Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

Hey,

I want to solve this equation and looking at the plot there are at least 3 solutions. I want the greatest/smallest negative solution. Unfortunately using solve with assumptions produces no results and solve without assumptions only finds two solutions.

Can you please help me?

#select greatest negative value from solution

restart:

expr:= ax*cos(lambda)+ay*sin(lambda)-(a+b*lambda)

ax*cos(lambda)+ay*sin(lambda)-b*lambda-a

(1)

ax:=1:ay:=2:a:=0.5:b:=0.25: #examplanatory values

plot(expr)

 

 

assume(-2*Pi<lambda,lambda<0): #does not work

 

sol_lambda:=[solve(expr=0,lambda, useassumptions)];# returns empty list even though without assumption one solution is found

Warning, solutions may have been lost

 

[]

(2)

sol_lambda:=[solve(expr=0,lambda)]; #returns only two solutions even though looking at the plot 3 are there

Warning, solve may be ignoring assumptions on the input variables.

 

Warning, solutions may have been lost

 

[2.190357220, -.2688724573]

(3)

sol_l_v:=evalb~(sol_lambda<~0); #dirty workaraound

[false, true]

(4)

sol_l_add:=[ListTools:-SearchAll(true,sol_l_v)] ; #this seems overly complicated

 

[2]

(5)

lambda:=sol_lambda[sol_l_add[-1]];  #to select the last entry

 

-.2688724573

(6)

expr; #test

 

0.

(7)

 


Download select_solution.mw

Thanks!

Honigmelone

Hi,

This is regarding numerical solution of a function and plot. I have a function in the form of f1(omega,arctan(f2(omega))), and i need to plot it with omega (as the expression is too long i cant insert it here). Now, if i am changing the range of omega in plot command then I am getting different plots for the small values of omega. Let's say if i change the range from 1..10 to 1..50 and look at the plot in the range of 1..3 then the plots looks different. Apart from this if i change the value of Digits  from 10 to 30 or 40 then every time i am getting an entire different  plot. As the expression if too long i cant convert it to Matlab expression and plot there. How to fix these issues. Please help me regarding this.

Regarding

Sunit

 

After using the Groebner and PolynomialIdeals packages, Maple goes into a long calculation when I make an entry of the form

name:=polynomial expression. This can take 10's of minutes for an expression of two lines. The only solution I have found is to save the sheet and restart it and enter the line name:= etc. before loading Groebner and PolynomialIdeals. This is most inconvenient. Is there a better workaround?

I would like compute the vertices of the convex hull of finitely many points in some \mathbb{R}^{n}, where the coordinates of these points could be rational numbers or irrational numbers like \sqrt{2}.

I know that PolyhedralSets[ConvexHull] is a direct command, however it does not support irrational numbers. But if I transform all coordinates into floating point numbers, for some rational numbers the rounding error would be large enough to affect the result. For example, after the transform some collinear points are no longer collinear.

Thanks!

 

 

 

USB and or RS232 porting from inside maple console. Title explains what i need, or how to port an externally built java app into the maple console, either which will engine my dispatch tonight

how to use Riemann matrix to output Riemann surface?

and plot this surface?

 

with(algcurves):
f:=y^3+2*x^7-x^3*y;
pm:=periodmatrix(f,x,y);
evalf(pm, 5);
rm:=evalf(periodmatrix(f,x,y,Riemann),10);
M := rm;
A := proc (x, y) options operator, arrow; RiemannTheta([x, y], M, [], 0.1e-1, output = list)[2] end proc;
plot3d(Re(A(x+I*y, 0)), x = 0 .. 1, y = 0 .. 4, grid = [40, 40]);

is this graph Riemann Surface?

if so, how to convert A into polynomials?

I'm displaying a series of point plots as an animation, and would like to update a displayed parameter as well.  I have a nested list L[t] where there's a set of points for each t, and for each t there's also a numerical value M that I'd like to display.  (In my real problem, L[t] is the number of particles in each of several states, and M is the rms deviation from am algebraic probability distribution.)  

The closest I've gotten (for a simple L and M) is the following, but it displays all of the M values in the legend at once:

with(plots); with(Statistics);

L := [[1, 2, 3, 4, 5, 6], [2, 4, 6, 8, 10, 12]];

M := [1, 2];

display([seq(PointPlot(L[t], legend = M[t]), t = 1 .. 2)], insequence = true)

 

I don't need this to be in the legend.  Is there a way to display only the current value of M for each t?  Thanks very much.

