Any integer in [129,129+13^2[ 1s written as the sum of squares of separate integers equal to or less than 12.
examples:: 129=10^2+5^2+2^2, 130=11^2+3^2... 132=9^2+5^2+4^2+3^2+1^2...
179=12^2+5^2+3^2+1^2...297=12^2+10^2+7^2+2^2. Thank you.

Hompotopy perturbation method

restart; with(LinearAlgebra);
PDEtools[declare](f(x), prime = x);
PDEtools[declare](g(x), prime = x);
N := 3;
F := sum(p^i*f[i](x), i = 0 .. N);
G := sum(p^i*g[i](x), i = 0 .. N);
FEq := (1-p)*(diff(F, x$3))+p*(diff(F, x$3)-(2*(diff(F, x$1))*(diff(F, x$1))-(5/2*F)*(diff(F, x$2))+M*(diff(F, x$1))) . A);
GEq := (1-p)*(diff(G, x$2))+p*(diff(G, x$2)+(5/2*(1/(1+R)) . Pr)*F*(diff(G, x$1)))*K(L);

M := 1;
A := (((1-W)^2.5*(1-W))*`ρf`+W*`ρt`)/`ρf`;
Pr := 6.2;
K := ((1-W)*`ρf`*Cf+W*`ρt`*Cs)/`ρf`;
L := .5;
`ρf` := 998.3;
`ρt` := 3970;
W := .2;
R := 1.0;
Cs := 765;
Cf := 4182;
coeff(FEq, p, 0);
coeff(GEq, p, 0);
for i from 0 to N do Fequ[i] := coeff(FEq, p, i) = 0 end do;
for i from 0 to N do Gequ[i] := coeff(GEq, p, i) = 0 end do;
Fcond[1][0] := f[0](0) = 0, (D(f[0]))(0) = 1, (D(f[0]))(5) = 0; for j to N do Fcond[1][j] := f[j](0) = 0, (D(f[j]))(0) = 0, (D(f[j]))(5) = 0 end do;
Gcond[0] := g[0](0) = 1, g[0](5) = 0; for j to N do Gcond[j] := g[j](0) = 0, g[j](5) = 0 end do;

for i from 0 to N do dsolve({Fequ[i], Fcond[1][i]}, f[i](x)); f[i](x) := rhs(%) end do;
for i from 0 to N do dsolve({Gcond[i], Gequ[i]}, g[i](x)); g[i](x) := rhs(%) end do;
Fa := simplify(sum(f[n](x), n = 0 .. N)); dFa := diff(Fa, x); subs(x = 2.4, dFa);
Ga := simplify(sum(g[n](x), n = 0 .. N)); dGa := diff(Ga, x); subs(x = 2.4, dGa);
plot(Ga, x = 0 .. 5);
plot(dFa, x = 0 .. 5);

ND sove solution 

Eq1 := diff(F(x), x$3)-(2*(diff(F(x), x$1))*(diff(F(x), x$1))-(5/2*F(x))*(diff(F(x), x$2))+M*(diff(F(x), x$1))) . A = 0;
Eq2 := (diff(G(x), x$2)+(5/2*(1/(1+R)))*Pr*F(x)*(diff(G(x), x$1)))*K(L) = 0;
M := 1;
Pr := 6.2;
A := (((1-W)^2.5*(1-W))*`ρf`+W*`ρt`)/`ρf`;
K := ((1-W)*`ρf`*Cf+W*`ρt`*Cs)/`ρf`;
L := 1;
`ρf` := 998.3;
`ρt` := 3970;
W := .2;
R := 2.0;
Cs := 765;
Cf := 4182;

Cd1 := F(0) = 0, (D(F))(0) = 1, (D(F))(5) = 0;
dsys := {Cd1, Eq1};
dsol := dsolve(dsys, numeric, output = operator);
dsol(.1);
plots[odeplot](dsol, [x, diff(F(x), x$1)], 0 .. 5, color = green);
Cd2 := G(0) = 1, G(5) = 0;
dsys := {Cd1, Cd2, Eq1, Eq2};
dsol := dsolve(dsys, numeric, output = operator);
plots[odeplot](dsol, [x, G(x)], 0 .. 5, color = green)

I find some book teach motion planning in topology 

but do it need to formulate the equations for the environments such as a map with obstacle in 2d or 3D?  the environment is quite complex, how can these equations be formulated?

