I was under the impression that I could declare the type of the return value from a procedure to be a tuple of two posints as follows:

  foo := proc () :: posint, posint; 12, 13; end proc;

and then use it for multiple assignment as

  i, j := foo();

Of course, I have to set

  kernelopts(assertlevel = 2):

if I want Maple to actually check that foo returns two posints as promised.

All this seems to work as expected, including getting an error message if the returned value has the wrong type.

So, why does Maple IDE claim that this is a syntax error? Is there a difference between the syntax accepted by Maple and Maple IDE, and if so which is correct?

Hello,

I could obtain the simulation of my multibody with kinematic closed chain (CKC).

However, it seems that from a specific time (around 12s) in my model I believe that I have some numerical instabilities. Indeed, I could compare my simulation results with another mulbody software. I obtain the same simulation until 12s and after in MapleSim, it appears many perturbations as you can see on the figures belows.

So, I think that I tune the numerical solver. This numerical solver must solve DAEs equations since my model contains 4 kinematic closed loops.

If i read correctly the help menu, there are the following methods to solve the DAEs :

- use specific DAE numerical solver (3 differents solvers are used : ck45 method, RKF45 method and Rosenbrock method

- use reformulation equations techniques (Baumgarte, Projection) which can be associated (I believe) with a classic solver like (RK4).

For the moment, I have obtained my results with the rosenbrock solver with error absolute : 1.0*10^(-4) and eror relative :error absolute : 1.0*10^(-4) 

Do you have some ideas or advices so as to find a better method to solve my multibody systems with kinematic closed loops ? This method should  prevent the creation of numerical instabilities.

Thanks a lot for your help

I have used the command "op" in a code that I have written with Maple 17. When I restart the maple server and run the whole code again, the result of the "op" command changes! why is this happening?

Hi,

I trying to simulate a force sensor on robot arm, but every time I try something, I get nothing from my sensor, can you help me?

Here it's my "design":

Also, if I add a rigid body I get this error:

Thanks!

Phil Yasskin (Texas A&M) has prepared a maplet for the Maplets for Calculus proiect. While this maplet works, in Malmem 18 it sometimes does NOT display the plot. We don't see this behavior in Maple 17, The maplet is attached for your convenience, if you are interested in seeing if it works for you.

HorAsymp-KD-ms-PY3.mw

The problem is difficult to describe. Basically, at the end of the problem, users can elect to see a plot of the function with(some) asymptotes. The code creates the plot when the problem is created, and displays this plot in the worksheet. But, when the plot is requested within the mapmlet, it sometimes does not show in the empty plot window.

Any explanations (or followup quesitons) will be greatly appreciated.

Doug

---------------------------------------------------------------------
Douglas B. Meade  <><
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu
Phone:  (803) 777-6183         URL:    http://www.math.sc.edu

My question is very similar to this question however my .txt files are in a different format.

I've generated a .txt file with Macaulay2 that looks like this

| -1 0 9  -17 4   |

| 1  2 -3 7    17 |

I would like to import this file into maple and define a matrix M as this matrix. Is there any way to accomplish this?

Hi

I'm dealing with 2nd order ODE on Maple. By using " infolevel 5" Maple tell me that it use Kovacic's algorithm to find the solution. Could anybody tell me how or at least some idea so that I can go on this my self. Following here my ODE

Thank you so much

Chaimongkol

Hi
I am trying to define commutation rules between operators a1, a2, b1, b2.

restart; 
with(Physics); 
with(Library); 
Setup(mathematicalnotation = true); 

Setup(op = {a1, a2, b1, b2}); 
alias(A = %AntiCommutator); 
algebra := [A(a1, a1) = 0, A(a2, a2) = 0, A(a1, a2) = 0, A(b2, a1) = 0, A(a1, b1) = 1, A(a2, b2) = 1];
Setup(algebrarules = algebra); 

However, the command Setup(algebrarules = algebra); causes an error. What is wrong? Noteworthy that if commutator is considered instead of anticommutator alias(A = %Commutator); then correct result follows.
Thank you.

Hello!