Dear All

In following I tried to find symmetries of certain partial differential equation taken from paper "Group classification and exact solutions of generalized modified Boussinesq equation". But the determining equations are not matching with equations obtained in paper.


with(PDEtools)

DepVars := [f(u(x, t)), u(x, t)]; declare(f(u(x, t)), u(x, t))

[f(u(x, t)), u(x, t)]

 

f(u(x, t))*`will now be displayed as`*f

 

u(x, t)*`will now be displayed as`*u

(1)

PDE1 := diff(u(x, t), t, t)-delta*(diff(u(x, t), x, x, t, t))-(diff(f(u(x, t)), x, x))

diff(diff(u(x, t), t), t)-delta*(diff(diff(diff(diff(u(x, t), t), t), x), x))-((D@@2)(f))(u(x, t))*(diff(u(x, t), x))^2-(D(f))(u(x, t))*(diff(diff(u(x, t), x), x))

(2)

G := [seq(xi[j](x, t, u), j = [x, t]), seq(eta[j](x, t, u), j = [u])]

[xi[x](x, t, u), xi[t](x, t, u), eta[u](x, t, u)]

(3)

declare(G)

eta(x, t, u)*`will now be displayed as`*eta

 

xi(x, t, u)*`will now be displayed as`*xi

(4)

DetSys := DeterminingPDE(PDE1, G, integrabilityconditions = false)

