Can I know how to write code about to solve the second kind of linear Fredholm and also Volterra approximation integral by Simpson's method and Galerkin method, and I need a book about advance math to the integral equation, thanks.

1. Does it have any detail manual for Matlab programming using Maple symbolic engine? (Except help documentation of Maple Symbolic Toolbox in Matlab).
2. How to maximize the running speed of the codes programmed by Maple symbolic toolbox? Any Notes?
3. How to use the function 'GenerateMatrix' of Maple in Matlab? What's the syntax to use this function in Matlab?

Best Regards.

Si

Hello

I wonder how integrate can be applied term by term to the following nonlinear differential equation

(diff(y(t), t))*(diff(y(t), t, t, t))-(diff(y(t), t))*y(t)^2-(diff(y(t), t))*(diff(y(t), t, t))-(diff(y(t), t))*A*y(t)

The expected output will be something like 

(diff(y(t), t))*(diff(y(t), t, t))-(1/3)*y(t)^3-(1/2)*A*y(t)^2-(1/2)*(diff(y(t), t))^2+C+int((diff(y(s), s, s))^2, s = 0 .. t)

map(x-> integrate(x,t),(diff(y(t), t))*(diff(y(t), t, t, t))-(diff(y(t), t))*y(t)^2-(diff(y(t), t))*(diff(y(t), t, t))-(diff(y(t), t))*A*y(t))

solves most of it but not the first part. 

Many thanks

Ed

I was attempting to construct  a log question and noticed a problem with the answers that are being resolved by maple.

restart:
with(StringTools):
a := 2:
b := 10:
 c := -4:
d := 5:
rs := 4:
#notice I use the word filler below, in order to randomize later and replace "filler" with various "log[base]" or "ln".
equation1 := convert(filler(a*x+b)-filler(c*x+d) = rs, string):
equationAct := parse(SubstituteAll(equation1, filler, cat(ln))):
answer := [solve(equationAct, x)]:

#it appears maple is applying the log properties and suggesting solutions outside the real domain, for the individual log expressions.  The plot of the equation seems to confirm this.
plotA := plot(lhs(equationAct), x = -10 .. 10):
plotB := plot(rhs(equationAct), x = -10 .. 10):
plots[display](plotA, plotB);

restart:
NewtonRaphsonSYS:=proc(X,F,X0,TOL,itmax)
local Xn,H,FX,J,i,m,n,Err;
m:=LinearAlgebra[Dimension](Vector(X));
Xn:=Vector(m);
H:=Vector(m);
FX:=Vector(m);
J:=Matrix(m,m);
Xn:=X0;

for n to itmax do
    FX:=eval(F,[seq(X[i]=Xn[i],i=1..m)]);
    J:=evalf(VectorCalculus[Jacobian](F,X=convert(Xn,list)));
H:=-Inverse(J).Vector(FX);
Xn:=Xn+H;

printf("%3d %.8f",n,Xn[1]);
 
for i from 2 to m do;
 printf("%.8f",Xn[i]);

end do;
for i from 1 to m do;
 printf("%.3g",H[i]);

end do;
printf("\n");
if (LinearAlgebra[VectorNorm](H,2)<TOL) then break end if;
end do;
end proc:
F:=[xy-z^2-1,xyz+y^2-x^2-2,e^x+z-e^y-3];
X:=[x,y,z];
X0:= <1,1,1>;
TOL:=0.00000001;
itmax:=10;

      [  2             2    2             x        y    ]
      [-z  + xy - 1, -x  + y  + xyz - 2, e  + z - e  - 3]
                           [x, y, z]
                Vector[column](%id = 4442374402)
                                 -8
                             1 10  
                               10
NewtonRaphsonSYS(X,F,X0,TOL,itmax);

Maple is not able to simplify x^3+a*x+b) -(y^3+a*y+b) )^2/(x-y)^4   into (x^2 + x*y + y^2 + a)^2/(x - y)^2 

wtf

p.s.  how do I get maple to show steps in simplifications

Hello people :) 

As the captian says, im trying to remove an old task i've made.
But i get this:

Error in Get, invalid object [_XML_reply_data_get("reference" =
"_Maplets_reference_12","parameter" =
"value",_XML_content("Task,UserTasks,Nyops",&Entity "#xc3",&Enity
"#xa6","tning"))]

And i have no idea what it is, but it won't erase my task :'D

Thanks a bunch in advance! 