Dear all

Using maple I can't obtain an exact solution, my goal for which initial condition can the solution diverge to infinity if maple can not give us a solution.

special_condition_diverge.mw

many thanks

I have two functions:

f(x)= (x)^(1/2)

g(x)=(x^2)/8

I want to get each function to rotate the y-axis and build the shape and I want the shaded region to build the 3D shape as it goes around the y-axis.

The domains for all would be 0 to 4.

The url link to what I am looking for it below.

https://en.wikipedia.org/wiki/Solid_of_revolution#/media/File:Rotationskoerper_animation.gif

Thank you in advanced!

Maple_question.mw

Hello everyone .

I asked Maple to compute a definite integral of a function, numerically. Unfortunately it does not give me any values . I briefly explain what I did.

As you can see in the picture first I define a real valued function BW_dilog(x) (with complex domain), where the function dilog  already exists in maple. Then I defined another function, V, (with real domain and codomain ). Now I need the approximate value of the bi integral of V, on a triangle. The Maple file is attached.

I would be grateful if any one could help me.

how do i Import part or all  PDF files into maple 

I believe this was easier in older versions of maple or worked partially.

I initialized a variable name using another variable name and := . I thought that Maple would assign the value, but I soon learned by debug that the address was assigned. This led to temporary problems.

Where can I learn the rules that Maple follows for assignment by value or address ?? Do I always have to initialize with a real number, like 0, to be safe ??

Thanks.

Mike Graber

x:=Proc
Local a,
b,

C;
use XML Tools in 
end use;

end proc;

Hello,

I have a problem, please help me to solve it.

I am trying to extract coefficients of some polynomial expressions but I receive Error.

For example:

>with(Physics):

>Setup(mathematicalnotation = true)

>S := a*(x^2)+b*x+c*(1/(x-h)):

>Coefficients(S, x, 1)

>Error, (in Physics:-Coefficients) unable to compute coeff.

**** Note that if instead of the term (1/(x-h)) we have (1/x), then we get the true result. The error occurs only when we have some extra things in the denominator namely "-h".

Regards

How I can pdsolve these equations in toroidal coordinates?

Initial conditions are arbitrary.

Please see attached pdf .

Thanks

Where.pdf

Weston1958

Can old maple version saved .m files in window be readable in maple 2015 Linux version?

Basically I need to include an if condition that assigns one set of values to a set of variables if the while loop completes a cycle without me interrupting it, and another set of values in the event I have pressed the interrupt button.

Is this able to be done?

Hello (again)

I thought I won't need help with that type of question but I came across an example that says otherwise.  Here it is

vars:=[x,y,z];

model7 := [x*(-RootOf(64*_Z^3+80*_Z^2+1104*_Z+561)-5/4)+y*alpha[1, 2]-33/(32*RootOf(64*_Z^3+80*_Z^2+1104*_Z+561)), x*z*alpha[2, 6]+y*RootOf(64*_Z^3+80*_Z^2+1104*_Z+561), x^2*(17*RootOf(64*_Z^3+80*_Z^2+1104*_Z+561)+17)/(alpha[1, 2]*alpha[2, 6])-17*x*y/alpha[2, 6]+2*z*x-z-(163/32+RootOf(64*_Z^3+80*_Z^2+1104*_Z+561)^2+5*RootOf(64*_Z^3+80*_Z^2+1104*_Z+561)*(1/4))/(alpha[1, 2]*alpha[2, 6])]

then I issued the command 

map(w->coeffs(w,vars),model7);

to get 

[-33/(32*RootOf(64*_Z^3+80*_Z^2+1104*_Z+561)), -RootOf(64*_Z^3+80*_Z^2+1104*_Z+561)-5/4, alpha[1, 2], RootOf(64*_Z^3+80*_Z^2+1104*_Z+561), alpha[2, 6], -(163/32+RootOf(64*_Z^3+80*_Z^2+1104*_Z+561)^2+5*RootOf(64*_Z^3+80*_Z^2+1104*_Z+561)*(1/4))/(alpha[1, 2]*alpha[2, 6]), -1, (17*RootOf(64*_Z^3+80*_Z^2+1104*_Z+561)+17)/(alpha[1, 2]*alpha[2, 6]), -17/alpha[2, 6], 2]

clearly the order does not follow model7's.  

I have also tried

[seq(coeffs(expand(model7[i]), indets(model7[i], suffixed({vars[]}))),i=1..nops(model7))];

Is there a solution to it?

Many thanks (again)

Ed

Dear all

I would like to compute a Laurent of a given function at an isolated point.

laurent_series.mw

thanks for your help