{diff(diff(xi[t](x, t, u), u), u)-(diff(diff(diff(diff(xi[t](x, t, u), u), u), x), x))*delta, (diff(diff(eta[u](x, t, u), x), x))*(diff(f(u), u))+(diff(diff(diff(diff(eta[u](x, t, u), t), t), x), x))*delta-(diff(diff(eta[u](x, t, u), t), t)), -(diff(diff(xi[x](x, t, u), u), u))*(diff(f(u), u))-(diff(diff(diff(diff(xi[x](x, t, u), t), t), u), u))*delta+(diff(diff(f(u), u), u))*(diff(xi[x](x, t, u), u)), 2*(diff(diff(diff(diff(xi[x](x, t, u), u), u), u), x))+2*(diff(diff(diff(diff(xi[t](x, t, u), t), u), u), u))-(diff(diff(diff(diff(eta[u](x, t, u), u), u), u), u)), 2*(diff(diff(diff(xi[x](x, t, u), u), u), x))+2*(diff(diff(diff(xi[t](x, t, u), t), u), u))-(diff(diff(diff(eta[u](x, t, u), u), u), u)), 4*(diff(diff(xi[x](x, t, u), t), x))-2*(diff(diff(eta[u](x, t, u), t), u))+diff(diff(xi[t](x, t, u), t), t), 2*(diff(diff(xi[x](x, t, u), u), x))+2*(diff(diff(xi[t](x, t, u), t), u))-(diff(diff(eta[u](x, t, u), u), u)), diff(diff(xi[x](x, t, u), x), x)-2*(diff(diff(eta[u](x, t, u), u), x))+4*(diff(diff(xi[t](x, t, u), t), x)), -2*(diff(xi[x](x, t, u), x))+(diff(diff(diff(eta[u](x, t, u), u), x), x))*delta-2*(diff(diff(diff(xi[t](x, t, u), t), x), x))*delta, -(diff(diff(diff(xi[x](x, t, u), u), x), x))*delta-4*(diff(diff(diff(xi[t](x, t, u), t), u), x))*delta+2*(diff(diff(diff(eta[u](x, t, u), u), u), x))*delta-2*(diff(xi[x](x, t, u), u)), (diff(diff(f(u), u), u))*eta[u](x, t, u)+(diff(diff(diff(eta[u](x, t, u), t), t), u))*delta-2*(diff(diff(diff(xi[x](x, t, u), t), t), x))*delta+2*(diff(xi[t](x, t, u), t))*(diff(f(u), u)), -2*(diff(xi[t](x, t, u), u))*(diff(f(u), u))+4*delta*(diff(diff(diff(eta[u](x, t, u), t), u), u))-2*(diff(diff(diff(xi[t](x, t, u), t), t), u))*delta-8*(diff(diff(diff(xi[x](x, t, u), t), u), x))*delta, 2*(diff(xi[t](x, t, u), u))*(diff(f(u), u))+2*delta*(diff(diff(diff(eta[u](x, t, u), t), u), u))-(diff(diff(diff(xi[t](x, t, u), t), t), u))*delta-4*(diff(diff(diff(xi[x](x, t, u), t), u), x))*delta, 2*(diff(diff(xi[t](x, t, u), t), u))-(diff(diff(eta[u](x, t, u), u), u))+(diff(diff(diff(diff(eta[u](x, t, u), u), u), x), x))*delta-2*(diff(diff(diff(diff(xi[t](x, t, u), t), u), x), x))*delta, diff(diff(xi[x](x, t, u), u), u)-4*(diff(diff(diff(diff(xi[t](x, t, u), t), u), u), x))*delta+2*(diff(diff(diff(diff(eta[u](x, t, u), u), u), u), x))*delta-(diff(diff(diff(diff(xi[x](x, t, u), u), u), x), x))*delta, 2*(diff(xi[x](x, t, u), u))-8*(diff(diff(diff(xi[t](x, t, u), t), u), x))*delta+4*(diff(diff(diff(eta[u](x, t, u), u), u), x))*delta-2*(diff(diff(diff(xi[x](x, t, u), u), x), x))*delta, -(diff(diff(xi[t](x, t, u), u), u))*(diff(f(u), u))-4*(diff(diff(diff(diff(xi[x](x, t, u), t), u), u), x))*delta-(diff(diff(diff(diff(xi[t](x, t, u), t), t), u), u))*delta+(diff(diff(f(u), u), u))*(diff(xi[t](x, t, u), u))+2*(diff(diff(diff(diff(eta[u](x, t, u), t), u), u), u))*delta, -(diff(diff(xi[t](x, t, u), x), x))*(diff(f(u), u))+diff(diff(xi[t](x, t, u), t), t)-2*(diff(diff(eta[u](x, t, u), t), u))+2*(diff(diff(diff(diff(eta[u](x, t, u), t), u), x), x))*delta-(diff(diff(diff(diff(xi[t](x, t, u), t), t), x), x))*delta, -2*(diff(xi[t](x, t, u), x))*(diff(f(u), u))+2*(diff(xi[x](x, t, u), t))-2*(diff(diff(diff(xi[x](x, t, u), t), x), x))*delta+4*(diff(diff(diff(eta[u](x, t, u), t), u), x))*delta-2*(diff(diff(diff(xi[t](x, t, u), t), t), x))*delta, (diff(diff(diff(diff(eta[u](x, t, u), t), t), u), u))*delta-2*(diff(diff(diff(diff(xi[x](x, t, u), t), t), u), x))*delta+(diff(diff(diff(f(u), u), u), u))*eta[u](x, t, u)+(diff(diff(eta[u](x, t, u), u), u))*(diff(f(u), u))-2*(diff(diff(xi[x](x, t, u), u), x))*(diff(f(u), u))+2*(diff(diff(f(u), u), u))*(diff(xi[t](x, t, u), t)+(1/2)*(diff(eta[u](x, t, u), u))), -(diff(diff(xi[x](x, t, u), x), x))*(diff(f(u), u))+2*(diff(diff(eta[u](x, t, u), u), x))*(diff(f(u), u))+2*(diff(diff(f(u), u), u))*(diff(eta[u](x, t, u), x))+diff(diff(xi[x](x, t, u), t), t)-delta*(diff(diff(diff(diff(xi[x](x, t, u), t), t), x), x))+2*delta*(diff(diff(diff(diff(eta[u](x, t, u), t), t), u), x)), 2*(diff(diff(xi[x](x, t, u), t), u))-2*(diff(diff(xi[t](x, t, u), u), x))*(diff(f(u), u))-2*(diff(xi[t](x, t, u), x))*(diff(diff(f(u), u), u))+4*(diff(diff(diff(diff(eta[u](x, t, u), t), u), u), x))*delta-2*(diff(diff(diff(diff(xi[t](x, t, u), t), t), u), x))*delta-2*(diff(diff(diff(diff(xi[x](x, t, u), t), u), x), x))*delta, diff(diff(diff(diff(xi[t](x, t, u), u), u), u), u), diff(diff(diff(diff(xi[t](x, t, u), u), u), u), x), diff(diff(diff(diff(xi[x](x, t, u), t), u), u), u), diff(diff(diff(diff(xi[x](x, t, u), u), u), u), u), diff(diff(diff(xi[t](x, t, u), u), u), u), diff(diff(diff(xi[t](x, t, u), u), u), x), diff(diff(diff(xi[t](x, t, u), u), x), x), diff(diff(diff(xi[x](x, t, u), t), t), u), diff(diff(diff(xi[x](x, t, u), t), u), u), diff(diff(diff(xi[x](x, t, u), u), u), u), diff(diff(xi[t](x, t, u), u), u), diff(diff(xi[t](x, t, u), u), x), diff(diff(xi[t](x, t, u), x), x), diff(diff(xi[x](x, t, u), t), t), diff(diff(xi[x](x, t, u), t), u), diff(diff(xi[x](x, t, u), u), u), diff(xi[t](x, t, u), u), diff(xi[t](x, t, u), x), diff(xi[x](x, t, u), t), diff(xi[x](x, t, u), u)}

