Unanswered Questions

This page lists MaplePrimes questions that have not yet received an answer

I'm having sone trouble with my matricies after running restart. When creating the matrice, everything is fine and they are defined as normal. But, if I run restart and try to erdefine them, they are defined as some form of 

The only way I've been able to fix this besides restarting Maple is to either add or remove the colon after the matrix, depending on wether there was one. If ther was, when I remove it the matrix is defined normally and vice versa. I'm relatively new to Maple coming from Matlab and would like to start using it more, but this matrix thing is very frustrating. I've attached a copy of the maple file. Thanks

First definition, everything is normal:

After restart, everything goes bad:

I want to animate a ball rolling on the surface cos(abs(x)+abs(y)).  The ball mass m is 1kg, radius r is 0.1meters starts at (0.5,0.5,cos(abs(5)+abs(5))) meters using g=9.8.  If we say the initial velocity of the ball is pushed in some random direction.  How do I show the path of the ball and animate?

Hi everibody 

I work with Maple 2015 under OS-X El Capitan.

Using more than one matrix vector product (either M.V  or MatrixVectorMultiply(M,V)  ; M is a n by p matrix and V a column vector of size p) within the same block of commands generates an error.

Do other people have the same problem ?
Thanks for your feedback.

SomethingGoesWrong.mw


PS : I know I can do this   X . <<1, 1, -1> | <-1, 2, 0>> but this doesn't explain the error I get

 

I have many expressions in a worksheet like this:

latex(%, "equations.tex", append = true)

I should have defined a file name like this:

fname := "C:/home/MyStuff/Economics/MICRO NOTES/equations.tex"

And then replaced the first expression throughit the worksheet by:

latex(%, fname, append = true)

To acheive this I open the Find/Replace dialogue as in picture below:

This does not work. Instead of replacing with fname the result is "fname" .  Is there any way of doing what I want?

interface(prettyprint=0):
interface(screenwidth=500):
with(LinearAlgebra):

expect 

Matrix([[a1,a2,3],[5,6,7],[9,10,12]])

but

it print datatype = anything,storage = rectangular,order = Fortran_order,shape  and (2,1) etc

Matrix(3,3,{(2, 1) = 1, (3, 1) = 1, (3, 2) = 1},datatype = anything,storage = rectangular,order = Fortran_order,shape = []), 

what are the dynamical system which act on invariant manifold?

Is it a complete set ? How to search matrix?

Hey, this is not the I've had this encounter. I want to open this saved document but when I open it and Maple starts up it just hits me with "A problem was encountered while opening the workbook. Database is not opened". How can I get to open it properly and see my math notes?

How can this be prevented?

Any help?

 

Christian

evalf(Int(x*(1-2*x^(3/10))^(10./3),x=0..1));  # Crashes Maple

Note that:

int(x*(1-2*x^(3/10))^(10./3),x=0..1);
int(x*(1-2*x^(3/10))^(10/3),x=0..1);

are OK.

(Windows 7, Maple 2017.3, 64 bit)

Hi 

I want to solve these equations in MAPLE, but something goes wrong. 


 

``

restart

``

NULL

NULL

NULL

phi[j] := sin(j*Pi*x)

sin(j*Pi*x)

(1)

phi[i] := sin(i*Pi*x)

sin(i*Pi*x)

(2)

phi[k] := sin(k*Pi*x)

sin(k*Pi*x)

(3)

phi[l] := sin(l*Pi*x)

sin(l*Pi*x)

(4)

phi[1] := sin(Pi*x)

sin(Pi*x)

(5)

NULL

pp1 := sum((int(phi[i]*phi[j], x = 0 .. 1, numeric))*(diff(p(t), t, t))[j], j = 1 .. 8)-beta^2*(sum((int(phi[i]*(diff(phi[j], x, x)), x = 0 .. 1, numeric))*p(t)[j], j = 1 .. 8)+sum((int(AA0*(diff(phi[1], x, x))*phi[i]*(diff(phi[j], x)), x = 0 .. 1, numeric))*q[j], j = 1 .. 7)+sum((int(AA0*(diff(phi[1], x))*phi[i]*(diff(phi[j], x, x)), x = 0 .. 1, numeric))*q[j], j = 1 .. 7)+sum(sum((int(phi[i]*(diff(phi[j], x))*(diff(phi[k], x, x)), x = 0 .. 1, numeric))*q[j]*q[k], k = 1 .. 7), j = 1 .. 7))+Cd*(sum((int(phi[i]*phi[j], x = 0 .. 1, numeric))*(diff(p(t), t))[j], j = 1 .. 8)):

