Maple 2018 Questions and Posts

These are Posts and Questions associated with the product, Maple 2018

i want to gain diff(p(t), t) and diff(q(t), t) and Jacobian matrix
 according to the attached pdf file.

please help me.

thanks

simplify.mw
 

k := diff(a(t), t) = -mu*a(t)-(1/4)*alpha6*a(t)*sin(gamma(t))

diff(a(t), t) = -mu*a(t)-(1/4)*alpha6*a(t)*sin(gamma(t))

(1)

j := a(t)*(diff(gamma(t), t)) = 2*a(t)*sigma-(6*(1/8))*(alpha1-alpha2+(1/3)*alpha3)*a(t)^3-(1/2)*alpha6*a(t)*cos(gamma(t))

a(t)*(diff(gamma(t), t)) = 2*a(t)*sigma-(3/4)*(alpha1-alpha2+(1/3)*alpha3)*a(t)^3-(1/2)*alpha6*a(t)*cos(gamma(t))

(2)

"p(t):=a(t)*cos(gamma(t))"

proc (t) options operator, arrow, function_assign; a(t)*cos(gamma(t)) end proc

(3)

"q(t):=a(t)*sin(gamma(t))"

proc (t) options operator, arrow, function_assign; a(t)*sin(gamma(t)) end proc

(4)

diff(p(t), t)

(diff(a(t), t))*cos(gamma(t))-a(t)*(diff(gamma(t), t))*sin(gamma(t))

(5)

(-mu*a(t)-(1/4)*alpha6*a(t)*sin(gamma(t)))*cos(gamma(t))-a(t)*(2*sigma-(6*(1/8))*(alpha1-alpha2+(1/3)*alpha3)*a(t)^2-(1/2)*alpha6*cos(gamma(t)))*sin(gamma(t))

(-mu*a(t)-(1/4)*alpha6*a(t)*sin(gamma(t)))*cos(gamma(t))-a(t)*(2*sigma-(3/4)*(alpha1-alpha2+(1/3)*alpha3)*a(t)^2-(1/2)*alpha6*cos(gamma(t)))*sin(gamma(t))

(6)

diff(p(t), t)

2*t

(7)

``


subs.pdf

Download simplify.mw

 

 

Hi

I am having some trouble with a procedure. One of the procedures arguments is a mathematical function g(var). For simplification lets say I wish to make a procedure which calculates some values of the unknown function, g: 

SomeProc:=proc(g,var:=x)
f(var):=g
return f(2)
end proc

This does not seem to work. No matter what value of var is inserted into f, the return is g(var). 

Any help would be much appreciated:

Hello

I have an expression which invokes the LambertW function.

LambertW(-ln(1+i)*EP*p*(1+i)^(-(365*EP*hr*kw*p+SC*i)/(365*FIT*hr*i*kw*(-1+p)))/(FIT*i*(-1+p)))

I was trying to import this expression into Excel, but my version doesn't have LambertW.

Does someone know an analagous function in a form Excel can compute?

According to wiki The Lambert W relation cannot be expressed in terms of elementary functions.

I have gotten around the problem using Newton-Raphson method, but it takes a few cells to converge....

 

how i can remove root of from result.

I want to plot function.