(5)

for EQ in sort([op(DetSys)], length) do EQ = 0 end do

diff(xi[t](x, t, u), u) = 0

 

diff(xi[t](x, t, u), x) = 0

 

diff(xi[x](x, t, u), t) = 0

 

diff(xi[x](x, t, u), u) = 0

 

diff(diff(xi[t](x, t, u), u), u) = 0

 

diff(diff(xi[t](x, t, u), u), x) = 0

 

diff(diff(xi[t](x, t, u), x), x) = 0

 

diff(diff(xi[x](x, t, u), t), t) = 0

 

diff(diff(xi[x](x, t, u), t), u) = 0

 

diff(diff(xi[x](x, t, u), u), u) = 0

 

diff(diff(diff(xi[t](x, t, u), u), u), u) = 0

 

diff(diff(diff(xi[t](x, t, u), u), u), x) = 0

 

diff(diff(diff(xi[t](x, t, u), u), x), x) = 0

 

diff(diff(diff(xi[x](x, t, u), t), t), u) = 0

 

diff(diff(diff(xi[x](x, t, u), t), u), u) = 0

 

diff(diff(diff(xi[x](x, t, u), u), u), u) = 0

 

diff(diff(diff(diff(xi[t](x, t, u), u), u), u), u) = 0

 

diff(diff(diff(diff(xi[t](x, t, u), u), u), u), x) = 0

 

diff(diff(diff(diff(xi[x](x, t, u), t), u), u), u) = 0

 

diff(diff(diff(diff(xi[x](x, t, u), u), u), u), u) = 0

 

diff(diff(xi[t](x, t, u), u), u)-(diff(diff(diff(diff(xi[t](x, t, u), u), u), x), x))*delta = 0

 

4*(diff(diff(xi[x](x, t, u), t), x))-2*(diff(diff(eta[u](x, t, u), t), u))+diff(diff(xi[t](x, t, u), t), t) = 0

 

2*(diff(diff(xi[x](x, t, u), u), x))+2*(diff(diff(xi[t](x, t, u), t), u))-(diff(diff(eta[u](x, t, u), u), u)) = 0

 

diff(diff(xi[x](x, t, u), x), x)-2*(diff(diff(eta[u](x, t, u), u), x))+4*(diff(diff(xi[t](x, t, u), t), x)) = 0

 

2*(diff(diff(diff(xi[x](x, t, u), u), u), x))+2*(diff(diff(diff(xi[t](x, t, u), t), u), u))-(diff(diff(diff(eta[u](x, t, u), u), u), u)) = 0

 

-2*(diff(xi[x](x, t, u), x))+(diff(diff(diff(eta[u](x, t, u), u), x), x))*delta-2*(diff(diff(diff(xi[t](x, t, u), t), x), x))*delta = 0

 

(diff(diff(eta[u](x, t, u), x), x))*(diff(f(u), u))+(diff(diff(diff(diff(eta[u](x, t, u), t), t), x), x))*delta-(diff(diff(eta[u](x, t, u), t), t)) = 0

 

2*(diff(diff(diff(diff(xi[x](x, t, u), u), u), u), x))+2*(diff(diff(diff(diff(xi[t](x, t, u), t), u), u), u))-(diff(diff(diff(diff(eta[u](x, t, u), u), u), u), u)) = 0

 

-(diff(diff(xi[x](x, t, u), u), u))*(diff(f(u), u))-(diff(diff(diff(diff(xi[x](x, t, u), t), t), u), u))*delta+(diff(diff(f(u), u), u))*(diff(xi[x](x, t, u), u)) = 0

 

-(diff(diff(diff(xi[x](x, t, u), u), x), x))*delta-4*(diff(diff(diff(xi[t](x, t, u), t), u), x))*delta+2*(diff(diff(diff(eta[u](x, t, u), u), u), x))*delta-2*(diff(xi[x](x, t, u), u)) = 0

 

2*(diff(xi[x](x, t, u), u))-8*(diff(diff(diff(xi[t](x, t, u), t), u), x))*delta+4*(diff(diff(diff(eta[u](x, t, u), u), u), x))*delta-2*(diff(diff(diff(xi[x](x, t, u), u), x), x))*delta = 0

 

2*(diff(diff(xi[t](x, t, u), t), u))-(diff(diff(eta[u](x, t, u), u), u))+(diff(diff(diff(diff(eta[u](x, t, u), u), u), x), x))*delta-2*(diff(diff(diff(diff(xi[t](x, t, u), t), u), x), x))*delta = 0

 

(diff(diff(f(u), u), u))*eta[u](x, t, u)+(diff(diff(diff(eta[u](x, t, u), t), t), u))*delta-2*(diff(diff(diff(xi[x](x, t, u), t), t), x))*delta+2*(diff(xi[t](x, t, u), t))*(diff(f(u), u)) = 0

 

-2*(diff(xi[t](x, t, u), u))*(diff(f(u), u))+4*delta*(diff(diff(diff(eta[u](x, t, u), t), u), u))-2*(diff(diff(diff(xi[t](x, t, u), t), t), u))*delta-8*(diff(diff(diff(xi[x](x, t, u), t), u), x))*delta = 0

 

2*(diff(xi[t](x, t, u), u))*(diff(f(u), u))+2*delta*(diff(diff(diff(eta[u](x, t, u), t), u), u))-(diff(diff(diff(xi[t](x, t, u), t), t), u))*delta-4*(diff(diff(diff(xi[x](x, t, u), t), u), x))*delta = 0

