Como interpreto los resultados de rootof?

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Junior Joel Aguilar Hancco
评论： Junior Joel Aguilar Hancco 2019-9-21
>> format bank
>> syms x5;
>> y5=-x5.^4/3518583760000 - (16883*x5.^3)/32986722750000 + (96727912574431*x5.^2)/386872375742379851776 - (3987519411663877*x5)/226683032661550694400 - 43900/43982297;
>> solve(y5)
ans =
RootOf(z^4 + (135064*z^3)/75 - (60454945359019375*z^2)/68719476736 + (99687985291596925*z)/1610612736 + 126533135130601452584060625/36028797018963968, z)[1]
RootOf(z^4 + (135064*z^3)/75 - (60454945359019375*z^2)/68719476736 + (99687985291596925*z)/1610612736 + 126533135130601452584060625/36028797018963968, z)[2]
RootOf(z^4 + (135064*z^3)/75 - (60454945359019375*z^2)/68719476736 + (99687985291596925*z)/1610612736 + 126533135130601452584060625/36028797018963968, z)[3]
RootOf(z^4 + (135064*z^3)/75 - (60454945359019375*z^2)/68719476736 + (99687985291596925*z)/1610612736 + 126533135130601452584060625/36028797018963968, z)[4]

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采纳的回答

Walter Roberson
Walter Roberson 2019-9-20
>> solve(y5,'MaxDegree',4)
ans =
- ((270053049741483176957*((2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/154019547927729872281849439453184 + 8340947500315093062750600098110806121940757524027/2920666982925840541048404185186304)^(1/3))/21474836480000 + 9*((2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/154019547927729872281849439453184 + 8340947500315093062750600098110806121940757524027/2920666982925840541048404185186304)^(2/3) + 6824144844545663996288226600305251/14167099448608935641088)^(1/2)/(6*(8340947500315093062750600098110806121940757524027/2920666982925840541048404185186304 + (2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/154019547927729872281849439453184)^(1/6)) - (- (6824144844545663996288226600305251*((270053049741483176957*((2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/154019547927729872281849439453184 + 8340947500315093062750600098110806121940757524027/2920666982925840541048404185186304)^(1/3))/21474836480000 + 9*((2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/154019547927729872281849439453184 + 8340947500315093062750600098110806121940757524027/2920666982925840541048404185186304)^(2/3) + 6824144844545663996288226600305251/14167099448608935641088)^(1/2))/14167099448608935641088 + (270053049741483176957*((2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/154019547927729872281849439453184 + 8340947500315093062750600098110806121940757524027/2920666982925840541048404185186304)^(1/3)*((270053049741483176957*((2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/154019547927729872281849439453184 + 8340947500315093062750600098110806121940757524027/2920666982925840541048404185186304)^(1/3))/21474836480000 + 9*((2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/154019547927729872281849439453184 + 8340947500315093062750600098110806121940757524027/2920666982925840541048404185186304)^(2/3) + 6824144844545663996288226600305251/14167099448608935641088)^(1/2))/10737418240000 - 9*((2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/154019547927729872281849439453184 + 8340947500315093062750600098110806121940757524027/2920666982925840541048404185186304)^(2/3)*((270053049741483176957*((2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/154019547927729872281849439453184 + 8340947500315093062750600098110806121940757524027/2920666982925840541048404185186304)^(1/3))/21474836480000 + 9*((2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/154019547927729872281849439453184 + 8340947500315093062750600098110806121940757524027/2920666982925840541048404185186304)^(2/3) + 6824144844545663996288226600305251/14167099448608935641088)^(1/2) + (11480946291063714818364437*6^(1/2)*((2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/2852213850513516153367582212096 + 25022842500945279188251800294332418365822272572081/162259276829213363391578010288128)^(1/2))/2415919104000000)^(1/2)/(6*(8340947500315093062750600098110806121940757524027/2920666982925840541048404185186304 + (2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/154019547927729872281849439453184)^(1/6)*((270053049741483176957*(8340947500315093062750600098110806121940757524027/2920666982925840541048404185186304 + (2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/154019547927729872281849439453184)^(1/3))/21474836480000 + 9*(8340947500315093062750600098110806121940757524027/2920666982925840541048404185186304 + (2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/154019547927729872281849439453184)^(2/3) + 6824144844545663996288226600305251/14167099448608935641088)^(1/4)) - 33766/75