NULL

NULL

NULL

for z to 8 do limit(pp1, i = z) end do

limit(.1591549431*(sin(3.141592654*i-3.141592654)*i-1.*sin(3.141592654*i+3.141592654)*i+sin(3.141592654*i-3.141592654)+sin(3.141592654*i+3.141592654))*(diff(diff(p(t), t), t))[1]/((i-1.)*(i+1.))+.1591549431*(sin(3.141592654*i-6.283185308)*i-1.*sin(3.141592654*i+6.283185308)*i+2.*sin(3.141592654*i-6.283185308)+2.*sin(3.141592654*i+6.283185308))*(diff(diff(p(t), t), t))[2]/((i-2.)*(i+2.))+.1591549431*(sin(3.141592654*i-9.424777962)*i-1.*sin(3.141592654*i+9.424777962)*i+3.*sin(3.141592654*i-9.424777962)+3.*sin(3.141592654*i+9.424777962))*(diff(diff(p(t), t), t))[3]/((i-3.)*(i+3.))+.1591549431*(sin(3.141592654*i-12.56637062)*i-1.*sin(3.141592654*i+12.56637062)*i+4.*sin(3.141592654*i-12.56637062)+4.*sin(3.141592654*i+12.56637062))*(diff(diff(p(t), t), t))[4]/((i-4.)*(i+4.))+.1591549431*(sin(3.141592654*i-15.70796327)*i-1.*sin(3.141592654*i+15.70796327)*i+5.*sin(3.141592654*i-15.70796327)+5.*sin(3.141592654*i+15.70796327))*(diff(diff(p(t), t), t))[5]/((i-5.)*(i+5.))+.1591549431*(sin(3.141592654*i-18.84955592)*i-1.*sin(3.141592654*i+18.84955592)*i+6.*sin(3.141592654*i-18.84955592)+6.*sin(3.141592654*i+18.84955592))*(diff(diff(p(t), t), t))[6]/((i-6.)*(i+6.))+.1591549431*(sin(3.141592654*i-21.99114858)*i-1.*sin(3.141592654*i+21.99114858)*i+7.*sin(3.141592654*i-21.99114858)+7.*sin(3.141592654*i+21.99114858))*(diff(diff(p(t), t), t))[7]/((i-7.)*(i+7.))+.1591549431*(sin(3.141592654*i-25.13274123)*i-1.*sin(3.141592654*i+25.13274123)*i+8.*sin(3.141592654*i-25.13274123)+8.*sin(3.141592654*i+25.13274123))*(diff(diff(p(t), t), t))[8]/((i-8.)*(i+8.))-beta^2*(-1.570796327*(sin(3.141592654*i-3.141592654)*i-1.*sin(3.141592654*i+3.141592654)*i+sin(3.141592654*i-3.141592654)+sin(3.141592654*i+3.141592654))*p(t)[1]/((i-1.)*(i+1.))-6.283185308*(sin(3.141592654*i-6.283185308)*i-1.*sin(3.141592654*i+6.283185308)*i+2.*sin(3.141592654*i-6.283185308)+2.*sin(3.141592654*i+6.283185308))*p(t)[2]/((i-2.)*(i+2.))-14.13716694*(sin(3.141592654*i-9.424777962)*i-1.*sin(3.141592654*i+9.424777962)*i+3.*sin(3.141592654*i-9.424777962)+3.*sin(3.141592654*i+9.424777962))*p(t)[3]/((i-3.)*(i+3.))-25.13274123*(sin(3.141592654*i-12.56637062)*i-1.*sin(3.141592654*i+12.56637062)*i+4.*sin(3.141592654*i-12.56637062)+4.*sin(3.141592654*i+12.56637062))*p(t)[4]/((i-4.)*(i+4.))-39.26990818*(sin(3.141592654*i-15.70796327)*i-1.*sin(3.141592654*i+15.70796327)*i+5.*sin(3.141592654*i-15.70796327)+5.*sin(3.141592654*i+15.70796327))*p(t)[5]/((i-5.)*(i+5.))-56.54866777*(sin(3.141592654*i-18.84955592)*i-1.*sin(3.141592654*i+18.84955592)*i+6.*sin(3.141592654*i-18.84955592)+6.*sin(3.141592654*i+18.84955592))*p(t)[6]/((i-6.)*(i+6.))-76.96902003*(sin(3.141592654*i-21.99114858)*i-1.*sin(3.141592654*i+21.99114858)*i+7.*sin(3.141592654*i-21.99114858)+7.*sin(3.141592654*i+21.99114858))*p(t)[7]/((i-7.)*(i+7.))-100.5309649*(sin(3.141592654*i-25.13274123)*i-1.*sin(3.141592654*i+25.13274123)*i+8.*sin(3.141592654*i-25.13274123)+8.*sin(3.141592654*i+25.13274123))*p(t)[8]/((i-8.)*(i+8.))-66.61982973*(sin(3.141592654*i-18.84955592)*i^3-1.*sin(3.141592654*i+18.84955592)*i^3+6.*sin(3.141592654*i-18.84955592)*i^2+6.*sin(3.141592654*i+18.84955592)*i^2)*q[3]^2/(i^2*(i+6.)*(i-6.))-157.9136704*(-64.*sin(-0.4000000000e-8+3.141592654*i)*i+64.*sin(0.4000000000e-8+3.141592654*i)*i+sin(-0.4000000000e-8+3.141592654*i)*i^3-1.*sin(25.13274124+3.141592654*i)*i^3+sin(-25.13274124+3.141592654*i)*i^3-1.*sin(0.4000000000e-8+3.141592654*i)*i^3+8.*sin(25.13274124+3.141592654*i)*i^2+8.*sin(-25.13274124+3.141592654*i)*i^2)*q[4]^2/(i^2*(i+8.)*(i-8.))+308.4251376*(-10.*sin(31.41592654+3.141592654*i)*i^2-10.*sin(-31.41592654+3.141592654*i)*i^2+sin(31.41592654+3.141592654*i)*i^3-1.*sin(-31.41592654+3.141592654*i)*i^3)*q[5]^2/(i^2*(10.+i)*(-10.+i))-532.9586378*(144.*sin(-0.4000000000e-8+3.141592654*i)*i-144.*sin(0.4000000000e-8+3.141592654*i)*i-1.*sin(-0.4000000000e-8+3.141592654*i)*i^3+sin(0.4000000000e-8+3.141592654*i)*i^3-1.*sin(37.69911184+3.141592654*i)*i^3+sin(-37.69911184+3.141592654*i)*i^3+12.*sin(37.69911184+3.141592654*i)*i^2+12.*sin(-37.69911184+3.141592654*i)*i^2)*q[6]^2/(i^2*(12.+i)*(-12.+i))-846.3185773*(sin(-43.98229716+3.141592654*i)*i^3-1.*sin(0.2000000000e-8+3.141592654*i)*i^3+14.*sin(43.98229716+3.141592654*i)*i^2+14.*sin(-43.98229716+3.141592654*i)*i^2-196.*sin(-0.2000000000e-8+3.141592654*i)*i+196.*sin(0.2000000000e-8+3.141592654*i)*i+sin(-0.2000000000e-8+3.141592654*i)*i^3-1.*sin(43.98229716+3.141592654*i)*i^3)*q[7]^2/(i^2*(14.+i)*(-14.+i))-19.73920881*(sin(3.141592654*i-12.56637062)*i^3-1.*sin(3.141592654*i+12.56637062)*i^3+4.*sin(3.141592654*i-12.56637062)*i^2+4.*sin(3.141592654*i+12.56637062)*i^2)*q[2]^2/(i^2*(i+4.)*(i-4.))-4.934802202*AA0*(sin(3.141592654*i-6.283185308)*i-1.*sin(3.141592654*i+6.283185308)*i+2.*sin(3.141592654*i-6.283185308)+2.*sin(3.141592654*i+6.283185308))*q[1]/((i-2.)*(i+2.))-2.467401101*(sin(3.141592654*i-6.283185308)*i^3-1.*sin(3.141592654*i+6.283185308)*i^3+2.*sin(3.141592654*i-6.283185308)*i^2+2.*sin(3.141592654*i+6.283185308)*i^2)*q[1]^2/(i^2*(i+2.)*(i-2.))-9.869604403*(sin(3.141592654*i-9.424777962)*i^3-1.*sin(3.141592654*i+3.141592654)*i^3+sin(3.141592654*i-3.141592654)*i^3-1.*sin(3.141592654*i+9.424777962)*i^3+3.*sin(3.141592654*i-9.424777962)*i^2+sin(3.141592654*i+3.141592654)*i^2+sin(3.141592654*i-3.141592654)*i^2+3.*sin(3.141592654*i+9.424777962)*i^2-1.*sin(3.141592654*i-9.424777962)*i+9.*sin(3.141592654*i+3.141592654)*i-9.*sin(3.141592654*i-3.141592654)*i+sin(3.141592654*i+9.424777962)*i-3.*sin(3.141592654*i-9.424777962)-9.*sin(3.141592654*i+3.141592654)-9.*sin(3.141592654*i-3.141592654)-3.*sin(3.141592654*i+9.424777962))*q[1]*q[2]/((i-1.)*(i+3.)*(i-3.)*(i+1.))-22.20660991*(sin(3.141592654*i-12.56637062)*i^3-1.*sin(3.141592654*i+12.56637062)*i^3+sin(3.141592654*i-6.283185308)*i^3-1.*sin(3.141592654*i+6.283185308)*i^3+4.*sin(3.141592654*i-12.56637062)*i^2+4.*sin(3.141592654*i+12.56637062)*i^2+2.*sin(3.141592654*i-6.283185308)*i^2+2.*sin(3.141592654*i+6.283185308)*i^2-4.*sin(3.141592654*i-12.56637062)*i+4.*sin(3.141592654*i+12.56637062)*i-16.*sin(3.141592654*i-6.283185308)*i+16.*sin(3.141592654*i+6.283185308)*i-16.*sin(3.141592654*i-12.56637062)-16.*sin(3.141592654*i+12.56637062)-32.*sin(3.141592654*i-6.283185308)-32.*sin(3.141592654*i+6.283185308))*q[1]*q[3]/((i-2.)*(i+4.)*(i-4.)*(i+2.))-39.47841761*(-25.*sin(-9.424777966+3.141592654*i)*i+9.*sin(3.141592654*i+15.70796327)*i-9.*sin(3.141592654*i-15.70796327)*i+25.*sin(9.424777966+3.141592654*i)*i+sin(-9.424777966+3.141592654*i)*i^3-1.*sin(3.141592654*i+15.70796327)*i^3+sin(3.141592654*i-15.70796327)*i^3-1.*sin(9.424777966+3.141592654*i)*i^3+3.*sin(-9.424777966+3.141592654*i)*i^2+5.*sin(3.141592654*i+15.70796327)*i^2+5.*sin(3.141592654*i-15.70796327)*i^2+3.*sin(9.424777966+3.141592654*i)*i^2-45.*sin(3.141592654*i+15.70796327)-45.*sin(3.141592654*i-15.70796327)-75.*sin(9.424777966+3.141592654*i)-75.*sin(-9.424777966+3.141592654*i))*q[1]*q[4]/((i-3.)*(i+5.)*(i-5.)*(i+3.))+61.68502752*(-1.*sin(3.141592654*i-18.84955592)*i^3+sin(3.141592654*i+18.84955592)*i^3-6.*sin(3.141592654*i-18.84955592)*i^2-6.*sin(3.141592654*i+18.84955592)*i^2+96.*sin(3.141592654*i-18.84955592)+96.*sin(3.141592654*i+18.84955592)+16.*sin(3.141592654*i-18.84955592)*i-16.*sin(3.141592654*i+18.84955592)*i-1.*sin(3.141592654*i-12.56637062)*i^3+sin(3.141592654*i+12.56637062)*i^3-4.*sin(3.141592654*i-12.56637062)*i^2-4.*sin(3.141592654*i+12.56637062)*i^2+144.*sin(3.141592654*i+12.56637062)+144.*sin(3.141592654*i-12.56637062)+36.*sin(3.141592654*i-12.56637062)*i-36.*sin(3.141592654*i+12.56637062)*i)*q[1]*q[5]/((i-4.)*(i+6.)*(i-6.)*(i+4.))-88.82643963*(-49.*sin(3.141592654*i-15.70796327)*i+25.*sin(21.99114857+3.141592654*i)*i-25.*sin(-21.99114857+3.141592654*i)*i+49.*sin(3.141592654*i+15.70796327)*i+sin(3.141592654*i-15.70796327)*i^3-1.*sin(21.99114857+3.141592654*i)*i^3+sin(-21.99114857+3.141592654*i)*i^3-1.*sin(3.141592654*i+15.70796327)*i^3+5.*sin(3.141592654*i-15.70796327)*i^2+7.*sin(21.99114857+3.141592654*i)*i^2+7.*sin(-21.99114857+3.141592654*i)*i^2+5.*sin(3.141592654*i+15.70796327)*i^2-245.*sin(3.141592654*i-15.70796327)-175.*sin(21.99114857+3.141592654*i)-175.*sin(-21.99114857+3.141592654*i)-245.*sin(3.141592654*i+15.70796327))*q[1]*q[6]/((i-5.)*(i+7.)*(i-7.)*(i+5.))