Maple 2017 Questions and Posts

These are Posts and Questions associated with the product, Maple 2017

I used the implicit function to draw two images, how to display only the intersection of two images? Or, how do I draw the x^2+y^2+z^2=1 image under x+y+z=0 condition? Code show as above.Thank you.

 

I want to solve for the coefficients in some multivariate polynomials by equating them to other known multivariate polynomials.

 

Something like this. I have

p[1]=(a+b)*x^2+(a+c)*x*y+d*z;

p[2]=(a-b)*x+e*y*z+f*z^2;

 

I want to impose that p[1]=x^2+2*x*y+3*z and that p[2]=x+4*y*z and I want Maple to tell me the values of (a,b,c,d,e,f).

 

Sounds simple enough, but I have not been able to do it

I am providing analysis for a Graph I have made using the GraphTheory kit. I am attempting to find a way to find the Betweeness Centrality. So far I have only found one example of the code which is being used to find the Betweeness Centrality of a Network found in a pdf (Attatched below). I have been able to alter the code accordingly to my data but the last line requires some further understanding of how Matrices work in Maple. This is the line I fail to understand completely:

"""""""" BetweenessCentrality_data := < node_data[1.., 1] | < seq(add (ad_mat[i, j] * wt_mat[i, j], j = 1.. num_characters), i = 1. . num_characters)> >: BetweenessCentrality_sorted := FlipDimension( x[2])))>, 1)  """"""""

And this is all the code leading up to the line in question:

"""""""" data := FileTools:-JoinPath(["Excel", "Inter station database (2).xls"], base = datadir);

M := ExcelTools:-Import(data, "Hoja2");

edge_data := Matrix(727, 3, (i, j) --> M[i, j+2] );

with(ListTools);

node_data := Matrix(727, 2, (i, j) -->M[i, j+2] );

convert(Matrix(<<node_data>>), list);


listednode_data := convert(Matrix(<<node_data>>), list);

MakeUnique(listednode_data);

UniqueListedNode_data := MakeUnique(listednode_data);

node_data := Matrix(numelems(UniqueListedNode_data), 1, (i, j) -->UniqueListedNode_data[i]);
 

num_edges := RowDimension(edge_data);
 

num_characters := RowDimension(node_data);
 

G := Graph(node_data[() .. (), 1], weighted);
 

for i from 1 to num_edges do

AddEdge(G, [{edge_data[i, 1], edge_data[i, 2]}, edge_data[i, 3]])

end do;

wt_mat := WeightMatrix(G);
ad_mat := AdjacencyMatrix(G); """"""""

To provide further context, my graph is strongly connected.

If anyone could kindly provide a breakdown of the line of code in question, It would be very appreciated. 

Here is the link to the pdf I used as source for my code:https://www.maplesoft.com/applications/view.aspx?SID=154530

 

Hello, I am wondering if Maple is capable of generating a subgraph for a directed, weighed graph with the GraphTheory package. The online resources I can find only include undirected, unweighed graphs. 

can you please include an example with commands that is able to perform the said task?

My name is Viorel Popescu and I am a Ph.D. candidate at University Politehnica of Bucharest, Europe. I was impressed by the article that I found on the internet about Series Solution to Differential Equation with Maple. I am trying to solve the equation g''(r)- r/R*g(r)=0 with initial condition g(2R)=0 and g'(0)=R where R>0 is a positive constant.

I am using Maple 2017 and the following equations gives me in correct result when I run `maple m.mpl` in terminal, however, when I run in using the GUI, the result is correct. (one result is postive while one is negative)

 

 

res := solve({
T000000=1/(1*4.57*10^(-06)+1*2.07*10^(-06)+1*2.83*10^(-06)) + T100000*1*4.57*10^(-06)/(1*4.57*10^(-06)+1*2.07*10^(-06)+1*2.83*10^(-06)) + T010000*1*2.07*10^(-06)/(1*4.57*10^(-06)+1*2.07*10^(-06)+1*2.83*10^(-06)) + T000010*1*2.83*10^(-06)/(1*4.57*10^(-06)+1*2.07*10^(-06)+1*2.83*10^(-06)) ,
T000010=1/(1*4.57*10^(-06)+1*2.07*10^(-06)+4) + T100010*1*4.57*10^(-06)/(1*4.57*10^(-06)+1*2.07*10^(-06)+4) + T010010*1*2.07*10^(-06)/(1*4.57*10^(-06)+1*2.07*10^(-06)+4) + T000000*4/(1*4.57*10^(-06)+1*2.07*10^(-06)+4) ,
T010000=1/(1*4.57*10^(-06)+1*2.83*10^(-06)+4) + T110000*1*4.57*10^(-06)/(1*4.57*10^(-06)+1*2.83*10^(-06)+4) + T010010*1*2.83*10^(-06)/(1*4.57*10^(-06)+1*2.83*10^(-06)+4) + T000000*4/(1*4.57*10^(-06)+1*2.83*10^(-06)+4) ,
T010010=1/(1*4.57*10^(-06)+4) + T000010*4/2/(1*4.57*10^(-06)+4) + T010000*4/2/(1*4.57*10^(-06)+4) ,
T100000=1/(1*2.07*10^(-06)+1*2.83*10^(-06)+4) + T110000*1*2.07*10^(-06)/(1*2.07*10^(-06)+1*2.83*10^(-06)+4) + T100010*1*2.83*10^(-06)/(1*2.07*10^(-06)+1*2.83*10^(-06)+4) + T000000*4/(1*2.07*10^(-06)+1*2.83*10^(-06)+4) ,
T100010=1/(1*2.07*10^(-06)+4) + T000010*4/2/(1*2.07*10^(-06)+4) + T100000*4/2/(1*2.07*10^(-06)+4) ,
T110000=1/(1*2.83*10^(-06)+4) + T010000*4/2/(1*2.83*10^(-06)+4) + T100000*4/2/(1*2.83*10^(-06)+4) }, { T000000,T000010,T010000,T010010,T100000,T100010,T110000 }):
T0 := subs(res, T000000):
printf("%g\n", T0);

 

Hi!

