How to convert D(floor) results into meaningful numbers?
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il 19 Dic 2019
Commentato: Walter Roberson
il 19 Dic 2019
The following results come from iLaplace of exponential functions applied to a system. Is there any way to convert them into meaningful numbers. I tried vpa() and it does not work.
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(56.240759341013409534260599373548 - 0.00000000000013606823531578978773053936699721i) - D(floor)(-37502291582195/2186280779104)*(0.25082825162799291866461491211747 + 0.00000000000000000000000023766846775708450148602766237522i) - D(floor)(-35316010803091/2186280779104)*(0.25082825162443326255224555529554 - 0.000000000000068034117655724846401157493545727i)
(56.241158633506651601044645552568 - 0.00000000000012480305931315181342276447193347i) - D(floor)(-6015952021081463/349804924656640)*(0.23006202066613085729738175242261 + 0.00000000000000000000000051090138401796784937183960969758i) - D(floor)(-5666147096424823/349804924656640)*(0.23006202066286590738534886574889 - 0.000000000000062401529654058621559197843631116i)
(56.235256023736908836092916667669 - 0.00000000000011109671301070566491753803076047i) - D(floor)(-1206307477802345/69960984931328)*(0.20479573517792250823562148871178 + 0.00000000000000000000000077414097726528085084719623267315i) - D(floor)(-1136346492871017/69960984931328)*(0.20479573517501612753176702882629 - 0.000000000000055548356502537548169101522076862i)
(56.226657491952465683852675204128 - 0.000000000000095217295008728883961911240208161i) - D(floor)(-1511780689235497/87451231164160)*(0.17552360825445199980707395856514 + 0.0000000000000000000000010222382336823627947827620821529i) - D(floor)(-1424329458071337/87451231164160)*(0.17552360825196103764099959817473 - 0.000000000000047608647501306226021151386961044i)
(56.218844284171322499646516889589 - 0.000000000000077475409581011859909343564103763i) - D(floor)(-5712903200215611/349804924656640)*(0.14281820796414905017691056378738 - 0.000000000000038737704787264601579263214667079i) - D(floor)(-6062708124872251/349804924656640)*(0.14281820796617587013696115581293 + 0.0000000000000000000000012503403262859262868331960199891i)
(56.21504136752541423771457256615 - 0.000000000000058218091199362568758262993763544i) - D(floor)(-3039146746401257/174902462328320)*(0.10731925782841899560807434869757 + 0.0000000000000000000000014539855370952371911208375667805i) - D(floor)(-2864244284072937/174902462328320)*(0.10731925782689596281721402028546 - 0.000000000000029109045596320244554453257178957i)
(56.218096779073345090116231613327 - 0.000000000000037822016476886252083678308922337i) - D(floor)(-6093878860732777/349804924656640)*(0.069721123694291236726418014699771 + 0.0000000000000000000000016291905291387338965491446291249i) - D(floor)(-5744073936076137/349804924656640)*(0.069721123693301781900223200206276 - 0.000000000000018911008235028117311716973318841i)
(56.230374334052602713594123491152 - 0.000000000000016686136305646097698424155421805i) - D(floor)(-4499733831255/273285097388)*(0.030759231833205532666108352928874 - 0.0000000000000083430681494208693989744505663963i) - D(floor)(-4773018928643/273285097388)*(0.030759231833642055613174315958524 + 0.0000000000000000000000017725282612420355090215988744932i)
D(floor)(-6125049596593303/349804924656640)*(0.0088043161371255537787915912234192 - 0.0000000000000000000000018811950215700452685748474368362i) + D(floor)(-5775244671936663/349804924656640)*(0.0088043161370006063793271245646387 - 0.000000000000002388063850613298719715223417708i) + (56.253661844963763806899211836779 + 0.0000000000000047761276945809915833346772271689i)
D(floor)(-1158166007973385/69960984931328)*(0.04819565009913375699584192944367 - 0.00000000000001307248489197118797744314127138i) + D(floor)(-1228126992904713/69960984931328)*(0.048195650099817730748217645838292 - 0.000000000000000000000001953065268734999334324914463984i) + (56.28909664892960680018903114424 + 0.000000000000026144969777585512389662980689961i)
D(floor)(-1539055083113457/87451231164160)*(0.086644268473237872723343390874044 - 0.000000000000000000000001986733207768541662161029706948i) + D(floor)(-1451603851949297/87451231164160)*(0.086644268472008251267741241775284 - 0.000000000000023501205776309491779375566665773i) + (56.337109854612977762576036033202 + 0.000000000000047002411546675203679721594915671i)
D(floor)(-5822000775727451/349804924656640)*(0.12339810936100847461075855405675 - 0.000000000000033470238846370123558451659136718i) + D(floor)(-6171805700384091/349804924656640)*(0.12339810936275969215263204002882 - 0.0000000000000000000000019815402877242649503433046421559i) + (56.397390309363130599230687188233 + 0.000000000000066940477687325812328148051520334i)