 

diff(diff(xi[x](x, t, u), u), u)-4*(diff(diff(diff(diff(xi[t](x, t, u), t), u), u), x))*delta+2*(diff(diff(diff(diff(eta[u](x, t, u), u), u), u), x))*delta-(diff(diff(diff(diff(xi[x](x, t, u), u), u), x), x))*delta = 0

 

-2*(diff(xi[t](x, t, u), x))*(diff(f(u), u))+2*(diff(xi[x](x, t, u), t))-2*(diff(diff(diff(xi[x](x, t, u), t), x), x))*delta+4*(diff(diff(diff(eta[u](x, t, u), t), u), x))*delta-2*(diff(diff(diff(xi[t](x, t, u), t), t), x))*delta = 0

 

-(diff(diff(xi[t](x, t, u), x), x))*(diff(f(u), u))+diff(diff(xi[t](x, t, u), t), t)-2*(diff(diff(eta[u](x, t, u), t), u))+2*(diff(diff(diff(diff(eta[u](x, t, u), t), u), x), x))*delta-(diff(diff(diff(diff(xi[t](x, t, u), t), t), x), x))*delta = 0

 

-(diff(diff(xi[t](x, t, u), u), u))*(diff(f(u), u))-4*(diff(diff(diff(diff(xi[x](x, t, u), t), u), u), x))*delta-(diff(diff(diff(diff(xi[t](x, t, u), t), t), u), u))*delta+(diff(diff(f(u), u), u))*(diff(xi[t](x, t, u), u))+2*(diff(diff(diff(diff(eta[u](x, t, u), t), u), u), u))*delta = 0

 

-(diff(diff(xi[x](x, t, u), x), x))*(diff(f(u), u))+2*(diff(diff(eta[u](x, t, u), u), x))*(diff(f(u), u))+2*(diff(diff(f(u), u), u))*(diff(eta[u](x, t, u), x))+diff(diff(xi[x](x, t, u), t), t)-delta*(diff(diff(diff(diff(xi[x](x, t, u), t), t), x), x))+2*delta*(diff(diff(diff(diff(eta[u](x, t, u), t), t), u), x)) = 0

 

2*(diff(diff(xi[x](x, t, u), t), u))-2*(diff(diff(xi[t](x, t, u), u), x))*(diff(f(u), u))-2*(diff(xi[t](x, t, u), x))*(diff(diff(f(u), u), u))+4*(diff(diff(diff(diff(eta[u](x, t, u), t), u), u), x))*delta-2*(diff(diff(diff(diff(xi[t](x, t, u), t), t), u), x))*delta-2*(diff(diff(diff(diff(xi[x](x, t, u), t), u), x), x))*delta = 0

 

(diff(diff(diff(diff(eta[u](x, t, u), t), t), u), u))*delta-2*(diff(diff(diff(diff(xi[x](x, t, u), t), t), u), x))*delta+(diff(diff(diff(f(u), u), u), u))*eta[u](x, t, u)+(diff(diff(eta[u](x, t, u), u), u))*(diff(f(u), u))-2*(diff(diff(xi[x](x, t, u), u), x))*(diff(f(u), u))+2*(diff(diff(f(u), u), u))*(diff(xi[t](x, t, u), t)+(1/2)*(diff(eta[u](x, t, u), u))) = 0

(6)

DetSys1 := dsubs(diff(xi[t](x, t, u), u) = 0, diff(xi[t](x, t, u), x) = 0, diff(xi[x](x, t, u), t) = 0, diff(xi[x](x, t, u), u) = 0, diff(eta[u](x, t, u), u, u) = 0, diff(eta[u](x, t, u), x, u, t) = 0, DetSys)

{0, diff(diff(xi[t](x, t, u), t), t)-2*(diff(diff(eta[u](x, t, u), t), u)), diff(diff(xi[x](x, t, u), x), x)-2*(diff(diff(eta[u](x, t, u), u), x)), -2*(diff(xi[x](x, t, u), x))+(diff(diff(diff(eta[u](x, t, u), u), x), x))*delta, (diff(diff(diff(f(u), u), u), u))*eta[u](x, t, u)+2*(diff(diff(f(u), u), u))*(diff(xi[t](x, t, u), t))+(diff(diff(f(u), u), u))*(diff(eta[u](x, t, u), u)), (diff(diff(f(u), u), u))*eta[u](x, t, u)+(diff(diff(diff(eta[u](x, t, u), t), t), u))*delta+2*(diff(xi[t](x, t, u), t))*(diff(f(u), u)), (diff(diff(eta[u](x, t, u), x), x))*(diff(f(u), u))+(diff(diff(diff(diff(eta[u](x, t, u), t), t), x), x))*delta-(diff(diff(eta[u](x, t, u), t), t)), -(diff(diff(xi[x](x, t, u), x), x))*(diff(f(u), u))+2*(diff(diff(eta[u](x, t, u), u), x))*(diff(f(u), u))+2*(diff(diff(f(u), u), u))*(diff(eta[u](x, t, u), x))}