Have a great weekend you all
Best regards Lucas :)

Hi

I am a student of economics writing my thesis. I have an inverse demand function defined:

p[i,j]=1-q[i,j]-αq[i,k]-β(q[h,j]+αq[h,k])

where α,β are scalars, i{1,2,}, j {1,2,3}, h/=i and k/=j.

I wanted to know how do i input this kind of function in the program and how do i calculate the function of q[i,j] (the inverse)

Thank you!

I would like to extract the x and y values from a list containing ordered pairs, [x,y], and display as a list.

For example, given 

  A:= [ [4,2], [9,1], [6,8] ] 

how can I obtain 

 X:=[4,9,6] and Y:=[2,1,8] 

using a simple command?

Thank you!

Why is lamba protected as something it traditionally isnt for this package?

Download main.mw

My learning exercise today is the Calkin-Wilf Tree, and the first worksheet I have the issue, due to needing to use a set operator and at that point of computation losing the ordering if it were to be a list (I have tried with a list, and was unsuccessful) none the less my question is, can I alter the ordering condition for Sets in a worksheet produced therein? 

I also encountered a strange result that I would appreciate an explaination for as seen below in the uploaded worksheet

Download Q1_MP_08112019.mw

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

Hello. Here is my question.

Download ORDERED.mw

Good day.

My question involves a set of prescribed points in the Cartesian plane. The x and y ranges are fixed. The points are connected by (imaginary) horizontal and vertical lines to produce a fixed number of blocks / grids.

An example is given in the attached file.  Grid_Example.mw

Now, I wish to reduce the intervals between these points by a scaling factor, n, so as to generate more blocks within the plane that is constrained by the x and y-ranges.

In doing so, I need to find the (x,y)-location of these points in the plane and it would also be great if I could obtain a simple plot.  

As I have several scaling factors to investigate, I was hoping someone may be able to guide me towards a simple routine to help obtain these solutions.

Once again, thanks for taking the time to read this.

Dear Maple Users, 

First of all I would like to thank for your great support and hints on making a package for Maple. It has made possible for me to construct this package here: 

restart; 
MyMat:=module()
description "My Package";
option package; 
export RegModelPlot,RegModel;
RegModelPlot :=proc(c::algebraic,xd::list,yd::list,x::algebraic)
    uses Statistics, plots:
     display
                            (  [ plot
                                 ( Fit(c, xd, yd, x),
                                   x=min(xd)..max(xd),
                                   color=blue,gridlines,
                                   title=typeset("Regressionformula\n f(x) = ", evalf[4](Fit(c, xd, yd, x))),caption=typeset("Residuals = ", Fit(c, xd, yd, x, output = residuals) ))                    
                                 ,
                            
                                 plot
                                 ( xd, yd,
                                   style=point,
                                   symbol=solidcircle,
                                   symbolsize=10,
                                   color=red
                                 )
                               ],
                               size=[800,600]
                            );
                           
                           end proc; 

    RegModel:=proc(c::algebraic,xd::list,yd::list,x::algebraic)
            uses Statistics, plots:
return  Fit(c, xd, yd, x);
end proc; 
    end module

My question is now. How do I make it installable ? Meaning, making it so I can be accessed using with the with() argument alene? I have tried to convert it to into an MLA-file and place it in the lib folder. 
 

But if I type with(MyMat) it gives me the error: 

Error, invalid input: with expects its 1st argument, pname, to be of type {`module`, package}, but received MyMat 
 

So anyone with an idea/hint on what I need to add to make the package installable? 

Thanks in advance :)