- ((270053049741483176957*((2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/154019547927729872281849439453184 + 8340947500315093062750600098110806121940757524027/2920666982925840541048404185186304)^(1/3))/21474836480000 + 9*((2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/154019547927729872281849439453184 + 8340947500315093062750600098110806121940757524027/2920666982925840541048404185186304)^(2/3) + 6824144844545663996288226600305251/14167099448608935641088)^(1/2)/(6*(8340947500315093062750600098110806121940757524027/2920666982925840541048404185186304 + (2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/154019547927729872281849439453184)^(1/6)) + (- (6824144844545663996288226600305251*((270053049741483176957*((2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/154019547927729872281849439453184 + 8340947500315093062750600098110806121940757524027/2920666982925840541048404185186304)^(1/3))/21474836480000 + 9*((2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/154019547927729872281849439453184 + 8340947500315093062750600098110806121940757524027/2920666982925840541048404185186304)^(2/3) + 6824144844545663996288226600305251/14167099448608935641088)^(1/2))/14167099448608935641088 + (270053049741483176957*((2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/154019547927729872281849439453184 + 8340947500315093062750600098110806121940757524027/2920666982925840541048404185186304)^(1/3)*((270053049741483176957*((2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/154019547927729872281849439453184 + 8340947500315093062750600098110806121940757524027/2920666982925840541048404185186304)^(1/3))/21474836480000 + 9*((2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/154019547927729872281849439453184 + 8340947500315093062750600098110806121940757524027/2920666982925840541048404185186304)^(2/3) + 6824144844545663996288226600305251/14167099448608935641088)^(1/2))/10737418240000 - 9*((2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/154019547927729872281849439453184 + 8340947500315093062750600098110806121940757524027/2920666982925840541048404185186304)^(2/3)*((270053049741483176957*((2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/154019547927729872281849439453184 + 8340947500315093062750600098110806121940757524027/2920666982925840541048404185186304)^(1/3))/21474836480000 + 9*((2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/154019547927729872281849439453184 + 8340947500315093062750600098110806121940757524027/2920666982925840541048404185186304)^(2/3) + 6824144844545663996288226600305251/14167099448608935641088)^(1/2) + (11480946291063714818364437*6^(1/2)*((2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/2852213850513516153367582212096 + 25022842500945279188251800294332418365822272572081/162259276829213363391578010288128)^(1/2))/2415919104000000)^(1/2)/(6*(8340947500315093062750600098110806121940757524027/2920666982925840541048404185186304 + (2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/154019547927729872281849439453184)^(1/6)*((270053049741483176957*(8340947500315093062750600098110806121940757524027/2920666982925840541048404185186304 + (2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/154019547927729872281849439453184)^(1/3))/21474836480000 + 9*(8340947500315093062750600098110806121940757524027/2920666982925840541048404185186304 + (2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/154019547927729872281849439453184)^(2/3) + 6824144844545663996288226600305251/14167099448608935641088)^(1/4)) - 33766/75
((270053049741483176957*((2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/154019547927729872281849439453184 + 8340947500315093062750600098110806121940757524027/2920666982925840541048404185186304)^(1/3))/21474836480000 + 9*((2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/154019547927729872281849439453184 + 8340947500315093062750600098110806121940757524027/2920666982925840541048404185186304)^(2/3) + 6824144844545663996288226600305251/14167099448608935641088)^(1/2)/(6*(8340947500315093062750600098110806121940757524027/2920666982925840541048404185186304 + (2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/154019547927729872281849439453184)^(1/6)) - (- (6824144844545663996288226600305251*((270053049741483176957*((2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/154019547927729872281849439453184 + 8340947500315093062750600098110806121940757524027/2920666982925840541048404185186304)^(1/3))/21474836480000 + 9*((2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/154019547927729872281849439453184 + 8340947500315093062750600098110806121940757524027/2920666982925840541048404185186304)^(2/3) + 6824144844545663996288226600305251/14167099448608935641088)^(1/2))/14167099448608935641088 + (270053049741483176957*((2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/154019547927729872281849439453184 + 8340947500315093062750600098110806121940757524027/2920666982925840541048404185186304)^(1/3)*((270053049741483176957*((2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/154019547927729872281849439453184 + 8340947500315093062750600098110806121940757524027/2920666982925840541048404185186304)^(1/3))/21474836480000 + 9*((2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/154019547927729872281849439453184 + 8340947500315093062750600098110806121940757524027/2920666982925840541048404185186304)^(2/3) + 6824144844545663996288226600305251/14167099448608935641088)^(1/2))/10737418240000 - 9*((2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/154019547927729872281849439453184 + 8340947500315093062750600098110806121940757524027/2920666982925840541048404185186304)^(2/3)*((270053049741483176957*((2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/154019547927729872281849439453184 + 8340947500315093062750600098110806121940757524027/2920666982925840541048404185186304)^(1/3))/21474836480000 + 9*((2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/154019547927729872281849439453184 + 8340947500315093062750600098110806121940757524027/2920666982925840541048404185186304)^(2/3) + 6824144844545663996288226600305251/14167099448608935641088)^(1/2) - (11480946291063714818364437*6^(1/2)*((2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/2852213850513516153367582212096 + 25022842500945279188251800294332418365822272572081/162259276829213363391578010288128)^(1/2))/2415919104000000)^(1/2)/(6*(8340947500315093062750600098110806121940757524027/2920666982925840541048404185186304 + (2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/154019547927729872281849439453184)^(1/6)*((270053049741483176957*(8340947500315093062750600098110806121940757524027/2920666982925840541048404185186304 + (2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/154019547927729872281849439453184)^(1/3))/21474836480000 + 9*(8340947500315093062750600098110806121940757524027/2920666982925840541048404185186304 + (2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/154019547927729872281849439453184)^(2/3) + 6824144844545663996288226600305251/14167099448608935641088)^(1/4)) - 33766/75
