Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

Hello, i have been trying to use the foldl function as a means of generating data as i do by iterating the seq call in the worksheet attached, but it has not been as straight forward as i thought. Im certain at least someone here already does this for the same reason, so if you know the code, sharing would be much appreciated.
 

F := frac(m[1]^2+m[2]^2+m[3]^2-2*m[1]*m[2]*m[3]/(m[1]*m[2]+m[1]*m[3]+m[2]*m[3]))

`minus`({seq(seq(seq(piecewise(F = 0, [m[1], m[2], m[3]], F <> 0, 0), m[1] = 1 .. 100), m[2] = 1 .. 100), m[3] = 1 .. 100)}, {0})

``


 

Download ASK_FOR_HELP_AGAIN.mw

the final value of an equation is displayed in the form of combination of many values like following

-503.3433660*1[3]^2-2068.935708*1[4]^2-591.1244880*1[4]*1[1]-443.3433660*1[1]^2

I prefer to display it identically just an absolute value like 5.66

please help me how do that

Assume that f:=(s+2)^2*(s-3). How do we get the order of the two factors reversed?
In other words, how do we get g:=(s-3)*(s+2)^2 by manipulating f? As usually,
I don't have f fixed. It is a product of two algebraic factors generated within the Maple program.
Thank you!

mapleatha

with(ArrayTools):
Operator:= proc(F::Array,X::Array) local f_11, f_12, f_21, f_22, f, P, S;

f_11:= diff(F[1],X[1]);

f_12:= diff(F[1],X[2]);

f_21:= diff(F[2],X[1]);

f_22:= diff(F[2],X[2]);

P:=Matrix(2,2,[f_11,f_21,f_12,f_22]);

S:=Matrix(2,1,[diff(G(x,y),x), diff(G(x,y),y)]);

if Size(P,2) = Size(S,1)

then return P.S;

else return

false;

end if;

end proc;

My procedure so far (I think) computes the deformation gradient and returns the transformed gradient. I am now tasked with generalisng this to arbitrary curvilinear orthogonal coordinate systems. I am unsure of how to do this in maple and what packages are available to do this. Would I simply be able to input a new line that would allow these types of coordinates, or would i have to involve a transformation that turns the coordinates into Cartesian? I also ideally want to make it work for N-dimensions, but I am unsure how to do an array with n variables 

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

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