Hello,

I need to order a set of polynomials based on a given ranking. For example:

F:=[F1,F2,F3,F4,F5,F6]:
F1 := x1*x4^2+x4^2-x1*x2*x4-x2*x4+x1*x2+3*x2;
F2 := x1*x4-x3-x1*x2;
F3 := x3*x4-2*x2^2-x1*x2-1;
F4 := x1*x3^2+x3^2-x1^2*x2*x3-x1*x2*x3+x1^3*x2+3*x1^2*x2;
F5 := -x3^2 + x1*x2*x3 -2*x1*x2^2-x1^2*x2-x1;
F6 := 2*x1*x2^2+2*x1^2*x2^2-2*x1^2*x2+x1^2+x1;

The order used to rank the polynomials is based on the variables in the following order: x1 < x2 < x3 < x4.

The ranking criteria are:

1. The first polynomial should be the one involving x4 with the lowest degree of nonlinearity in x4 and the fewest number of terms (in this case, F2).
2. The next polynomial should also involve x4, but with the lowest degree of nonlinearity and the next fewest number of terms and so on.
3. Once the polynomials in x4 are exhausted, the ranking continues similarly for the next variable x3, followed by x2, and finally x1.

How can I do this efficiently?

Obs.:If necessary, I can share my solution to the problem, though it's far from efficient.

Hello,

I am attempting to solve what appears to be a simple system of two ordinary differential equations (ODEs) (please find the attached file). However, I encountered an error message from Maple stating: "division by zero."

Could anyone suggest an approach to obtain a closed-form solution for this system?

Please note that the system includes two variables: S(t) and K(t). All other symbols represent positive parameters.

Thank you in advance for your assistance!

Best regards,

Dmitry

Download ODE.mw

Good morning, please tell us how to graph on a map the graph that is seen in the image with those colors and their areas for the following exercise:

1. Draw the graph and find the area of ​​the region that is inside the cardioid r=2+2 cosθ and outside the circumference r=3

Calculate the area of ​​the region common to the two regions limited by the following curves:

r1= -6*cos(θ) Circle
r2= 2-2*cos(θ) Cardioid

A classic task from surveying that is unfortunately no longer taught in our GPS age and is worth remembering:

A hiker has lost his way and wants to know where he is. He has a map, a compass, paper, pen and calculator in his bag. From his position he sees three distant objects from left to right: a radio mast F, a chimney S and a church tower K. He also finds these objects on his map. Using his compass he aims at the three objects and measures the angles at which the distances FS and SK appear: angle for FS=alpha, angle for SK=beta. The hiker also manages to get the approximate coordinates of the three objects from the map to scale: F=(xf;yf), S=(xs;ys) and K=(xk;yk).
Question:
What are the hiker's coordinates?

Hello, I am having problem in solving the pde in the image using maple. Due to its nonlinear nature it has been solved for small value of v using first order perturbation technique and seperation of variable method into radial and angular part in many papers. I am having trouble in proceeding as Maple complains about Boundary/Initial condition.Please tell me if Maple can provide any help in improving existing solution or providing new solution? I can post the full solution procedure by the method i mentioned if needed.

Download Nonlinear_Elliptic_PDE_in_Spherical_Coordinate.mw

I need to modify only one entry in a .m file (which happens to be table entry). How do I do this?

Hi! 

I want to create a matrix of variables, and another matrix of variables that are different from the first matrix.

The idea is to generate a matrix of equations, then reshape the matrix into an array of functions, and then enter the array into "solve" to solve the system of equations.  

I was able to do this in a different software package, and I was able to do it.

Basically, (matrix a - matrix b - identity matrix).  Then, "equate" this matrix to a matrix of zeros to generate the right hand side.

Can this be done in maple? How would one do this?

Given a conventionally labeled triangle ABC with the two sides a=3 and b=4, c is not given. What is the side length of the largest inscribed square whose "base" lies on the triangle side c?

Hi

How merge or combine two or more 3D plot together ? and How many 3D plot exist for describe graph ? and how we can transfer this combine plot to another program like matlab?