Thnaks

root_of.mw
 

sigma2 := RootOf(43980465111040000000000000000*sqrt(3)*Pi^25*sqrt(32*Pi^2+2)*sigma+21990232555520000000000000000*sqrt(3)*Pi^23*sqrt(32*Pi^2+2)*sigma-98268851732480000000000000000*sqrt(3)*Pi^21*sqrt(32*Pi^2+2)*sigma-44495861186560000000000000000*sqrt(3)*Pi^19*sqrt(32*Pi^2+2)*sigma+82188225740800000000000000000*sqrt(3)*Pi^17*sqrt(32*Pi^2+2)*sigma+33095407370240000000000000000*sqrt(3)*Pi^15*sqrt(32*Pi^2+2)*sigma-30136000839680000000000000000*sqrt(3)*Pi^13*sqrt(32*Pi^2+2)*sigma-10618895073280000000000000000*sqrt(3)*Pi^11*sqrt(32*Pi^2+2)*sigma+3822293002240000000000000000*sqrt(3)*Pi^9*sqrt(32*Pi^2+2)*sigma+1210118016000000000000000000*sqrt(3)*Pi^7*sqrt(32*Pi^2+2)*sigma+118805400000000000000000000*sqrt(3)*Pi^5*sqrt(32*Pi^2+2)*sigma+5028750000000000000000000*sqrt(3)*Pi^3*sqrt(32*Pi^2+2)*sigma+79101562500000000000000*sqrt(3)*sigma*Pi*sqrt(32*Pi^2+2)+111484894360500000*Pi^2*20^RootOf8+1765920726670320000*Pi^4*20^RootOf8-569534208772147200*Pi^6*20^RootOf8-4505569481375428608*Pi^8*20^RootOf8+972005049637797888*Pi^10*20^RootOf8+5143616921914048512*Pi^12*20^RootOf8-554194415829123072*Pi^14*20^RootOf8-2216777663316492288*Pi^16*20^RootOf8+(-9231519020818020433920000000000*Pi^22+195541371952408496701440000000000*Pi^20+89300299589267320995840000000000*Pi^18-333503605675043554590720000000000*Pi^16-115500365322956203622400000000000*Pi^14+204706142659640339988480000000000*Pi^12+55783620627641021399040000000000*Pi^10-43454880575740151285760000000000*Pi^8-9286786763553830541120000000000*Pi^6-635208422610519981000000000000*Pi^4-16054449064166199375000000000*Pi^2-85686765999732421875000000)*_Z+(1683627180032000000000000000000*Pi^28+947040288768000000000000000000*Pi^26-243897798836910985052160000000000*Pi^24-105849518880314282213376000000000*Pi^22+543806205557386676011008000000000*Pi^20+206745517628405562998784000000000*Pi^18-493535946568048375234560000000000*Pi^16-161556685841710476165120000000000*Pi^14+209521703041307302907904000000000*Pi^12+57932333046211895115008000000000*Pi^10-32606166808014116503296000000000*Pi^8-7574931806403147431400000000000*Pi^6-916854325001083153125000000000*Pi^4-60848666758777034179687500000*Pi^2-1531121744500488281250000000)*_Z^2+(14538675656595603456000000000000*Pi^20+6360670599760576512000000000000*Pi^18-24363640065154351104000000000000*Pi^16-9459367828326973440000000000000*Pi^14+10040437028153917440000000000000*Pi^12+3693930616897744896000000000000*Pi^10+1609933205706216192000000000000*Pi^8+58674582771546096000000000000*Pi^6-1202653471578517170000000000000*Pi^4-149668239567146343750000000000*Pi^2-4663745768352832031250000000)*_Z^3+(-8723205391669003498291200000000*Pi^24-4361602695834501749145600000000*Pi^22+19490912047010429691494400000000*Pi^20+8825430454852624633036800000000*Pi^18-16301436833461042151424000000000*Pi^16-6564233354119088386867200000000*Pi^14+5977256592087501137510400000000*Pi^12+2106180608207148770918400000000*Pi^10-758124018049754123827200000000*Pi^8-240018107472837924480000000000*Pi^6-23564187036740637000000000000*Pi^4-997415989180706250000000000*Pi^2-15689219628471679687500000)*_Z^4-13647882752248245117187500000-261292721157421875*20^RootOf8-535230827832343213125000000000*Pi^2-90526382422649463214540800000000*Pi^8-18587959930253464168320000000000*Pi^6-5863377073505044924800000000000*Pi^4+305811336261213249011712000000000*Pi^12+79115470702645314657484800000000*Pi^10-239241111641945951698944000000000*Pi^16-79895480796476508576153600000000*Pi^14+7986315188014109687808000000000*Pi^22-60346149989113268482867200000000*Pi^20-18258684357505568263372800000000*Pi^18+14855623787650488886886400000000*Pi^24)

