Hi all!

F is a delta function:

F:=delta(x-x[0])*delta(y-y[0])

I want it be expaned through trigonometric series:

F:=sum(sum(Q[k*l]*sin(l*Pi*x/a)*sin(k*Pi*y/b), k = 1 .. infinity), l = 1 .. infinity)

So I want to get every Q:

Q[k, l] := `assuming`([4*(int(int(f[z1]*sin(l*Pi*x/a)*sin(k*Pi*y/b), x = 0 .. b), y = 0 .. a))/(a*b)], [k::posint, l::posint, a > 0, b > 0])

But it result in (when x[0]:=a/2, y[0]:=b/2):

4*(int(int(F[0]*exp(I*omega*t)*delta(x-x[0])*delta(y-y[0])*sin(l*Pi*x/a)*sin(k*Pi*y/b), x = 0 .. b), y = 0 .. a))/(a*b)

I wonder HOW CAN I GET THE EXACT RESULT:Q[k, l] := 4*sin(l*Pi/a)*sin(k*Pi/b)/(a*b)

THANKS!

http://en.wikipedia.org/wiki/Hypersurface

http://people.cs.uchicago.edu/~niyogi/papersps/surfacesampling.pdf

hypersurface is a homogenous polynomial

f(x,y) = 0

i do not understand how sampling hypersurface can generate this kind of polynomial

Have a good day;

Anyone know the correct command to plot functions (For Exact Solution). Here I have attached the file:

Exact.mw

For your information, I need to plot the different values of R in the same graph. The values of R are 

R=0, 0.1, 0.2 and 0.3.

Thank you very much in advance. 

May God bless you :)

Dear All,

i am solving a system of pde with boundar conditons then i got this error...

Error, (in pdsolve/numeric/plot) unable to compute solution for tau>HFloat(0.0):

Thank.

jeffrey_fluid.mw

Download jeffrey_fluid.mw

I am having issues when defining functions in a loop. First, I define the first two functions as follows (here, r(x) is a function already assigned).

f_0 := x -> r(x):

f_1 := x -> r(x)*f_0(r(x)):

Then, I define successive functions in a for loop as follows.

for i from 2 to 10 do

   f_i := x -> r(x)*f_[i - 1](r(x));

end do

The loop defines the function f_2 but compiles erroneously for f_3 which, and I do admit, relies on f_2. Does someone have an idea of how to fix this issue? Any help will be greatly appreciated. Thanks.

Aslam-u-Alikum. Hope you will be fine all.  I want to plot the follwing vector in the plan z=0 at time t=0 and A=1

v := `<,>`(VectorCalculus[`-`](VectorCalculus[`*`](VectorCalculus[`*`](VectorCalculus[`*`](A, y), 1/VectorCalculus[`+`](x^2, y^2)), exp(VectorCalculus[`-`](VectorCalculus[`*`](k, t))))), VectorCalculus[`*`](VectorCalculus[`*`](VectorCalculus[`*`](A, x), 1/VectorCalculus[`+`](x^2, y^2)), exp(VectorCalculus[`-`](VectorCalculus[`*`](k, t)))), VectorCalculus[`*`](B, t))

I am waiting for your positive answer.

I am trying to alter the Virtual Solar system Maple worksheet of Yi Xie in the way that I added several objects to the eight planets and Pluto (e.g. Hale-Bopp, Sedna, 2012 VP113 etc.) and would like to adjust the array such that when zooming out and the obrit and labels overlap so that it's unreadable anymore (orbits and labels) that I can switch on and off (respectively display/not display) specific parts, e.g. the inner solar system. In the original file a single array was created from 1..18 (including 9 orbital entries and 9 label entries). What I did is to create arrays for each part of the Solar system, e.g. Inner for the planets+Pluto 1..18, an array for Hale-Bopp with an orbital entry and a label entry, so [1,2], and an array with 6 entries for 3 additional objects like Sedna, Planet X and 2012 VP113. As well as the sun, which only has a single entry as there are no orbital elements necessary and one just makes a 3dplot (I did not label it, so just one entry). All arrays are converted into lists in the end and displayed. Here is the code:

> with(linalg);

> with(plots);

> with(plottools);

> P1 := matrix([[cos(omega[j]), -sin(omega[j]), 0], [sin(omega[j]), cos(omega[j]), 0], [0, 0, 1]]); P2 := matrix([[1, 0, 0], [0, cos(i[j]), -sin(i[j])], [0, sin(i[j]), cos(i[j])]]); P3 := matrix([[cos(Omega[j]), -sin(Omega[j]), 0], [sin(Omega[j]), cos(Omega[j]), 0], [0, 0, 1]]);

> A:=matrix([[a[j]*(cos(E[j])-e[j])],[a[j]*sqrt(1-e[j]^2)*sin(E[j])],[0]]);

> R:=multiply(P3,P2,P1);

> B:=multiply(R,A);

> a := [.38709893, .72333199, 1.00000011, 1.52366231, 5.20336301, 9.53707032, 19.19126393, 30.06896348, 39.48168677, 1/0.5454e-2, 268.2509283, 532.7838156, 300];

> e := [.20563069, 0.677323e-2, 0.1671022e-1, 0.9341233e-1, 0.4839266e-1, 0.5415060e-1, 0.4716771e-1, 0.858587e-2, .24880766, .994920, .7005635, .8570973, .1];

> i := [7.00487, 3.39471, 0.5e-4, 1.85061, 1.30530, 2.48446, .76986, 1.76917, 17.14175, 89.5328, 24.01830, 11.92859, 10];

> Omega := [48.33167, 76.68069, -11.26064, 49.57854, 100.55615, 113.71504, 74.22988, 131.72169, 110.30347, 282.1476, 90.88303, 144.53190, 45];

> omega := [77.45645, 131.53298, 102.94719, 336.04084, 14.75385, 92.43194, 170.96424, 44.97135, 224.06676, 130.8038, 293.03200, 311.18311, 150];

> i := map(x→ convert(x, units, deg, rad) end proc, i);

> Omega := map(x→ convert(x, units, deg, rad) end proc, Omega);

> omega := map(x→ convert(x, units, deg, rad) end proc, omega);

> for j to 13 do omega[j] := arcsin(sin(omega[j]-Omega[j])/sin(arccos(sin(i[j])*cos(omega[j]-Omega[j])))) end do;

> x := array(1 .. 13);

> y := array(1 .. 13);

> z := array(1 .. 13);

> for j to 13 do x[j] := B[1, 1]; y[j] := B[2, 1]; z[j] := B[3, 1] end do;

> Sun := array([1]);

> Inner := array(1 .. 18); for j to 9 do Colors := [black, green, blue, red, black, yellow, green, violet, brown, aquamarine, black, black, red]; Linestyle := [solid, solid, solid, solid, solid, solid, solid, solid, solid, longdash, solid, solid, longdash]; Inner[j] := spacecurve([subs(E[j] = E, x[j]), subs(E[j] = E, y[j]), subs(E[j] = E, z[j])], E = 0 .. 2*Pi, color = Colors[j], linestyle = Linestyle[j]) end do;

> Comet := array([1, 2]); if j = 10 then Colors := [aquamarine]; Linestyle := [longdash]; Comet[1] := spacecurve([subs(E[j] = E, x[j]), subs(E[j] = E, y[j]), subs(E[j] = E, z[j])], E = 0 .. 2*Pi, color = Colors[j], linestyle = Linestyle[j]) end if;

> Oort := array(1 .. 6); for j from 11 to 13 do Colors := [black, black, red]; Linestyle := [solid, solid, longdash]; Inner[j] := spacecurve([subs(E[j] = E, x[j]), subs(E[j] = E, y[j]), subs(E[j] = E, z[j])], E = 0 .. 2*Pi, color = Colors[j], linestyle = Linestyle[j]) end do;

