Maple Questions and Posts

How to plot two or more plane equations in maple?...

Asked by: ANANDMUNAGALA 175

October 28 2014

0 2

Good afternoon sir.

I request your kind suggestion to my cited query.

With thanks & Regards

M.Anand

Assistant Professor in Mathematics

SR International Institute of Technology,

Hyderabad, Andhra Pradesh, INDIA.

Could possibly (still) be a bug? Rank of a symboli...

Asked by: casperyc 962

October 27 2014

1 4

I am a research student and I am writing up my thesis. I was reading one of the paper written earlier by authors in 2003.

The authors calculated a symbolic rank of a matrix A, and got 9, using Maple 6.

Then new methods developed in 2012 and proved that the "true" rank should be 8. The later paper that "Most recent versions of Maple have this simplification built in and are able to return a rank of 8.".

I just noticed that in Maple 18.01, this matrix was still evaluted for a symbolic rank 9, if no simplifcaiton was done before using Rank(), see attached.

I didnt explore a lot, but just as a notice. I am a bit concerned as most of my research was trying to deal with exponentials.

Is that something to be fixed in future versions?

Thanks!

Bug.mw

piecewise function simplify / cancel out a variabl...

Asked by: Stephan 45

October 27 2014

1 3

Hello,
Maple does not cancel out a variable.

Why is that?

Is there a way to solve this?

(I pasted my code on the bottom of this message)

Thanks for your help/advice,

Stephan

restart:
M(x):=piecewise(x<=l,1/2*(q*x^2)/(EI)-3/8*(q*l*x)/(EI),l<x,1/2*(q*x^2)/(EI)-13/8*(q*l*x)/(EI)+5/4*(q*l^2)/(EI)):
M(x):=M(x)*(-EI);
# simplify() does not work.....?
M(x):=simplify(%) assuming EI>0;
# Wiht EI cancelled out by hand it schould look like:
M(x):=piecewise(x<=l,1/2*(q*x^2)-3/8*(q*l*x),l<x,1/2*(q*x^2)-13/8*(q*l*x)+5/4*(q*l^2));

Dos and don'ts of Maple programming w.r.t. the phy...

Asked by: NOh 55

October 27 2014

2 5

EDIT 2: Ok, here is what I am trying to do with Maple.

I have the following expression:

with

and

(j times)

Now the above expression should be zero. I get a set of equations in orders of lambda. The H matrices are known. I only need to find the S matrices.

Anyways, the HOffDiag is the sum above and the GetAdvCommutator0 is this nested commutator. And I need this sum evaluated up to order n (n is a given input-number) in lambda. The rest is really not that performance hungry.

EDIT: Ok, it realy seems that this sum of commutators is something that takes Maple forever. I have written a new MWE. Is it possible to speed things up? Maybe using assumptions or so?

>	restart;with(Physics):with(LinearAlgebra): Setup(mathematicalnotation=true):Setup(noncommutativeprefix={M,H,S});

(1)

>

GetAdvCommutator0:=proc(power::integer,order::integer,M)
if power <= 0 then return M fi:
if power = 1 then

return mtaylor(Commutator(M,add(lambda^l*S[l],l=1..order)),lambda, order+1) fi:

return mtaylor(Commutator(GetAdvCommutator0(power-1,order,M),add(lambda^l*S[l],l=1..order)),lambda,order+1):
end proc:

>	HOffDiag:=n->eval(add(1/((2j+1)!)'GetAdvCommutator0'(2j+1,n,H[0]),j=0..iquo(n-1,2)+1)+add(1/((2j+1)!)'GetAdvCommutator0'(2j+1,n,lambdaH[1]),j=0..iquo(n-2,2)+1)+add(1/((2j)!)'GetAdvCommutator0'(2j,n,lambda*H[2]),j=0..iquo(n-1,2)+1)):

>	HOffDiag(3); # still fast

lambda^3*Physics:-Commutator(H[0], S[3])+lambda^2*Physics:-Commutator(H[0], S[2])+lambda*Physics:-Commutator(H[0], S[1])+(1/6)*lambda^3*Physics:-Commutator(Physics:-Commutator(Physics:-Commutator(H[0], S[1]), S[1]), S[1])+lambda^2*Physics:-Commutator(H[1], S[1])+lambda^3*Physics:-Commutator(H[1], S[2])+lambda*H[2]+(1/2)*lambda^3*Physics:-Commutator(Physics:-Commutator(H[2], S[1]), S[1])