-120.9026539*(sin(3.141592654*i-25.13274123)*i^3-1.*sin(18.84955593+3.141592654*i)*i^3+6.*sin(-18.84955593+3.141592654*i)*i^2+8.*sin(3.141592654*i+25.13274123)*i^2+8.*sin(3.141592654*i-25.13274123)*i^2+6.*sin(18.84955593+3.141592654*i)*i^2-64.*sin(-18.84955593+3.141592654*i)*i+36.*sin(3.141592654*i+25.13274123)*i-36.*sin(3.141592654*i-25.13274123)*i+64.*sin(18.84955593+3.141592654*i)*i+sin(-18.84955593+3.141592654*i)*i^3-1.*sin(3.141592654*i+25.13274123)*i^3-384.*sin(18.84955593+3.141592654*i)-384.*sin(-18.84955593+3.141592654*i)-288.*sin(3.141592654*i+25.13274123)-288.*sin(3.141592654*i-25.13274123))*q[1]*q[7]/((i-6.)*(i+8.)*(i-8.)*(i+6.))-69.08723082*(-1.*sin(3.141592654*i-15.70796327)*i^3+sin(3.141592654*i+15.70796327)*i^3-5.*sin(3.141592654*i-15.70796327)*i^2-5.*sin(3.141592654*i+15.70796327)*i^2+405.*sin(3.141592654*i+15.70796327)+405.*sin(3.141592654*i-15.70796327)+81.*sin(3.141592654*i-15.70796327)*i-81.*sin(3.141592654*i+15.70796327)*i+9.*sin(28.27433389+3.141592654*i)*i^2+9.*sin(-28.27433389+3.141592654*i)*i^2+25.*sin(28.27433389+3.141592654*i)*i-25.*sin(-28.27433389+3.141592654*i)*i-1.*sin(28.27433389+3.141592654*i)*i^3+sin(-28.27433389+3.141592654*i)*i^3-225.*sin(-28.27433389+3.141592654*i)-225.*sin(28.27433389+3.141592654*i))*q[7]*q[2]/((i+5.)*(9.+i)*(-9.+i)*(i-5.))-155.4462694*(-1.*sin(3.141592654*i-12.56637062)*i^3+sin(3.141592654*i+12.56637062)*i^3-4.*sin(3.141592654*i-12.56637062)*i^2-4.*sin(3.141592654*i+12.56637062)*i^2+400.*sin(3.141592654*i+12.56637062)+400.*sin(3.141592654*i-12.56637062)+100.*sin(3.141592654*i-12.56637062)*i-100.*sin(3.141592654*i+12.56637062)*i+10.*sin(31.41592654+3.141592654*i)*i^2+10.*sin(-31.41592654+3.141592654*i)*i^2+16.*sin(31.41592654+3.141592654*i)*i-16.*sin(-31.41592654+3.141592654*i)*i-1.*sin(31.41592654+3.141592654*i)*i^3+sin(-31.41592654+3.141592654*i)*i^3-160.*sin(31.41592654+3.141592654*i)-160.*sin(-31.41592654+3.141592654*i))*q[7]*q[3]/((i+4.)*(10.+i)*(-10.+i)*(i-4.))-276.3489233*(121.*sin(-9.424777958+3.141592654*i)*i-121.*sin(9.424777958+3.141592654*i)*i-1.*sin(-9.424777958+3.141592654*i)*i^3+sin(9.424777958+3.141592654*i)*i^3-3.*sin(-9.424777958+3.141592654*i)*i^2-3.*sin(9.424777958+3.141592654*i)*i^2+9.*sin(34.55751920+3.141592654*i)*i-9.*sin(-34.55751920+3.141592654*i)*i-1.*sin(34.55751920+3.141592654*i)*i^3+sin(-34.55751920+3.141592654*i)*i^3+11.*sin(34.55751920+3.141592654*i)*i^2+11.*sin(-34.55751920+3.141592654*i)*i^2-99.*sin(34.55751920+3.141592654*i)-99.*sin(-34.55751920+3.141592654*i)+363.*sin(-9.424777958+3.141592654*i)+363.*sin(9.424777958+3.141592654*i))*q[7]*q[4]/((i+3.)*(11.+i)*(-11.+i)*(i-3.))+431.7951926*(sin(3.141592654*i-6.283185308)*i^3-1.*sin(3.141592654*i+6.283185308)*i^3+2.*sin(3.141592654*i-6.283185308)*i^2+2.*sin(3.141592654*i+6.283185308)*i^2-288.*sin(3.141592654*i+6.283185308)-288.*sin(3.141592654*i-6.283185308)+144.*sin(3.141592654*i+6.283185308)*i-144.*sin(3.141592654*i-6.283185308)*i-12.*sin(37.69911185+3.141592654*i)*i^2-12.*sin(-37.69911185+3.141592654*i)*i^2-4.*sin(37.69911185+3.141592654*i)*i+4.*sin(-37.69911185+3.141592654*i)*i+sin(37.69911185+3.141592654*i)*i^3-1.*sin(-37.69911185+3.141592654*i)*i^3+48.*sin(-37.69911185+3.141592654*i)+48.*sin(37.69911185+3.141592654*i))*q[7]*q[5]/((i+2.)*(12.+i)*(-12.+i)*(i-2.))-4.934802201*AA0*(sin(3.141592654*i-9.424777962)*i^3+sin(3.141592654*i+3.141592654)*i^3-1.*sin(3.141592654*i-3.141592654)*i^3-1.*sin(3.141592654*i+9.424777962)*i^3+3.*sin(3.141592654*i-9.424777962)*i^2-1.*sin(3.141592654*i+3.141592654)*i^2-1.*sin(3.141592654*i-3.141592654)*i^2+3.*sin(3.141592654*i+9.424777962)*i^2-1.*sin(3.141592654*i-9.424777962)*i-9.*sin(3.141592654*i+3.141592654)*i+9.*sin(3.141592654*i-3.141592654)*i+sin(3.141592654*i+9.424777962)*i-3.*sin(3.141592654*i-9.424777962)+9.*sin(3.141592654*i+3.141592654)+9.*sin(3.141592654*i-3.141592654)-3.*sin(3.141592654*i+9.424777962))*q[2]/((i-3.)*(i+1.)*(i-1.)*(i+3.))-7.402203302*AA0*(-1.*sin(3.141592654*i-6.283185308)*i^3+sin(3.141592654*i+6.283185308)*i^3+sin(3.141592654*i-12.56637062)*i^3-1.*sin(3.141592654*i+12.56637062)*i^3-2.*sin(3.141592654*i-6.283185308)*i^2-2.*sin(3.141592654*i+6.283185308)*i^2+4.*sin(3.141592654*i-12.56637062)*i^2+4.*sin(3.141592654*i+12.56637062)*i^2+16.*sin(3.141592654*i-6.283185308)*i-16.*sin(3.141592654*i+6.283185308)*i-4.*sin(3.141592654*i-12.56637062)*i+4.*sin(3.141592654*i+12.56637062)*i+32.*sin(3.141592654*i-6.283185308)+32.*sin(3.141592654*i+6.283185308)-16.*sin(3.141592654*i-12.56637062)-16.*sin(3.141592654*i+12.56637062))*q[3]/((i-4.)*(i+2.)*(i-2.)*(i+4.))+9.869604403*AA0*(sin(3.141592654*i-9.424777962)*i^3-1.*sin(3.141592654*i+9.424777962)*i^3-1.*sin(3.141592654*i-15.70796327)*i^3+sin(3.141592654*i+15.70796327)*i^3+3.*sin(3.141592654*i-9.424777962)*i^2+3.*sin(3.141592654*i+9.424777962)*i^2-5.*sin(3.141592654*i-15.70796327)*i^2-5.*sin(3.141592654*i+15.70796327)*i^2-25.*sin(3.141592654*i-9.424777962)*i+25.*sin(3.141592654*i+9.424777962)*i+9.*sin(3.141592654*i-15.70796327)*i-9.*sin(3.141592654*i+15.70796327)*i-75.*sin(3.141592654*i-9.424777962)-75.*sin(3.141592654*i+9.424777962)+45.*sin(3.141592654*i-15.70796327)+45.*sin(3.141592654*i+15.70796327))*q[4]/((i-5.)*(i+3.)*(i-3.)*(i+5.))-12.33700550*AA0*(sin(3.141592654*i-18.84955592)*i^3-1.*sin(3.141592654*i+18.84955592)*i^3-1.*sin(3.141592654*i-12.56637062)*i^3+sin(3.141592654*i+12.56637062)*i^3+6.*sin(3.141592654*i-18.84955592)*i^2+6.*sin(3.141592654*i+18.84955592)*i^2-4.*sin(3.141592654*i-12.56637062)*i^2-4.*sin(3.141592654*i+12.56637062)*i^2-16.*sin(3.141592654*i-18.84955592)*i+16.*sin(3.141592654*i+18.84955592)*i+36.*sin(3.141592654*i-12.56637062)*i-36.*sin(3.141592654*i+12.56637062)*i-96.*sin(3.141592654*i-18.84955592)-96.*sin(3.141592654*i+18.84955592)+144.*sin(3.141592654*i-12.56637062)+144.*sin(3.141592654*i+12.56637062))*q[5]/((i-6.)*(i+4.)*(i-4.)*(i+6.))-14.80440660*AA0*(sin(3.141592654*i-21.99114858)*i^3-1.*sin(3.141592654*i+21.99114858)*i^3-1.*sin(3.141592654*i-15.70796327)*i^3+sin(3.141592654*i+15.70796327)*i^3+7.*sin(3.141592654*i-21.99114858)*i^2+7.*sin(3.141592654*i+21.99114858)*i^2-5.*sin(3.141592654*i-15.70796327)*i^2-5.*sin(3.141592654*i+15.70796327)*i^2-25.*sin(3.141592654*i-21.99114858)*i+25.*sin(3.141592654*i+21.99114858)*i+49.*sin(3.141592654*i-15.70796327)*i-49.*sin(3.141592654*i+15.70796327)*i-175.*sin(3.141592654*i-21.99114858)-175.*sin(3.141592654*i+21.99114858)+245.*sin(3.141592654*i-15.70796327)+245.*sin(3.141592654*i+15.70796327))*q[6]/((i-7.)*(i+5.)*(i-5.)*(i+7.))+17.27180770*AA0*(sin(3.141592654*i-18.84955592)*i^3-1.*sin(3.141592654*i+18.84955592)*i^3-1.*sin(3.141592654*i-25.13274123)*i^3+sin(3.141592654*i+25.13274123)*i^3+6.*sin(3.141592654*i-18.84955592)*i^2+6.*sin(3.141592654*i+18.84955592)*i^2-8.*sin(3.141592654*i-25.13274123)*i^2-8.*sin(3.141592654*i+25.13274123)*i^2-64.*sin(3.141592654*i-18.84955592)*i+64.*sin(3.141592654*i+18.84955592)*i+36.*sin(3.141592654*i-25.13274123)*i-36.*sin(3.141592654*i+25.13274123)*i-384.*sin(3.141592654*i-18.84955592)-384.*sin(3.141592654*i+18.84955592)+288.*sin(3.141592654*i-25.13274123)+288.*sin(3.141592654*i+25.13274123))*q[7]/((i-8.)*(i+6.)*(i-6.)*(i+8.))-621.7850774*(169.*sin(-3.141592658+3.141592654*i)*i-169.*sin(3.141592658+3.141592654*i)*i-1.*sin(-3.141592658+3.141592654*i)*i^3+sin(3.141592658+3.141592654*i)*i^3-1.*sin(-3.141592658+3.141592654*i)*i^2-1.*sin(3.141592658+3.141592654*i)*i^2+sin(40.84070450+3.141592654*i)*i-1.*sin(-40.84070450+3.141592654*i)*i-1.*sin(40.84070450+3.141592654*i)*i^3+sin(-40.84070450+3.141592654*i)*i^3+13.*sin(40.84070450+3.141592654*i)*i^2+13.*sin(-40.84070450+3.141592654*i)*i^2-13.*sin(-40.84070450+3.141592654*i)-13.*sin(40.84070450+3.141592654*i)+169.*sin(3.141592658+3.141592654*i)+169.*sin(-3.141592658+3.141592654*i))*q[7]*q[6]/((i+1.)*(13.+i)*(-13.+i)*(i-1.))-133.2396595*(-1.*sin(3.141592654*i-9.424777962)*i^3+sin(3.141592654*i+9.424777962)*i^3-3.*sin(3.141592654*i-9.424777962)*i^2-3.*sin(3.141592654*i+9.424777962)*i^2+9.*sin(28.27433389+3.141592654*i)*i^2+9.*sin(-28.27433389+3.141592654*i)*i^2+9.*sin(28.27433389+3.141592654*i)*i-9.*sin(-28.27433389+3.141592654*i)*i-1.*sin(28.27433389+3.141592654*i)*i^3+sin(-28.27433389+3.141592654*i)*i^3+243.*sin(3.141592654*i+9.424777962)+243.*sin(3.141592654*i-9.424777962)+81.*sin(3.141592654*i-9.424777962)*i-81.