I would like to start with the following set of 9 elements,
A = { E11, E12, E21, E22, E11+E12, E11+E21, E12+E22, E21+E22, E11+E12+E21+E22 }.

I need a procedure that takes each of those elements and creates 3 new ones in the following way: Eij becomes Eij1, Eij2, Eij1+Eij2. So for example, E11 will become: E111, E112, and E111+E112. And for example the fifth element in A (i.e. E11+E12) will become the 3 new elements: E111+E121, E112+E122, and E111+E121 + E112+E122.

Since each of the 9 elements gets triplicated, there will be a new set, call it B, with 27 elements.

B = {E111, E112, E111+E112, E121, E122, E121+E122, ... }

Now I want to repeat this process of triplicating again so that, for example, E111 becomes: E1111, E1112, and E1111+E1112. And so on. This new set C will have 81 elements. Now I want to repeat this one last time. The final set, D, will have 243 (3^5) elements. 

Step 2: 

For every pair of elements x and y in D, I want to compute z:=(x+y)mod2. If z already belongs to D, discard it, otherwise, place z in the set D2. Do this until there are no more elements to add together (note that if x+y is computed then I don't want y+x to be computed also--that's inefficient). Maybe the most efficient way is to perform all possibly combinations of x+y mod 2 to create the set D2 and then just go: D2 setminus D.

Step 3: For x in D and y in D2 perform all possible combinations of z:=(x+y)mod2 and place these in D3 then perform set subtraction again: D3 minus D2 minus D.

Repeat this process again: x in D and y in D3 to create new elements in D4. Repeat again until Dm is empty (that is, D(m-1) will be the last set that contains new elements). I'm expecting around 12 sets... 

The issue with this whole algorithm is that I often run out of memory so I need a clever way to do this, since this algorithm is essentially classifying 2^32 elements into disjoint sets. Thank you! 

When the loop variable can be written as a unit step sequence, I never really distinguish between using

seq( f(i), i=m..n ), and

f(i) $ i=m..n

However I recent came across a case where the 'seq' construct ran about 2.5x faster. Is using 'seq' always faster? Does it depend on the function being evaluated? Why is there such a large difference in execution time

The original example which exhibited the problem is shown below, although after some experimentation, I have found other cases where 'seq' is faster (and plenty where it doesn't seem to make any difference!)

Example code for implementation using '$' is

restart:
ulim:=1000000:
t1:=time():
ans:= max
          ( { iquo(3*d, 7)/d $ d = 1..ulim }
             minus
            {3/7}
         ):
t2:= time()-t1;

Example code for for implementation using 'seq' is

restart:
ulim:=1000000:
t1:= time():
ans:= max
        ( { seq
            ( iquo(3*d, 7)/d, d=1..ulim )
          }
          minus
          {3/7}
        ):
t2:= time()-t1;

On my machine, the version using the 'seq' construct runs 2.5x faster

How to calculate the integral of (z-z0)*z/sqrt((x-x0)^2+(y-y0)^2+(z-z0)^2)
over the unit sphere {(x,y,z):x^2+y^2+z^2<=1}
under the assumtion x0^2+y0^2+z0^2<=1 (x0^2+y0^2+z0^2>1)?
Its physical interpretation suggests the integral can be expressed through  elementary functions of the parameters.

My tries are
VectorCalculus:-int((z-z0)*z/sqrt((x-x0)^2+(y-y0)^2+(z-z0)^2),[x,y,z]=Sphere(<0,0,0>,1)) assuming x0^2+y0^2+z0^2<=1;

and

VectorCalculus:-int(eval((z-z0)*z/sqrt((x-x0)^2+(y-y0)^2+(z-z0)^2),
[x=r*sin(psi)*cos(theta),y=r*cos(psi)*sin(theta),z=r*cos(psi)])*r^2*sin(psi),
[r,psi,theta]=Parallelepiped(0..1,0..Pi,0..2*Pi)) assuming x0^2+y0^2+z0^2<=1;

The both are spinning on my comp. Also

VectorCalculus:-int((z-1/4)*z/sqrt((x-1/2)^2+(y-1/3)^2+(z-1/4)^2),[x,y,z]=Sphere(<0,0,0>,1),numeric);

is spinning.
Edt. The omitted part of the code assuming x0^2+y0^2+z0^2<=1 is added.

