Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

Hello,

I am facing a problem, I have a system of nonlinear inequalities that has solutions for the sake of the example:
xy-1<0, x>0, y >= 1
Here we can just say that for any 1>x>0, the y for which it is satisfied are 1/x > y >=1, and in that sense it gives a depiction of the set of all (x,y) that satisfies the system. But I would rather like to know one particular solution say x=1/2, y=1 for example. Is there a way to generate a particular solution of such a system without having to write a procedure that tests all x,y with three digits after the comma within a given range?

Thank you

I occasionally need single left quotes placed around the value of number.
Let's say x=3. Is there a command on x that will make x=`3`?
Thank you!

mapleatha

Here's something neat to be done in Maple. 
This anaglyph or stereo image uses the red green glasses to make the model appear more 3 dimensional.  The static-non-stereo image of the animated plot below is done in maple by plot3d(sin(x*y)^2,x=-2..2,y=-2..2,scaling=constrained)

Anyone?

 

Why is this happening?

Thank you!
mapleatha

how to find infinitisimals of system of differential equations?

i have system of two dependent variables and two independent variables.

[-(diff(psi[2], x))+diff(psi[1], t, t)-2*n*(psi[1]^2+psi[2]^2)*psi[1]-beta*(diff(psi[1], x, t)) = 0,

diff(psi[1], x)+diff(psi[2], t, t)-2*n*(psi[1]^2+psi[2]^2)*psi[2]-beta*(diff(psi[2], x, t)) = 0]

Here is a possible situation tha appears very often in presentations:

How do I add a colon ":" after "ss3" in the second red line? And, while we are at it, how do I add the word "and" between ss2 and ss3?
Thank you all so much for your continuous and inexhaustible help!

mapleatha

Question:I've defined wave, but it's after that it gets sticky. This is my attempt:As you can see, not very fruitful. I have tried wave(x=-infinity..infinity, t=-infinity, infinity) which returns an error. 

When i sub in wave(1,1) i get an answer, or any other number for that matter, but I'm not sure how to actually aswer this question. 

Any and all help appreciated

Thank you

Question: You will observe that the two curves intersect at one or more places in the displayed region. Use fsolve to find the (x; y) coordinates of all the points of intersection in this region.

In theory this question has a very simple answer, but i am struggling no end finding it. 

P1 := y^2 = x^3+x^2

P2 := y = 2*x+1

This is what the graph looks like when plotted, and as we have already got the two equasions assigned as H and J, i just type in fsolve({P1,P2})? 

Apparently not, as this returns {x = 4.048917340, y = 9.097834679}, which is correct, but is only one of three points of intersection, and just so happens to be the one not shown in my plot (although it is still a valid point of intersection) and i need the ones within the region i have set for the graph (x=-1..2 and y=-1..1).

How do i get maple to show me the two points of intersection i need using the fsolve command? 

I've tried rearranging the equasions for y, rearranging for x, adding an option to solve for x [fsolve({P1,P2},x) but this returned an error] and am pretty stumped. For something so seemingly simple i dont really know where to turn.

Thank you :)

i have a matrix m[10,10] with some values, i want to PointPlot every rows with Explore command , here is my code:

Explore(PointPlot(m[a, 1 .. 10], [.1, .2, .3, .4, .5, .6, .7, .8, .9, 1]), parameters = [a = 1 .. 10]) 

but it does'nt work! how can i fix it?

thank you in advance

Hello!

 

I have the following situation that I'm having trouble with . I am a total beginner in Maple, btw.

I have a long equation, involving a variable (x) , several other variables, and a function of x, F(x). A priory, this function is unspecified (its a probability density function, that may depend on whichever distribution it follows). I would like to have Maple operate on this function as if its a function of x, but without specifying. For example, lets say I have

x + yF(x)=0

I would like to derive it and have Maple return me

1 + yF'(x)=0

Is this possible?

 

Thanks!