I am very interested in using the "phc.module", which is a module to work with "polynomial homotopy continuation" method. Please, see this paper       PHCmaple.pdf

I have downloaded the following files:  phc.zip

Then, I open (as an "ordinary" maple worksheet) the file "phc_savelib.maple" and execute it, but it seems that I can not use their functions and procedures because it returns errors. 

For instance, follwing the attached PDF,  in the phc_savelib.maple file, define the polynomial system:

 

T := makeSystem([x, y], [], [x^2+y^2-1, x^3+y^3-1])

 

and try to solve the above system 

sols := solve(T)

 

but returns the error 

Error, (in fopen) file or directory does not exist
 

Many thanks in advance for your help!

 

n is a Carmichael number iff for every prime factor p of n, p-1/n-1.

Question: How to find odd squarefree composite numbers n having k distinct prime divisors, and the property that exactly k-1 prime divisors satisfy the Carmichael requirement, p-1/n-1 ?

Examples: 231,1045,1635. In these cases k=3 and the prime divisors satisfying the criteria are the greatest and smallest. I have a code for this but would like to compute the general case, where the criteria is satisfied for precisely any k-1 divisors.

Any assistance greatly appreciated.

David. 

 

Hello everyone, I'm trying to run a simple calculation (Water flowing out of a pressurised container) using a combination of conservation of energy and conservation of mass. I have working models of the same system without pressurisation (purely gravity working) which work fine in Maple, but when re-writing the pressure as a function of the height of the water I receive the error:

"Error, (in DEtools/convertsys) unable to convert to an explicit first-order system".

 

The formula used is:

"Eq1:= -Rho_Water * A_Barrell * v_Barrel = Rho_Water * A_Nozzle * v_Nozzle"

Which returns:

"Eq1:= -25.23733555 * d/dt h_Water(t) = 0.5982 * (-190.1309944 - 13.64385474 * h_Water(t) + (d/dt h_Water(t))2)1/2"

With initial condition:

"ics1:= h_Water(0) = 0.2"

 

After giving the command:

"Sol1:= dsolve({Eq1, ics1}, numeric)"

Maple returns the aforementioned error. When trying to solve non-numerically the output is a list filled with "RootOf" and "_Z". Instinctively I would say the square root in the second part of the equation is the problem here, but I would not know how to fix this. Does anybody have a quick fix for this problem? Or is there a fundamental issue with the equation? Thank you in advance!

I'm trying to solve this set of two equations forn where (EQ1 and EQ2 are already défined in fontions of the followings variables (k, wr ,R,Pi), and i'm using the following loop 

 

eqns:={EQ1,EQ2}:

for i from 1 by 1 to 101 do R:=(i-1):S:=fsolve((eqns), {k, wr},{k=0..10,wr=0..10} ):v(i):=(subs(S,(wr))):w(i):=(subs(S,(k)))end do:
Error, invalid input: subs received fsolve({-0.6391108652e160*k+0.2384499927e160*wr+0.714075224e160*k^3-0.4729440685e160*wr^3-0.4025871558e160*k^5+0.1700629083e159*wr^5-0.4813673552e156*k^9+0.1033594302e160*k^7-0.1044324938e156*wr^7-0.1017755535e159*k^3*wr^4+0.2163976160e160*k^5*wr^2-0.7986601863e160*k^4*wr-0.2729449277e160*k^6*wr+0.8693579523e154*k^3*wr^6+0.4453377949e156*k^4*wr^5-0.2636332727e157*k^5*wr^4-0.5817233940e157*k^7*wr^2+0.5719400327e157*k^6*wr^3-0.2875232976e161*k^2*wr+0.2294793648e161*k*wr^2+0.1483050053e158*k^2*wr^5-0.3944893217e159*k^4*wr^3-0.464413477e159*k^2*wr^3+0.2760407324e157*k^8*wr+0.8238787577e156*k*wr^6-0.1081920595e...
 

i do get a solution for Pi/2 and Pi/3 but beyond this value i get the above error

Hi,

I am trying to write a code for the following simple recurrence:

a(1)=1,

a(n)+1prime—>a(n+1)=a(n)+1,

a(n)+1 composite —>a(n+1)=n+2

if a(n) even, or a(n)+ 3 if a(n) odd.

Data: 1,2,3,6,7,10,11,14,16,17.....

My first attempt is the following:

N:=10:

for k from 1 to N do

X:=1;

if isprime(X+1) then print(X+1);

elif not isprime(X+1) and mod(X,2)=0 

then print(X+2);

else print(X+3);

end if:

end do:

This does not work but I cannot see why. Would somebody mind to help me out with this?

 

Best regards

David.

 

 

 

Hi so the Maple 2017 software froze on the loading screen I have a MacBook Air 2018, I tried restarting my Mac but it says I have to Quit out of Maple 2017, however it isn't allowing me to do so, the software won't quit. Is there anyone that can help me out??? I would gladly appreciate it.

Hello

I am using Maple to solve a couple of differential equations.  Here is what I did so far

k := 141/10000;
yB0 := 296/1000;
e := -148/1000;
Ff0 := 67844/1000;
Far0 := 323066/1000;
FB0 := 135688/1000;
P0 := 10;
x0 := 0;
a := 38/1000;
dsys:={diff(x(w),w)=(k*((yB0*p(w)*(1 - x(w)))/(1 + e*x(w)))^(1/3)*(Ff0/(Far0 + FB0)*p(w)*((Ff0/FB0 - 1/2*x(w))/(1 + e*x(w))))^(2/3))/FB0,
diff(p(w),w)=P0*(-a)/(2*p(w)/P0)*(1 + e*x(w)),x(0)=x0,p(0)=P0}:
dsn1:≔dsolve(dsys,numeric,[x(w),p(w)],stiff=true);

Maple returns neither an error message or a solution.   I am sure I have mistyped something or did not understand how dsolve works at all.  

