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.
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!
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?
I did know about it (and did try it), but %i was the problem.
??????? ???????????? 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 "$" to specify which version of the function you need.
Grrrmbl. Will version 1.3.8 do better?
Martin.
On 6/19/2022 1:30 AM, clicliclic@freenet.de wrote:
??????? ???????????? schrieb:
I did know about it (and did try it), but %i was the problem.
I have no luck either when I submit the order-5 integrand with sqrt(-1)
in place of %i to the FriCAS web interface currently running version
1.3.7:
unparse(integrate(x/(x^2 - 1/5 - 2*sqrt(-1)/5)/sqrt(x^3 - x),
x)::InputForm)
There are 9 exposed and 6 unexposed library operations named -
having 2 argument(s) but none was determined to be applicable.
Use HyperDoc Browse, or issue
)display op -
to learn more about the available operations. Perhaps
package-calling the operation or using coercions on the arguments
will allow you to apply the operation.
Cannot find a definition or applicable library operation named -
with argument type(s)
Polynomial(Fraction(Integer))
AlgebraicNumber
Perhaps you should use "@" to indicate the required return type,
or "$" 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
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?
But that is the same integral, Nasser.
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.
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).
??????? ???????????? 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.
fricasFriCAS Computer Algebra System
[...] I always use setSimplifyDenomsFlag(true) anyway:
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.
"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.
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")]
"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.
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.
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.
Sysop: | Keyop |
---|---|
Location: | Huddersfield, West Yorkshire, UK |
Users: | 285 |
Nodes: | 16 (2 / 14) |
Uptime: | 62:29:03 |
Calls: | 6,488 |
Calls today: | 1 |
Files: | 12,096 |
Messages: | 5,274,568 |