(7)

for EQ in sort([op(DetSys1)], length) do EQ = 0 end do

0 = 0

 

diff(diff(xi[t](x, t, u), t), t)-2*(diff(diff(eta[u](x, t, u), t), u)) = 0

 

diff(diff(xi[x](x, t, u), x), x)-2*(diff(diff(eta[u](x, t, u), u), x)) = 0

 

-2*(diff(xi[x](x, t, u), x))+(diff(diff(diff(eta[u](x, t, u), u), x), x))*delta = 0

 

(diff(diff(f(u), u), u))*eta[u](x, t, u)+(diff(diff(diff(eta[u](x, t, u), t), t), u))*delta+2*(diff(xi[t](x, t, u), t))*(diff(f(u), u)) = 0

 

(diff(diff(eta[u](x, t, u), x), x))*(diff(f(u), u))+(diff(diff(diff(diff(eta[u](x, t, u), t), t), x), x))*delta-(diff(diff(eta[u](x, t, u), t), t)) = 0

 

(diff(diff(diff(f(u), u), u), u))*eta[u](x, t, u)+2*(diff(diff(f(u), u), u))*(diff(xi[t](x, t, u), t))+(diff(diff(f(u), u), u))*(diff(eta[u](x, t, u), u)) = 0

 

-(diff(diff(xi[x](x, t, u), x), x))*(diff(f(u), u))+2*(diff(diff(eta[u](x, t, u), u), x))*(diff(f(u), u))+2*(diff(diff(f(u), u), u))*(diff(eta[u](x, t, u), x)) = 0

(8)

The third equation in (8) can simplify last equation. This will give us eta[u][x] = 0as f[u, u] is non zero.

NULL


Download [1116]_Symmetries_Determination.mw[1116]_Group_classification_and_exact_solutions_of_generalized_modified_Boussinesq_equation.pdf

Regards

Still a little unclear what this error means tho

-f(X)/(X*(ln(X)-Psi(1-f(X))-Psi(f(X)))*GAMMA(1-m))+X*(ln(X)-Psi(1-f(X))-Psi(f(X)))/(f(X)*GAMMA(1-m)) = 0

 

Download dispatchTOshillCORE.mw

updated:

with(CurveFitting);
f := PolynomialInterpolation([[0, x0],[1, x1],[2, x2],[3, x3],[4, x4]], x);
f2 := solve(f=y,x);
area1 := int(f, x=0..1);
with(student):
area2 := trapezoid(f2[1], x = 0..1);
with(CurveFitting);
f := PolynomialInterpolation([[0, x0],[1, x1],[2, x2],[3, x3]], x);
f2 := solve(f=y,x);
area1 := int(f, x=0..1);
with(student):
area2 := trapezoid(f2[1], x = 0..1);

 

i use 5 points trapezoid got RootOf  in result,

only 4 points is acceptable

 

when i try 5 points, there is no problem, but when more points such as

30 points, got RootOf for c sharp code

 

moreover, i got a problem when i copy the area1 result into 

visual studio c# code, it has error Integral Constant is too large

 

with(CurveFitting);
f := PolynomialInterpolation([[0, x0],[1, x1],[2, x2],[3, x3],[4, x4],[5, x5],[6, x6],[7, x7],[8, x8],[9, x9],[10, x10],[11, x11],[12, x12],[13, x13],[14, x14],[15, x15],[16, x16],[17, x17],[18, x18],[19, x19],[20, x20],[21, x21],[22, x22],[23, x23],[24, x24],[25, x25],[26, x26],[27, x27],[28, x28],[29, x29]], x);
f2 := solve(f=y,x);
area1 := int(f, y=0..1);
with(student):
area2 := trapezoid(f2[1], x = 0..1);
with(CodeGeneration):
CSharp(area1, resultname = "area1");
CSharp(area2, resultname = "area2");

i find area2 has

Warning, the function names {RootOf, Sum} are not recognized in the target language
Warning, precedence for Range unspecified
Warning, cannot translate range
area2 = RootOf((System.Double) (19276689540529530246975515949293568 * x3 - 2626509155780373903082144116707328 * x2 + 239680950855919251544490932629504 * x1 -

Hi,

I am trying to solve a set of homogeneous equations for the non-trivial solutions. Mathematically it is possible to get it. But is there any way to get it in Maple. Please find the attached maple sheet for the question. Please help me regarding this.