(2)

>	HOffDiag(6); # takes a very long time, I didn't even try entering higher numbers

Warning, computation interrupted

>

SumOfCommutators.mw

Hi,

I know this question is really unspecific. However, since I am still new to Maple, and since you don't program with Maple as you would do with c++, I would appreciate some advise. I have written a program in Maple and I don't know if it works correctly. All I know is, it is pretty slow :(.

So if anyone of you could just have a short look at my attached worksheet and could tell me, if I at some point used an obvious "don't", I would greatly appreciate it.

Cheers

NOh

A Maple worksheet

Setup Maple

>	restart;with(Physics):with(LinearAlgebra):Setup(mathematicalnotation=true):Setup(noncommutativeprefix={MA,MB,H,S});

(1.1)

Input parameter

>	H0:=Matrix([[ 0 , 0 , 0 , 0 ], [ 0 , 0 , 0 , 0 ], [ 0 , 0 , U , 0 ], [ 0 , 0 , 0 , U ]]);

H0 := Matrix(4, 4, {(1, 1) = 0, (1, 2) = 0, (1, 3) = 0, (1, 4) = 0, (2, 1) = 0, (2, 2) = 0, (2, 3) = 0, (2, 4) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = U, (3, 4) = 0, (4, 1) = 0, (4, 2) = 0, (4, 3) = 0, (4, 4) = U})

(2.1)

>	H1:=Matrix([[ 0 , 0 , 0 , 0 ], [ 0 , 0 , 0 , 0 ], [ 0 , 0 , 0 , 0 ], [ 0 , 0 , 0 , 0 ]]);

H1 := Matrix(4, 4, {(1, 1) = 0, (1, 2) = 0, (1, 3) = 0, (1, 4) = 0, (2, 1) = 0, (2, 2) = 0, (2, 3) = 0, (2, 4) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 0, (3, 4) = 0, (4, 1) = 0, (4, 2) = 0, (4, 3) = 0, (4, 4) = 0})

(2.2)

>	H2:=Matrix([[ 0 , 0 , -t , -t ], [ 0 , 0 , t , t ], [ -t , t , 0 , 0 ], [ -t , t , 0 , 0 ]]);

H2 := Matrix(4, 4, {(1, 1) = 0, (1, 2) = 0, (1, 3) = -t, (1, 4) = -t, (2, 1) = 0, (2, 2) = 0, (2, 3) = t, (2, 4) = t, (3, 1) = -t, (3, 2) = t, (3, 3) = 0, (3, 4) = 0, (4, 1) = -t, (4, 2) = t, (4, 3) = 0, (4, 4) = 0})

(2.3)

>	orderNumber:= 4 ;

(2.4)

Define all necessary functions

>

GetAdvCommutator0:=proc(power::integer,order::integer)
    local Comm:
    if power <= 0 then return H[0] fi:
    if power = 1 then return add(coeff(Commutator(H[0],add(lambda^l*S[l],l=1..order)),lambda,n)*lambda^n,n=0..order) fi:

    return add(coeff(Commutator(GetAdvCommutator0(power-1,order),add(lambda^l*S[l],l=1..order)),lambda,n)*lambda^n,n=0..order):
end proc:

>

GetAdvCommutator1:=proc(power::integer,order::integer)
    local Comm:
    if power <= 0 then return lambda*H[1] fi:
    if power = 1 then return add(coeff(Commutator(lambda*H[1],add(lambda^l*S[l],l=1..order)),lambda,n)*lambda^n,n=0..order) fi:

    return add(coeff(Commutator(GetAdvCommutator1(power-1,order),add(lambda^l*S[l],l=1..order)),lambda,n)*lambda^n,n=0..order):
end proc:

>

GetAdvCommutator2:=proc(power::integer,order::integer)
    local Comm:
    if power <= 0 then return lambda*H[2] fi:
    if power = 1 then return add(coeff(Commutator(lambda*H[2],add(lambda^l*S[l],l=1..order)),lambda,n)*lambda^n,n=0..order) fi:

    return add(coeff(Commutator(GetAdvCommutator2(power-1,order),add(lambda^l*S[l],l=1..order)),lambda,n)*lambda^n,n=0..order):
end proc:

>	HOffDiag:=n->eval(add(1/((2j+1)!)'GetAdvCommutator0'(2j+1,n),j=0..iquo(n-1,2)+1)+add(1/((2j+1)!)'GetAdvCommutator1'(2j+1,n),j=0..iquo(n-2,2)+1)+add(1/((2j)!)'GetAdvCommutator2'(2*j,n),j=0..iquo(n-1,2)+1)):

>	HOnDiag:=n->eval(add(1/((2j)!)'GetAdvCommutator0'(2j,n),j=0..iquo(n,2)+1)+add(1/((2j)!)'GetAdvCommutator1'(2j,n),j=0..iquo(n-1,2)+1)+add(1/((2j+1)!)'GetAdvCommutator2'(2*j+1,n),j=0..iquo(n-2,2)+1)):

>

computeHBlockDiag:=proc( n::posint,firstBlockWidth::posint, H0::Matrix, H1::Matrix, H2::Matrix )
    local expr, Orders, i, eq, j, eq2, orders,smatrices,rows::posint,evallist,m,l,cols,Hdiag,ff;


    expr:=HOffDiag(n);       # !!!!! this one is one of the slowest parts I think
    Orders:=[$1..n];
    for i from 1 to n do
        eq:=add(coeff(expr,lambda,l)*lambda^l,l=0..i)=0;
        for j from 1 to i-1 do
            eq:=eval(eq,Commutator(H[0],S[j])=Orders[j]);
        od;
        eq:=subs(Commutator(H[0],S[i])=MX,eq);
        eq2:=solve(eq,MX);
        Orders[i]:=eq2;
    od;


    rows,cols:=Dimension(H0);
    smatrices:=[seq(H0,i=1..n)];
    for i from 1 to n do
        evallist:=[`*`=`.`,H[1]=H1,H[2]=H2];
        for j from 1 to i-1 do
            evallist:=[op(evallist),S[j]=smatrices[j]];
        od;
        smatrices[i]:=eval(Orders[i],evallist);
        for m from 1 to firstBlockWidth do
            for l from firstBlockWidth+1 to rows do
                smatrices[i][m,l]:=smatrices[i][m,l]*1/(H0[m][m]-H0[l][l]);
                smatrices[i][l,m]:=smatrices[i][l,m]*1/(H0[m][m]-H0[l][l]);
            od;
        od;
    od;

    expr:=HOnDiag(n);            # !!!!! and this one of course (almost identical to the one above)
    Hdiag:=eval(add(coeff(expr,lambda,l)*lambda^l,l=0..n),lambda=1);
    evallist:= [op(evallist), H[0]=H0,S[n]=smatrices[n]];
    Hdiag:=eval(Hdiag,evallist);


    return Hdiag;
end proc:

>

>	computeHBlockDiag(2,2,H0,H1,H2);

$Matrix(4, 4, {(1, 1) = -2*t^2/U, (1, 2) = 2*t^2/U, (1, 3) = 0, (1, 4) = 0, (2, 1) = 2*t^2/U, (2, 2) = -2*t^2/U, (2, 3) = 0, (2, 4) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = U+2*t^2/U, (3, 4) = 2*t^2/U, (4, 1) = 0, (4, 2) = 0, (4, 3) = 2*t^2/U, (4, 4) = U+2*t^2/U})$

(1)

>	Eigenvalues(%);

$Vector(4, {(1) = 0, (2) = U, (3) = -4*t^2/U, (4) = (U^2+4*t^2)/U})$

(2)

>

Testing

#Fast

>	computeHBlockDiag(2,2,H0,H1,H2);

$Matrix(4, 4, {(1, 1) = -2*t^2/U, (1, 2) = 2*t^2/U, (1, 3) = 0, (1, 4) = 0, (2, 1) = 2*t^2/U, (2, 2) = -2*t^2/U, (2, 3) = 0, (2, 4) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = U+2*t^2/U, (3, 4) = 2*t^2/U, (4, 1) = 0, (4, 2) = 0, (4, 3) = 2*t^2/U, (4, 4) = U+2*t^2/U})$