> Sun[1] := plot3d(0.1e-1, 0 .. 2*Pi, 0 .. Pi, style = PATCHNOGRID, coords = spherical, color = red);

> Inner[10] := textplot3d([subs(E[1] = 0, x[1]), subs(E[1] = 0, y[1]), subs(E[1] = 0, z[1]), "Mercury"]); Inner[11] := textplot3d([subs(E[2] = 0, x[2]), subs(E[2] = 0, y[2]), subs(E[2] = 0, z[2]), "Venus"]); Inner[12] := textplot3d([subs(E[3] = 0, x[3]), subs(E[3] = 0, y[3]), subs(E[3] = 0, z[3]), "Earth"]); Inner[13] := textplot3d([subs(E[4] = 0, x[4]), subs(E[4] = 0, y[4]), subs(E[4] = 0, z[4]), "Mars"]); Inner[14] := textplot3d([subs(E[5] = 0, x[5]), subs(E[5] = 0, y[5]), subs(E[5] = 0, z[5]), "Jupiter"]); Inner[15] := textplot3d([subs(E[6] = 0, x[6]), subs(E[6] = 0, y[6]), subs(E[6] = 0, z[6]), "Saturn"]); Inner[16] := textplot3d([subs(E[7] = 0, x[7]), subs(E[7] = 0, y[7]), subs(E[7] = 0, z[7]), "Uranus"]); Inner[17] := textplot3d([subs(E[8] = 0, x[8]), subs(E[8] = 0, y[8]), subs(E[8] = 0, z[8]), "Neptune"]); Inner[18] := textplot3d([subs(E[9] = 0, x[9]), subs(E[9] = 0, y[9]), subs(E[9] = 0, z[9]), "Pluto"]); Comet[2] := textplot3d([subs(E[10] = 0, x[10]), subs(E[10] = 0, y[10]), subs(E[10] = 0, z[10]), Hale-Bopp]); Oort[4] := textplot3d([subs(E[11] = 0, x[11]), subs(E[11] = 0, y[11]), subs(E[11] = 0, z[11]), "2012 VP113"]); Oort[5] := textplot3d([subs(E[12] = 0, x[12]), subs(E[12] = 0, y[12]), subs(E[12] = 0, z[12]), "Sedna"]); Oort[6] := textplot3d([subs(E[13] = 0, x[13]), subs(E[13] = 0, y[13]), subs(E[13] = 0, z[13]), "Planet X ?", color = red]);

> Sun1 := convert(Sun, 'list');
> Inner1 := convert(Inner, 'list');
> Comet1 := convert(Comet, 'list');
> Oort1 := convert(Oort, 'list');
> display(Sun1, Inner1, Comet1, Oort1, scaling = CONSTRAINED);

 

The first error message appears after the if-condition. Can you tell me where I am making a mistake? Beware: when copy paste the code from Maple to Word and from Word in here the colons at the end of lines have changed into semi-colons. Hope this is no problem in executing the code despite the lines being in the same ">..." e.g. where the labels are defined.

Good day everyone, could you please help use Gauss Elimination method for these system of equations. See the worksheet here F1.mw

Thanks.

Can we output a mixed number instead of  an improper fraction in Maple programmatically. For example  

                 instead  of

Dear All,

I am solving 6 ODE equations with boundary conditions using Runge kutta Felbergh 45 (Maple 12). then, i got this problem.. any suggestion??