Can you help me out?

Many thanks

Ed

PS. How to plot the solution?  

 

 

 

Hi all,

I am trying to find numerical integration of a complex function (Bessel+ trigonometric function) in (r, theta). MAPLE is unable to solve it due to high memory allocation issues. Function is like this f(r.theta)=Bessel(1,r)+cos(theta)*f(r)+....50 terms.

I am using  evalf( Int(f(r,theta), [r=0..1, theta=0..Pi])).

Will term by term integration be helpful? How to do it in maple?

PS: If I decrease the number of digits, I get the result fast.
 

restart;

F1 := 0.1e10 * (0.55776153956804000740336392666745e0 * r ^ 2 - 0.18915469024923561670746189899598e-134609736 * BesselJ(0.0e0, 0.15157937163140142799278350422223e3 * r) + 0.10159683864017545475828989384714e-98384011 * BesselJ(0.0e0, 0.12958780324510399675374141784136e3 * r) + 0.59829761821461366846048256106725e-56462782 * BesselJ(0.0e0, 0.98170950730790781973537759160851e2 * r) + 0.14811094053601555275542685914404e-80227782 * BesselJ(0.0e0, 0.11702112189889242502757649460146e3 * r) + 0.33892512681723589723181533606428e-7313754 * BesselJ(0.0e0, 0.35332307550083865102634479022519e2 * r) - 0.51262328796358933950059817332311e-2254297 * BesselJ(0.0e0, 0.19615858510468242021125065884138e2 * r) - 0.12881247566594125484600726823569e-19254076 * BesselJ(0.0e0, 0.57327525437901010745090504243751e2 * r) + 0.11118751423887112574088244798447e-31252221 * BesselJ(0.0e0, 0.73036895225573834826506117569092e2 * r) - 0.51777724984261891154172697895593e-33998785 * BesselJ(0.0e0, 0.76178699584641457572852614623535e2 * r) + 0.12182571270348008146031905708415e-42932343 * BesselJ(0.0e0, 0.85604019436350230965949425493380e2 * r) + 0.40737194122764952321439991068058e-36860993 * BesselJ(0.0e0, 0.79320487175476299391184484872488e2 * r) - 0.50622470024129990724764923292822e-6070573 * BesselJ(0.0e0, 0.32189679910974403626622984104460e2 * r) - 0.46336835054606228289459855037304e-46141486 * BesselJ(0.0e0, 0.88745767144926306903735916434854e2 * r) + 0.13326755919882635551499433439984e-71843536 * BesselJ(0.0e0, 0.11073775478089921510860865288827e3 * r) - 0.51549643524094258017297656487619e-15264332 * BesselJ(0.0e0, 0.51043535183571509468733034633224e2 * r) + 0.63020619016879105779529017065422e-17201382 * BesselJ(0.0e0, 0.54185553641061320532099966214534e2 * r) - 0.34143530857990731804462883496266e-75977837 * BesselJ(0.0e0, 0.11387944084759499813488417492843e3 * r) + 0.29817206128159554191843363526765e-49466273 * BesselJ(0.0e0, 0.91887504251694985280553622214490e2 * r) - 0.32466998108445575875801048023258e-52906705 * BesselJ(0.0e0, 0.95029231808044695268050998187174e2 * r) - 0.18661427630098737592148946513116e-60134503 * BesselJ(0.0e0, 0.10131266182303873013714105638865e3 * r) - 0.88067954684538428870806207522441e-67824881 * BesselJ(0.0e0, 0.10759606325950917218267036427761e3 * r) + 0.13287757851408088906808371290053e-1290876``98 * BesselJ(0.0e0, 0.14843772662034223039593927702627e3 * r) - 0.28491383339723867983586755114008e-93671487 * BesselJ(0.0e0, 0.12644613869851659569779448049584e3 * r) + 0.44151440493072282554074854252808e-21422416 * BesselJ(0.0e0, 0.60469457845347491559398749808383e2 * r) - 0.25433459757254658126695515265514e-23706400 * BesselJ(0.0e0, 0.63611356698481232631039762417874e2 * r) + 0.31838472287249562307154488541348e-118390557 * BesselJ(0.0e0, 0.14215442965585902903270090809976e3 * r) + 0.24664036351722993558633516210405e-26106029 * BesselJ(0.0e0, 0.66753226734098493415305259750042e2 * r) - 0.35291670105094410350434844041935e-8672580 * BesselJ(0.0e0, 0.38474766234771615112052197557717e2 * r) + 0.58664491893391140222815167210588e-10147051 * BesselJ(0.0e0, 0.41617094212814450885863516805060e2 * r) - 0.15835272073861680035000959411566e-11737166 * BesselJ(0.0e0, 0.44759318997652821732779352713212e2 * r) + 0.70213789662657167106991346854437e-13442927 * BesselJ(0.0e0, 0.47901460887185447121274008722508e2 * r) + 0.20203042047105171656770921613101e-86016 * BesselJ(0.0e0, 0.38317059702075123156144358863082e1 * r) + 0.45595799288913858149685893872177e-140247419 * BesselJ(0.0e0, 0.15472101451628595352476655565184e3 * r) - 0.18611154629569865685380386607775e-146000746 * BesselJ(0.0e0, 0.15786265540193029780509466960866e3 * r) + 0.98529688671644920915913795962299e-63921870 * BesselJ(0.0e0, 0.10445436579128276007136342813961e3 * r) - 0.15806285101030450527944027463056e-123681305 * BesselJ(0.0e0, 0.14529607934519590723242215085501e3 * r) - 0.40315574736579460691059726643094e-28621303 * BesselJ(0.0e0, 0.69895071837495773969730536435500e2 * r) + 0.62723521218202757338090566184844e-108155995 * BesselJ(0.0e0, 0.13587112236478900059180156821946e3 * r) - 0.10859734567264554119513113490716e-113215453 * BesselJ(0.0e0, 0.13901277738865970417843354613596e3 * r) - 0.54175511325922018873646654014932e-39838846 * BesselJ(0.0e0, 0.82462259914373556453986610648781e2 * r) + 0.11283650227585469604741653680022e-4943036 * BesselJ(0.0e0, 0.29046828534916855066647819883532e2 * r) - 