 

NULL

restart; with(LinearAlgebra)

kernelopts(version); interface(version)

`Maple 2017.3, X86 64 WINDOWS, Sep 27 2017, Build ID 1265877`

 

`Standard Worksheet Interface, Maple 2017.3, Windows 10, September 27 2017 Build ID 1265877`

(1)



The following equation contains so many regularities, that it is tantalizing to find a compact matrix formulation.
I found a matrix expression, but it seems unnecessairy complex. Is there a Maple procedure that can help me to find a more concise matrix formulation?

eq1 := i2*i3*i4*(i2+i3+i4)+i1*i3*i4*(i1+i3+i4)+i1*i2*i4*(i1+i2+i4)+i1*i2*i3*(i1+i2+i3)

i2*i3*i4*(i2+i3+i4)+i1*i3*i4*(i1+i3+i4)+i1*i2*i4*(i1+i2+i4)+i1*i2*i3*(i1+i2+i3)

(2)

expand(eq1)

i1^2*i2*i3+i1^2*i2*i4+i1^2*i3*i4+i1*i2^2*i3+i1*i2^2*i4+i1*i2*i3^2+i1*i2*i4^2+i1*i3^2*i4+i1*i3*i4^2+i2^2*i3*i4+i2*i3^2*i4+i2*i3*i4^2

(3)

V := Matrix(4, 1, [i1, i2, i3, i4])

Matrix(%id = 18446745919887783806)

(4)

one := Matrix(4, 1, 1)

Matrix(%id = 18446745919887784886)

(5)

This matrix expression works, but seems overly complex. Using Maple, is there a way to simplify it?

Trace(MatrixScalarMultiply(one^%T.(V.one^%T-DiagonalMatrix(Diagonal(V.one^%T))).convert(Diagonal(Adjoint(V.one^%T-DiagonalMatrix(Diagonal(V.one^%T)))), Matrix), 1/2))-eq1

0

(6)

Alternatively, but also not very simple:

Trace(DiagonalMatrix(Diagonal(MatrixScalarMultiply(1/(V.one^%T-DiagonalMatrix(Diagonal(V.one^%T))), (1/2)*Determinant(V.one^%T-DiagonalMatrix(Diagonal(V.one^%T)))))).(KroneckerProduct(V^%T.one, IdentityMatrix(4))-DiagonalMatrix(V)))-eq1

0

(7)

Obviously, this does not help:

A, B := LinearAlgebra:-GenerateMatrix([eq1], [x])

Matrix(%id = 18446745919887762006), Vector[column](%id = 18446745919887761886)

(8)

NULL


 

Download Matrix_formulation.mw

When i input: i get returned.and with this i have no idea what im supposed to do. I dont understand what it means, how to correct it or how to actually answer the question using the information. 

This is what i am returned with when i try to input a sequence using my previous result.

 

Could someone please put me on the right tracks and help me with this problem?

 

Thank you

Hi, 

I'm new to maple and have a problem when using the dsolve in a for loop. I get the error message Error, (in dsolve/numeric/process_input) the independent variable (t in phi(t)) cannot be a procedure name and I dont now why. 

The code design is 

for k to kk do
vars := x(t), y(t), phi(t);
ic := x(0) = xx, y(0) = yy, phi(0) = zz;
sys := diff(x(t), t) = y(t),
diff(y(t), t) = -2*gamma*y(t)-alpha*x(t)-beta*x(t)^3+F*cos(phi(t)),
diff(phi(t), t) = 1;
sol := dsolve({ic, sys}, {vars}, numeric, output = listprocedure, numeric = -1);
assign(sol);
x := x(t);
y := y(t);
phi := phi(t);
numpts := 50;
pts := seq([x(2*Pi*i), y(2*Pi*i)], i = 1 .. numpts);
plt(k) := plot([pts], view = [-1.5 .. 1.5, -.5 .. 1], color = black);
xx := 'xx'; yy := 'yy'; zz := 'zz';
xx := x(2*Pi*numpts);
yy := y(2*Pi*numpts);
zz := phi(2*Pi*numpts);
unassign(x, y, phi);
c := x(0) = xx, y(0) = yy, phi(0) = zz
end do

Let's say you have a m times n matrix and you want to ask Maple to computes all of its p minors (p smaller than minimum of m and n). Is there any prepared command for it at Maple? I can write a procedure myself, I just want to know if there is a command in Maple or not. The minor command in LinearAlgebra package is just computing determinant of a square matrix after removing a given row and a given column which is not what I'm talking about.

Hi all,

 

I am totally stuck in the question:

I can do it for seperate cases, but how to do it, with somekind of sequence

 

Integral for x= 0 to infinity of [2 sin(x/2)/x] ^ 2n 

this has to be equal to:

2n* pi (sum of [(-1)^j * (n-j)^(2n-1)] / [j! * (2n-j)!]

I showed it for j=0 and n=1

But how to do it for n =1,2,3 and 4

 

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