Thank you :)

ISPC3.mw

Download ISPC3.mw

restart; with(linalg); with(stats); with(plots); with(Statistics); with(LinearAlgebra); 

s := 1/(273.16+50); s1 := 1/(273.16+145); s3 := 1/(273.16+250); s2 := 1/(273.16+197.5); gamma0 := 0.1e-3; gamma1 := .5; gamma2 := 0.15e-2; beta := -3800;
c := 300; n := 200; tau1 := 99; tau2 := 120;

Delta := solve(1-exp(-(gam0*tau1+(1/2)*gam1*tau1^2)*exp(beta*s1)) = 1-exp(-(gam0*a+(1/2)*gam1*a^2)*exp(beta*s2)), a);
a := Delta[1];

Theta := solve(1-exp(-(gam0*(a+tau2-tau1)+(1/2)*gam1*(a+tau2-tau1)^2)*exp(beta*s2)) = 1-exp(-(gam0*b+(1/2)*gam1*b^2)*exp(beta*s3)), b);
b := Theta[1];

n1 := n*(int((gam1*t+gam0)*exp(beta*s1)*exp(-(gam0*t+(1/2)*gam1*t^2)*exp(beta*s1)), t = 0 .. tau1));
200. - 200. exp(-0.01119474511 gam0 - 0.5541398828 gam1)
n2 := (n-n1)*(int((gam1*t+gam0)*exp(beta*s2)*exp(-(gam0*t+(1/2)*gam1*t^2)*exp(beta*s2)), t = a .. a+tau2-tau1));

g1 := -n1(gam0, gam1)*(int((1/(gam1*t+gam0)-t*exp(beta*s1))*(gamma2*t^2+gamma1*t+gamma0)*exp(beta*s1)*exp(-(gamma0*t+(1/2)*gamma1*t^2+(1/3)*gamma2*t^3)*exp(beta*s1)), t = 0 .. tau1))-evalf(n2(gam0, gam1)*(int((1/(gam0+gam1*(a+t-tau1))-(a+t-tau1)*exp(beta*s2))*(gamma0+gamma1*(a+t-tau1)+gamma2*(a+t-tau1)^2)*exp(beta*s2)*exp(-(gamma0*(a+t-tau1)+(1/2)*gamma1*(a+t-tau1)^2+(1/3)*gamma2*(a+t-tau1)^3)*exp(beta*s2)), t = tau1 .. tau2)))

g2 := -n1*(int((t/(gam1*t+gam0)-(1/2)*t^2*exp(beta*s1))*(gamma2*t^2+gamma1*t+gamma0)*exp(beta*s1)*exp(-(gamma0*t+(1/2)*gamma1*t^2+(1/3)*gamma2*t^3)*exp(beta*s1)), t = 0 .. tau1))-evalf(n2*(int(((a+t-tau1)/(gam0+gam1*(a+t-tau1))-(1/2)*(a+t-tau1)^2*exp(beta*s2))*(gamma0+gamma1*(a+t-tau1)+gamma2*(a+t-tau1)^2)*exp(beta*s2)*exp(-(gamma0*(a+t-tau1)+(1/2)*gamma1*(a+t-tau1)^2+(1/3)*gamma2*(a+t-tau1)^3)*exp(beta*s2)), t = tau1 .. tau2)))

solve({g1 = 0, g2 = 0}, {gam0, gam1})

I want to find the answer of gam0 and gam1. It takes me 20 hours until now...and still evaluating...

Please Help ..

I can't directly copy Maple code into messages but have to insert into Word first, apply some changes that for better readability and copy it from there via Word-paste. Is there a direct way?

how do minor generate 2*2 matrix from 5*5 matrix or n*n matrix which n >= 3

first case is the symmetric or nonsymmetric ladder matrix which fill full upper right and lower left corner

{0,1,1,1,1}
{1,0,1,1,1}
{1,0,0,0,1}
{1,1,1,0,0}
{1,1,1,1,0}

second case is overlap two different first case , one is 1 and another is 0 which is for display partial fill the upper right corner and lower right corner

{0,1,0,0,0}
{1,0,1,1,0}
{1,0,0,0,1}
{0,1,1,0,0}
{0,0,0,1,0}