How to convert D(floor) results into meaningful numbers?

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)

Answer 1

[Walter Roberson]

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.

https://math.stackexchange.com/questions/1806824/what-is-the-inverse-laplace-transform-of-lfloor-s-rfloor

http://math.armstrong.edu/faculty/hollis/classes/DE/book3411/Chapter7.pdf

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.

[Walter Roberson]

https://math.stackexchange.com/questions/2095674/floor-function-in-complex-plane

The definition of floor on the complex plane is dubious.

[S H]

Thank you Robert for sending me refrences. They were all very helful.

[Walter Roberson]

You need the very obscure https://www.mathworks.com/help/symbolic/sym.mapsymtype.html mapSymType() for R2019a or later. If you have an earlier release then the work has to be done through calls to evalin(symengine) in order to execute raw MuPAD code .

D(floor)*(r1*(a1+jb1)) - D(floor)*(r2*(a2+jb2)) == floor(abs(r1*(a1+jb1))-abs(r2*(a2+jb2)))

looks dubious to me. On the right hand side, the floor() is being applied to the combined expression, but on the left hand side, the D(floor) are being applied to the individual expressions. The left hand side has seperable terms but the right hand side does not. Put in some sample values: floor(sqrt(2)-exp(1)) is floor(-1.3) approximately which is -2 but floor(sqrt(2)) - floor(exp(1)) is 1-2 = -1 . Therefore whether the floor() is around the subtracted abs or around the individual abs makes a difference mathematically. I think you have gotten the formula wrong.

[S H]

Yes I confirmed that your original comment of Dfloor of non-integer should be 0 is correct.

[Walter Roberson]

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.