F := plot([sigma2], sigma = -10 .. 10, color = [RED], thickness = 1)

Warning, expecting only range variable sigma in expression RootOf(-2216777663316492288*Pi^16*20^RootOf8-554194415829123072*Pi^14*20^RootOf8+5143616921914048512*Pi^12*20^RootOf8+33095407370240000000000000000*3^(1/2)*Pi^15*(32*Pi^2+2)^(1/2)*sigma-30136000839680000000000000000*3^(1/2)*Pi^13*(32*Pi^2+2)^(1/2)*sigma+5028750000000000000000000*3^(1/2)*Pi^3*(32*Pi^2+2)^(1/2)*sigma+79101562500000000000000*3^(1/2)*sigma*Pi*(32*Pi^2+2)^(1/2)-10618895073280000000000000000*3^(1/2)*Pi^11*(32*Pi^2+2)^(1/2)*sigma+3822293002240000000000000000*3^(1/2)*Pi^9*(32*Pi^2+2)^(1/2)*sigma+1210118016000000000000000000*3^(1/2)*Pi^7*(32*Pi^2+2)^(1/2)*sigma+118805400000000000000000000*3^(1/2)*Pi^5*(32*Pi^2+2)^(1/2)*sigma+43980465111040000000000000000*3^(1/2)*Pi^25*(32*Pi^2+2)^(1/2)*sigma+21990232555520000000000000000*3^(1/2)*Pi^23*(32*Pi^2+2)^(1/2)*sigma-98268851732480000000000000000*3^(1/2)*Pi^21*(32*Pi^2+2)^(1/2)*sigma-44495861186560000000000000000*3^(1/2)*Pi^19*(32*Pi^2+2)^(1/2)*sigma+82188225740800000000000000000*3^(1/2)*Pi^17*(32*Pi^2+2)^(1/2)*sigma+14855623787650488886886400000000*Pi^24-18587959930253464168320000000000*Pi^6-5863377073505044924800000000000*Pi^4+79115470702645314657484800000000*Pi^10-90526382422649463214540800000000*Pi^8-239241111641945951698944000000000*Pi^16-79895480796476508576153600000000*Pi^14+305811336261213249011712000000000*Pi^12-60346149989113268482867200000000*Pi^20-18258684357505568263372800000000*Pi^18+7986315188014109687808000000000*Pi^22-535230827832343213125000000000*Pi^2+111484894360500000*Pi^2*20^RootOf8+1765920726670320000*Pi^4*20^RootOf8-569534208772147200*Pi^6*20^RootOf8-4505569481375428608*Pi^8*20^RootOf8+972005049637797888*Pi^10*20^RootOf8+(-9231519020818020433920000000000*Pi^22+195541371952408496701440000000000*Pi^20+89300299589267320995840000000000*Pi^18-333503605675043554590720000000000*Pi^16-115500365322956203622400000000000*Pi^14+204706142659640339988480000000000*Pi^12+55783620627641021399040000000000*Pi^10-43454880575740151285760000000000*Pi^8-9286786763553830541120000000000*Pi^6-635208422610519981000000000000*Pi^4-16054449064166199375000000000*Pi^2-85686765999732421875000000)*_Z+(1683627180032000000000000000000*Pi^28+947040288768000000000000000000*Pi^26-243897798836910985052160000000000*Pi^24-105849518880314282213376000000000*Pi^22+543806205557386676011008000000000*Pi^20+206745517628405562998784000000000*Pi^18-493535946568048375234560000000000*Pi^16-161556685841710476165120000000000*Pi^14+209521703041307302907904000000000*Pi^12+57932333046211895115008000000000*Pi^10-32606166808014116503296000000000*Pi^8-7574931806403147431400000000000*Pi^6-916854325001083153125000000000*Pi^4-60848666758777034179687500000*Pi^2-1531121744500488281250000000)*_Z^2+(14538675656595603456000000000000*Pi^20+6360670599760576512000000000000*Pi^18-24363640065154351104000000000000*Pi^16-9459367828326973440000000000000*Pi^14+10040437028153917440000000000000*Pi^12+3693930616897744896000000000000*Pi^10+1609933205706216192000000000000*Pi^8+58674582771546096000000000000*Pi^6-1202653471578517170000000000000*Pi^4-149668239567146343750000000000*Pi^2-4663745768352832031250000000)*_Z^3+(-8723205391669003498291200000000*Pi^24-4361602695834501749145600000000*Pi^22+19490912047010429691494400000000*Pi^20+8825430454852624633036800000000*Pi^18-16301436833461042151424000000000*Pi^16-6564233354119088386867200000000*Pi^14+5977256592087501137510400000000*Pi^12+2106180608207148770918400000000*Pi^10-758124018049754123827200000000*Pi^8-240018107472837924480000000000*Pi^6-23564187036740637000000000000*Pi^4-997415989180706250000000000*Pi^2-15689219628471679687500000)*_Z^4-13647882752248245117187500000-261292721157421875*20^RootOf8) to be plotted but found name RootOf8

