Issues in using isolating variables from constrain...

I can't isolate a variable from the constraint and move it to one side of the inequality. For example, it's like having theta <= all other terms. I've tried using the isolate and eval functions, but they aren't producing any results or simplifying the expression. What am I doing wrong?

Attaching sheet below (issue marked yellow in background): N_1.mw

Minimization of a function...

Can anyone helps me with my optimization Problem.  Following are the issues :-

• I have to minimize the function TRC, i am unable to do.
• I am unable to add a constraint with if statement.
• Check whether i have represented I1 and I2 with respect to alpha and beta right or wrong

Attaching the sheet below, the background marked in yellow is the problem area. Thankyou

Basic_model.mw

Need to Obtain Bifurcation Points and Bifurcation ...

Hello Everyone;

I need to find the bifurcation point and further bifarcation diagram for the given model. But facing error. Can anybody help to do this? Can you refer some library for bifurcation analysis of ODE's? Code is attched. Thanks in Advance.

123.mw

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 > bif_eq1 := eq1 = 0;

 > bif_eq2 := diff( eq1, V) = 0;

 > bif_sol := solve({ bif_eq1,bif_eq2}, {V, g_Na});

as the solutions, which are then expressed as the points  via

LagrangeMultipliers...

Hi, I have an homework where I need to find the highest point and the lowest point on an ellipse form by the intersection of two equations wich are 4x-3y+8z=5 and z^2=x^2+y^2 and I have to use the LagrangeMultiplier command. I get how it works but I can't get the correct form. How should I do it ?

{r} values in eigenvectors ...

Hello everyone,

I'm trying to symbolically diagonalize a 5x5 matrix in Maple. I can determine the eigenvalues for my matrix, but when it comes to evaluating the eigenvectors, Maple gives me the following results:

eigenvalues(A): -a + u, a + u, u, u, u

eigenvectors(A): [a + u, 1, {r}], [-a + u, 1, {r}], [u, 5, {r, r, r, r, r}]

I don't understand why I'm getting `{r}` in the eigenvectors. How can I display the eigenvectors for my matrix A?

5x5

 (1.1)

 (1.2)

 (1.3)

 (1.4)

 (1.5)

 (1.6)

 (1.7)

minimax optimization error and failure...

Error, (in minimize/cell/function/multidependence/univariate)

Error, n should be an integer for integer[n]
Error, (in minimize/cell/function/multidependence/univariate) invalid input: `minimize/continuous` expects its 2nd argument, yFP, to be of type {name, list(name)}, but received `X[4,3]` = -infinity

Error, invalid input: `convert/Array` expects its 1st argument, A, to be of type {Array, Matrix, Vector, array, sequential}, but received 0

my design optimization objective function is to carry out a minimize the maximum assignments from vector B overlap  between any two members in A , such that in vector A all members fall under a group and there is no duplication of membership, further   a member from each group representing the group  is to be assigned to vector B such that only one member of a group should be assigned each member of vector B, while ensuring that every member in vector B has represntation from every group in vector A.

 (1)

Unevaluate Expression...

Sorry if this is already known, but I haven't found the proper function call.

I just want to "print" this expression without evaluating the boolean calls

restart;
P(X <= 5) = P(-5 <= -X) = P(E(X) - 5 <= E(X) - X);

As it stands, this will evaluate to "false" which I obviously don't want.

I just want to use it as a displayer.

How do I solve this nonlinear system in Maple?...

Hi, I'm trying to solve these 2 nonlinear equations in f, g, and x, where x is from 0 to 1 with an increment of 0.1.

I am new to Maple and do not know the basics. Please try and help me. I'd highly appreciate it.

Since this is a nonlinear system, multiple solutions exist, I need to find the first 3 or 5 solutions. Once I solve the system, I would like to plot 2 plots, y-x and z-x.

How do I convert ordinary code to parallel computi...

I currently do extensive modeling that involves Monte Carlo simulations. This kind of analysis seems idially suited to parallel computing. To begin the process I have been following the teachings of chapter 15 of the Programming Guide 2023. As a first excersize I copyied the code on pages 583-584 and attempted to run it on my system. My Maple program is a 2019  Student Version running on anHP laptop using Windows11. The code yields an error code "Error, invalid input: add_range uses a 1st argument, lo, which is missing"

This is an exact copy of the ccode in the guide. Is there posibly a probem with my installation? I am willing to update and upgrade as may be needed. Any suuggestions how to procced?

Thanks

Ray

power as fraction, Maple...

I defined the following function L1 and L2 to test, if  Maple is returning the same results. Mathematically they are identical. For all testpoints, L1 returns the correct results (for y := -5 the result is -15).  L2  returns identical results exept for y:=-5. For y:= -5, where you can see on the first glance that the result must be -15,  Maple is returning for L2 a complex number. I am worried about this different treatment of the functions L1 and L2, because I am calculating with functions, where you cannot prove the result as easy as it can be done here.