0.61345791140260163801601678872534e-103212181 * BesselJ(0.0e0, 0.13272946438850961588677459735175e3 * r) - 0.10878629914720505255262338938331e-84593372 * BesselJ(0.0e0, 0.12016279832814900375811940782917e3 * r) - 0.35054349658929943485990383440882e-3931145 * BesselJ(0.0e0, 0.25903672087618382625495855445980e2 * r) + 0.13529453916914935758397358737774e-89074607 * BesselJ(0.0e0, 0.12330447048863571801676003206877e3 * r) + 0.13471689526126410315073637771645e-3034898 * BesselJ(0.0e0, 0.22760084380592771898053005152182e2 * r) - 0.21295581245266175979652384428576e-288353 * BesselJ(0.0e0, 0.70155866698156187535370499814765e1 * r) + 0.46293568384524693637583038682636e-606366 * BesselJ(0.0e0, 0.10173468135062722077185711776776e2 * r) - 0.65373336840252622743371660187403e-1040030 * BesselJ(0.0e0, 0.13323691936314223032393684126948e2 * r) + 0.12271878942218097649114096289979e-1589340 * BesselJ(0.0e0, 0.16470630050877632812552460470990e2 * r) + 0.30096533794321654779481815801012e5) * (-0.84195432401461277308031602263610e-5 * r ^ 2 - 0.59149959490724929627371164952978e-2 * r ^ 6 * cos(0.6e1 * theta) + 0.44528672504236299477606103483348e-2 * r ^ 9 * cos(0.9e1 * theta) + 0.2112306765385091377525007041829e-2 * r ^ 25 * cos(0.25e2 * theta) - 0.67200617360940427597733246769568e-3 * r ^ 4 * cos(0.4e1 * theta) + 0.8077651557524848874997646779728e-4 * r ^ 38 * cos(0.38e2 * theta) + 0.6431431133931729186611840353106e-3 * r ^ 39 * cos(0.39e2 * theta) + 0.6638764085868884552072751263020e-3 * r ^ 40 * cos(0.40e2 * theta) + 0.3077586813267194148977094233961e-3 * r ^ 41 * cos(0.41e2 * theta) - 0.1856408707409825202502168626613e-3 * r ^ 42 * cos(0.42e2 * theta) - 0.4195028383398335941571877904622e-3 * r ^ 43 * cos(0.43e2 * theta) - 0.3706398326158304378037548737582e-3 * r ^ 44 * cos(0.44e2 * theta) - 0.7999587757612915190037434403564e-4 * r ^ 45 * cos(0.45e2 * theta) + 0.1737050010593172373976692973078e-3 * r ^ 46 * cos(0.46e2 * theta) + 0.2156346448293426610250334073280e-3 * r ^ 47 * cos(0.47e2 * theta) + 0.8688707406587637755715273073496e-4 * r ^ 48 * cos(0.48e2 * theta) - 0.2566545888070136544474329645476e-4 * r ^ 49 * cos(0.49e2 * theta) + 0.10879633813910334336257501999693e-1 * cos(theta) * r + 0.1887562703232630941270016328998e-2 * r ^ 24 * cos(0.24e2 * theta) + 0.9513343462787182229625573235371e-3 * r ^ 26 * cos(0.26e2 * theta) - 0.6163648649547716429383661026270e-3 * r ^ 27 * cos(0.27e2 * theta) - 0.1638476483444926784339005153548e-2 * r ^ 28 * cos(0.28e2 * theta) - 0.1544747773264052898936010069036e-2 * r ^ 29 * cos(0.29e2 * theta) - 0.5206686266979668543527923877478e-3 * r ^ 30 * cos(0.30e2 * theta) + 0.7031766719478684183248753358164e-3 * r ^ 31 * cos(0.31e2 * theta) + 0.1364403772746535517159915014059e-2 * r ^ 32 * cos(0.32e2 * theta) + 0.10540246948583098852767644351809e-2 * r ^ 33 * cos(0.33e2 * theta) + 0.1949337811874134263703020015791e-3 * r ^ 34 * cos(0.34e2 * theta) - 0.7191715359288498000802128285804e-3 * r ^ 35 * cos(0.35e2 * theta) - 0.10227876151057534138247065986153e-2 * r ^ 36 * cos(0.36e2 * theta) - 0.6867126825080510201446558832207e-3 * r ^ 37 * cos(0.37e2 * theta) - 0.51907452513946892830363140141895e-2 * r ^ 5 * cos(0.5e1 * theta) + 0.15481206149695126077925147166938e-2 * r ^ 11 * cos(0.11e2 * theta) - 0.18891064144929437714573633077525e-2 * r ^ 12 * cos(0.12e2 * theta) - 0.3811736195725823688361734620913e-2 * r ^ 13 * cos(0.13e2 * theta) - 0.32257343081162300403533436479469e-2 * r ^ 14 * cos(0.14e2 * theta) - 0.6456518231629053621129825002098e-3 * r ^ 15 * cos(0.15e2 * theta) + 0.20319096805014454478199422911684e-2 * r ^ 16 * cos(0.16e2 * theta) + 0.3233144446775015541635116158538e-2 * r ^ 17 * cos(0.17e2 * theta) + 0.23137228128708316785559166203584e-2 * r ^ 18 * cos(0.18e2 * theta) + 0.6898483226498941349817978084256e-4 * r ^ 19 * cos(0.19e2 * theta) - 0.20285262491678306920628881668352e-2 * r ^ 20 * cos(0.20e2 * theta) - 0.2671173199674743523515178373090e-2 * r ^ 21 * cos(0.21e2 * theta) - 0.15775142288031750532503075313091e-2 * r ^ 22 * cos(0.22e2 * theta) + 0.3622094777240520457049718035053e-3 * r ^ 23 * cos(0.23e2 * theta) + 0.14579067481459940998484958894370e-2 * r ^ 8 * cos(0.8e1 * theta) + 0.43385218600667457865829805287215e-2 * r ^ 10 * cos(0.10e2 * theta) - 0.29324228962818139404116534560943e-2 * r ^ 7 * cos(0.7e1 * theta) + 0.54771662980043457997274959739776e-2 * r ^ 3 * cos(0.3e1 * theta) - 0.11907324829492592983826593268542e-1 + 0.99737018277250342942042004599405e6 * (0.10375843065514893709650453544669e-7 * r ^ 4 - 0.24066724220589275560649004814238e-8 * r ^ 2) * cos(0.2e1 * theta) / r ^ 2 - 0.18524693450872080736996040590111e-1589345 * BesselJ(0.0e0, 0.16470630050877632812552460470990e2 * r) - 0.20335836094200343189896872255293e-3034903 * BesselJ(0.0e0, 0.22760084380592771898053005152182e2 * r) + 0.32146186927377989454999075542184e-288358 * BesselJ(0.0e0, 0.70155866698156187535370499814765e1 * r) - 0.69881243704258704205303920297122e-606371 * BesselJ(0.0e0, 