I have a great problem with this integral and Maple gives two answers completely different:

so I get two different results :

or this:

In the first integral A get Lommels2 and If I get the Integral by using Taylor of  and after that I resum I get Lommels1.

Thank you.

Hi All,

I have a problem with regard to partial differential equations. I am using Lagrangian dynamics for a problem. First i have a function First i defined a function with two speeds of angles (first derivatives):

ODE := 5*(diff(theta1(t), t))+diff(theta2(t), t). This gives:

Now this gives an output. Lagrange (just a simple example now) demands that i now derive the obtained function with regard to the first derivative of theta1. In this case, the answer i want is 5. Now, if i give the command: 

diff(ODE, diff(theta1(t),t)), maple says go home. Does anybody know how to solve this? I have been searching for a solution all afternoon.

Thnx in advance!

three equations,

f1=(256*((256*(-24610976415716501050652227*x+256*(-10153609683556422184100+374519398571124540883*y-4145573659500944095488*z))*(29427736469514379027531261659072347+58899562724319710108573382000184640*y-1732944474195510410991057714955859184*z))/((5042560366642267*x-256*(2446745837411900+4901398098088043*y-144207654645973248*z))^3)-(256*(-308518681989548429992935348850261+41445095210006425938788783390458*y-1638970396838251453451269879637336*z)*(-801790542801929135637671-732048260009923946735424*x+56975701334774517040256*y-187552638032246240630656*z))/((-3075770275504817+198931044892562752*x+14199788245258112*y-1122852841901814912*z)^3)+(5*(-89303793175477833893354121208000+6533090911353242906294143748495*y-32276910383172707359896832089932*z)*(-61468981380127448102256-5328427636421850183140*x+4647710007810227520885*y-13344414478836548348450*z))/((-46366672189358032-18896234711237580*x+3927118781169095*y+14705346416259850*z)^3)-(3*(9101665097092871812176+3063507166600182944940*x+6945927557350563805665*y+1052001549322007294950*z)*(19493858980629008651267653094056+93282964805436900100617577630195*y+42271355681070699741325611572830*z))/((46366672189358032+18896234711237580*x-3927118781169095*y-14705346416259850*z)^3)-(4*(39553725461800043367392+17203831108841472538824*x+45483386678520344593037*y+2703260049547565568088*z)*(52830583937680669669892057655944+303023948138837354463602341532495*y+134962043561465977901954677856080*z))/((92856945980914656+51329763147513032*x-8586501277743859*y-56199770659759016*z)^3)-((22670037111266004087968+12461845278544574559640*x+39219302812923818032157*y-46563087562792926056*z)*(95973949246309465842551069546976+723429769797021053206211106031819*y+317530466286898645427564085427048*z))/((50159316775994592+36243094308305160*x-4827156544231217*y-52318895858217464*z)^3)-(80*(4157117722725769078952+4534359335248895646832*x+26193979470458655189977*y-2382852476120229696128*z)*(205429639975670471114284923188348+2095815907391732802212116237430935*y+883539023887333564964405237094400*z))/((45070329471431608+130124049256651728*x-5583613021604317*y-387630670566282112*z)^3)-(16*(9439334964924689507817+17499514376929345709248*x+187907876794815451253888*y-21704870055089718153088*z)*(943164674716649969807523653958385+18130967224506023673179633045358720*y+7486136216172114262568716503454336*z))/((-3075770275504817+198931044892562752*x+14199788245258112*y-1122852841901814912*z)^3)+(80*(2304705299858575630109*x-256*(204828849006588248100+19508530860149228990861*y-2445924471668591306496*z))*(-179928369646271075844345534739549+3401432279430696137250330740801392*y+12500875943051297916024009205116096*z))/((5042560366642