*sin(3.141592654*i+9.424777962)*i-81.*sin(-28.27433389+3.141592654*i)-81.*sin(28.27433389+3.141592654*i))*q[6]*q[3]/((i+3.)*(9.+i)*(-9.+i)*(i-3.))-236.8705057*(100.*sin(-6.283185304+3.141592654*i)*i-100.*sin(6.283185304+3.141592654*i)*i-1.*sin(-6.283185304+3.141592654*i)*i^3+sin(6.283185304+3.141592654*i)*i^3-2.*sin(-6.283185304+3.141592654*i)*i^2-2.*sin(6.283185304+3.141592654*i)*i^2+4.*sin(31.41592654+3.141592654*i)*i-4.*sin(-31.41592654+3.141592654*i)*i-1.*sin(31.41592654+3.141592654*i)*i^3+sin(-31.41592654+3.141592654*i)*i^3+10.*sin(31.41592654+3.141592654*i)*i^2+10.*sin(-31.41592654+3.141592654*i)*i^2-40.*sin(31.41592654+3.141592654*i)-40.*sin(-31.41592654+3.141592654*i)+200.*sin(6.283185304+3.141592654*i)+200.*sin(-6.283185304+3.141592654*i))*q[6]*q[4]/((i+2.)*(10.+i)*(-10.+i)*(i-2.))+370.1101651*(-1.*sin(3.141592654*i+3.141592654)*i^3+sin(3.141592654*i-3.141592654)*i^3+sin(3.141592654*i+3.141592654)*i^2+sin(3.141592654*i-3.141592654)*i^2-121.*sin(3.141592654*i+3.141592654)+121.*sin(3.141592654*i+3.141592654)*i-121.*sin(3.141592654*i-3.141592654)*i-121.*sin(3.141592654*i-3.141592654)-11.*sin(34.55751919+3.141592654*i)*i^2-11.*sin(-34.55751919+3.141592654*i)*i^2-1.*sin(34.55751919+3.141592654*i)*i+sin(-34.55751919+3.141592654*i)*i+sin(34.55751919+3.141592654*i)*i^3-1.*sin(-34.55751919+3.141592654*i)*i^3+11.*sin(34.55751919+3.141592654*i)+11.*sin(-34.55751919+3.141592654*i))*q[6]*q[5]/((i+1.)*(11.+i)*(-11.+i)*(i-1.))-725.4159234*(sin(-40.84070450+3.141592654*i)*i^3-1.*sin(3.141592656+3.141592654*i)*i^3+sin(-3.141592656+3.141592654*i)*i^2+13.*sin(40.84070450+3.141592654*i)*i^2+13.*sin(-40.84070450+3.141592654*i)*i^2+sin(3.141592656+3.141592654*i)*i^2-169.*sin(-3.141592656+3.141592654*i)*i+sin(40.84070450+3.141592654*i)*i-1.*sin(-40.84070450+3.141592654*i)*i+169.*sin(3.141592656+3.141592654*i)*i+sin(-3.141592656+3.141592654*i)*i^3-1.*sin(40.84070450+3.141592654*i)*i^3-169.*sin(3.141592656+3.141592654*i)-169.*sin(-3.141592656+3.141592654*i)-13.*sin(40.84070450+3.141592654*i)-13.*sin(-40.84070450+3.141592654*i))*q[6]*q[7]/((i-1.)*(13.+i)*(-13.+i)*(i+1.))-17.27180771*(-1.*sin(3.141592654*i-18.84955592)*i^3+sin(3.141592654*i+18.84955592)*i^3-6.*sin(3.141592654*i-18.84955592)*i^2-6.*sin(3.141592654*i+18.84955592)*i^2-288.*sin(3.141592654*i-25.13274123)-288.*sin(3.141592654*i+25.13274123)-36.*sin(3.141592654*i-25.13274123)*i+36.*sin(3.141592654*i+25.13274123)*i+384.*sin(3.141592654*i-18.84955592)+384.*sin(3.141592654*i+18.84955592)+64.*sin(3.141592654*i-18.84955592)*i-64.*sin(3.141592654*i+18.84955592)*i+sin(3.141592654*i-25.13274123)*i^3-1.*sin(3.141592654*i+25.13274123)*i^3+8.*sin(3.141592654*i-25.13274123)*i^2+8.*sin(3.141592654*i+25.13274123)*i^2)*q[7]*q[1]/((i+6.)*(i+8.)*(i-8.)*(i-6.))-12.33700550*(sin(3.141592654*i-18.84955592)*i^3-1.*sin(3.141592654*i+18.84955592)*i^3-1.*sin(3.141592654*i-12.56637062)*i^3+sin(3.141592654*i+12.56637062)*i^3+6.*sin(3.141592654*i-18.84955592)*i^2+6.*sin(3.141592654*i+18.84955592)*i^2-4.*sin(3.141592654*i-12.56637062)*i^2-4.*sin(3.141592654*i+12.56637062)*i^2-16.*sin(3.141592654*i-18.84955592)*i+16.*sin(3.141592654*i+18.84955592)*i+36.*sin(3.141592654*i-12.56637062)*i-36.*sin(3.141592654*i+12.56637062)*i-96.*sin(3.141592654*i-18.84955592)-96.*sin(3.141592654*i+18.84955592)+144.*sin(3.141592654*i-12.56637062)+144.*sin(3.141592654*i+12.56637062))*q[5]*q[1]/((i+4.)*(i+6.)*(i-6.)*(i-4.))-49.34802202*(sin(3.141592654*i-21.99114858)*i^3-1.*sin(3.141592654*i+21.99114858)*i^3+7.*sin(3.141592654*i-21.99114858)*i^2+7.*sin(3.141592654*i+21.99114858)*i^2-63.*sin(3.141592654*i-21.99114858)-63.*sin(3.141592654*i+21.99114858)-9.*sin(3.141592654*i-21.99114858)*i+9.*sin(3.141592654*i+21.99114858)*i-1.*sin(3.141592654*i-9.424777962)*i^3+sin(3.141592654*i+9.424777962)*i^3-3.*sin(3.141592654*i-9.424777962)*i^2-3.*sin(3.141592654*i+9.424777962)*i^2+147.*sin(3.141592654*i+9.424777962)+147.*sin(3.141592654*i-9.424777962)+49.*sin(3.141592654*i-9.424777962)*i-49.*sin(3.141592654*i+9.424777962)*i)*q[5]*q[2]/((i+3.)*(i+7.)*(i-7.)*(i-3.))-111.0330496*(-32.*sin(3.141592654*i-25.13274123)-32.*sin(3.141592654*i+25.13274123)-4.*sin(3.141592654*i-25.13274123)*i+4.*sin(3.141592654*i+25.13274123)*i-1.*sin(3.141592654*i-6.283185308)*i^3+sin(3.141592654*i+6.283185308)*i^3-2.*sin(3.141592654*i-6.283185308)*i^2-2.*sin(3.141592654*i+6.283185308)*i^2+128.*sin(3.141592654*i+6.283185308)+128.*sin(3.141592654*i-6.283185308)-64.*sin(3.141592654*i+6.283185308)*i+64.*sin(3.141592654*i-6.283185308)*i+sin(3.141592654*i-25.13274123)*i^3-1.*sin(3.141592654*i+25.13274123)*i^3+8.*sin(3.141592654*i-25.13274123)*i^2+8.*sin(3.141592654*i+25.13274123)*i^2)*q[5]*q[3]/((i+2.)*(i+8.)*(i-8.)*(i-2.))-197.3920880*(-81.*sin(3.141592650+3.141592654*i)*i+sin(28.27433389+3.141592654*i)*i-1.*sin(-28.27433389+3.141592654*i)*i+81.*sin(-3.141592650+3.141592654*i)*i+sin(3.141592650+3.141592654*i)*i^3-1.*sin(28.27433389+3.141592654*i)*i^3+sin(-28.27433389+3.141592654*i)*i^3-1.*sin(-3.141592650+3.141592654*i)*i^3-1.*sin(3.141592650+3.141592654*i)*i^2+9.*sin(28.27433389+3.141592654*i)*i^2+9.*sin(-28.27433389+3.141592654*i)*i^2-1.*sin(-3.141592650+3.141592654*i)*i^2+81.*sin(-3.141592650+3.141592654*i)+81.*sin(3.141592650+3.141592654*i)-9.*sin(28.27433389+3.141592654*i)-9.*sin(-28.27433389+3.141592654*i))*q[5]*q[4]/((i+1.)*(9.+i)*(-9.+i)*(i-1.))-444.1321982*(121.*sin(3.141592650+3.141592654*i)*i-121.*sin(-3.141592650+3.141592654*i)*i-1.*sin(3.141592650+3.141592654*i)*i^3+sin(-3.141592650+3.141592654*i)*i^3+sin(3.141592650+3.141592654*i)*i^2+sin(-3.141592650+3.141592654*i)*i^2+sin(34.55751919+3.141592654*i)*i-1.*sin(-34.55751919+3.141592654*i)*i-1.*sin(34.55751919+3.141592654*i)*i^3+sin(-34.55751919+3.141592654*i)*i^3+11.*sin(34.55751919+3.141592654*i)*i^2+11.*sin(-34.55751919+3.141592654*i)*i^2-11.*sin(34.55751919+3.141592654*i)-11.*sin(-34.55751919+3.141592654*i)-121.*sin(-3.141592650+3.141592654*i)-121.*sin(3.141592650+3.141592654*i))*q[5]*q[6]/((i-1.)*(11.+i)*(-11.+i)*(i+1.))-39.47841761*AA0*(sin(3.141592654*i-9.424777962)*i^3-1.*sin(3.141592654*i+9.424777962)*i^3+sin(3.141592654*i-15.70796327)*i^3-1.*sin(3.141592654*i+15.70796327)*i^3+3.*sin(3.141592654*i-9.424777962)*i^2+3.*sin(3.141592654*i+9.424777962)*i^2+5.*sin(3.141592654*i-15.70796327)*i^2+5.*sin(3.141592654*i+15.70796327)*i^2-25.*sin(3.141592654*i-9.424777962)*i+25.*sin(3.141592654*i+9.424777962)*i-9.*sin(3.141592654*i-15.70796327)*i+9.*sin(3.141592654*i+15.70796327)*i-75.*sin(3.141592654*i-9.424777962)-75.*sin(3.141592654*i+9.424777962)-45.*sin(3.141592654*i-15.70796327)-45.*sin(3.141592654*i+15.70796327))*q[4]/((i-5.)*(i+3.)*(i-3.)*(i+5.))-61.68502752*AA0*(sin(3.141592654*i-18.84955592)*i^3-1.*sin(3.141592654*i+18.84955592)*i^3+sin(3.141592654*i-12.56637062)*i^3-1.*sin(3.141592654*i+12.56637062)*i^3+6.*sin(3.141592654*i-18.84955592)*i^2+6.*sin(3.141592654*i+18.84955592)*i^2+4.*sin(3.141592654*i-12.56637062)*i^2+4.*sin(3.141592654*i+12.56637062)*i^2-16.*sin(3.141592654*i-18.84955592)*i+16.*sin(3.141592654*i+18.84955592)*i-36.*sin(3.141592654*i-12.56637062)*i+36.*sin(3.141592654*i+12.56637062)*i-96.*sin(3.141592654*i-18.84955592)-96.*sin(3.141592654*i+18.84955592)-144.*sin(3.141592654*i-12.56637062)-144.*sin(3.141592654*i+12.56637062))*q[5]/((i-6.)*(i+4.)*(i-4.)*(i+6.))-88.82643963*AA0*(sin(3.141592654*i-21.99114858)*i^3-1.*sin(3.141592654*i+21.99114858)*i^3+sin(3.141592654*i-15.70796327)*i^3-1.*sin(3.141592654*i+15.70796327)*i^3+7.*sin(3.141592654*i-21.99114858)*i^2+7.*sin(3.141592654*i+21.99114858)*i^2+5.*sin(3.141592654*i-15.70796327)*i^2+5.*sin(3.141592654*i+15.70796327)*i^2-25.*sin(3.141592654*i-21.99114858)*i+25.*sin(3.141592654*i+21.99114858)*i-49.*sin(3.141592654*i-15.70796327)*i+49.*sin(3.141592654*i+15.70796327)*i-175.*sin(3.141592654*i-21.99114858)-175.*sin(3.141592654*i+21.99114858)-245.*sin(3.141592654*i-15.70796327)-245.*sin(3.141592654*i+15.70796327))*q[6]/((i-7.)*(i+5.)*(i-5.)*(i+7.))-120.9026539*AA0*(sin(3.141592654*i-18.84955592)*i^3-1.*sin(3.141592654*i+18.84955592)*i^3+sin(3.141592654*i-25.13274123)*i^3-1.*sin(3.141592654*i+25.13274123)*i^3+6.*sin(3.141592654*i-18.84955592)*i^2+6.*sin(3.141592654*i+18.84955592)*i^2+8.*sin(3.141592654*i-25.13274123)*i^2+8.*sin(3.141592654*i+25.13274123)*i^2-64.*sin(3.141592654*i-18.84955592)*i+64.*sin(3.141592654*i+18.84955592)*i-36.