0.10173468135062722077185711776776e2 * r) + 0.98682608468381340045946744187651e-1040035 * BesselJ(0.0e0, 0.13323691936314223032393684126948e2 * r) - 0.20423032817438260168628393904163e-89074612 * BesselJ(0.0e0, 0.12330447048863571801676003206877e3 * r) + 0.16393027894394588837550747507414e-113215458 * BesselJ(0.0e0, 0.13901277738865970417843354613596e3 * r) + 0.81779224239606095156885663441587e-39838851 * BesselJ(0.0e0, 0.82462259914373556453986610648781e2 * r) - 0.17032938676879018403348115316985e-4943041 * BesselJ(0.0e0, 0.29046828534916855066647819883532e2 * r) + 0.92602932340297485357655867631396e-103212186 * BesselJ(0.0e0, 0.13272946438850961588677459735175e3 * r) + 0.16421550871268572218657911635481e-84593377 * BesselJ(0.0e0, 0.12016279832814900375811940782917e3 * r) + 0.52915375437527581357423578813141e-3931150 * BesselJ(0.0e0, 0.25903672087618382625495855445980e2 * r) + 0.77815414272085141864206462412262e-15264337 * BesselJ(0.0e0, 0.51043535183571509468733034633224e2 * r) - 0.95131124896907983486241420998755e-17201387 * BesselJ(0.0e0, 0.54185553641061320532099966214534e2 * r) + 0.51540472771347914200070162230077e-75977842 * BesselJ(0.0e0, 0.11387944084759499813488417492843e3 * r) - 0.45009782583936088946734982085640e-49466278 * BesselJ(0.0e0, 0.91887504251694985280553622214490e2 * r) + 0.49009706668463083583947296301775e-52906710 * BesselJ(0.0e0, 0.95029231808044695268050998187174e2 * r) + 0.28169869327339522936720076403132e-60134508 * BesselJ(0.0e0, 0.10131266182303873013714105638865e3 * r) + 0.13294067445237467596212175135530e-67824885 * BesselJ(0.0e0, 0.10759606325950917218267036427761e3 * r) - 0.20058186851887448492658350947366e-129087703 * BesselJ(0.0e0, 0.14843772662034223039593927702627e3 * r) + 0.43008421517583172146652387481621e-93671492 * BesselJ(0.0e0, 0.12644613869851659569779448049584e3 * r) - 0.66647650649066255093532041895905e-21422421 * BesselJ(0.0e0, 0.60469457845347491559398749808383e2 * r) + 0.38392413062141555362678468281752e-23706405 * BesselJ(0.0e0, 0.63611356698481232631039762417874e2 * r) - 0.48060931976467196435085585083844e-118390562 * BesselJ(0.0e0, 0.14215442965585902903270090809976e3 * r) - 0.37230950111886614086127736374754e-26106034 * BesselJ(0.0e0, 0.66753226734098493415305259750042e2 * r) + 0.53273616301499657528989740768063e-8672585 * BesselJ(0.0e0, 0.38474766234771615112052197557717e2 * r) - 0.88555447286690435479201942884554e-10147056 * BesselJ(0.0e0, 0.41617094212814450885863516805060e2 * r) + 0.23903720225781678909977638730792e-11737171 * BesselJ(0.0e0, 0.44759318997652821732779352713212e2 * r) - 0.10598938725267772368055360453741e-13442931 * BesselJ(0.0e0, 0.47901460887185447121274008722508e2 * r) - 0.30496972994915901977125629292157e-86021 * BesselJ(0.0e0, 0.38317059702075123156144358863082e1 * r) - 0.68827944640884252540240135035619e-140247424 * BesselJ(0.0e0, 0.15472101451628595352476655565184e3 * r) + 0.28093981036064987725074202641260e-146000751 * BesselJ(0.0e0, 0.15786265540193029780509466960866e3 * r) - 0.14873291099481638062068892057166e-63921874 * BesselJ(0.0e0, 0.10445436579128276007136342813961e3 * r) + 0.23859963700126918177896460503756e-123681310 * BesselJ(0.0e0, 0.14529607934519590723242215085501e3 * r) + 0.60857319959503281138409206408861e-28621308 * BesselJ(0.0e0, 0.69895071837495773969730536435500e2 * r) - 0.94682648696048924172260521336169e-108156000 * BesselJ(0.0e0, 0.13587112236478900059180156821946e3 * r) + 0.28553350861432233569650200943679e-134609741 * BesselJ(0.0e0, 0.15157937163140142799278350422223e3 * r) - 0.15336284689969342456370426833116e-98384016 * BesselJ(0.0e0, 0.12958780324510399675374141784136e3 * r) - 0.90314449987634539477129986599199e-56462787 * BesselJ(0.0e0, 0.98170950730790781973537759160851e2 * r) - 0.22357699119008062011176340166029e-80227787 * BesselJ(0.0e0, 0.11702112189889242502757649460146e3 * r) - 0.51161554857649418772612124539227e-7313759 * BesselJ(0.0e0, 0.35332307550083865102634479022519e2 * r) + 0.77381705849741819343661724258774e-2254302 * BesselJ(0.0e0, 0.19615858510468242021125065884138e2 * r) + 0.19444549898144465612468716205102e-19254081 * BesselJ(0.0e0, 0.57327525437901010745090504243751e2 * r) - 0.16784020006534355647552255243370e-31252226 * BesselJ(0.0e0, 0.73036895225573834826506117569092e2 * r) + 0.78159708666719140456536882061442e-33998790 * BesselJ(0.0e0, 0.76178699584641457572852614623535e2 * r) - 0.18389881393811040868057686236036e-42932348 * BesselJ(0.0e0, 0.85604019436350230965949425493380e2 * r) - 0.61493764461507094694745129374163e-36860998 * BesselJ(0.0e0, 0.79320487175476299391184484872488e2 * r) + 0.76415823798329557427383241351545e-6070578 * BesselJ(0.0e0, 0.32189679910974403626622984104460e2 * r) + 0.69946555772905592227422733556311e-46141491 * BesselJ(0.0e0, 0.88745767144926306903735916434854e2 * r) - 0.20117055364775216522977716192738e-71843541 * BesselJ(0.0e0, 0.11073775478089921510860865288827e3 * r) + 0.24003433134624560908493351044670e-2 * cos(0.2e1 * theta)) * r;