Regards

Sunit

restart

with(plots):

with(LinearAlgebra):

eq[1] := diff(x[1](t), t)-x[2](t)

diff(x[1](t), t)-x[2](t)

(1)

eq[2] := diff(x[2](t), t)+2*zeta*beta*x[2](t)+beta^2*x[1](t)+n*psi*(-v*(phi[1](t)-phi[1](t-2*Pi/(n*omega0)))+x[1](t)-x[1](t-2*Pi/(n*omega0)))

diff(x[2](t), t)+2*zeta*beta*x[2](t)+beta^2*x[1](t)+n*psi*(-v*(phi[1](t)-phi[1](t-2*Pi/(n*omega0)))+x[1](t)-x[1](t-2*Pi/(n*omega0)))

(2)

eq[3] := diff(phi[1](t), t)-phi[2](t)

diff(phi[1](t), t)-phi[2](t)

(3)

eq[4] := diff(phi[2](t), t)+2*kappa*phi[2](t)+phi[1](t)+n*(-v*(phi[1](t)-phi[1](t-2*Pi/(n*omega0)))+x[1](t)-x[1](t-2*Pi/(n*omega0)))

diff(phi[2](t), t)+2*kappa*phi[2](t)+phi[1](t)+n*(-v*(phi[1](t)-phi[1](t-2*Pi/(n*omega0)))+x[1](t)-x[1](t-2*Pi/(n*omega0)))

(4)

for k to 4 do eqn[k] := simplify(coeff(map(expand, eval(eq[k], [x[1] = (proc (t) options operator, arrow; x[1]*exp(lambda*t) end proc), x[2] = (proc (t) options operator, arrow; x[2]*exp(lambda*t) end proc), phi[1] = (proc (t) options operator, arrow; phi[1]*exp(lambda*t) end proc), phi[2] = (proc (t) options operator, arrow; phi[2]*exp(lambda*t) end proc)])), exp(lambda*t))) end do

x[1]*lambda-x[2]

 

x[2]*lambda+2*zeta*beta*x[2]+beta^2*x[1]-n*psi*v*phi[1]+n*psi*v*phi[1]*exp(-2*lambda*Pi/(n*omega0))+n*psi*x[1]-n*psi*x[1]*exp(-2*lambda*Pi/(n*omega0))

 

phi[1]*lambda-phi[2]

 

phi[2]*lambda+2*kappa*phi[2]+phi[1]-n*v*phi[1]+n*v*phi[1]*exp(-2*lambda*Pi/(n*omega0))+n*x[1]-n*x[1]*exp(-2*lambda*Pi/(n*omega0))

(5)

A, b := GenerateMatrix([seq(eqn[k], k = 1 .. 4)], [x[1], x[2], phi[1], phi[2]])

A, b := Matrix(4, 4, {(1, 1) = lambda, (1, 2) = -1, (1, 3) = 0, (1, 4) = 0, (2, 1) = beta^2+n*psi-n*psi*exp(-2*lambda*Pi/(n*omega0)), (2, 2) = 2*Zeta*beta+lambda, (2, 3) = n*psi*v*exp(-2*lambda*Pi/(n*omega0))-n*psi*v, (2, 4) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = lambda, (3, 4) = -1, (4, 1) = n-n*exp(-2*lambda*Pi/(n*omega0)), (4, 2) = 0, (4, 3) = -n*v+1+n*v*exp(-2*lambda*Pi/(n*omega0)), (4, 4) = 2*kappa+lambda}), Vector(4, {(1) = 0, (2) = 0, (3) = 0, (4) = 0})

(6)

right_vector := Matrix(4, 1, [r[1], r[2], r[3], r[4]])

right_vector := Matrix(4, 1, {(1, 1) = r[1], (2, 1) = r[2], (3, 1) = r[3], (4, 1) = r[4]})

(7)

junk := MatrixVectorMultiply(subs(lambda = I*omega, A), right_vector)

junk := Matrix(4, 1, {(1, 1) = I*omega*r[1]-r[2], (2, 1) = (beta^2+n*psi-n*psi*exp(-(2*I)*omega*Pi/(n*omega0)))*r[1]+(2*Zeta*beta+I*omega)*r[2]+(n*psi*v*exp(-(2*I)*omega*Pi/(n*omega0))-n*psi*v)*r[3], (3, 1) = I*omega*r[3]-r[4], (4, 1) = (n-n*exp(-(2*I)*omega*Pi/(n*omega0)))*r[1]+(-n*v+1+n*v*exp(-(2*I)*omega*Pi/(n*omega0)))*r[3]+(2*kappa+I*omega)*r[4]})

(8)

junk(1)

I*omega*r[1]-r[2]

(9)

for k to 4 do eqnn[k] := junk(k) end do

I*omega*r[1]-r[2]

 

(beta^2+n*psi-n*psi*exp(-(2*I)*omega*Pi/(n*omega0)))*r[1]+(2*zeta*beta+I*omega)*r[2]+(n*psi*v*exp(-(2*I)*omega*Pi/(n*omega0))-n*psi*v)*r[3]

 