*sin(3.141592654*i-25.13274123)*i+36.*sin(3.141592654*i+25.13274123)*i-384.*sin(3.141592654*i-18.84955592)-384.*sin(3.141592654*i+18.84955592)-288.*sin(3.141592654*i-25.13274123)-288.*sin(3.141592654*i+25.13274123))*q[7]/((i-8.)*(i+6.)*(i-6.)*(i+8.))-9.869604403*AA0*(sin(3.141592654*i-9.424777962)*i^3-1.*sin(3.141592654*i+3.141592654)*i^3+sin(3.141592654*i-3.141592654)*i^3-1.*sin(3.141592654*i+9.424777962)*i^3+3.*sin(3.141592654*i-9.424777962)*i^2+sin(3.141592654*i+3.141592654)*i^2+sin(3.141592654*i-3.141592654)*i^2+3.*sin(3.141592654*i+9.424777962)*i^2-1.*sin(3.141592654*i-9.424777962)*i+9.*sin(3.141592654*i+3.141592654)*i-9.*sin(3.141592654*i-3.141592654)*i+sin(3.141592654*i+9.424777962)*i-3.*sin(3.141592654*i-9.424777962)-9.*sin(3.141592654*i+3.141592654)-9.*sin(3.141592654*i-3.141592654)-3.*sin(3.141592654*i+9.424777962))*q[2]/((i-3.)*(i+1.)*(i-1.)*(i+3.))-22.20660991*AA0*(sin(3.141592654*i-12.56637062)*i^3-1.*sin(3.141592654*i+12.56637062)*i^3+sin(3.141592654*i-6.283185308)*i^3-1.*sin(3.141592654*i+6.283185308)*i^3+4.*sin(3.141592654*i-12.56637062)*i^2+4.*sin(3.141592654*i+12.56637062)*i^2+2.*sin(3.141592654*i-6.283185308)*i^2+2.*sin(3.141592654*i+6.283185308)*i^2-4.*sin(3.141592654*i-12.56637062)*i+4.*sin(3.141592654*i+12.56637062)*i-16.*sin(3.141592654*i-6.283185308)*i+16.*sin(3.141592654*i+6.283185308)*i-16.*sin(3.141592654*i-12.56637062)-16.*sin(3.141592654*i+12.56637062)-32.*sin(3.141592654*i-6.283185308)-32.*sin(3.141592654*i+6.283185308))*q[3]/((i-4.)*(i+2.)*(i-2.)*(i+4.))-604.5132695*(sin(-37.69911185+3.141592654*i)*i^3-1.*sin(6.283185310+3.141592654*i)*i^3+2.*sin(-6.283185310+3.141592654*i)*i^2+12.*sin(37.69911185+3.141592654*i)*i^2+12.*sin(-37.69911185+3.141592654*i)*i^2+2.*sin(6.283185310+3.141592654*i)*i^2-144.*sin(-6.283185310+3.141592654*i)*i+4.*sin(37.69911185+3.141592654*i)*i-4.*sin(-37.69911185+3.141592654*i)*i+144.*sin(6.283185310+3.141592654*i)*i+sin(-6.283185310+3.141592654*i)*i^3-1.*sin(37.69911185+3.141592654*i)*i^3-288.*sin(6.283185310+3.141592654*i)-288.*sin(-6.283185310+3.141592654*i)-48.*sin(37.69911185+3.141592654*i)-48.*sin(-37.69911185+3.141592654*i))*q[5]*q[7]/((i-2.)*(12.+i)*(-12.+i)*(i+2.))-14.80440661*(sin(3.141592654*i-21.99114858)*i^3-1.*sin(3.141592654*i+21.99114858)*i^3-1.*sin(3.141592654*i-15.70796327)*i^3+sin(3.141592654*i+15.70796327)*i^3+7.*sin(3.141592654*i-21.99114858)*i^2+7.*sin(3.141592654*i+21.99114858)*i^2-5.*sin(3.141592654*i-15.70796327)*i^2-5.*sin(3.141592654*i+15.70796327)*i^2-25.*sin(3.141592654*i-21.99114858)*i+25.*sin(3.141592654*i+21.99114858)*i+49.*sin(3.141592654*i-15.70796327)*i-49.*sin(3.141592654*i+15.70796327)*i-175.*sin(3.141592654*i-21.99114858)-175.*sin(3.141592654*i+21.99114858)+245.*sin(3.141592654*i-15.70796327)+245.*sin(3.141592654*i+15.70796327))*q[6]*q[1]/((i+5.)*(i+7.)*(i-7.)*(i-5.))-59.21762642*(-128.*sin(3.141592654*i-25.13274123)-128.*sin(3.141592654*i+25.13274123)-16.*sin(3.141592654*i-25.13274123)*i+16.*sin(3.141592654*i+25.13274123)*i-1.*sin(3.141592654*i-12.56637062)*i^3+sin(3.141592654*i+12.56637062)*i^3-4.*sin(3.141592654*i-12.56637062)*i^2-4.*sin(3.141592654*i+12.56637062)*i^2+256.*sin(3.141592654*i+12.56637062)+256.*sin(3.141592654*i-12.56637062)+64.*sin(3.141592654*i-12.56637062)*i-64.*sin(3.141592654*i+12.56637062)*i+sin(3.141592654*i-25.13274123)*i^3-1.*sin(3.141592654*i+25.13274123)*i^3+8.*sin(3.141592654*i-25.13274123)*i^2+8.*sin(3.141592654*i+25.13274123)*i^2)*q[6]*q[2]/((i+4.)*(i+8.)*(i-8.)*(i-4.))-4.934802202*(sin(3.141592654*i-9.424777962)*i^3+sin(3.141592654*i+3.141592654)*i^3-1.*sin(3.141592654*i-3.141592654)*i^3-1.*sin(3.141592654*i+9.424777962)*i^3+3.*sin(3.141592654*i-9.424777962)*i^2-1.*sin(3.141592654*i+3.141592654)*i^2-1.*sin(3.141592654*i-3.141592654)*i^2+3.*sin(3.141592654*i+9.424777962)*i^2-1.*sin(3.141592654*i-9.424777962)*i-9.*sin(3.141592654*i+3.141592654)*i+9.*sin(3.141592654*i-3.141592654)*i+sin(3.141592654*i+9.424777962)*i-3.*sin(3.141592654*i-9.424777962)+9.*sin(3.141592654*i+3.141592654)+9.*sin(3.141592654*i-3.141592654)-3.*sin(3.141592654*i+9.424777962))*q[2]*q[1]/((i+1.)*(i+3.)*(i-3.)*(i-1.))-44.41321982*(sin(3.141592654*i-15.70796327)*i^3-1.*sin(3.141592654*i+15.70796327)*i^3+5.*sin(3.141592654*i-15.70796327)*i^2+5.*sin(3.141592654*i+15.70796327)*i^2-5.*sin(3.141592654*i+15.70796327)-5.*sin(3.141592654*i-15.70796327)-1.*sin(3.141592654*i-15.70796327)*i+sin(3.141592654*i+15.70796327)*i-1.*sin(3.141592654*i+3.141592654)*i^3+sin(3.141592654*i-3.141592654)*i^3+sin(3.141592654*i+3.141592654)*i^2+sin(3.141592654*i-3.141592654)*i^2-25.*sin(3.141592654*i+3.141592654)+25.*sin(3.141592654*i+3.141592654)*i-25.*sin(3.141592654*i-3.141592654)*i-25.*sin(3.141592654*i-3.141592654))*q[2]*q[3]/((i-1.)*(i+5.)*(i-5.)*(i+1.))-78.95683522*(-36.*sin(-6.283185312+3.141592654*i)*i+4.*sin(18.84955593+3.141592654*i)*i-4.*sin(-18.84955593+3.141592654*i)*i+36.*sin(6.283185312+3.141592654*i)*i+sin(-6.283185312+3.141592654*i)*i^3-1.*sin(18.84955593+3.141592654*i)*i^3+sin(-18.84955593+3.141592654*i)*i^3-1.*sin(6.283185312+3.141592654*i)*i^3+2.*sin(-6.283185312+3.141592654*i)*i^2+6.*sin(18.84955593+3.141592654*i)*i^2+6.*sin(-18.84955593+3.141592654*i)*i^2+2.*sin(6.283185312+3.141592654*i)*i^2-24.*sin(-18.84955593+3.141592654*i)-72.*sin(6.283185312+3.141592654*i)-72.*sin(-6.283185312+3.141592654*i)-24.*sin(18.84955593+3.141592654*i))*q[2]*q[4]/((i-2.)*(i+6.)*(i-6.)*(i+2.))+123.3700550*(-1.*sin(3.141592654*i-21.99114858)*i^3+sin(3.141592654*i+21.99114858)*i^3-7.*sin(3.141592654*i-21.99114858)*i^2-7.*sin(3.141592654*i+21.99114858)*i^2+63.*sin(3.141592654*i-21.99114858)+63.*sin(3.141592654*i+21.99114858)+9.*sin(3.141592654*i-21.99114858)*i-9.*sin(3.141592654*i+21.99114858)*i-1.*sin(3.141592654*i-9.424777962)*i^3+sin(3.141592654*i+9.424777962)*i^3-3.*sin(3.141592654*i-9.424777962)*i^2-3.*sin(3.141592654*i+9.424777962)*i^2+147.*sin(3.141592654*i+9.424777962)+147.*sin(3.141592654*i-9.424777962)+49.*sin(3.141592654*i-9.424777962)*i-49.*sin(3.141592654*i+9.424777962)*i)*q[2]*q[5]/((i-3.)*(i+7.)*(i-7.)*(i+3.))-177.6528793*(-64.*sin(-12.56637061+3.141592654*i)*i+16.*sin(3.141592654*i+25.13274123)*i-16.*sin(3.141592654*i-25.13274123)*i+64.*sin(12.56637061+3.141592654*i)*i+sin(-12.56637061+3.141592654*i)*i^3-1.*sin(3.141592654*i+25.13274123)*i^3+sin(3.141592654*i-25.13274123)*i^3-1.*sin(12.56637061+3.141592654*i)*i^3+4.*sin(-12.56637061+3.141592654*i)*i^2+8.*sin(3.141592654*i+25.13274123)*i^2+8.*sin(3.141592654*i-25.13274123)*i^2+4.*sin(12.56637061+3.141592654*i)*i^2-256.*sin(12.56637061+3.141592654*i)-256.*sin(-12.56637061+3.141592654*i)-128.*sin(3.141592654*i+25.13274123)-128.*sin(3.141592654*i-25.13274123))*q[2]*q[6]/((i-4.)*(i+8.)*(i-8.)*(i+4.))-241.8053078*(sin(-28.27433389+3.141592654*i)*i^3-1.*sin(3.141592654*i+15.70796327)*i^3+5.*sin(3.141592654*i-15.70796327)*i^2+9.*sin(28.27433389+3.141592654*i)*i^2+9.*sin(-28.27433389+3.141592654*i)*i^2+5.*sin(3.141592654*i+15.70796327)*i^2-81.*sin(3.141592654*i-15.70796327)*i+25.*sin(28.27433389+3.141592654*i)*i-25.*sin(-28.27433389+3.141592654*i)*i+81.*sin(3.141592654*i+15.70796327)*i+sin(3.141592654*i-15.70796327)*i^3-1.*sin(28.27433389+3.141592654*i)*i^3-225.*sin(28.27433389+3.141592654*i)-225.*sin(-28.27433389+3.141592654*i)-405.*sin(3.141592654*i+15.70796327)-405.*sin(3.141592654*i-15.70796327))*q[2]*q[7]/((i-5.)*(9.+i)*(-9.+i)*(i+5.))-7.402203303*(-1.*sin(3.141592654*i-6.283185308)*i^3+sin(3.141592654*i+6.283185308)*i^3+sin(3.141592654*i-12.56637062)*i^3-1.*sin(3.141592654*i+12.56637062)*i^3-2.*sin(3.141592654*i-6.283185308)*i^2-2.*sin(3.141592654*i+6.283185308)*i^2+4.*sin(3.141592654*i-12.56637062)*i^2+4.*sin(3.141592654*i+12.56637062)*i^2+16.*sin(3.141592654*i-6.283185308)*i-16.*sin(3.141592654*i+6.283185308)*i-4.*sin(3.141592654*i-12.56637062)*i+4.*sin(3.141592654*i+12.56637062)*i+32.*sin(3.141592654*i-6.283185308)+32.*sin(3.141592654*i+6.283185308)-16.*sin(3.141592654*i-12.56637062)-16.*sin(3.141592654*i+12.56637062))*q[3]*q[1]/((i+2.)*(i+4.)*(i-4.)*(i-2.))-29.60881321*(sin(3.141592654*i-15.70796327)*i^3-1.*sin(3.141592654*i+15.70796327)*i^3+5.*sin(3.141592654*i-15.70796327)*i^2+5.*sin(3.141592654*i+15.70796327)*i^2-5.*sin(3.141592654*i+15.70796327)-5.*sin(3.141592654*i-15.70796327)-1.*sin(3.141592654*i-15.70796327)*i+sin(3.141592654*i+15.70796327)*i+sin(3.141592654*i+3.141592654)*i^3-1.