Maple 2017 Questions and Posts

Problem in Solving integral in Maple...

Asked by: pooyan1990 35

September 11 2019

1 3

Hello,

I have a problem in solving an integral in maple. I can't solve the below integral in maple and it returns the integral itself to me. I also attach an image from the integral if here is not clearly shown. I want maple to return me just a number. can anyone help me in this?

Thank you

int(sin(beta)*(-0.4447569104e-1*beta(10)^3+1.846983291*beta(10)^2+78.88888890*beta(10)+620.4645491)/(9.+.6366197724*beta(10))^2, beta = 0 .. (1/2)*Pi)

How do I plot a function under some constrainets...

Asked by: dingtianlidi 55

August 31 2019

2 2

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.

Equating multiple multivariate polynomials to find...

Asked by: mnovaes 25

August 26 2019

1 1

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

Struggling to understand a line of code...

Asked by: Scythor 30

August 20 2019

1 2

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

How to create subgraph for a directed graph...

Asked by: Scythor 30

August 08 2019

2 2

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?

How do I solve a Series Solution to Differential E...

Asked by: MichaelVio 40

July 24 2019

2 6

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.

Maple 2017 gives wrong results...

Asked by: 1a1a11a 5

July 12 2019

1 4

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);

How to find “almost Carmichael” numbers...

Asked by: David Sycamore 95

June 17 2019

0 5

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.

Error, unable to convert to an explicit first-orde...

Asked by: IvarvanStraaten 5

June 13 2019

1 2

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!

Error, invalid input: subs received fsolve...

Asked by: tarik_mohamadi 25

June 12 2019

1 8

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

Integer sequence recurrence...

Asked by: David Sycamore 95

June 05 2019

0 7

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 I need help Maple 2017 froze on loading screen...

Asked by: fungkevin8 15

May 21 2019

3 2

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.

Help on using dsolve...

Asked by: emendes 455

May 18 2019

0 2

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?

Numerical intergration ...

Asked by: gaurav_rs 65

May 14 2019

1 11

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-129087698 * 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;