267*x-256*(2446745837411900+4901398098088043*y-144207654645973248*z))^3)+(80*(-805507884940017483975376678503744+52529278437993151034132605337909*y-620040027953848498781390188900552*z)*(-716026618045942942760*x+243780804476456624597*y-8*(408351630952413337484+89777022692195474597*z)))/((-50159316775994592-36243094308305160*x+4827156544231217*y+52318895858217464*z)^3)+(768*(61889933231497708820968+30294916915069669525488*x-4484037822343607626207*y+13934625423713945278848*z)*(16858970779944867265671037333379*y-176*(1546216290476124632111328928258+3134171189636832381705249359145*z)))/((45070329471431608+130124049256651728*x-5583613021604317*y-387630670566282112*z)^3)-(40*(1717566388539311579248*x+7025931019459451548321*y+48*(46537098413809906919-8301700878138964680*z))*(3434616943638241443585000648954199*y+320*(1107265969195848092307625165761+4643932844541992753284837619195*z)))/((85141430232132048+97951351741329392*x-8855616621991191*y-199920422688690560*z)^3)+(12*(88457226224862447127008+13504083955712971035976*x-6622138801690554356387*y+19322683651036147287512*z)*(36451820000039413375829754767131*y-8*(66864837166560711793644210325852+35619205657210451197984743698883*z)))/((92856945980914656+51329763147513032*x-8586501277743859*y-56199770659759016*z)^3)+(512*(45619694076424722199344+14936846773318822792976*x-3365788117861218576473*y+10130491989577935272320*z)*(12048859085295019197936041733505*y-6*(32519187452933223586671104614156+40471151781636260063426632487709*z)))/((85141430232132048+97951351741329392*x-8855616621991191*y-199920422688690560*z)^3)))/125;
f2=(128*((32768*(24610976415716501050652227*x-256*(-10153609683556422184100+374519398571124540883*y-4145573659500944095488*z))*(98990697209366584150952278657452+920305667567495470446459093752885*x-65799721166407263195366683527104*z))/((5042560366642267*x-256*(2446745837411900+4901398098088043*y-144207654645973248*z))^3)+(1024*(-10864227594859409007678067839115+566592725765813239786863532667460*x-3214793226869529893757297514562848*z)*(9439334964924689507817+17499514376929345709248*x+187907876794815451253888*y-21704870055089718153088*z))/((-3075770275504817+198931044892562752*x+14199788245258112*y-1122852841901814912*z)^3)+(40*(2938923392457131154149055759247753+8383263629566931208848464949723740*x-24821520393182477390523323699174560*z)*(4157117722725769078952+4534359335248895646832*x+26193979470458655189977*y-2382852476120229696128*z))/((45070329471431608+130124049256651728*x-5583613021604317*y-387630670566282112*z)^3)+(80*(1717566388539311579248*x+7025931019459451548321*y+48*(46537098413809906919-8301700878138964680*z))*(3017477155357435955713408172820441+3434616943638241443585000648954199*x-6875761229715351344214913955270620*z))/((85141430232132048+97951351741329392*x-8855616621991191*y-199920422688690560*z)^3)+(2*(1013986939222028224203834326214704+723429769797021053206211106031819*x-1002019231842824621894736024449560*z)*(22670037111266004087968+12461845278544574559640*x+39219302812923818032157*y-46563087562792926056*z))/((50159316775994592+36243094308305160*x-4827156544231217*y-52318895858217464*z)^3)+(2*(698833722744934775627393528218146+279848894416310700301852732890585*x-191427609122898840477329914007915*z)*(9101665097092871812176+3063507166600182944940*x+6945927557350563805665*y+1052001549322007294950*z))/((46366672189358032+18896234711237580*x-3927118781169095*y-14705346416259850*z)^3)+(8*(557016173590538671691101855964863+303023948138837354463602341532495*x-309197308873592242001670976702725*z)*(39553725461800043367392+17203831108841472538824*x+45483386678520344593037*y+2703260049547565568088