*sin(3.141592654*i-3.141592654)*i^3-1.*sin(3.141592654*i+3.141592654)*i^2-1.*sin(3.141592654*i-3.141592654)*i^2+25.*sin(3.141592654*i+3.141592654)-25.*sin(3.141592654*i+3.141592654)*i+25.*sin(3.141592654*i-3.141592654)*i+25.*sin(3.141592654*i-3.141592654))*q[3]*q[2]/((i+1.)*(i+5.)*(i-5.)*(i-1.))-118.4352528*(-49.*sin(-3.141592658+3.141592654*i)*i+sin(3.141592654*i+21.99114858)*i-1.*sin(3.141592654*i-21.99114858)*i+49.*sin(3.141592658+3.141592654*i)*i+sin(-3.141592658+3.141592654*i)*i^3-1.*sin(3.141592654*i+21.99114858)*i^3+sin(3.141592654*i-21.99114858)*i^3-1.*sin(3.141592658+3.141592654*i)*i^3+sin(-3.141592658+3.141592654*i)*i^2+7.*sin(3.141592654*i+21.99114858)*i^2+7.*sin(3.141592654*i-21.99114858)*i^2+sin(3.141592658+3.141592654*i)*i^2-7.*sin(3.141592654*i+21.99114858)-7.*sin(3.141592654*i-21.99114858)-49.*sin(3.141592658+3.141592654*i)-49.*sin(-3.141592658+3.141592654*i))*q[3]*q[4]/((i-1.)*(i+7.)*(i-7.)*(i+1.))+185.0550826*(32.*sin(3.141592654*i-25.13274123)+32.*sin(3.141592654*i+25.13274123)+4.*sin(3.141592654*i-25.13274123)*i-4.*sin(3.141592654*i+25.13274123)*i-1.*sin(3.141592654*i-6.283185308)*i^3+sin(3.141592654*i+6.283185308)*i^3-2.*sin(3.141592654*i-6.283185308)*i^2-2.*sin(3.141592654*i+6.283185308)*i^2+128.*sin(3.141592654*i+6.283185308)+128.*sin(3.141592654*i-6.283185308)-64.*sin(3.141592654*i+6.283185308)*i+64.*sin(3.141592654*i-6.283185308)*i-1.*sin(3.141592654*i-25.13274123)*i^3+sin(3.141592654*i+25.13274123)*i^3-8.*sin(3.141592654*i-25.13274123)*i^2-8.*sin(3.141592654*i+25.13274123)*i^2)*q[3]*q[5]/((i-2.)*(i+8.)*(i-8.)*(i+2.))-266.4793189*(-81.*sin(-9.424777958+3.141592654*i)*i+9.*sin(28.27433388+3.141592654*i)*i-9.*sin(-28.27433388+3.141592654*i)*i+81.*sin(9.424777958+3.141592654*i)*i+sin(-9.424777958+3.141592654*i)*i^3-1.*sin(28.27433388+3.141592654*i)*i^3+sin(-28.27433388+3.141592654*i)*i^3-1.*sin(9.424777958+3.141592654*i)*i^3+3.*sin(-9.424777958+3.141592654*i)*i^2+9.*sin(28.27433388+3.141592654*i)*i^2+9.*sin(-28.27433388+3.141592654*i)*i^2+3.*sin(9.424777958+3.141592654*i)*i^2-243.*sin(-9.424777958+3.141592654*i)-81.*sin(28.27433388+3.141592654*i)-81.*sin(-28.27433388+3.141592654*i)-243.*sin(9.424777958+3.141592654*i))*q[3]*q[6]/((i-3.)*(9.+i)*(-9.+i)*(i+3.))-362.7079617*(sin(-31.41592654+3.141592654*i)*i^3-1.*sin(3.141592654*i+12.56637062)*i^3+4.*sin(3.141592654*i-12.56637062)*i^2+10.*sin(31.41592654+3.141592654*i)*i^2+10.*sin(-31.41592654+3.141592654*i)*i^2+4.*sin(3.141592654*i+12.56637062)*i^2-100.*sin(3.141592654*i-12.56637062)*i+16.*sin(31.41592654+3.141592654*i)*i-16.*sin(-31.41592654+3.141592654*i)*i+100.*sin(3.141592654*i+12.56637062)*i+sin(3.141592654*i-12.56637062)*i^3-1.*sin(31.41592654+3.141592654*i)*i^3-160.*sin(-31.41592654+3.141592654*i)-400.*sin(3.141592654*i+12.56637062)-400.*sin(3.141592654*i-12.56637062)-160.*sin(31.41592654+3.141592654*i))*q[3]*q[7]/((i-4.)*(10.+i)*(-10.+i)*(i+4.))-9.869604404*(sin(3.141592654*i-15.70796327)*i^3-1.*sin(3.141592654*i+15.70796327)*i^3+5.*sin(3.141592654*i-15.70796327)*i^2+5.*sin(3.141592654*i+15.70796327)*i^2-45.*sin(3.141592654*i+15.70796327)-45.*sin(3.141592654*i-15.70796327)-9.*sin(3.141592654*i-15.70796327)*i+9.*sin(3.141592654*i+15.70796327)*i-1.*sin(3.141592654*i-9.424777962)*i^3+sin(3.141592654*i+9.424777962)*i^3-3.*sin(3.141592654*i-9.424777962)*i^2-3.*sin(3.141592654*i+9.424777962)*i^2+75.*sin(3.141592654*i+9.424777962)+75.*sin(3.141592654*i-9.424777962)+25.*sin(3.141592654*i-9.424777962)*i-25.*sin(3.141592654*i+9.424777962)*i)*q[4]*q[1]/((i+3.)*(i+5.)*(i-5.)*(i-3.))-39.47841761*(sin(3.141592654*i-18.84955592)*i^3-1.*sin(3.141592654*i+18.84955592)*i^3+6.*sin(3.141592654*i-18.84955592)*i^2+6.*sin(3.141592654*i+18.84955592)*i^2-24.*sin(3.141592654*i-18.84955592)-24.*sin(3.141592654*i+18.84955592)-4.*sin(3.141592654*i-18.84955592)*i+4.*sin(3.141592654*i+18.84955592)*i-1.*sin(3.141592654*i-6.283185308)*i^3+sin(3.141592654*i+6.283185308)*i^3-2.*sin(3.141592654*i-6.283185308)*i^2-2.*sin(3.141592654*i+6.283185308)*i^2+72.*sin(3.141592654*i+6.283185308)+72.*sin(3.141592654*i-6.283185308)-36.*sin(3.141592654*i+6.283185308)*i+36.*sin(3.141592654*i-6.283185308)*i)*q[4]*q[2]/((i+2.)*(i+6.)*(i-6.)*(i-2.))-88.82643964*(sin(3.141592654*i-21.99114858)*i^3-1.*sin(3.141592654*i+21.99114858)*i^3+7.*sin(3.141592654*i-21.99114858)*i^2+7.*sin(3.141592654*i+21.99114858)*i^2-7.*sin(3.141592654*i-21.99114858)-7.*sin(3.141592654*i+21.99114858)-1.*sin(3.141592654*i-21.99114858)*i+sin(3.141592654*i+21.99114858)*i+sin(3.141592654*i+3.141592654)*i^3-1.*sin(3.141592654*i-3.141592654)*i^3-1.*sin(3.141592654*i+3.141592654)*i^2-1.*sin(3.141592654*i-3.141592654)*i^2+49.*sin(3.141592654*i+3.141592654)-49.*sin(3.141592654*i+3.141592654)*i+49.*sin(3.141592654*i-3.141592654)*i+49.*sin(3.141592654*i-3.141592654))*q[4]*q[3]/((i+1.)*(i+7.)*(i-7.)*(i-1.))+246.7401101*(sin(3.141592654*i+3.141592654)*i^3-1.*sin(3.141592654*i-3.141592654)*i^3-1.*sin(3.141592654*i+3.141592654)*i^2-1.*sin(3.141592654*i-3.141592654)*i^2-9.*sin(28.27433389+3.141592654*i)*i^2-9.*sin(-28.27433389+3.141592654*i)*i^2-1.*sin(28.27433389+3.141592654*i)*i+sin(-28.27433389+3.141592654*i)*i+sin(28.27433389+3.141592654*i)*i^3-1.*sin(-28.27433389+3.141592654*i)*i^3+81.*sin(3.141592654*i+3.141592654)-81.*sin(3.141592654*i+3.141592654)*i+81.*sin(3.141592654*i-3.141592654)*i+81.*sin(3.141592654*i-3.141592654)+9.*sin(-28.27433389+3.141592654*i)+9.*sin(28.27433389+3.141592654*i))*q[4]*q[5]/((i-1.)*(9.+i)*(-9.+i)*(i+1.))-355.3057585*(-100.*sin(-6.283185304+3.141592654*i)*i+4.*sin(31.41592654+3.141592654*i)*i-4.*sin(-31.41592654+3.141592654*i)*i+100.*sin(6.283185304+3.141592654*i)*i+sin(-6.283185304+3.141592654*i)*i^3-1.*sin(31.41592654+3.141592654*i)*i^3+sin(-31.41592654+3.141592654*i)*i^3-1.*sin(6.283185304+3.141592654*i)*i^3+2.*sin(-6.283185304+3.141592654*i)*i^2+10.*sin(31.41592654+3.141592654*i)*i^2+10.*sin(-31.41592654+3.141592654*i)*i^2+2.*sin(6.283185304+3.141592654*i)*i^2-40.*sin(31.41592654+3.141592654*i)-40.*sin(-31.41592654+3.141592654*i)-200.*sin(6.283185304+3.141592654*i)-200.*sin(-6.283185304+3.141592654*i))*q[4]*q[6]/((i-2.)*(10.+i)*(-10.+i)*(i+2.))-483.6106156*(sin(-34.55751920+3.141592654*i)*i^3-1.*sin(9.424777964+3.141592654*i)*i^3+3.*sin(-9.424777964+3.141592654*i)*i^2+11.*sin(34.55751920+3.141592654*i)*i^2+11.*sin(-34.55751920+3.141592654*i)*i^2+3.*sin(9.424777964+3.141592654*i)*i^2-121.*sin(-9.424777964+3.141592654*i)*i+9.*sin(34.55751920+3.141592654*i)*i-9.*sin(-34.55751920+3.141592654*i)*i+121.*sin(9.424777964+3.141592654*i)*i+sin(-9.424777964+3.141592654*i)*i^3-1.*sin(34.55751920+3.141592654*i)*i^3-363.*sin(9.424777964+3.141592654*i)-363.*sin(-9.424777964+3.141592654*i)-99.*sin(34.55751920+3.141592654*i)-99.*sin(-34.55751920+3.141592654*i))*q[4]*q[7]/((i-3.)*(11.+i)*(-11.+i)*(i+3.)))+Cd*(.1591549431*(sin(3.141592654*i-3.141592654)*i-1.*sin(3.141592654*i+3.141592654)*i+sin(3.141592654*i-3.141592654)+sin(3.141592654*i+3.141592654))*(diff(p(t), t))[1]/((i-1.)*(i+1.))+.1591549431*(sin(3.141592654*i-6.283185308)*i-1.*sin(3.141592654*i+6.283185308)*i+2.*sin(3.141592654*i-6.283185308)+2.*sin(3.141592654*i+6.283185308))*(diff(p(t), t))[2]/((i-2.)*(i+2.))+.1591549431*(sin(3.141592654*i-9.424777962)*i-1.*sin(3.141592654*i+9.424777962)*i+3.*sin(3.141592654*i-9.424777962)+3.*sin(3.141592654*i+9.424777962))*(diff(p(t), t))[3]/((i-3.)*(i+3.))+.1591549431*(sin(3.141592654*i-12.56637062)*i-1.*sin(3.141592654*i+12.56637062)*i+4.*sin(3.141592654*i-12.56637062)+4.*sin(3.141592654*i+12.56637062))*(diff(p(t), t))[4]/((i-4.)*(i+4.))+.1591549431*(sin(3.141592654*i-15.70796327)*i-1.*sin(3.141592654*i+15.70796327)*i+5.*sin(3.141592654*i-15.70796327)+5.*sin(3.141592654*i+15.70796327))*(diff(p(t), t))[5]/((i-5.)*(i+5.))+.1591549431*(sin(3.141592654*i-18.84955592)*i-1.*sin(3.141592654*i+18.84955592)*i+6.*sin(3.141592654*i-18.84955592)+6.*sin(3.141592654*i+18.84955592))*(diff(p(t), t))[6]/((i-6.)*(i+6.))+.1591549431*(sin(3.141592654*i-21.99114858)*i-1.*sin(3.141592654*i+21.99114858)*i+7.*sin(3.141592654*i-21.99114858)+7.*sin(3.141592654*i+21.99114858))*(diff(p(t), t))[7]/((i-7.)*(i+7.))+.1591549431*(sin(3.141592654*i-25.13274123)*i-1.*sin(3.141592654*i+25.13274123)*i+8.*sin(3.141592654*i-25.13274123)+8.*sin(3.141592654*i+25.13274123))*(diff(p(t), t))[8]/((i-8.)*(i+8.))), i = 1)

