Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

Hi dears,

How can I detect two equivalent matrices? Is there any Maple command for this?

Also, Is there any command to verify that two matrices have the same Smith normalform?

Sincerely yours

I would like to return local variable y (line 4 in showstat) in the attached dummy procedure (s1) without manually adding any comment inside the procedure s1. This procedure is a simple one and easy to copy paste/or change. When we have a long procedure, it is difficult to do so. I will always know the name of the local variable I want (say, y) and/or line number in showstat

Thanks

PS, I want to get y:=array(1..,2[(1)=x,2=zz])
 

restart;

s1:=proc(n,x)
local y,xx,i,j,zz::array(1..n,1..n);
for i from 1 to n do for j from 1 to n do zz[i,j]:=x[i]*(1+x[j]^2);od:
od:
y:=array(1..2,[(1)=x, (2)=zz]):
for j from 1 to n do xx[i]:=zz[i,i]/(add(zz[i,j],j=1..n));od:
0;
end proc;

s1 := proc (n, x) local y, xx, i, j, zz::(array(1 .. n, 1 .. n)); for i to n do for j to n do zz[i, j] := x[i]*(1+x[j]^2) end do end do; y := array(1 .. 2, [1 = x, 2 = zz]); for j to n do xx[i] := zz[i, i]/add(zz[i, j], j = 1 .. n) end do; 0 end proc

(1)

showstat(s1);

 

s1 := proc(n, x)

local y, xx, i, j, zz::array(1 .. n,1 .. n);

   1   for i to n do

   2     for j to n do

   3       zz[i,j] := x[i]*(1+x[j]^2)

         end do

       end do;

   4   y := array(1 .. 2,[1 = x, 2 = zz]);

   5   for j to n do

   6     xx[i] := zz[i,i]/add(zz[i,j],j = 1 .. n)

       end do;

   7   0

end proc

 

 

x0:=Vector(2,[1,1]);

x0 := Vector(2, {(1) = 1, (2) = 1})

(2)

s1(2,x0);

0

(3)

 


 

Download showstatexample.mws

Dear All

I am trying to use differential operator two times in sucession but I am not getting desired differentiation. Please see content below:


 

with(PDEtools):

DepVars := [u(x, t), v(x, t), phi(x, t), psi(x, t)]; 1; declare(u(x, t), v(x, t), phi(x, t), psi(x, t))

[u(x, t), v(x, t), phi(x, t), psi(x, t)]

 

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

 

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

 

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

 

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

(1)

_local(I):

I := phi(x, t)*(diff(v(x, t), x)+b*(diff(u(x, t), x, x)))+psi(x, t)*(diff(u(x, t), x, x, x)+d*(diff(v(x, t), x, x)))

phi(x, t)*(diff(v(x, t), x)+b*(diff(diff(u(x, t), x), x)))+psi(x, t)*(diff(diff(diff(u(x, t), x), x), x)+d*(diff(diff(v(x, t), x), x)))

(2)

ToJet(I, DepVars)

phi*(b*u[x, x]+v[x])+psi*(d*v[x, x]+u[x, x, x])

(3)

T[1] := proc (f) options operator, arrow; diff(f, u[x]) end proc; 1; T[2] := proc (f) options operator, arrow; diff(f, u[x, x]) end proc; 1; T[3] := proc (f) options operator, arrow; diff(f, u[x, x, x]) end proc; 1; U[1] := proc (f) options operator, arrow; diff(f, v[x]) end proc; 1; U[2] := proc (f) options operator, arrow; diff(f, v[x, x]) end proc

proc (f) options operator, arrow; diff(f, u[x]) end proc

 

proc (f) options operator, arrow; diff(f, u[x, x]) end proc

 

proc (f) options operator, arrow; diff(f, u[x, x, x]) end proc

 

proc (f) options operator, arrow; diff(f, v[x]) end proc

 

proc (f) options operator, arrow; diff(f, v[x, x]) end proc

(4)

d := proc (f) options operator, arrow; diff(f, x)+u[x]*(diff(f, u))+u[x, x]*(diff(f, u[x]))+u[x, x, x]*(diff(f, u[x, x])) end proc

proc (f) options operator, arrow; diff(f, x)+u[x]*(diff(f, u))+u[x, x]*(diff(f, u[x]))+u[x, x, x]*(diff(f, u[x, x])) end proc

(5)

T[2](I)

0

(6)

Why this is giving zero result ?

If I change Ito jet notation then I get result non zero result like:

T[2](phi*(b*u[x, x]+v[x])+psi*(d*v[x, x]+u[x, x, x]))

phi*b

(7)

d(T[2](phi*(b*u[x, x]+v[x])+psi*(d*v[x, x]+u[x, x, x])))

0

(8)

I was expecting this to be "phi[x]*b, "but instead I am getting zero result.``


 

Download operator_for_differentiation.mw

Let us consider 

Student[Precalculus]:-LimitTutor(sqrt(x), x = 2);

One expects a nice illustration of the result sqrt(2). But instead of that one reads "f(x) approaches 1.41 as x approaches 2". This is simply clueless and forms a wrong understanding of limits. It should also be noticed that all the entries (left, 2-sided, and right) produce the same animation. The same issue with other limits I tried, e.g.

Student[Precalculus]:-LimitTutor(sqrt(x), x = 1);

. I think this command should be completely rewritten or excluded from Maple. 

I am working to minimize an objective function concerning a facility location problem (p-median technique).

Can somebody explain how to formulate the constraint equation that involves  1 or 0?