D(floor)(-3093695534157177/174902462328320)*(0.15773826102633780860027994285598 - 0.0000000000000000000000019375880830527567935475936278415i) + D(floor)(-2918793071828857/174902462328320)*(0.15773826102409924910240447147099 - 0.000000000000042784588021268690629354433788216i) + (56.468868860387575668327443988242 + 0.0000000000000855691760377581988790813116331i)
D(floor)(-5853171511587977/349804924656640)*(0.18899302391487334887969517010608 - 0.000000000000051262062954927531647702522255081i) + D(floor)(-6202976436244617/349804924656640)*(0.18899302391755546370694148503009 - 0.0000000000000000000000018557363067870605515283354551885i) + (56.549723049093535484210182727775 + 0.00000000000010252412590580461499231564315555i)
D(floor)(-36679730496989/2186280779104)*(0.21655104924655873506329328816894 - 0.000000000000058736842712032094902525336246277i) + D(floor)(-38866011276093/2186280779104)*(0.21655104924963194257121429074338 - 0.0000000000000000000000017375859944010349778699111720551i) + (56.637401943906359521193088948741 + 0.0000000000001174736854208217030762293004231i)
D(floor)(-5884342247448503/349804924656640)*(0.23987329708430656246083679803668 - 0.000000000000065062719255366939832250976822508i) + D(floor)(-6234147172105143/349804924656640)*(0.23987329708771075015752102929346 - 0.0000000000000000000000015854481872673616813784682915594i) + (56.728670392398371093037153843115 + 0.00000000000013012543850836277813388448432932i)
D(floor)(-1179985523075753/69960984931328)*(0.25850358006332178163895175281582 - 0.000000000000070115957301335088228329270004716i) + D(floor)(-1249946508007081/69960984931328)*(0.25850358006699036300043210927562 - 0.0000000000000000000000014022987282724117852338572915893i) + (56.819671566782533271791189816496 + 0.00000000000014023191460121683929688884399305i)
D(floor)(-1478878245827257/87451231164160)*(0.2720774864958187800437633090733 - 0.000000000000073797714604373877053865540654735i) + D(floor)(-1566329476991417/87451231164160)*(0.27207748649967999695840884424851 - 0.0000000000000000000000011917200537938049351289133566953i) + (56.906006295696587522278544114938 + 0.0000000000001475954292082406088551978604913i)
D(floor)(-5931098351239291/349804924656640)*(0.28032950832920708454352323098246 - 0.000000000000076035975329063940018119375384224i) + D(floor)(-6280903275895931/349804924656640)*(0.28032950833318541091361624248182 - 0.00000000000000000000000095783112060023555602648187211957i) + (56.98282732715009354923957842228 + 0.00000000000015207195065857684654334776128373i)
(57.044946358636559657165276622897 - 0.0000000000000000000000025253101365232451924993310276108i) - D(floor)(-2973341859584777/174902462328320)*(0.28309823453138612917956898455014 - 0.000000000000076786958692831409262551553225254i) - D(floor)(-3148244321913097/174902462328320)*(0.28309823453540374822536811968001 - 0.00000000000000000000000070520683830624586266808892596842i)
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Risposta accettata
Walter Roberson
il 19 Dic 2019
Yes there are ways, but they are obscure and very likely wrong for your situation.
You appear to have applied ilaplace to a function defined in terms of floor(s) and then substituted numeric values in to the result. Possibly floor did not appear directly in the original: possibly the original was defined in terms of mod()
The derivative of floor(x) is mathematically
sum(dirac(x-n), n=-infinity to infinity)
Which is a functional (not a function) with integral 1 if x is an integer, and 0 otherwise.
If you examine the values that the derivative of floor is being applied to, none of the values are integers, so the values are all 0.
Each of your lines is the sum of some of of those derivatives together with a constant. Because the derivatives will all be 0, the value of each expression is the constant that is outside of the derivative.
For your purposes.... Use children() to break up the expression and then select just the constant portion of each line.
However I really have to wonder whether that is appropriate for your situation.
The later shows how the inverse transform of some exponential forms can effectively end up being the floor function, but you appear to be taking the inverse transform of the floor function. It would make more sense to see floor showing up in an original function that you wanted to do a forward transform on and get out an exponential.
5 Commenti
Walter Roberson
il 19 Dic 2019
In that case use children() to extract the portions that are of interest to you.
I have seen D(floor) show up at one point, but I do not have any sample code to produce it at the moment in order to test with.
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