Maple is  good for decribe plot  and very faster from other program but for visualization and some other stuff we need other language program, so how we can combine the plot and how we transfer this plot another program like matlab i know the matlab have special template for this kind plot but i didn't have the template if any one have it it will be  awesome?

Download combine_graph.mw

Dear all, I tried to run the test.java example in the Eclipse IDE but receive the following error message:

Error: Unable to initialize main class examples.test2
Caused by: java.lang.NoClassDefFoundError: com/maplesoft/externalcall/MapleException

May be there is s.o. who has an idea.

Thanks

If we have the system of difference equations

x_n=y_n-1x_n-1+2,             y_n=0.5 x_n-1+y_n-1+1,      n=1,2,...,

 where x₀ and y₀ are positive initial valyes.

How can I plot the solution {x_n,y_n} ??

The usual ODE must be solved:
y´´*(y^3-y)+y´^2 *(y^2+1)=0
"Dangerous places" of the definition domain must be described: Where are the general solution y(x) and its derivatives continuous?

This is probably asked before but can't find it. 

After making a plot, then RIGHT-CLICKing on it, option menu comes up that allows one to modify the plot (like adding gridlines, or change the line style).

How does one find the Maple command after doing such changes, so one can use the command in the code?

Here is an example. I modified a little acers plot in this answer and added the points to the plot

eq:=-0.0004*x^2 - 2.7680*10^(-28)*x^12 - 2.1685*10^(-43)*x^18 - 1.3245*10^(-37)*x^16 - 1.6917*10^(-32)*x^14 + 0.7650 + 6.6773*10^(-18)*x^8 - 2.5543*10^(-23)*x^10 - 8.0002*10^(-13)*x^6 + 3.6079*10^(-8)*x^4 = 0:
the_roots:=fsolve(eq):	
the_roots:=map(X->[X,0],[the_roots]):
p1:=plot(lhs(eq),x=-210..210,size=[500,200]):
p2:=plot(the_roots,style=point, color=red, symbol=solidcircle, symbolsize=20):
plots:-display(p1,p2)

I was lazy to look up the grid option syntax. So right clicked on the plot and found option to add gridline. So said, great. And the above is the result.

But now I'd like to see the command used so I know where the grid option goes and how its syntax is. There does not seem to be option in the interface to display the Maple command used.

How would one find it?

Maple 2024.1 on windows 10

hi...

how can I just find the real roots of this equation in Maple:

eq:=-0.0004*x^2 - 2.7680*10^(-28)*x^12 - 2.1685*10^(-43)*x^18 - 1.3245*10^(-37)*x^16 - 1.6917*10^(-32)*x^14 + 0.7650 + 6.6773*10^(-18)*x^8 - 2.5543*10^(-23)*x^10 - 8.0002*10^(-13)*x^6 + 3.6079*10^(-8)*x^4 = 0:

I want to solve it first with fsolve (with options) command and second other command than fsolve. 

tnx...

I am trying to plot the shearforce of a hollow section circular beam along the hight of the cross section.

I don't seem to be able to solve the equation. I get the message:"Warning, solutions may have been lost"
Can anyone help?

The tricky part is the distance of the "point of grafity of the area above y' to the 'point of grafity of the cross section (y=0)'. This distance is a function of y and is called y_

this is de code: M_V_as_function_of_hight_cc__temporary.mw

restart: with(LinearAlgebra): with(plots, textplot, display): #Digits :=5: evalf(%): with(RealDomain):
Rout:=168.3/2:
Rin :=Rout-12.5:

T:=V*Q/(II*b):
Q:=A_*y_:
bout:=2*sqrt(Rout**2 - y**2):
bin:=piecewise( y<Rin,2*sqrt(Rin**2 - y**2)  ,  y>=Rin,0):
#bin:=Re(2*sqrt(Rin**2 - y**2)):
b:=bout-bin;
A_ :=piecewise(  y<=0,0   ,    y<Rin,evalf( int(b ,  y=y..Rout ) ) ,    y>=Rin,int(bout , y=y..Rout)    ,    y>=Rout,0);
y:=y_: AA_:=A_;
y:='y':
eq1:=2*AA_ = A_:
sol1:=solve(eq1, y_ );
y_ := sol1:
y_;
#plot(y_,y=0..Rout);