*z))/((92856945980914656+51329763147513032*x-8586501277743859*y-56199770659759016*z)^3)-(128*(-57335208466953058729715954197164+96390872682360153583488333868040*x-372364031472286149332017066304111*z)*(45619694076424722199344+14936846773318822792976*x-3365788117861218576473*y+10130491989577935272320*z))/((85141430232132048+97951351741329392*x-8855616621991191*y-199920422688690560*z)^3)-(5*(-5058036108182894712997605343704+13066181822706485812588287496990*x-23584235630998237996607750176151*z)*(61468981380127448102256+5328427636421850183140*x-4647710007810227520885*y+13344414478836548348450*z))/((46366672189358032+18896234711237580*x-3927118781169095*y-14705346416259850*z)^3)-(256*(-35027435322808897803896166913833+101153824679669203594026224000274*x-443348667941077090029000877418626*z)*(61889933231497708820968+30294916915069669525488*x-4484037822343607626207*y+13934625423713945278848*z))/((45070329471431608+130124049256651728*x-5583613021604317*y-387630670566282112*z)^3)-(24*(-23539469566855513950637813409344+36451820000039413375829754767131*x-87577625291530403453057402554096*z)*(88457226224862447127008+13504083955712971035976*x-6622138801690554356387*y+19322683651036147287512*z))/((92856945980914656+51329763147513032*x-8586501277743859*y-56199770659759016*z)^3)-(112*(97743545586690977941666831119873+189463292388600804291605866927808*x-534599264249120709692835475330432*z)*(801790542801929135637671+732048260009923946735424*x-56975701334774517040256*y+187552638032246240630656*z))/((-3075770275504817+198931044892562752*x+14199788245258112*y-1122852841901814912*z)^3)-(2560*(2304705299858575630109*x-256*(204828849006588248100+19508530860149228990861*y-2445924471668591306496*z))*(-29205293090710790323990469408790736+212589517464418508578145671300087*x+1750806894610755007047140949242022912*z))/((5042560366642267*x-256*(2446745837411900+4901398098088043*y-144207654645973248*z))^3)-(160*(3266813047619306699872+716026618045942942760*x-243780804476456624597*y+718216181537563796776*z)*(52529278437993151034132605337909*x-4*(8646336391489439377118003754263+39602745269819371968458588313429*z)))/((50159316775994592+36243094308305160*x-4827156544231217*y-52318895858217464*z)^3)))/125;
f3=(128*((-24576*(3839508863935892182987929073642496+36103009879073133562313702394913733*x-87732961555209684260488911369472*y)*(24610976415716501050652227*x-256*(-10153609683556422184100+374519398571124540883*y-4145573659500944095488*z)))/((5042560366642267*x-256*(2446745837411900+4901398098088043*y-144207654645973248*z))^3)-(30720*(65108728870058843312625047943313*x-256*(4791937744017588738333042319232+569924119339438478856491194414721*y))*(2304705299858575630109*x-256*(204828849006588248100+19508530860149228990861*y-2445924471668591306496*z)))/((5042560366642267*x-256*(2446745837411900+4901398098088043*y-144207654645973248*z))^3)+(256*(650985307933227267490679218098413+935767027021514282821089562931792*x+12859172907478119575029190058251392*y)*(9439334964924689507817+17499514376929345709248*x+187907876794815451253888*y-21704870055089718153088*z))/((-3075770275504817+198931044892562752*x+14199788245258112*y-1122852841901814912*z)^3)+(1280*(114748411888321695540849692963124+110442377985916695620550654636800*x+775672512286952418453853865599205*y)*(4157117722725769078952+4534359335248895646832*x+26193979470458655189977*y-2382852476120229696128*z))/((45070329471431608+130124049256651728*x-5583613021604317*y-387630670566282112*z)^3)+(1600*(100744894915663705876272277122960+74302925512671884052557401907120*x+343788061485767567210745697763531*y)*(1717566388539311579248*x+7025931019459451548321*y