0.1e10*(30096.533794321654779481815801012+.55776153956804000740336392666745*r^2-0.18915469024923561670746189899598e-134609736*BesselJ(0., 151.57937163140142799278350422223*r)+0.10159683864017545475828989384714e-98384011*BesselJ(0., 129.58780324510399675374141784136*r)+0.59829761821461366846048256106725e-56462782*BesselJ(0., 98.170950730790781973537759160851*r)+0.14811094053601555275542685914404e-80227782*BesselJ(0., 117.02112189889242502757649460146*r)+0.33892512681723589723181533606428e-7313754*BesselJ(0., 35.332307550083865102634479022519*r)-0.51262328796358933950059817332311e-2254297*BesselJ(0., 19.615858510468242021125065884138*r)-0.12881247566594125484600726823569e-19254076*BesselJ(0., 57.327525437901010745090504243751*r)+0.11118751423887112574088244798447e-31252221*BesselJ(0., 73.036895225573834826506117569092*r)-0.51777724984261891154172697895593e-33998785*BesselJ(0., 76.178699584641457572852614623535*r)+0.12182571270348008146031905708415e-42932343*BesselJ(0., 85.604019436350230965949425493380*r)+0.40737194122764952321439991068058e-36860993*BesselJ(0., 79.320487175476299391184484872488*r)-0.50622470024129990724764923292822e-6070573*BesselJ(0., 32.189679910974403626622984104460*r)-0.46336835054606228289459855037304e-46141486*BesselJ(0., 88.745767144926306903735916434854*r)+0.13326755919882635551499433439984e-71843536*BesselJ(0., 110.73775478089921510860865288827*r)-0.51549643524094258017297656487619e-15264332*BesselJ(0., 51.043535183571509468733034633224*r)+0.63020619016879105779529017065422e-17201382*BesselJ(0., 54.185553641061320532099966214534*r)-0.34143530857990731804462883496266e-75977837*BesselJ(0., 113.87944084759499813488417492843*r)+0.29817206128159554191843363526765e-49466273*BesselJ(0., 91.887504251694985280553622214490*r)-0.32466998108445575875801048023258e-52906705*BesselJ(0., 95.029231808044695268050998187174*r)-0.18661427630098737592148946513116e-60134503*BesselJ(0., 101.31266182303873013714105638865*r)-0.88067954684538428870806207522441e-67824881*BesselJ(0., 107.59606325950917218267036427761*r)+0.13287757851408088906808371290053e-129087698*BesselJ(0., 148.43772662034223039593927702627*r)-0.28491383339723867983586755114008e-93671487*BesselJ(0., 126.44613869851659569779448049584*r)+0.44151440493072282554074854252808e-21422416*BesselJ(0., 60.469457845347491559398749808383*r)-0.25433459757254658126695515265514e-23706400*BesselJ(0., 63.611356698481232631039762417874*r)+0.31838472287249562307154488541348e-118390557*BesselJ(0., 142.15442965585902903270090809976*r)+0.24664036351722993558633516210405e-26106029*BesselJ(0., 66.753226734098493415305259750042*r)-0.35291670105094410350434844041935e-8672580*BesselJ(0., 38.474766234771615112052197557717*r)+0.58664491893391140222815167210588e-10147051*BesselJ(0., 41.617094212814450885863516805060*r)-0.15835272073861680035000959411566e-11737166*BesselJ(0., 44.759318997652821732779352713212*r)+0.70213789662657167106991346854437e-13442927*BesselJ(0., 47.901460887185447121274008722508*r)+0.20203042047105171656770921613101e-86016*BesselJ(0., 3.8317059702075123156144358863082*r)+0.45595799288913858149685893872177e-140247419*BesselJ(0., 154.72101451628595352476655565184*r)-0.18611154629569865685380386607775e-146000746*BesselJ(0., 157.86265540193029780509466960866*r)+0.98529688671644920915913795962299e-63921870*BesselJ(0., 104.45436579128276007136342813961*r)-0.15806285101030450527944027463056e-123681305*BesselJ(0., 145.29607934519590723242215085501*r)-0.40315574736579460691059726643094e-28621303*BesselJ(0., 69.895071837495773969730536435500*r)+0.62723521218202757338090566184844e-108155995*BesselJ(0., 135.87112236478900059180156821946*r)-0.10859734567264554119513113490716e-113215453*BesselJ(0., 139.01277738865970417843354613596*r)-0.54175511325922018873646654014932e-39838846*BesselJ(0., 82.462259914373556453986610648781*r)+0.11283650227585469604741653680022e-4943036*BesselJ(0., 29.046828534916855066647819883532*r)-0.61345791140260163801601678872534e-103212181*BesselJ(0., 132.72946438850961588677459735175*r)-0.10878629914720505255262338938331e-84593372*BesselJ(0., 120.16279832814900375811940782917*r)-0.35054349658929943485990383440882e-3931145*BesselJ(0., 25.903672087618382625495855445980*r)+0.13529453916914935758397358737774e-89074607*BesselJ(0., 123.30447048863571801676003206877*r)+0.13471689526126410315073637771645e-3034898*BesselJ(0., 22.760084380592771898053005152182*r)-0.21295581245266175979652384428576e-288353*BesselJ(0., 7.0155866698156187535370499814765*r)+0.46293568384524693637583038682636e-606366*BesselJ(0., 10.173468135062722077185711776776*r)-0.65373336840252622743371660187403e-1040030*BesselJ(0., 13.323691936314223032393684126948*r)+0.12271878942218097649114096289979e-1589340*BesselJ(0., 16.470630050877632812552460470990*r))*(-0.11907324829492592983826593268542e-1-0.59149959490724929627371164952978e-2*r^6*cos(6.