2)), FAILS = ("gosper", "lookup", "derivativedivides", "norman", "trager", "meijerg", "risch")]


    ---- 4 -----
    integrate(x/((x^2 + 2*sqrt(10*sqrt(2) + 14) + 4*sqrt(2) + 5)*sqrt(x^3 - x)), x,method=_RETURNVERBOSE)


    ["default" = 1/2*(x+1)^(1/2)*(-2*x+2)^(1/2)*(-x)^(1/2)/(x^3-x)^(1/2)/(-1-I*(2*( 10*2^(1/2)+14)^(1/2)+4*2^(1/2)+5)^(1/2))*EllipticPi((x+1)^(1/2),-1/(-1-I*(2*(10 *2^(1/2)+14)^(1/2)+4*2^(1/2)+5)^(1/2)),1/2*2^(1/2))+1/2*(x+1)^(1/2)*(-2*x+2)^(1 /2)*(-x)^(1/2)/(x^3-x)^(1/2)/(I*(2*(10*2^(1/2)+14)^(1/2)+4*2^(1/2)+5)^(1/2)-1)* EllipticPi((x+1)^(1/2),-1/(I*(2*(10*2^(1/2)+14)^(1/2)+4*2^(1/2)+5)^(1/2)-1),1/2 *2^(1/2)), "trager" = 1/19216*(64*(10*2^(1/2)+14)^(1/2)*2^(1/2)-114*(10*2^(1/2) +14)^(1/2)-60*2^(1/2)+257)*(5*ln(( etc
    .... outout too large to post.... ....EllipticPi((x+1)^(1/2),-1/(I*(2*(10*2^(1/2)+14)^(1/2)+4*2^(1/2)+5)^(1/2)-1),1/2
    *2^(1/2)), FAILS = ("gosper", "lookup", "derivativedivides", "norman", "meijerg", "risch")]


    --Nasser

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  • From nobody@nowhere.invalid@21:1/5 to Nasser M. Abbasi on Sun Jun 26 19:58:52 2022
    "Nasser M. Abbasi" schrieb:

    On 6/25/2022 3:58 AM, clicliclic@freenet.de wrote:

    "clicliclic@freenet.de" schrieb:

    For:

    integrate(x/((x^2 - (1 - 2*sqrt(3)/3))*sqrt(x^3 - x)), x)

    on the web interface running version 1.3.7 I get the instantaneous
    result (hopefully I didn't mess it up):

    [...]

    A much shorter version appears earlier in this thread.


    One more question on the Masser-Zannier integrals. Can Maple do this
    one and the other cases from

    <https://www.math.uni.wroc.pl/~hebisch/fricas/p3>
    <https://www.math.uni.wroc.pl/~hebisch/fricas/p5>
    <https://www.math.uni.wroc.pl/~hebisch/fricas/p6>
    <https://www.math.uni.wroc.pl/~hebisch/fricas/p8>

    too? Especially newer versions of Maple in which the Risch-Trager
    algorithm is applied even to integrands not converted to root
    objects.


    The first 3 all give result using Elliptic functions. It says all
    these failed

    "gosper", "lookup", "derivativedivides", "norman", "trager",
    "meijerg", "risch"

    I used integrate(...., x,method=_RETURNVERBOSE) on all of them.

    Only last one "trager" gave answer but it also had
    Elliptic function in its output

    Here is the result in same order

    [...]

    ---- 4 -----
    integrate(x/((x^2 + 2*sqrt(10*sqrt(2) + 14) + 4*sqrt(2) + 5)*sqrt(x^3 - x)), x,method=_RETURNVERBOSE)

    ["default" = 1/2*(x+1)^(1/2)*(-2*x+2)^(1/2)*(-x)^(1/2)/(x^3-x)^(1/2)/(-1-I*(2*(
    10*2^(1/2)+14)^(1/2)+4*2^(1/2)+5)^(1/2))*EllipticPi((x+1)^(1/2),-1/(-1-I*(2*(10
    *2^(1/2)+14)^(1/2)+4*2^(1/2)+5)^(1/2)),1/2*2^(1/2))+1/2*(x+1)^(1/2)*(-2*x+2)^(1
    /2)*(-x)^(1/2)/(x^3-x)^(1/2)/(I*(2*(10*2^(1/2)+14)^(1/2)+4*2^(1/2)+5)^(1/2)-1)*
    EllipticPi((x+1)^(1/2),-1/(I*(2*(10*2^(1/2)+14)^(1/2)+4*2^(1/2)+5)^(1/2)-1),1/2
    *2^(1/2)), "trager" = 1/19216*(64*(10*2^(1/2)+14)^(1/2)*2^(1/2)-114*(10*2^(1/2)
    +14)^(1/2)-60*2^(1/2)+257)*(5*ln(( etc
    .... outout too large to post.... ....EllipticPi((x+1)^(1/2),-1/(I*(2*(10*2^(1/2)+14)^(1/2)+4*2^(1/2)+5)^(1/2)-1),1/2
    *2^(1/2)), FAILS = ("gosper", "lookup", "derivativedivides", "norman", "meijerg", "risch")]


    I suspect that the EllipticPi() appearing in Maple's evaluation of the
    fourth integral actually belongs not to its "trager" but to its
    "elliptic" evaluation. Along with the "default" evaluation, the latter
    seems to work for all integrands of this type.

