A simple tutorial task on optimization from one of the forums. We need to find the minimum of the function 
g1 = (x1-x2)*(x2-x3)*(x3-x4)*(x4-x1) with the following constraint g2 = x1^2+x2^2+x3^2+x4^2-1. 
It reduces to solving polynomial equations.  
Minimum = - 0.25. It's  solution:
[x1 = .683012702, x2 = .183012702, x3 = -.183012702, x4 = -.683012702],
[x1 = .183012702, x2 = .683012702, x3 = -.683012702, x4 = -.183012702],
[x1 = -.183012702, x2 = .183012702, x3 = .683012702, x4 = -.683012702],
[x1 = -.683012702, x2 = .683012702, x3 = .183012702, x4 = -.183012702],
[[x1 = .683012702, x2 = -.683012702, x3 = -.183012702, x4 = .183012702],
[x1 = .183012702, x2 = -.183012702, x3 = -.683012702, x4 = .683012702],
[x1 = -.183012702, x2 = -.683012702, x3 = .683012702, x4 = .183012702],
[x1 = -.683012702, x2 = -.183012702, x3 = .183012702, x4 = .683012702]
when x5 =0 .25

But so far I have not found an easy way to solve it using Maple. First we need to be able to successfully use fsolve, and only then "polynomial" functions.

restart; with(RootFinding):
g1 := (x1-x2)*(x2-x3)*(x3-x4)*(x4-x1); 
g2 := x1^2+x2^2+x3^2+x4^2-1;
 g :=g1+x5*g2; 
f1 := diff(g, x1); 
f2 := diff(g, x2); 
f3 := diff(g, x3); 
f4 := diff(g, x4); 
f5 := diff(g, x5); 
#solve([f1, f2, f3, f4, f5], [x1, x2, x3, x4, x5]);
Isolate([f1, f2, f3, f4, f5], [x1, x2, x3, x4, x5]); 
S := fsolve([f1, f2, f3, f4, f5], {x1, x2, x3, x4, x5}, maxsols = 8); 
x5 := rhs(op(5, S));
Isolate([f1, f2, f3, f4], [x1, x2, x3, x4]); 
solve([f1, f2, f3, f4], [x1, x2, x3, x4])

The optimization package doesn't help much either.
The task itself is of no interest, it is interesting to look at its simplest solution in Maple.
(By the way, Draghilev's method works well, but, of course, this is not the easiest way).

Hellow maple users, I am getting an error while solving system of differential equations analytically. Please help to recify the error. Thanks in advance. Here is my codes;

restart:
with(DETools):
# S, N  are constant
Eq1:=diff(u(y),y,y)-u(y)=C(y):
Eq2:=diff(T(y),y,y)=u(y)-diff(u(y),y)^2-u(y)^2+S*T(y)+N*T(y):
Eq3:=diff(C(y),y,y)-C(y)=0:
desys:={Eq1,Eq2,Eq3};ics:={u(0)=0,D(u)(0)=h,T(1)=h,D(T)(0)=0,C(1)=h,D(C)(0)=0}:
combine(dsolve(desys union ics,{u(y),T(y),C(y)}));

Dear all

How can I solve the system of equations with unknowns  c[2] and Z

system_eqs.mw

Maybe the question can be solved by hand.

thanks

Hello Everyone;

Hope you are fine. I need to solve the system of equation. I am using fsolve command but it is not working. Kindly guide me.

Thanks

ques.mw

Download ques.mw

Fitting procedures in Maple are self explaning and easy to perform. However, I was wondering if it is possible to fit data vectors with units. For example one vector would have units of seconds and the other units of length. Thank you for your help.

Is there any command that allows me to extract the input number of any function f?

exmple:

f: (x₁; x₂;...;x_n)-> y

command (f)=n

thanks for the help!

I have string of length

StringTools:-Length(str);
                            1073105

When doing

p:=StringTools:-LengthSplit(str,100):

Maple gives

From help:

LengthSplit
split a string into equal length pieces
 

This is all done in .mpl  file actually, not interactive, but I made the above worksheet to show  the problem. The string is read from a file by a program and it wants to split it to 100 length smaller strings.

I have lots of RAM. 128 GB.  So why does Maple crash and is there a workaround this?

This string was generated by another software.

I have attached the above example below as worksheet.  Maple 2022.1 on windows 10.