 

Warning,  computation interrupted

 

``

``

NULL

pp2 := sum((int(phi[i]*phi[j], x = 0 .. 1, numeric))*(diff(q(t), t, t))[j], j = 1 .. 7)+(1+`&eta;&eta;`)*(sum((int(phi[i]*(diff(phi[j], x, x, x, x)), x = 0 .. 1, numeric))*q(t)[j], j = 1 .. 7))+Cd*(sum((int(phi[i]*phi[j], x = 0 .. 1, numeric))*(diff(q(t), t))[j], j = 1 .. 7))-beta^2*(sum(sum((int(phi[i]*(diff(phi[j], x, x))*(diff(phi[k], x)), x = 0 .. 1, numeric))*q(t)[j]*p[k], k = 1 .. 8), j = 1 .. 7)+sum(sum((int(phi[i]*(diff(phi[j], x))*(diff(phi[k], x, x)), x = 0 .. 1, numeric))*q(t)[j]*p[k], k = 1 .. 8), j = 1 .. 7)+sum((int(AA0*(diff(phi[1], x, x))*phi[i]*(diff(phi[j], x)), x = 0 .. 1, numeric))*p[j], j = 1 .. 8)+sum((int(AA0*(diff(phi[1], x))*phi[i]*(diff(phi[j], x, x)), x = 0 .. 1, numeric))*p[j], j = 1 .. 8)+(3/2)*(sum(sum(sum((int(phi[i]*(diff(phi[j], x))*(diff(phi[k], x))*(diff(phi[l], x, x)), x = 0 .. 1, numeric))*q(t)[j]*q(t)[k]*q(t)[l], l = 1 .. 7), k = 1 .. 7), j = 1 .. 7))+(3/2)*(sum(sum((int(AA0*(diff(phi[1], x, x))*phi[i]*(diff(phi[j], x))*(diff(phi[k], x)), x = 0 .. 1, numeric))*q(t)[j]*q(t)[k], k = 1 .. 7), j = 1 .. 7))+sum((int((AA0*(diff(phi[1], x)))^2*phi[i]*(diff(phi[j], x, x)), x = 0 .. 1, numeric))*q(t)[j], j = 1 .. 7)+3*(sum(sum((int(AA0*(diff(phi[1], x))*phi[i]*(diff(phi[j], x))*(diff(phi[k], x, x)), x = 0 .. 1, numeric))*q(t)[j]*q(t)[k], k = 1 .. 7), j = 1 .. 7))+2*(sum((int(AA0^2*(diff(phi[1], x))*(diff(phi[1], x, x))*phi[i]*(diff(phi[j], x)), x = 0 .. 1, numeric))*q(t)[j], j = 1 .. 7)))-(int(f1*phi[1]*phi[i], x = 0 .. 1, numeric))*cos(Omega*t)

NULL

NULL

``

for z to 7 do limit(pp2, i = z) end do

Warning,  computation interrupted

 

``

NULL

``

``

``

``

``

``

``

``

``

``

``

``

``

``

``


 

Download 11111111111111.mwWould you mind please check out my code11111111111111.mw

11111111111111.mw

Hello everyone,

I am experiencing a strange result. The Theta_double_dot got equated to zero in line 1.7. Please see the red arrow.

(I am using the Physics package)

How can I solve this issue?

x/2 seems completely wrong as a CDF. In other cases Maple correctly writes the CDF as a piecewise-constant function clipped to 0..1:

with(Statistics):

dd := Distribution(ProbabilityFunction = 1/2, Support = 1 .. 2);

PDF(dd, x); # OK
                   (1/2)*Dirac(x-1)+(1/2)*Dirac(x-2)

CDF(dd, x);
                                (1/2)*x

Also CDF seems to have issues with DiscreteValueMap specified using a list, a table or piecewise():

dd := Distribution(ProbabilityFunction = 1/2, DiscreteValueMap = (n -> [1, 2][n]), Support = 1 .. 2);

PDF(dd, x); # OK
                    (1/2)*Dirac(x-1)+(1/2)*Dirac(x-2)

CDF(dd, x); # indeterminate
  int((1/2)*Dirac(0)*Dirac(_t-1)+(1/2)*Dirac(0)*Dirac(_t-2), _t = -infinity .. x)

 

with(Statistics):

CDF(Binomial(2, 1/2), x); # wrong
               piecewise(x < 0, 0, 2 <= x, 1, 1)

CDF(Binomial(2, p), x); # also wrong
     piecewise(x < 0, 0, 2 <= x, 1, p = 0, 1, p = 1, 0, 1)

Maple can actually generate PDFs for discrete distributions:

bpdf := unapply(PDF(Binomial(2, 1/2), x), x);
          x -> (1/4)*Dirac(x)+(1/2)*Dirac(x-1)+(1/4)*Dirac(x-2)

int(bpdf(t), t = -infinity .. x); # correct CDF
         (1/4)*Heaviside(x)+(1/2)*Heaviside(x-1)+(1/4)*Heaviside(x-2)

But then functions of random variables do not seem to work :

bdist := Distribution(PDF = bpdf, Support = -infinity .. infinity);

CDF(bdist, x); # OK
           piecewise(x < 0, 0, x = 0, undefined, x < 1, 1/4, x = 1, undefined, x < 2, 3/4, x = 2,
           undefined, 2 < x, 1)

CDF(add(RandomVariable(bdist), i = 1 .. 2), x); # indeterminate
          int((1/16)*Dirac(_t)^2+(1/4)*Dirac(0)*Dirac(_t-1)+(3/8)*Dirac(0)*Dirac(_t-2)+(1/4)*Dirac(0)*
          Dirac(_t-3)+(1/16)*Dirac(0)*Dirac(_t-4), _t = -infinity .. x)

It's a bit disappointing that Maple generates PDFs in terms of the delta function but doesn't support them properly, because that could be an easy and natural way to define mixed distributions.

Apologies for possible double post, it seemingly locked up upon trying to post the first time. 

So before I get as far as to ask for how to get a certain PDE system solved and plotted, I tried to fiddle a little bit around with linear algebra. 

  • First, the file SystemGoesWrong.mw . I have issues with declaring (same result if I remove the with(VectorCalculus)); as far as I can see, EQ0 and EQ00 should be the same, except that I have summed the vector in one of them. And the first that "works", is wrong: it returns a scaling of a vector. How come?
  • But then I copy everything from the heading and down into a worksheet where I was already fighting some linear algebra things (can someone please explain?): SystemDeclaresBut.mw 
    Then EQ0 and EQ00 declare just fine! What is the issue?
  • How do I get Maple to list the equations in "compact" form with vector-valued functions so that I can read and debug?  The actual PDE system I want to solve (numerically, of course), looks as follows: DE4Maple.pdf 
    That was also the reason why I tried to declare procedures (coordinate-wise maximum ...), but I guess that questions on how to extract a solution and plot it in a particular way will be its own posting after I have learned how to declare it.

 

The contents of the first file:


 

restart

# Since I do not have any idea of how to get vectors nicely, ...

... I replace U0, U1, U2 by u,v,w and use difftables U,V,W.  And y1, y2 replaced by y,z.

with(PDEtools):

declare(u(y, z), v(y, z), w(y, z), q1(y, z), r1(y, z), s1(y, z), q2(y, z), r2(y, z), s2(y, z), F1(y, z), F2(y, z)):

u(y, z)*`will now be displayed as`*u

 

v(y, z)*`will now be displayed as`*v

 

w(y, z)*`will now be displayed as`*w

 

q1(y, z)*`will now be displayed as`*q1

 

r1(y, z)*`will now be displayed as`*r1

 

s1(y, z)*`will now be displayed as`*s1

 

q2(y, z)*`will now be displayed as`*q2

 

r2(y, z)*`will now be displayed as`*r2

 

s2(y, z)*`will now be displayed as`*s2

 

F1(y, z)*`will now be displayed as`*F1

 

F2(y, z)*`will now be displayed as`*F2

(1)

``

M := `<|>`(`<,>`(2, -1), `<,>`(-1, 2))

M := Matrix(2, 2, {(1, 1) = 2, (1, 2) = -1, (2, 1) = -1, (2, 2) = 2})

(2)

1/M

Matrix([[2/3, 1/3], [1/3, 2/3]])

(3)

 

# The system

 