*theta)+0.44528672504236299477606103483348e-2*r^9*cos(9.*theta)+0.2112306765385091377525007041829e-2*r^25*cos(25.*theta)-0.67200617360940427597733246769568e-3*r^4*cos(4.*theta)+0.8077651557524848874997646779728e-4*r^38*cos(38.*theta)+0.6431431133931729186611840353106e-3*r^39*cos(39.*theta)+0.6638764085868884552072751263020e-3*r^40*cos(40.*theta)+0.3077586813267194148977094233961e-3*r^41*cos(41.*theta)-0.1856408707409825202502168626613e-3*r^42*cos(42.*theta)-0.4195028383398335941571877904622e-3*r^43*cos(43.*theta)-0.3706398326158304378037548737582e-3*r^44*cos(44.*theta)-0.7999587757612915190037434403564e-4*r^45*cos(45.*theta)+0.1737050010593172373976692973078e-3*r^46*cos(46.*theta)+0.2156346448293426610250334073280e-3*r^47*cos(47.*theta)+0.8688707406587637755715273073496e-4*r^48*cos(48.*theta)-0.2566545888070136544474329645476e-4*r^49*cos(49.*theta)+0.10879633813910334336257501999693e-1*cos(theta)*r+0.1887562703232630941270016328998e-2*r^24*cos(24.*theta)+0.9513343462787182229625573235371e-3*r^26*cos(26.*theta)-0.6163648649547716429383661026270e-3*r^27*cos(27.*theta)-0.1638476483444926784339005153548e-2*r^28*cos(28.*theta)-0.1544747773264052898936010069036e-2*r^29*cos(29.*theta)-0.5206686266979668543527923877478e-3*r^30*cos(30.*theta)+0.7031766719478684183248753358164e-3*r^31*cos(31.*theta)+0.1364403772746535517159915014059e-2*r^32*cos(32.*theta)+0.10540246948583098852767644351809e-2*r^33*cos(33.*theta)+0.1949337811874134263703020015791e-3*r^34*cos(34.*theta)-0.7191715359288498000802128285804e-3*r^35*cos(35.*theta)-0.10227876151057534138247065986153e-2*r^36*cos(36.*theta)-0.6867126825080510201446558832207e-3*r^37*cos(37.*theta)-0.51907452513946892830363140141895e-2*r^5*cos(5.*theta)+0.15481206149695126077925147166938e-2*r^11*cos(11.*theta)-0.18891064144929437714573633077525e-2*r^12*cos(12.*theta)-0.3811736195725823688361734620913e-2*r^13*cos(13.*theta)-0.32257343081162300403533436479469e-2*r^14*cos(14.*theta)-0.6456518231629053621129825002098e-3*r^15*cos(15.*theta)+0.20319096805014454478199422911684e-2*r^16*cos(16.*theta)+0.3233144446775015541635116158538e-2*r^17*cos(17.*theta)+0.23137228128708316785559166203584e-2*r^18*cos(18.*theta)+0.6898483226498941349817978084256e-4*r^19*cos(19.*theta)-0.20285262491678306920628881668352e-2*r^20*cos(20.*theta)-0.2671173199674743523515178373090e-2*r^21*cos(21.*theta)-0.15775142288031750532503075313091e-2*r^22*cos(22.*theta)+0.3622094777240520457049718035053e-3*r^23*cos(23.*theta)+0.14579067481459940998484958894370e-2*r^8*cos(8.*theta)+0.43385218600667457865829805287215e-2*r^10*cos(10.*theta)-0.29324228962818139404116534560943e-2*r^7*cos(7.*theta)+0.54771662980043457997274959739776e-2*r^3*cos(3.*theta)-0.84195432401461277308031602263610e-5*r^2+0.28553350861432233569650200943679e-134609741*BesselJ(0., 151.57937163140142799278350422223*r)-0.15336284689969342456370426833116e-98384016*BesselJ(0., 129.58780324510399675374141784136*r)-0.90314449987634539477129986599199e-56462787*BesselJ(0., 98.170950730790781973537759160851*r)-0.22357699119008062011176340166029e-80227787*BesselJ(0., 117.02112189889242502757649460146*r)-0.51161554857649418772612124539227e-7313759*BesselJ(0., 35.332307550083865102634479022519*r)+0.77381705849741819343661724258774e-2254302*BesselJ(0., 19.615858510468242021125065884138*r)+0.19444549898144465612468716205102e-19254081*BesselJ(0., 57.327525437901010745090504243751*r)-0.16784020006534355647552255243370e-31252226*BesselJ(0., 73.036895225573834826506117569092*r)+0.78159708666719140456536882061442e-33998790*BesselJ(0., 76.178699584641457572852614623535*r)-0.18389881393811040868057686236036e-42932348*BesselJ(0., 85.604019436350230965949425493380*r)-0.61493764461507094694745129374163e-36860998*BesselJ(0., 79.320487175476299391184484872488*r)+0.76415823798329557427383241351545e-6070578*BesselJ(0., 