I*omega*r[3]-r[4]

 

(n-n*exp(-(2*I)*omega*Pi/(n*omega0)))*r[1]+(1-n*v+n*v*exp(-(2*I)*omega*Pi/(n*omega0)))*r[3]+(2*kappa+I*omega)*r[4]

(10)

solve({seq(eqnn[k], k = 1 .. 4)}, {seq(r[k], k = 1 .. 4)})

{r[1] = 0, r[2] = 0, r[3] = 0, r[4] = 0}

(11)

``

``

``

 

Download question4.mw

pls help review this code, its doesnt return a solution

 

 

restart;
Digits := 16;
M := .5; lambda := .5; Pr := .72; beta := 1; L[w] := 0; m := 1; R := 1; Ec := 1;
N := 7;
for j from 0 to N do J[j] := sum(f[k](t)*(diff(f[j-k](t), `$`(t, 2))), k = 0 .. j) end do;
for i from 0 to N do K[i] := sum((diff(f[k](t), t))*(diff(f[i-k](t), t)), k = 0 .. i) end do;
for j from 0 to N do G[j] := sum(f[k](t)*(diff(theta[j-k](t), t)), k = 0 .. j) end do;
for j from 0 to N do H[j] := sum((diff(f[k](t), t))*theta[j-k](t), k = 0 .. j) end do;
for i from 0 to N do P[i] := sum((diff(f[k](t), t, t))*(diff(f[i-k](t), t)), k = 0 .. i) end do;
epsilon := 1; delta := 0;
f[0] := proc (t) options operator, arrow; L[w]+epsilon+delta*A*t+(1/2)*A*t^2 end proc;
1 2
t -> L[w] + epsilon + delta A t + - A t
2
theta[0] := proc (t) options operator, arrow; 1+B*t end proc;
t -> 1 + B t
NULL;
;
NULL;
NULL;
NULL;
NULL;
for i to N do f[i] := simplify(-((m+1)*(1/2))*(int(int(int(J[i-1], t = 0 .. eta), t = 0 .. eta), t = 0 .. eta))+m*(int(int(int(1-K[i-1], t = 0 .. eta), t = 0 .. eta), t = 0 .. eta))-M*(int(int(int(diff(f[i-1](t), t)-1, t = 0 .. eta), t = 0 .. eta), t = 0 .. eta))-lambda*(int(int(int(theta[i-1](t), t = 0 .. eta), t = 0 .. eta), t = 0 .. eta))); f[i] := unapply(f[i], eta); theta[i] := simplify(-3*Pr*R*(((m+1)*(1/2))*(int(int(G[i-1], t = 0 .. eta), t = 0 .. eta))-(2*m-1)*(int(int(H[i-1], t = 0 .. eta), t = 0 .. eta))+Ec*(int(int(P[i-1], t = 0 .. eta), t = 0 .. eta)))/(4+3*R)); theta[i] := unapply(theta[i], eta) end do;
NULL;
F(eta):=collect((&sum;)f[z](eta),eta):
Theta(eta):=collect((&sum;)theta[z](eta),eta):
with(numapprox);
for k from 2 to 5 do W[k] := pade(diff(F(eta), eta), eta, [k, k]); Q[k] := pade(Theta(eta), eta, [k, k]); SOLL1[k] := expand(coeff(numer(W[k]), eta^k)) = 1; SOLL2[k] := expand(coeff(numer(Q[k]), eta^k)) = 0; SOL[k] := solve({SOLL1[k], SOLL2[k]}, {A, B}); print([k] = SOL[k]) end do;
Warning, computation interrupted

 

 

 

 

 

 

im just getting a generic recursive assignment plus first unused arg error

thats what the maple engine says im doing wrong ill get the number of recursives counted but i guess it just makes me the most angry because its like the same type of error for me every ******* time

Hi all,

I was wondering how to go about validating some airfoil designs for my Formula SAE team's CFD results.  I know this is more common with simplier calculations but I'm hoping using Maple and maybe the new algebraic manipulation of non-comunitive differential operators, I could achive what I am after.   The two calculations of interest are the drag force and downforce.  Can someone shed some light? Thanks

Hello people in mapleprimes,

I think that I found a bug.

Using the screen opened with command + f, I tried to find a v__1211 in the file I appended here.

But, when the cursor is trapped on an output part, which is a blue part, maple wouldn't continue to find the next

v__1211 anymore even if I clicked the Find Next on the screen.

If I move the cursol one line below with a hand, the Find Next butttons works again, but it is intricate.

Isn't there any good way to avoid this trouble other than not using double _, that is __.?

I hope you will give me some hint.

taro

v_1211.mw

P.S. I clicked the above link and opened that file with maple. Then, the notification telling that this is read-only file and

you cannot save this file after some modification, appeared. I don't know whether there is any problem. 

Does appending a maple file on a post on this mapleprimes always done in such a way? 

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