+48*(46537098413809906919-8301700878138964680*z)))/((85141430232132048+97951351741329392*x-8855616621991191*y-199920422688690560*z)^3)+(16*(72249495731635781189477972681776+39691308285862330678445510678381*x+125252403980353077736842003056195*y)*(22670037111266004087968+12461845278544574559640*x+39219302812923818032157*y-46563087562792926056*z))/((50159316775994592+36243094308305160*x-4827156544231217*y-52318895858217464*z)^3)+(640*(505227745581172894057712966825000+155010006988462124695347547225138*x-39602745269819371968458588313429*y)*(3266813047619306699872+716026618045942942760*x-243780804476456624597*y+718216181537563796776*z))/((50159316775994592+36243094308305160*x-4827156544231217*y-52318895858217464*z)^3)+(2*(356681541401645116923690413208956+126814067043212099223976834718490*x+191427609122898840477329914007915*y)*(9101665097092871812176+3063507166600182944940*x+6945927557350563805665*y+1052001549322007294950*z))/((46366672189358032+18896234711237580*x-3927118781169095*y-14705346416259850*z)^3)+(8*(301993014170585471859024964195112+134962043561465977901954677856080*x+309197308873592242001670976702725*y)*(39553725461800043367392+17203831108841472538824*x+45483386678520344593037*y+2703260049547565568088*z))/((92856945980914656+51329763147513032*x-8586501277743859*y-56199770659759016*z)^3)+(128*(4874430224431350455160317539284048+1942615285518540483044478359410032*x-372364031472286149332017066304111*y)*(45619694076424722199344+14936846773318822792976*x-3365788117861218576473*y+10130491989577935272320*z))/((85141430232132048+97951351741329392*x-8855616621991191*y-199920422688690560*z)^3)+((1486971442137244004077030949061728+322769103831727073598968320899320*x-117921178154991189983038750880755*y)*(61468981380127448102256+5328427636421850183140*x-4647710007810227520885*y+13344414478836548348450*z))/((46366672189358032+18896234711237580*x-3927118781169095*y-14705346416259850*z)^3)+(512*(3005184872892536482128059816733656+1654842388128247497540371661628560*x-221674333970538545014500438709313*y)*(61889933231497708820968+30294916915069669525488*x-4484037822343607626207*y+13934625423713945278848*z))/((45070329471431608+130124049256651728*x-5583613021604317*y-387630670566282112*z)^3)+(192*(137644881571986015841084811827840+35619205657210451197984743698883*x-10947203161441300431632175319262*y)*(88457226224862447127008+13504083955712971035976*x-6622138801690554356387*y+19322683651036147287512*z))/((92856945980914656+51329763147513032*x-8586501277743859*y-56199770659759016*z)^3)+(64*(13728575451141247570683309821008705+13111763174706011627610159037098688*x-935548712435961241962462081828256*y)*(801790542801929135637671+732048260009923946735424*x-56975701334774517040256*y+187552638032246240630656*z))/((-3075770275504817+198931044892562752*x+14199788245258112*y-1122852841901814912*z)^3)))/125;

thank you in advance.

RandomCompositions:= proc(n::posint, k::posint)
local
C,
Compositions:= [seq(C-~1, C= combinat:-composition(n+k, k))],
Rand:= rand(1..nops(Compositions))
;
()-> Compositions[Rand()]
end proc:

R:= RandomCompositions(9,6):
n:= 10:
S:= 'R()' $ n;

S := [4, 1, 1, 1, 2, 0], [3, 2, 1, 1, 0, 2], [0, 1, 1, 0, 0, 7], [0, 1, 1, 5, 0, 2], [1, 0, 3, 1, 3, 1],

        [1, 3, 1, 1, 0, 3], [1, 4, 2, 0, 2, 0], [5, 0, 0, 3, 1, 0], [1, 1, 1, 4, 0, 2], [0, 1, 2, 1, 0, 5]

[4, 1, 1, 1, 2, 0] , [1, 1, 1, 4, 0, 2]  and [0, 1, 1, 5, 0, 2] , [0, 1, 2, 1, 0, 5]  are same number 

  but different order.

There are two same sequence. I want to  count  as one, and compile statistics the summation, and 

divide by 8.

the result

0=14/8

1=17/8

2=6/8

...

4=2/8

5=2/8

...