32.189679910974403626622984104460*r)+0.69946555772905592227422733556311e-46141491*BesselJ(0., 88.745767144926306903735916434854*r)-0.20117055364775216522977716192738e-71843541*BesselJ(0., 110.73775478089921510860865288827*r)+0.77815414272085141864206462412262e-15264337*BesselJ(0., 51.043535183571509468733034633224*r)-0.95131124896907983486241420998755e-17201387*BesselJ(0., 54.185553641061320532099966214534*r)+0.51540472771347914200070162230077e-75977842*BesselJ(0., 113.87944084759499813488417492843*r)-0.45009782583936088946734982085640e-49466278*BesselJ(0., 91.887504251694985280553622214490*r)+0.49009706668463083583947296301775e-52906710*BesselJ(0., 95.029231808044695268050998187174*r)+0.28169869327339522936720076403132e-60134508*BesselJ(0., 101.31266182303873013714105638865*r)+0.13294067445237467596212175135530e-67824885*BesselJ(0., 107.59606325950917218267036427761*r)-0.20058186851887448492658350947366e-129087703*BesselJ(0., 148.43772662034223039593927702627*r)+0.43008421517583172146652387481621e-93671492*BesselJ(0., 126.44613869851659569779448049584*r)-0.66647650649066255093532041895905e-21422421*BesselJ(0., 60.469457845347491559398749808383*r)+0.38392413062141555362678468281752e-23706405*BesselJ(0., 63.611356698481232631039762417874*r)-0.48060931976467196435085585083844e-118390562*BesselJ(0., 142.15442965585902903270090809976*r)-0.37230950111886614086127736374754e-26106034*BesselJ(0., 66.753226734098493415305259750042*r)+0.53273616301499657528989740768063e-8672585*BesselJ(0., 38.474766234771615112052197557717*r)-0.88555447286690435479201942884554e-10147056*BesselJ(0., 41.617094212814450885863516805060*r)+0.23903720225781678909977638730792e-11737171*BesselJ(0., 44.759318997652821732779352713212*r)-0.10598938725267772368055360453741e-13442931*BesselJ(0., 47.901460887185447121274008722508*r)-0.30496972994915901977125629292157e-86021*BesselJ(0., 3.8317059702075123156144358863082*r)-0.68827944640884252540240135035619e-140247424*BesselJ(0., 154.72101451628595352476655565184*r)+0.28093981036064987725074202641260e-146000751*BesselJ(0., 157.86265540193029780509466960866*r)-0.14873291099481638062068892057166e-63921874*BesselJ(0., 104.45436579128276007136342813961*r)+0.23859963700126918177896460503756e-123681310*BesselJ(0., 145.29607934519590723242215085501*r)+0.60857319959503281138409206408861e-28621308*BesselJ(0., 69.895071837495773969730536435500*r)-0.94682648696048924172260521336169e-108156000*BesselJ(0., 135.87112236478900059180156821946*r)+0.16393027894394588837550747507414e-113215458*BesselJ(0., 139.01277738865970417843354613596*r)+0.81779224239606095156885663441587e-39838851*BesselJ(0., 82.462259914373556453986610648781*r)-0.17032938676879018403348115316985e-4943041*BesselJ(0., 29.046828534916855066647819883532*r)+0.92602932340297485357655867631396e-103212186*BesselJ(0., 132.72946438850961588677459735175*r)+0.16421550871268572218657911635481e-84593377*BesselJ(0., 120.16279832814900375811940782917*r)+0.52915375437527581357423578813141e-3931150*BesselJ(0., 25.903672087618382625495855445980*r)-0.20423032817438260168628393904163e-89074612*BesselJ(0., 123.30447048863571801676003206877*r)-0.20335836094200343189896872255293e-3034903*BesselJ(0., 22.760084380592771898053005152182*r)+0.32146186927377989454999075542184e-288358*BesselJ(0., 7.0155866698156187535370499814765*r)-0.69881243704258704205303920297122e-606371*BesselJ(0., 10.173468135062722077185711776776*r)+0.98682608468381340045946744187651e-1040035*BesselJ(0., 13.323691936314223032393684126948*r)-0.18524693450872080736996040590111e-1589345*BesselJ(0., 16.470630050877632812552460470990*r)+0.24003433134624560908493351044670e-2*cos(2.*theta)+997370.18277250342942042004599405*(0.10375843065514893709650453544669e-7*r^4-0.24066724220589275560649004814238e-8*r^2)*cos(2.*theta)/r^2)*r

(1)

evalf(subs(r=1,theta=Pi/4,F1))

0.7135632392e12

(2)

Digits:=16;

16

(3)

int_F1:=evalf(Int(F1,[theta=Pi/4..2*Pi-Pi/4,r=0..1]));

Warning,  computation interrupted

 

``


 

Download Maple_prime_integration.mw

Thanks.

Hi, I am trying to solve a recurrence with rsolve:

rsolve({f(1) = 1, f(n) = n + sum(f(i), i=1..n-1)}, f)

Unfontunately, maple just prints the same function without evaluation:

rsolve({f(1) = 1, f(n) = n + sum(f(i), i=1..n-1)}, f)

How to get the expected result 2^n - 1 from maple?

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