 

``


 

Download root_of.mw

 

Hi, I'm using Maple 2018 and I tried to run coding from https://www.maplesoft.com/applications/view.aspx?sid=4194&view=html

however, it said : unable to parse. I figured out that the problem maybe is in the if loop. though it seems perfectly fine, but it has some goto commands that i cannot search on maple website. does this mean that the goto cannot be used here and should be replaced? if yes, then how? 

i am still learning on how to use maple. any help would be much appreciated. thank you!

this is the coding for if loop:

 

label_7;

rv:=vector([p1(x1pt,x2pt),p2(x1pt,x2pt)]):

numgeval:=numgeval+1;

printf("%5d (%8.4f,%8.4f)",numIter,rv[1],rv[2]);

max:=n;

mg:=convert(sqrt(dotprod(rv,rv)),float);

printf("%12.4f",mg);

if(mg<tol or numIter>=max) then

goto(label_6);

else

numIter:=numIter+1;

fi;

v1:=x1pt+t*rv[1];

v2:=x2pt+t*rv[2];

newt:=evalf(subs({x1=v1,x2=v2},f1));

numfeval:=numfeval+1;

lam:=fsolve(diff(newt,t)=0,t,maxsols=1);

nv1:=evalf(subs({t=lam},v1));

nv2:=evalf(subs({t=lam},v2));

printf(" (%8.4f,%8.4f)%13.4f\n",x1pt,x2pt,lam);

x1pt:=nv1;

x2pt:=nv2;

goto(label_7);

label_6;

printf("\n\n-----------------------------------------");

printf("---------------------------------------------");

printf("\n\n Approximate Solution: ");

printf(" (%8.4f,%8.4f)\n",x1pt,x2pt);

Fvalue:=evalf(subs(x1=x1pt,x2=x2pt,f));

printf(" Maximum Functional Value: ");

printf("%21.4f",Fvalue);

printf("\n Number gradient evaluations:");

printf("%22d",numgeval);

printf("\n Number function evaluations:");

printf("%22d",numfeval);

printf("\n\n-----------------------------------------");

printf("---------------------------------------------");

end:

If q := [q1(t),q2(t),q3(t)];

and L=cos(q1(t))+sin(q2(t))+5*dq1 + 4*dq3

now I want to get the result of the following expression

d(dL/d dq1)/dt=?,

how can i write the expression?

In above expression dq1 is the derivative of q1(t), and dq3 is that of q3(t),

How do I solve (1/2)*n^2 +2n-1=O(n^2) in maple2018?Thank you

I have plotted a 3d figure with MAPLE. How can I snap a point in 3d figure and  show  the coordinate value of snaped point ?It  can be  carried out  easily in MATLAB,but I  cann‘t  snap the point used  point probe tool in MAPLE ?

Hi,

with the Physics package, I want to represent a discrete two-dimensional Hilbert space in a direct-product basis.