((270053049741483176957*((2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/154019547927729872281849439453184 + 8340947500315093062750600098110806121940757524027/2920666982925840541048404185186304)^(1/3))/21474836480000 + 9*((2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/154019547927729872281849439453184 + 8340947500315093062750600098110806121940757524027/2920666982925840541048404185186304)^(2/3) + 6824144844545663996288226600305251/14167099448608935641088)^(1/2)/(6*(8340947500315093062750600098110806121940757524027/2920666982925840541048404185186304 + (2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/154019547927729872281849439453184)^(1/6)) + (- (6824144844545663996288226600305251*((270053049741483176957*((2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/154019547927729872281849439453184 + 8340947500315093062750600098110806121940757524027/2920666982925840541048404185186304)^(1/3))/21474836480000 + 9*((2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/154019547927729872281849439453184 + 8340947500315093062750600098110806121940757524027/2920666982925840541048404185186304)^(2/3) + 6824144844545663996288226600305251/14167099448608935641088)^(1/2))/14167099448608935641088 + (270053049741483176957*((2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/154019547927729872281849439453184 + 8340947500315093062750600098110806121940757524027/2920666982925840541048404185186304)^(1/3)*((270053049741483176957*((2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/154019547927729872281849439453184 + 8340947500315093062750600098110806121940757524027/2920666982925840541048404185186304)^(1/3))/21474836480000 + 9*((2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/154019547927729872281849439453184 + 8340947500315093062750600098110806121940757524027/2920666982925840541048404185186304)^(2/3) + 6824144844545663996288226600305251/14167099448608935641088)^(1/2))/10737418240000 - 9*((2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/154019547927729872281849439453184 + 8340947500315093062750600098110806121940757524027/2920666982925840541048404185186304)^(2/3)*((270053049741483176957*((2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/154019547927729872281849439453184 + 8340947500315093062750600098110806121940757524027/2920666982925840541048404185186304)^(1/3))/21474836480000 + 9*((2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/154019547927729872281849439453184 + 8340947500315093062750600098110806121940757524027/2920666982925840541048404185186304)^(2/3) + 6824144844545663996288226600305251/14167099448608935641088)^(1/2) - (11480946291063714818364437*6^(1/2)*((2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/2852213850513516153367582212096 + 25022842500945279188251800294332418365822272572081/162259276829213363391578010288128)^(1/2))/2415919104000000)^(1/2)/(6*(8340947500315093062750600098110806121940757524027/2920666982925840541048404185186304 + (2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/154019547927729872281849439453184)^(1/6)*((270053049741483176957*(8340947500315093062750600098110806121940757524027/2920666982925840541048404185186304 + (2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/154019547927729872281849439453184)^(1/3))/21474836480000 + 9*(8340947500315093062750600098110806121940757524027/2920666982925840541048404185186304 + (2^(1/2)*3^(1/2)*573897224629626001025423965510526852271292582270353705606829052391889249765897296843924125328233^(1/2)*1i)/154019547927729872281849439453184)^(2/3) + 6824144844545663996288226600305251/14167099448608935641088)^(1/4)) - 33766/75
RootOf(expression_in_z, z) stands for the set of values, z, such that expression_in_z comes out zero -- the roots of a polynomial. The indexing you are seeing such as [3] means the third such root out of 4 possible roots. It is not publicly documented how MATLAB sorts the roots; it mostly appears to be by absolute value first and then complex angle within the same absolute value, but this is not done consistently.
In later versions of MATLAB than yours, you would start seeing root() instead of RootOf, such as
root(z^4 + (135064*z^3)/75 - (60454945359019375*z^2)/68719476736 + (99687985291596925*z)/1610612736 + 126533135130601452584060625/36028797018963968, z, 1)
root(z^4 + (135064*z^3)/75 - (60454945359019375*z^2)/68719476736 + (99687985291596925*z)/1610612736 + 126533135130601452584060625/36028797018963968, z, 2)
This is the same basic functionality as RootOf(), except that it incorperates the root index as part of the expression, which can be important for differentiating between the roots.

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