Here is a simpler way to generate this problem

restart;
str:=StringTools:-Random(1073104,'upper'):
str[1..10];

StringTools:-Length(str);
p:=StringTools:-LengthSplit(str,100):

Using trial and error, the crash happens when the length reaches 1073101. At 1073100 there was no crash.

I need to define a simple recursive algorithm (i'm not a programmer) such that:

x_i=x_i-1+b 

with i=0,1,...,n; 

and with all x_i's elements of a Set A

how can i achieve this?

I have some expressions like 3%/5 and would like to get the numerator and denominators numer(3%/5) does not return 3.

I cannot evaluate it since it might reduce the fraction which will make my results invalid.

Hi,

I want to get the coefficient of some terms but I can't define suitable codes to do it:

I used the codes of one question on this site namely

https://www.mapleprimes.com/questions/229770-How-To-Find-The-Coefficient-Of-X-X2and

but they do not work for my case.

My case is as follows:

restart;
F:=2*y*sin(beta*x)+6*z*cos(beta*x)+24*sin(beta*x)*cos(beta*x):
coeff(F,sin(beta*x));
                      2 y + 24 cos(beta x)
coeff(F,cos(beta*x));
                      6 z + 24 sin(beta x)

coeff(coeff(F,cos(beta*x)),sin(beta*x));
                      24
The last one is true but for the first two cases, I want to get 2y and 6z respectively.

Maple code for finding optimum maximum value of function TOTP given below when D is kept in the range of 300 to 2000?Also give maple code to find 3Dplot to determine the convexity of function TOTP with respect to y and Sr?

D^γ S(t)=(b-ev)S-α_1 (1-ev)SI_1-α_2 (1-ev)SI_2-dS,
D^γ I_1 (t)=α_1 (1-ev)SI_1-(β_1+d_1+d)I_1,                                           
D^γ I_2 (t)=α_2 (1-ev)SI_2-(β_2+d_2+d) I_2                  , 
D^γ R(t)=β_1 I_1+β_2 I_2+evS-dR 

Found case where PDEtools:-Solve gives exception but not solve.

Is this known issue?

Download exception_from_Solve_august_8_2022.mw

I create a plot, then later on, I want to use the same view for a second plot or using the same starting x, ending x and starting y and ending y. For reasons no need to get into into, I need to do this and I have no access to this information at this time. I only have access to the p variable used to store the plot into as in this example below.

I am not sure what is the correct way to do read this information from the PLOTS structure as I never used it before. 

Help describes the PLOTS structure under "PLOT and PLOT3D Data Structures" , but do not see how is one supposed to read different parts of it. I could have missed it. Maple help pages are very hard for me to read in order to obtain the information needed. From help it says:

The Maple plotting functions, plot, plot3d, and others, produce PLOT and PLOT3D data structures describing the images to be displayed.

By trial and error, for standard plot this worked

p:=plot(sin(x),x=-1..10):
op([4,1,2,2],p)

returns

           "originalview" = [-0.9862500000 .. 9.9862500000, -1.0000000000 .. 1.0000000000]

I see also that command plottools:-getdata(p):  returns the data. So I could also do (it is stored in matrix, in third entry):

p0:=plottools:-getdata(p);
startingx:=p0[3][1,1];
startingy:=p0[3][1,2];
endingx:=p0[3][-1,1];
endingy:=p0[3][-1,2];

Will the above work all the time? should this command be used to obtain this information or is there a better way?

When I lprint(p) I see these fields have actual names. For example  , here is screen shot of lprint(p)  

it looks like  a RECORD data structure. But when I tried p:-originalview  Error, `p` does not evaluate to a module 

The question is: What is the correct way to find what x range and y range was used for an earlier plot, given one has access only to p variable used to store the output of the plot command?  This is for 2D plot only.

in MapleFlow 2022 ...
1i means 1*sqrt(-1) while 2i means 2*sqrt(-1) ... etc ... right?

In electronics "j" is used for  the sqrt(-1) ... since "i" is used for electric current.

That said I just discovered that MapleFlow will also interperit "j" as sqrt(-1) when used in this context...
1j = 1*sqrt(-1)
2j= 2*sqrt(-1)
Right?

But how can I have MapleFlow express answers using j as sqrt(-1) instead of using i?

I want 2 * 2j= 4j
not 2*2j = 4i

Also, on another topic...
On this forum... what is the difference between a "Post" and a "Question"... as when I ask a question ...
 consider it "posting" a question.

Thanks for any help or  clairfication.