I have looked at https://www.mapleprimes.com/posts/209099-Tensor-Product-Of-Quantum-State-Spaces but am not sure how to implement bracketrules.

Let's assume I have one-dimensional bases A and B that span a two-dimensional space C. A is of size Na and B is of size Nb. Consequently, C is of size Na * Nb.

If I understand it correclty, this can be done with

Setup(hilbertspaces = {{A, C}, {B, C}}, quantumbasisdimension = {A = 1 .. Na, B = 1 .. Nb, C = 1 .. Na*Nb}, quantumdiscretebasis = {A, B, C})

First question: Is this correct and if yes, why do I need to specify quantumbasisdimension for C?

Then, I want to define, using bracketrules, <A[i]| <B[j]| |Psi> = X[i,j],

where |Psi> lives in the full, two-dimensional space C and X is a matrix.

<B[j]|Psi> would be a state living in A and <A[i]||Psi> would be a state in B.

How do I define this?

bracketrules = {%Bracket(Bra(A, i)*Bra(B, j), Ket(C, t)) = X[i,j](t)}

gives me an error.

I found a way using the nested expression

bracketrules = {%Bracket(Bra(A, i), Ket(A, j)) = X[i,j], %Bracket(Bra(B, j), Ket(C)) = Ket(A, j)}

giving

Bracket(Bra(A, i), Bracket(Bra(B, j), Ket(C, t))) = X[i,j]

but this is error prone, clumsy and only works in one direction:

Bracket(Bra(B, j), Bracket(Bra(A, i), Ket(C)))

does not work. Of course, I could also specify rules for the reverse direction but this is quite an effort for higher-dimensional spaces (I have, e.g., 9-dimensional spaces in mind).

So how do I do this properly?

Please have a look at the attached example, where I also included time-dependence.

Thanks,

Henrik

 


 

-------``

First try

-------

restart; restart, with(Physics)

Setup(hilbertspaces = {{A, C}, {B, C}}, quantumbasisdimension = {A = 1 .. Na, B = 1 .. Nb, C = 1 .. Na*Nb}, quantumdiscretebasis = {A, B, C}, bracketrules = {%Bracket(Bra(A, i)*Bra(B, j), Ket(C, t)) = X[i, j](t)})

Error, (in Physics:-Setup) expected first argument in the Bracket defining a bracket rule to be a 'Bra'; received: Physics:-`*`(%Bra(A, i), %Bra(B, j))

 

 

---------

Second try

---------

 

restart; restart, with(Physics)

Setup(hilbertspaces = {{A, C}, {B, C}}, quantumbasisdimension = {A = 1 .. Na, B = 1 .. Nb, C = 1 .. Na*Nb}, quantumdiscretebasis = {A, B, C}, bracketrules = {%Bracket(Bra(A, i), Bra(B, j), Ket(C, t)) = X[i, j](t)})

[bracketrules = {%Bracket(%Bra(A, i), %Bra(B, j), %Ket(C, t)) = X[i, j](t)}, disjointedspaces = {{A, C}, {B, C}}, quantumbasisdimension = {A = 1 .. Na, B = 1 .. Nb, C = 1 .. Na*Nb}, quantumdiscretebasis = {A, B, C}]

(1)

Bracket(Bra(A, i), Bra(B, j), Ket(C, t))

Physics:-`*`(Physics:-Bra(A, i), Physics:-Bra(B, j), Physics:-Ket(C, t))

(2)

--------

Third try

--------

 

 

restart; restart, with(Physics)

Setup(hilbertspaces = {{A, C}, {B, C}}, quantumbasisdimension = {A = 1 .. Na, B = 1 .. Nb, C = 1 .. Na*Nb}, quantumdiscretebasis = {A, B, C}, bracketrules = {%Bracket(Bra(A, i), Ket(A, j, t)) = X[i, j](t), %Bracket(Bra(B, j), Ket(C, t)) = Ket(A, j, t)})