For instance, the constraint x[i,j]  is an element of {0,1}; namely, x[i,j] = 1 if a point is assigned to a facility located at the point j; 0 otherwise.

Thanks in advance.

 

I am attempting to minimize an objective function that is related to a p-median problem (facility location). Can somebody please tell me how to impose a constraint that comprises 0 or 1? For instance, I wish to assign the condition, x[i,j] = 0 or 1; in other words, x[i,j] = 1 if the point i is assigned to facilty located at point j; 0 otherwise.

 

Thanks in advance!

Hi!

I'm currently using Maple 17 and I'm trying to programatically export .eps 3D plots using the following code:

plotsetup(eps, plotoutput = `square_of_x`, plotoptions = `color=rgb , portrait, noborder, height=4in,width=4in, shrinkby=0.1`)

The problem that I'm facing is:

1- The z-axis label is outside of my figure (see uploaded figure). This happens even if I try to save the figure in .png and it seems that the 'shrinkby' option its not working properly;

Could you help me solving this?

Thanks!

 

Hi

I have a set P which is filled with 2D elements e.g.

P:={[1,1],[1,2],[1,3]...}


Later I'm wanting to add a new element e.g. {[1,10]}
At the moment I have

P union {[10, 10]}


If I were to print this I get what I want, but I want to update P.
When I try and do

 P:= P union {[10,10]}

I get an error "Error, illegal use of an object as a name"

What am I doing wrong and how can I solve this? Much appreciated!

I have upload the attachment here. in this problem I want to find the comparison. Please check it and please tell me the correction

 

Ask.mw

AB44.mwAdded these tasks by highlighting object and then choosing
Edit > Create Task

Is there some way to delete a task from my Tasks palette

At some point I created "My second palette" is there a way
to delete individual items from this palette and how are tasks
added to a customized palette.

Any help appreciated, Thanks! Les

AB44.mw

Hello!

Hope everything fine with you. Please check the following program

restart; a := 0; b := 1; Rd := .5; Ra := .2; Nc := .6; e := .2; Nr := .3; H := .9; Digits := 20;
with(LinearAlgebra);
L[0] := 1; L[1] := a+1-x;
M := 4; K := 1;
for n while n <= M do
L[n+1] := expand(-((x-2*n-a-1)*L[n]+(n+a)*L[n-1])/(n+1))
end do; printlevel := 2;
for m from 0 while m < M do
for n to 2^(K-1) do
psi[n, m] := simplify(sqrt(m+1/2.)*2^((1/2)*K)*(eval(L[m], x = 2^K*x-2*n+1)))
end do
end do;
f1 := simplify(sum(sum(c[p, q]*psi[p, q], q = 0 .. M-1), p = 1 .. 2^(K-1)));
u := collect(f1, [x], recursive);

u := -3.5276684147527874541*c[1, 3]*x^3+(4.4721359549995793928*c[1, 2]+21.166010488516724724*c[1, 3])*x^2+(-3.4641016151377545871*c[1, 1]-13.416407864998738178*c[1, 2]-34.394767043839677677*c[1, 3])*x+c[1, 0]+3.4641016151377545871*c[1, 1]+7.8262379212492639373*c[1, 2]+14.992590762699346680*c[1, 3]

f := 1+sum(A[i]*(x^(i+1)-(i+1)*x), i = 1 .. M-2)

f:=1+A[1]*(x^2-2*x)+A[2]*(x^3-3*x)

 

I want to equate the like powers of "x" in f ( mention as red) and u ( mention as red) for any values of M make a system of equations as

Eq[1]:=-3.5276684147527874541*c[1, 3] = A[2];

Eq[2]:=4.4721359549995793928*c[1, 2]+21.166010488516724724*c[1, 3] = A[1];

Eq[3]:=-3.4641016151377545871*c[1, 1]-13.416407864998738178*c[1, 2]-34.394767043839677677*c[1, 3] = -2*A[1]-3*A[2];

Eq[4]:=c[1, 0]+3.4641016151377545871*c[1, 1]+7.8262379212492639373*c[1, 2]+14.992590762699346680*c[1, 3] = 1;

and solve them for any values of A[1] and A[2];

Also attached the program Equate.mw

With my best regards and sincerely.

Muhammad Usman

School of Mathematical Sciences 
Peking University, Beijing, China

For the PDE, I can't seem to plot T' as the y-axis, it gives me the error, "Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct". Anyone knows what seem to be the problem? I am open to all ideas and would appreciate any help:)

fyp3.mw

Hello, 

I have just started using Maple, and it seems very powerful. I am trying to solve trigonometric equations and get all the solutions in a range, but when I use fsolve I only get one solution. 

Is this by design of the function or is there another way to do this? 

 

Tom

Im attempting some very basic calculations where numbers are stored in variables with correct units. However i wish to take a variable to the power 2 without altering it's unit. This is a really easy but strange calculation to make which is why i guess Maple is having trouble with it. 

e.g. I have a variable A with a number 4 stored inside with unit in Meters. I want to take A2 = 16 meters and and not A2 = 16 meters2

Is there a function or way to select the base number without having to write an entire line about it? 

convert(A,'unit_free')^(2)*Unit('m')

can do the trick but i believe there has to be an easier, less complicated, way to achieve this? 

i need to find the graph of exp(v(r)) from 0 to 2e6.

i obtained the graph of v(r) by taking log but how to obtained in exp form

graph_of_exp_form_of_u(r).mw 

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