EQ0 := VectorCalculus:-`+`(VectorCalculus:-`+`(Typesetting:-delayDotProduct(`<|>`(F1, F2), VectorCalculus:-`+`(Typesetting:-delayDotProduct(1/M, `<,>`(q1, q2)), VectorCalculus:-`-`(`<,>`(U[y], V[z])))), VectorCalculus:-`-`(Typesetting:-delayDotProduct(VectorCalculus:-`*`(1/4, VectorCalculus:-`+`(Typesetting:-delayDotProduct(1/M, `<,>`(q1, q2)), VectorCalculus:-`-`(`<,>`(U[y], V[z])))^%T), VectorCalculus:-`+`(Typesetting:-delayDotProduct(1/M, `<,>`(q1, q2)), VectorCalculus:-`-`(`<,>`(U[y], V[z])))))), VectorCalculus:-`-`(Typesetting:-delayDotProduct(Typesetting:-delayDotProduct(VectorCalculus:-`*`(1/2, `<|>`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`*`(2, F1), U[y]), VectorCalculus:-`-`(s1)), VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`*`(2, F2), V[z]), VectorCalculus:-`-`(s2)))), 1/M), `<,>`(q1, q2))))

EQ0 := -((1/6)*q1+(1/12)*q2-(1/4)*(diff(u(y, z), y)))*((2/3)*q1+(1/3)*q2-(diff(u(y, z), y)))-((1/12)*q1+(1/6)*q2-(1/4)*(diff(v(y, z), z)))*((1/3)*q1+(2/3)*q2-(diff(v(y, z), z)))+(Vector(1, {(1) = F1*((2/3)*q1+(1/3)*q2-(diff(u(y, z), y)))+F2*((1/3)*q1+(2/3)*q2-(diff(v(y, z), z)))}, attributes = [coords = cartesian]))+(Vector(1, {(1) = -((2/3)*F1+(1/3)*(diff(u(y, z), y))-(1/3)*s1+(1/3)*F2+(1/6)*(diff(v(y, z), z))-(1/6)*s2)*q1-((1/3)*F1+(1/6)*(diff(u(y, z), y))-(1/6)*s1+(2/3)*F2+(1/3)*(diff(v(y, z), z))-(1/3)*s2)*q2}, attributes = [coords = cartesian]))

(4)

EQ00 := `<|>`(F1, F2).(1/M.`<,>`(q1, q2)-`<,>`(U[y], V[z]))-(1/4)*LinearAlgebra:-Transpose(1/M.`<,>`(q1, q2)-`<,>`(U[y], V[z])).(1/M.`<,>`(q1, q2)-`<,>`(U[y], V[z]))-1/2*(2*`<|>`(F1, F2)+`<|>`(U[y], V[z])-`<|>`(s1, s2)).(1/M).`<,>`(q1, q2)

Error, (in rtable/Sum) invalid input: dimensions do not match: Matrix(1 .. 1, 1 .. 2) cannot be added to Vector[row](1 .. 2)

 

``

``


 

Download SystemGoesWrong.mw

 

 

 

... and of the second:

 

 


 

``

Over to some linear algebra.  

 

 

restart; with(LinearAlgebra); with(VectorCalculus)

NULL

LinearAlgebra:-Transpose(`<|>`(3, 4)).`<,>`(2, 3)

18

(1)

VectorCalculus:-DotProduct(VectorCalculus:-`<,>`(3, 4), VectorCalculus:-`<,>`(2, 3))

18

(2)

DotProduct(`<,>`(2, 3), `<|>`(3, 4))

Matrix([[6, 8], [9, 12]])

(3)

Trace(Matrix(%id = 18446746888362217830));

18

(4)

                                                                 

define(normsqbyDot, normsqbyDot(y::Vector) = VectorCalculus:-DotProduct(y, y))

showstat(normsqbyDot)


normsqbyDot := proc()
local theArgs, arg, look, me, cf, term;
   1   me := eval(procname,1);
   2   theArgs := args;
   3   look := tablelook(('procname')(theArgs),'[`/POS`(1,normsqbyDot,1), `/BIND`(1,1,`/y1`::VectorCalculus:-Vector), `/PATTERN`(`/y1`^2)]');
   4   if look <> FAIL then
   5     eval(look,`/FUNCNAME` = procname)
       else
   6     ('procname')(theArgs)
       end if
end proc

 

define, "%1 is assigned", normsqbyMatrixProduct

showstat(normsqbyMatrixProduct)


normsqbyMatrixProduct := proc()
local theArgs, arg, look, me, cf, term;
   1   me := eval(procname,1);
   2   theArgs := args;
   3   look := tablelook(('procname')(theArgs),'[`/POS`(1,normsqbyMatrixProduct,1), `/BIND`(1,1,`/y1`::Matrix), `/PATTERN`(`/y1`^2)]');
   4   if look <> FAIL then
   5     eval(look,`/FUNCNAME` = procname)
       else
   6     ('procname')(theArgs)
       end if
end proc

 

normsqbyDot(`<,>`(2, 3))

Error, (in rtable/Power) exponentiation operation not defined for Vectors

 

normsqbyMatrixProduct(VectorCalculus:-`<,>`(2, 3))

normsqbyMatrixProduct(Vector(2, {(1) = 2, (2) = 3}, attributes = [coords = cartesian]))

(5)

convert(n*ormsqbyMatrixProduct(`<,>`(2, 3)), float)

n*ormsqbyMatrixProduct(Vector(2, {(1) = 2, (2) = 3}, attributes = [coords = cartesian]))

(6)

NULL

# Since I do not have any idea of how to get vectors nicely, ...

... I replace U0, U1, U2 by u,v,w and use difftables U,V,W.  And y1, y2 replaced by y,z.

with(PDEtools); -1; with(plots)

[animate, animate3d, animatecurve, arrow, changecoords, complexplot, complexplot3d, conformal, conformal3d, contourplot, contourplot3d, coordplot, coordplot3d, densityplot, display, dualaxisplot, fieldplot, fieldplot3d, gradplot, gradplot3d, implicitplot, implicitplot3d, inequal, interactive, interactiveparams, intersectplot, listcontplot, listcontplot3d, listdensityplot, listplot, listplot3d, loglogplot, logplot, matrixplot, multiple, odeplot, pareto, plotcompare, pointplot, pointplot3d, polarplot, polygonplot, polygonplot3d, polyhedra_supported, polyhedraplot, rootlocus, semilogplot, setcolors, setoptions, setoptions3d, shadebetween, spacecurve, sparsematrixplot, surfdata, textplot, textplot3d, tubeplot]

(7)

declare(u(y, z), v(y, z), w(y, z), q1(y, z), r1(y, z), s1(y, z), q2(y, z), r2(y, z), s2(y, z), F1(y, z), F2(y, z)):

u(y, z)*`will now be displayed as`*u

 

v(y, z)*`will now be displayed as`*v

 

w(y, z)*`will now be displayed as`*w

 

q1(y, z)*`will now be displayed as`*q1

 

r1(y, z)*`will now be displayed as`*r1

 

s1(y, z)*`will now be displayed as`*s1

 

q2(y, z)*`will now be displayed as`*q2

 

r2(y, z)*`will now be displayed as`*r2

 

s2(y, z)*`will now be displayed as`*s2

 

F1(y, z)*`will now be displayed as`*F1

 

F2(y, z)*`will now be displayed as`*F2

(8)

NULL

M := `<|>`(`<,>`(2, -1), `<,>`(-1, 2))

M := Matrix(2, 2, {(1, 1) = 2, (1, 2) = -1, (2, 1) = -1, (2, 2) = 2})

(9)

1/M

Matrix([[2/3, 1/3], [1/3, 2/3]])

(10)

 

# The system

 

EQ0 := Typesetting:-delayDotProduct(`<|>`(F1, F2), Typesetting:-delayDotProduct(1/M, `<,>`(q1, q2))+`-`(`<,>`(U[y], V[z])))+`-`(Typesetting:-delayDotProduct(VectorCalculus:-`*`(1/4, (Typesetting:-delayDotProduct(1/M, `<,>`(q1, q2))+`-`(`<,>`(U[y], V[z])))^%T), Typesetting:-delayDotProduct(1/M, `<,>`(q1, q2))+`-`(`<,>`(U[y], V[z]))))+`-`(Typesetting:-delayDotProduct(Typesetting:-delayDotProduct(VectorCalculus:-`*`(1/2, `<|>`(VectorCalculus:-`*`(2, F1)+U[y]+`-`(s1), VectorCalculus:-`*`(2, F2)+V[z]+`-`(s2))), 1/M), `<,>`(q1, q2)))

F1*((2/3)*q1+(1/3)*q2-(diff(u(y, z), y)))+F2*((1/3)*q1+(2/3)*q2-(diff(v(y, z), z)))-((1/6)*q1+(1/12)*q2-(1/4)*(diff(u(y, z), y)))*((2/3)*q1+(1/3)*q2-(diff(u(y, z), y)))-((1/12)*q1+(1/6)*q2-(1/4)*(diff(v(y, z), z)))*((1/3)*q1+(2/3)*q2-(diff(v(y, z), z)))-((2/3)*F1+(1/3)*(diff(u(y, z), y))-(1/3)*s1+(1/3)*F2+(1/6)*(diff(v(y, z), z))-(1/6)*s2)*q1-((1/3)*F1+(1/6)*(diff(u(y, z), y))-(1/6)*s1+(2/3)*F2+(1/3)*(diff(v(y, z), z))-(1/3)*s2)*q2

(11)

EQ00 := VectorCalculus:-`+`(VectorCalculus:-`+`(Typesetting:-delayDotProduct(`<|>`(F1, F2), VectorCalculus:-`+`(Typesetting:-delayDotProduct(1/M, `<,>`(q1, q2)), VectorCalculus:-`-`(`<,>`(U[y], V[z])))), VectorCalculus:-`-`(Typesetting:-delayDotProduct(VectorCalculus:-`*`(1/4, VectorCalculus:-`+`(Typesetting:-delayDotProduct(1/M, `<,>`(q1, q2)), VectorCalculus:-`-`(`<,>`(U[y], V[z])))^%T), VectorCalculus:-`+`(Typesetting:-delayDotProduct(1/M, `<,>`(q1, q2)), VectorCalculus:-`-`(`<,>`(U[y], V[z])))))), VectorCalculus:-`-`(Typesetting:-delayDotProduct(Typesetting:-delayDotProduct(VectorCalculus:-`*`(1/2, VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`*`(2, `<|>`(F1, F2)), `<|>`(U[y], V[z])), VectorCalculus:-`-`(`<|>`(s1, s2)))), 1/M), `<,>`(q1, q2))))

F1*((2/3)*q1+(1/3)*q2-(diff(u(y, z), y)))+F2*((1/3)*q1+(2/3)*q2-(diff(v(y, z), z)))-((1/6)*q1+(1/12)*q2-(1/4)*(diff(u(y, z), y)))*((2/3)*q1+(1/3)*q2-(diff(u(y, z), y)))-((1/12)*q1+(1/6)*q2-(1/4)*(diff(v(y, z), z)))*((1/3)*q1+(2/3)*q2-(diff(v(y, z), z)))-((2/3)*F1+(1/3)*(diff(u(y, z), y))-(1/3)*s1+(1/3)*F2+(1/6)*(diff(v(y, z), z))-(1/6)*s2)*q1-((1/3)*F1+(1/6)*(diff(u(y, z), y))-(1/6)*s1+(2/3)*F2+(1/3)*(diff(v(y, z), z))-(1/3)*s2)*q2

(12)

``

 


 

Download SystemDeclaresBut.mw

 

 

Hi,

What is the procedure to follow for importing a maple file into Mobius?

Thanks

1 2 3 4 5 6 7 Last Page 3 of 216