[bracketrules = {%Bracket(%Bra(A, i), %Ket(A, j, t)) = X[i, j](t), %Bracket(%Bra(B, j), %Ket(C, t)) = Physics:-Ket(A, j, t)}, disjointedspaces = {{A, C}, {B, C}}, quantumbasisdimension = {A = 1 .. Na, B = 1 .. Nb, C = 1 .. Na*Nb}, quantumdiscretebasis = {A, B, C}]

(3)

Bracket(Bra(A, i).Bra(B, j), Ket(C, t))

Physics:-`*`(Physics:-Bra(A, i), Physics:-Bra(B, j), Physics:-Ket(C, t))

(4)

Bracket(Bra(A, i), Bracket(Bra(B, j), Ket(C, t)))

X[i, j](t)

(5)

Bracket(Bra(B, j), Bracket(Bra(A, i), Ket(C, t)))

Error, (in Physics:-Bracket) expected a Bra and a Ket as a first and last arguments, or no Bra and no Ket when using the shortcut notation; received: Physics:-Bra(B,j), Physics:-Bracket(Physics:-Bra(A,i),Physics:-Ket(C,t))

 

``


 

Download twoD.mw

 

hi

I want to mix two curve and have only one figure(I want to compare two curve in one plot domain )?

Thank you

plot.mw
 

h1 := solve(Vdc = 0.1500000000e-2*sqrt(2.53669508*10^8*u^3-6.06101011*10^8*u^2+3.46343435*10^8*u), u); plot([h1], Vdc = 0 .. 11.5, color = [magenta], thickness = 1); plot(Vector([0, 3.38, 5.21, 6.97, 8.4108, 10.099, 10.9232, 11.8091]), Vector([0, 0.760e-1, .1275, .1994, .2286, .3222, .3637, .999]), style = point, symbol = asterisk, color = "Blue")

 

 

``


 

Download plot.mw

 

 

Hi, fairly simple question,

I solve a simple equation:

solve(x^x = 4, allsolutions, explicit);

#(2*(I*Pi*_Z7+ln(2)))/LambertW(_Z9, 2*ln(2)+(2*I)*Pi*_Z7)

Maple  gave me solution with prefix _Z for integer values, but why  _Z9 must be exactly equal  Zero  to be correct ?.

If _Z9 is integer it can also take other values than zero ?

Thanks in advance.



More information see attached file:

Download Allsolution.mw

 

We have just released an update to Maple, Maple 2018.2. This release includes improvements in a variety of areas, including code edit regions, Workbooks, and Physics, as well as support for macOS 10.14.

This update is available through Tools>Check for Updates in Maple, and is also available from our website on the Maple 2018.2 download page, where you can also find more details.

For MapleSim users, the update includes optimizations for handling large models, improvements to model import and export, updates to the hydraulics and pneumatics libraries, and more. For more details and download instructions, visit the MapleSim 2018.2 download page.

Is it possible to output to the console without a new line being added. The code:

prints each number on a separate line. I want to print them all on the same line.

Hello!

I am trying to determine the type of Lie algebra originating from Killing vectors. However, Maple says that some variable x is protected (though, I guess, it shouldn't even be in the L). Is there any way to solve this issue?

Best regards, 
Nick

error.mw

restart

with(DifferentialGeometry); with(Tensor); with(LieAlgebras); with(GroupActions); with(Library)

DGsetup([x, y], M)

g := evalDG((`&t`(dx, dx)+`&t`(dy, dy))/y^2)

_DG([["tensor", M, [["cov_bas", "cov_bas"], []]], [[[1, 1], 1/y^2], [[2, 2], 1/y^2]]])

(1)

kv := KillingVectors(g)

[_DG([["vector", M, []], [[[1], (1/2)*x^2-(1/2)*y^2], [[2], y*x]]]), _DG([["vector", M, []], [[[1], x], [[2], y]]]), _DG([["vector", M, []], [[[1], 1]]])]

(2)

L := LieAlgebraData(kv, Poincare)

_DG([["LieAlgebra", Poincare, [3]], [[[1, 2, 1], -1], [[1, 3, 2], -1], [[2, 3, 3], -1]]])

(3)

DGsetup(L); MultiplicationTable("LieTable")

Query(Poincare, "Semisimple")

true

(4)

CSA := CartanSubalgebra(Poincare)

[_DG([["vector", Poincare, []], [[[2], 1]]])]

(5)

RSD := RootSpaceDecomposition(CSA)

Error, (in MultiSet:-Entries) attempting to assign to `x` which is protected.  Try declaring `local x`; see ?protect for details.