L1 := y -> 3*y*((y + 4)^2)^(1/3);
L1 := proc (y) options operator, arrow, function_assign;

3*y*((y+4)^2)^(1/3) end proc

L2 := y -> 3*y*(y + 4)^(2/3);
L2 := proc (y) options operator, arrow, function_assign;

3*y*(y+4)^(2/3) end proc
NULL;
for y from -5 to 0 do
print("y = ", y, "L1(y)   =  ", L1(1.0*y), "          L2(y)  =,  ", L2(1.0*y));
end do;
"y =  ", -5, "L1(y)   =  ", -15.0, "          L2(y)  =,  ",     7.500000000 - 12.99038105 I
"y =  ", -4, "L1(y)   =  ", -0., "          L2(y)  =,  ", -0.
"y =  ", -3, "L1(y)   =  ", -9.0, "          L2(y)  =,  ", -9.0
"y =  ", -2, "L1(y)   =  ", -9.524406312,              "          L2(y)  =,  ", -9.524406312
"y =  ", -1, "L1(y)   =  ", -6.240251469,              "          L2(y)  =,  ", -6.240251469
"y =  ", 0, "L1(y)   =  ", 0., "          L2(y)  =,  ", 0.

Command Extrempoints...

Question about using the command „ExtremPoints“

I am using Maple 2019.

Using the command ExtremPoints I got different list when defining the function over a closed intervall piecewise or with f(x), x=a..b.

Maple desciption states:
ExtremePoints(f(x), x = a..b) command returns all extreme points of f(x) in the interval [a,b] as a list of values.

An extreme point is defined as any point which is a local minimum or maximum, which includes any finite end points.

So I expected, Maple returns the same list, independend of how the same function is defined (see example below). Instead: with the piecewise definition Maple returns as extrempoints only the local extrempoints without the finite endpoints.
Defining the same function with f(x),x=a..b Maple returns the list with local minimum or maximum, which includes any finite end points.

Example:

f := x -> piecewise(-1 <= x and x <= 2, x^2, undefined);

Return:  ExtremePoints(f(x));

[0]

g := x -> x^2

ExtremePoints(g(x), x = -1 .. 2);

[-1, 0, 2]

I am not able to solve these equation, can anyone ...

restart;
Pr:=0.71: n:=-1:

eta0:=0.0699;

EQ1:=diff(H(x), x ) - x*diff(F(x), x ) ;

EQ2:=(1+x^2)*diff(F(x), x\$2) + (3*x + x*F(x)-H(x))*diff(F(x), x) + F(x)^2 + G(x)^2 +2*P(x) + x*diff(P(x), x) ;

EQ3:=(1+x^2)*diff(G(x), x\$2) + (3*x + x*F(x)-H(x))*diff(G(x), x) ;

EQ4:=(1+x^2)*diff(H(x), x\$2) + (3*x + x*F(x)-H(x))*diff(H(x), x) + (1+F(x))*H(x)- diff(P(x), x);

EQ5:=(1+x^2)*diff(theta(x), x\$2) + x*(1-2*n)*diff(theta(x), x) + n^2*theta(x) - Pr*( n*F(x)*theta(x) + ( H(x)-x*F(x) )*diff(theta(x), x)  ) ;

EQ:={EQ1=0, EQ2=0,EQ3=0,EQ4=0 ,EQ5=0}:

IC:={ F(0)=0, G(0)=12, H(0)=0, theta(0)= 1, F(eta0)=0, G(eta0)=12, H(eta0)=0, theta(eta0)= 0, P(0)=0};

sol:= dsolve(EQ union IC,numeric,output=Array([0,0.0699]));

ques.mw

What will be the range of p and q to get the plot ...

What will be the range of p and q to get the plot and to get the optimum solution?
If possible get a solution for particular value of p and q.
file attached: q1.mw

Problem in IntegrationTools:-Change ?...

Just wanted to ask, what the issue here is:

restart;
Int(1/(1 - x*ln(x)), x);
IntegrationTools:-Change(%,u=1-x*ln(x),u);

doesn't give the proper transformation. It gives

Int(1/u,u)

Solving for x and writing the transformation in terms of LambertW gives something else, if I'm not mistaken.

Problem with a function defined using procedure...

tortoise_draft2.mw
I am trying to use the function "rt" defined below to solve the equation "eq1", but I get an error "Error, (in PDEtools:-Solve) x is in the equation, and is not solved for". I don't quite understand what prevents me from using this function freely in expressions (for example, to plot it I must use unevaluation, etc.). Could you, please, clarify why this error occurs and how to fix it?

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