    It would be odd if Maple's Risch-Trager procedure could do an 8th-order Masser-Zannier integral while it fails on the 3rd-, 5th-, and 6th-order integrands.

    Martin.

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  • From antispam@math.uni.wroc.pl@21:1/5 to clicliclic@freenet.de on Sun Jun 26 20:56:20 2022
    clicliclic@freenet.de <nobody@nowhere.invalid> wrote:

    "Nasser M. Abbasi" schrieb:

    On 6/19/2022 8:15 AM, ?????????????? ???????????????????????? wrote:
    But that is the same integral, Nasser.

    You are right. But they are written differently. Since one gave an
    error and not the second, I assumed they are different and I thought
    I copied the wrong one from somewhere else.

    This looks like bug in Fricas parser in this case?

    (1) -> setSimplifyDenomsFlag(true)
    (2) -> r=integrate(x/((x^2 - ((1 + 2*sqrt(-1))/5))*sqrt(x^3 - x)), x);
    Type: Equation(Expression(Integer))

    (3) -> r2=integrate(x/(x^2 - 1/5 - 2*sqrt(-1)/5)/sqrt(x^3 - x),x);
    There are 9 exposed and 6 unexposed library operations named -
    having 2 argument(s) but none was determined to be applicable.
    Use HyperDoc Browse, or issue
    )display op -
    to learn more about the available operations. Perhaps
    package-calling the operation or using coercions on the arguments
    will allow you to apply the operation.

    Cannot find a definition or applicable library operation named -
    with argument type(s)
    Polynomial(Fraction(Integer))
    AlgebraicNumber

    Perhaps you should use "@" to indicate the required return type,
    or "$" to specify which version of the function you need.


    I would consider it a natural behaviour for the FriCAS parser to
    resolve:

    Polynomial(Fraction(Integer)) - AlgebraicNumber

    by automatically downgrading to Polynomial(AlgebraicNumber), assuming
    that is a valid FriCAS type. Presumably, the integrand would then again
    end up as Expression(Integer) and thus be palatable to the integrator.

    Martin.

    Yes, this should happen. And now developement version works in this
    way.

    --
    Waldek Hebisch

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  • From Nasser M. Abbasi@21:1/5 to clicliclic@freenet.de on Sun Jun 26 15:32:29 2022
    On 6/26/2022 12:58 PM, clicliclic@freenet.de wrote:


    I suspect that the EllipticPi() appearing in Maple's evaluation of the
    fourth integral actually belongs not to its "trager" but to its
    "elliptic" evaluation. Along with the "default" evaluation, the latter
    seems to work for all integrands of this type.

    It would be odd if Maple's Risch-Trager procedure could do an 8th-order Masser-Zannier integral while it fails on the 3rd-, 5th-, and 6th-order integrands.

    Martin.

    Opps, sorry, you are right. That is why I thought it is strange trager had elliptic special function in its output. I missed it since output was so
    large.

    Here is the full output for the 4th integral

    https://12000.org/tmp/06262022/maple.txt


    --Nasser

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  • From antispam@math.uni.wroc.pl@21:1/5 to Nasser M. Abbasi on Sun Jun 26 21:17:56 2022
    Nasser M. Abbasi <nma@12000.org> wrote:
    On 6/22/2022 1:25 AM, clicliclic@freenet.de wrote:

    ??????? ???????????? schrieb:

    Yep, it is a second minus that is the problem.

    I also does not like removal of 1/5

    integrate(x/(x^2 - 2*sqrt(-1)/5)/sqrt(x^3 - x),x);

    That again causes catdef: division by zero if
    you do it 2 times very fast (and I mean VERY).
    That still requires setSimplifyDenomsFlag(true).

    On the FriCAS web interface, which runs version 1.3.7, your modified integral:

    integrate(x/(x^2 - 2*sqrt(-1)/5)/sqrt(x^3 - x), x)

    is immediately returned unevaluated.

    When calling it first time the catdef happens, but it also must load some code into memory or causes something internall to change, because the
    second time same call is made, it now hangs and no longer gives catdef.

    This is strange.

    FriCAS integrator uses (pseudo)random numbers. Call to integrate
    changes state of random number generator, so second call gets
    different numbers and works...

    --
    Waldek Hebisch

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