 

``


 

Download error.mw

 

hi.

I can not gain answer for integral.

Best

int.mw
 

restart

PDE := (12*kappa^2*psi^2*(-upsilon^2+1)*((3*Pi^2*Q^2*(nu*psi^2+1)/(32*(-nu^2+1))+Q^2*(Pi^2*cos(2*Pi*y)/(8*psi^2)+psi^2*cos(2*Pi*x)*Pi^2*cos(2*Pi*y)/(4*(psi^2+1)^2)+Pi^2*cos(4*Pi*y)/(32*psi^2)+psi^2*cos(2*Pi*x)*Pi^2*cos(4*Pi*y)/(2*(4*psi^2+1)^2)+psi^2*cos(4*Pi*x)*Pi^2*cos(2*Pi*y)/(8*(psi^2+4)^2)))*(2*Q*Pi^2*sin(Pi*x)^2*cos(Pi*y)^2-2*Q*cos(Pi*x)^2*cos(Pi*y)^2*Pi^2)+(2*Q*cos(Pi*x)^2*Pi^2*sin(Pi*y)^2-2*Q*cos(Pi*x)^2*cos(Pi*y)^2*Pi^2)*(3*Pi^2*Q^2*(psi^2+nu)/(32*(-nu^2+1))+Q^2*((1/8)*psi^2*cos(2*Pi*x)*Pi^2+psi^2*cos(2*Pi*x)*Pi^2*cos(2*Pi*y)/(4*(psi^2+1)^2)+(1/32)*psi^2*cos(4*Pi*x)*Pi^2+psi^2*cos(2*Pi*x)*Pi^2*cos(4*Pi*y)/(8*(4*psi^2+1)^2)+psi^2*cos(4*Pi*x)*Pi^2*cos(2*Pi*y)/(2*(psi^2+4)^2)))-8*Q^3*cos(Pi*x)*cos(Pi*y)*Pi^2*sin(Pi*x)*sin(Pi*y)*(-psi^2*Pi^2*sin(2*Pi*x)*sin(2*Pi*y)/(4*(psi^2+1)^2)-psi^2*Pi^2*sin(2*Pi*x)*sin(4*Pi*y)/(4*(4*psi^2+1)^2)-psi^2*Pi^2*sin(4*Pi*x)*sin(2*Pi*y)/(4*(psi^2+4)^2)))+beta*V^2/(1-Q*cos(Pi*x)^2*cos(Pi*y)^2)^2-8*Q*Pi^4*cos(Pi*x)^2*cos(Pi*y)^2+8*Q*Pi^4*sin(Pi*x)^2*cos(Pi*y)^2-2*psi^2*(4*Q*Pi^4*sin(Pi*x)^2*sin(Pi*y)^2-4*Q*Pi^4*sin(Pi*x)^2*cos(Pi*y)^2-4*Q*cos(Pi*x)^2*Pi^4*sin(Pi*y)^2+4*Q*Pi^4*cos(Pi*x)^2*cos(Pi*y)^2)-psi^4*(-8*Q*cos(Pi*x)^2*Pi^4*sin(Pi*y)^2+8*Q*Pi^4*cos(Pi*x)^2*cos(Pi*y)^2))*(1-Q*cos(Pi*x)^2*cos(Pi*y)^2)^2*cos(Pi*x)^2*cos(Pi*y)^2

int(int(PDE, y = -1/2 .. 1/2), x = -1/2 .. 1/2)


 

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