How to simplify polynomial expansion?

2011 4 18
5 个回答
回答已采纳
8 次查看（30 天）

0 个投票

Hi Matlab Expert,
I would like to know whether a very long polynomial/ transfer function can be simplified into simple equation? Here is the example:
(204968618250053*(584538599205637399086599987135947635451994771705480410605494724605739664408576*z^2 + 422925278262421791614499596366110068734536615324831654028242248627900121088*z - 562034690169857024583161294350028872841265995589812041494482936727596957696000))/(386856262276681335905976320*(- 28948022309329048855892746252171976963317496166410141009864396001978282409984*z^4 + 57027603102903937905953706302347020088167616191162366204531808022443679809536*z^3 - 28380639403170911505711693007325694555593766082052861983585512887619317399552*z^2 + 278131765835133701917335118393270798796155394262861496597754401087939411968*z + 9422688258172540988705649901718163109010916071792709435376038033183)) - (447741983102391*(6981406932819801854409645172378584299508358365678721409026875796016332800*z^2 - 14060267183868235010495647745615491862070477638281599174319088939466489856*z + 7076949635759948779787857807944294354431191559659510600954019088246505472))/(142962266571249025024*(- 28948022309329048855892746252171976963317496166410141009864396001978282409984*z^4 + 57027603102903937905953706302347020088167616191162366204531808022443679809536*z^3 - 28380639403170911505711693007325694555593766082052861983585512887619317399552*z^2 + 278131765835133701917335118393270798796155394262861496597754401087939411968*z + 9422688258172540988705649901718163109010916071792709435376038033183)) - (5788597805039735*(196845455631738875350006527089503631641108477737992176481075200*z^2 + 213499342509751794414898651875580780507177983147674932525137920*z + 17492749683950302063970526297851198891671980880519887444770816))/(12781822672896*(- 28948022309329048855892746252171976963317496166410141009864396001978282409984*z^4 + 57027603102903937905953706302347020088167616191162366204531808022443679809536*z^3 - 28380639403170911505711693007325694555593766082052861983585512887619317399552*z^2 + 278131765835133701917335118393270798796155394262861496597754401087939411968*z + 9422688258172540988705649901718163109010916071792709435376038033183)) - (1024843091250265*(430627536192026783897911635856137629357959544584379917182598905856*z^2 + 4240917730283025791189675815432061078943960832707948157312434176*z + 692690418279477323535171459109694039392635377988006571178721280))/(6755399441055744*(- 28948022309329048855892746252171976963317496166410141009864396001978282409984*z^4 + 57027603102903937905953706302347020088167616191162366204531808022443679809536*z^3 - 28380639403170911505711693007325694555593766082052861983585512887619317399552*z^2 + 278131765835133701917335118393270798796155394262861496597754401087939411968*z + 9422688258172540988705649901718163109010916071792709435376038033183)) - (3731183192519925*(44411111195987892257013963188850689410654266331841974763520*z^2 + 87915803750142195349768749557328505454356254637028798365696*z + 8722123876189377499121331979872612611687774916817123803136))/(4160749568*(- 28948022309329048855892746252171976963317496166410141009864396001978282409984*z^4 + 57027603102903937905953706302347020088167616191162366204531808022443679809536*z^3 - 28380639403170911505711693007325694555593766082052861983585512887619317399552*z^2 + 278131765835133701917335118393270798796155394262861496597754401087939411968*z + 9422688258172540988705649901718163109010916071792709435376038033183)) - (6525747434972147*(- 11573813613581748956010638412113825149809693402020063798372600910038141415456768*z^2 + 220792948692657246210195123361446121736065131965637842292725081136480345128960*z + 11353020665395612576938494406006621945911326392702098405589742127336896606502912))/(49121460758843889307997249208320*(- 28948022309329048855892746252171976963317496166410141009864396001978282409984*z^4 + 57027603102903937905953706302347020088167616191162366204531808022443679809536*z^3 - 28380639403170911505711693007325694555593766082052861983585512887619317399552*z^2 + 278131765835133701917335118393270798796155394262861496597754401087939411968*z + 9422688258172540988705649901718163109010916071792709435376038033183)) - (32628737174860735*(431359146674410236714672241392314090778194310760649159697657763987456*z^3 - 418432845497916413092305581509467403560566486519288197204122454196224*z^2 + 4314153037836787092795079253967787795533372338423225076243924779008*z + 13992391003240178627509484721241720424970472273946691630794801152))/(857773599427494150144*(- 28948022309329048855892746252171976963317496166410141009864396001978282409984*z^4 + 57027603102903937905953706302347020088167616191162366204531808022443679809536*z^3 - 28380639403170911505711693007325694555593766082052861983585512887619317399552*z^2 + 278131765835133701917335118393270798796155394262861496597754401087939411968*z + 9422688258172540988705649901718163109010916071792709435376038033183)) + (1157719561007947*(- 28948022309329048855892746252171976963317496166410141009864396001978282409984*z^3 + 43127593764229068021205536538769243451079788478656972231027650840051748700160*z^2 + 2217781511180268625048049772868654016016138954548982171034168902274777088*z - 14193252661797991997041663248028912493491531820174568492234112553274000277504))/(731966804844795008122880*(- 28948022309329048855892746252171976963317496166410141009864396001978282409984*z^4 + 57027603102903937905953706302347020088167616191162366204531808022443679809536*z^3 - 28380639403170911505711693007325694555593766082052861983585512887619317399552*z^2 + 278131765835133701917335118393270798796155394262861496597754401087939411968*z + 9422688258172540988705649901718163109010916071792709435376038033183))
This is unreasonable equation yet it is supposed to be 4th order simple equation. It just shows all the lengthy number which I don't even know how to read. Can you guys come up with function to make this simple to read?
Thank you,
Raymond Sutjiono

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 采纳的回答

Walter Roberson
Walter Roberson 2011-4-18

0 个投票

Maple pretty quickly calculates it as the ratio of a cubic divided by a quartic. The coefficients involved are quite large.
You can get very long coefficients such as that if you input floating point numbers, as by default MuPad converts floating point numbers in to rational values. For example, in a problem earlier today someone wanted to use 0.707 which would have led to a _much _messier answer than what the probable value was, 1/sqrt(2)
I have confirmed that the numerator and denominator of the ratio do not have any roots in common (not even close), so it is not possible to reduce the expression to a polynomial instead of a ratio of polynomials.

更多回答（4 个）

Andrei Bobrov
Andrei Bobrov 2011-4-18

1 个投票

factor(v)
ans =
(1050073985609136376117577180218721828864*z^3 - 1065633110957905273283671547044295504128*z^2 - 1005605039090954507740748057427872845024*z + 1030036145611443176612944407325409289073)/(34310943977099766005760*(19342813113834066795298816*z^4 - 38105341268646458384449536*z^3 + 18963692861661811782451200*z^2 - 185845192119942907953152*z - 6296157162660917))
Oleg Komarov
Oleg Komarov 2011-4-18

0 个投票

syms z
% Now set f = ... all the expression here
f = simplify(f);
Raymond
Raymond 2011-4-18

0 个投票

I used simplify, but it does not calculate the fraction itself. It still create very long fraction.
Any ideas?
Thank you anyway for your answer, Oleg
Raymond
Raymond 2011-4-18

0 个投票

Thank you for all the response.
that helps me.

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