(4.1)

#Not so fast

>	computeHBlockDiag(4,2,H0,H1,H2);

$Matrix(4, 4, {(1, 1) = -2*t^2/U-(8/3)*t^4/U^3, (1, 2) = 2*t^2/U+(8/3)*t^4/U^3, (1, 3) = 0, (1, 4) = 0, (2, 1) = 2*t^2/U+(8/3)*t^4/U^3, (2, 2) = -2*t^2/U-(8/3)*t^4/U^3, (2, 3) = 0, (2, 4) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = U+2*t^2/U+(8/3)*t^4/U^3, (3, 4) = 2*t^2/U+(8/3)*t^4/U^3, (4, 1) = 0, (4, 2) = 0, (4, 3) = 2*t^2/U+(8/3)*t^4/U^3, (4, 4) = U+2*t^2/U+(8/3)*t^4/U^3})$

(4.2)

#Already pretty slow :(

>	computeHBlockDiag(6,2,H0,H1,H2);

Warning, computation interrupted

>

Download MapleWorksheet.mw

How to correct error of invalid range...

Asked by: emmantop 40

October 27 2014

0 1

How can error of invalid range be corrected FDM.mw

Memory allocation question...

Asked by: Mac Dude 1576

October 27 2014

1 2

I am running a Maple procedure in CLI Maple (mainly because it just provides colored random numbers for other work). When the procedure runs I am getting this kind of output scrolling by:

memory used=10732.9MB, alloc=344.0MB, time=895.85
memory used=10809.2MB, alloc=345.6MB, time=904.26
memory used=10885.5MB, alloc=347.3MB, time=912.67
memory used=10961.8MB, alloc=348.9MB, time=921.27
.
.
.

So I am wondering what "memory used" and "memory allocated" mean here. In "Activity Monitor" (this is Mac OS X) I see that the "memory allocated" values correspond rather closely to the "real memory" usage. No idea what the "memory used" column is. Note that this is a 32 bit process running on a PPS Mac, and it merrily "uses" unlimited amounts of memory that don't exist on the machine and that a 32 bit process should not be able to use (I think Mac OS X limits 32 bit processes to 4 GB). It is clearly not paging as the machine stays perfectly useable.

So, what am I to make of these numbers?

Mac Dude.

Multiple pointplots...

Asked by: jonlg 55

October 26 2014

1 6

Hi there,

I am trying to display multiple pointplots in the same plot. I would like to either distinguish the plots by their color or by the symbol (square, traiangle, circle) at each data-point. May be both, although I ignore whether using symbols at data-points is possible in Maple.

The plot i would like to achieve is this:

Maple says that my points are not in the correct format: MapleSimulation_test6.mw

My data array N has two parameters, and the free variable. The two parameters are also varied over a certain range. For plotting purposes, I would like to have one of the variables fixed, select three parameters for the other variable, and plot all data-points for them.

The resulting data array N seems to be OK, but I am aware that my attempt for plotting multiple arrays may be wrong. May be pointplot is not even the best choice.

Any ideas?

Thank you,

jon

A concho-spiral ...

Asked by: laporte bernard 45

October 26 2014

0 1

A concho-spiral is a curve C that has a parametrization :

$x=a(e)^mu(t)*cos(t)$

y= $a(e)^mu(t)*sin(t)$

$z=b(e)^mu(t)$

$t>=0$

where a, b, $mu$ , are constants.

Show that C lies on the cone a^2*z^2=b^2*(x^2+y^2).
Sketch C for a = b = 4 and $mu$ =-1.
Find the length of C corresponding to the t-interval [0, $infinity$ ].

PDE- Boundary Condition...

Asked by: kjell 40

October 26 2014

1 2

How to include a derivative boundry condition in pde?

diff(u(1,t),x)=0. I got 0=0

Any advice?

How we use Gamma function...

Asked by: oguner 0

October 26 2014

0 0

Hi!

Please find my Maple-worksheet attached below.

How do I solve this problem? I can not drawn it.

I would really appriciate if somebody could help me.

How to plot if variables are given in form of equa...

Asked by: harkirat 5

October 26 2014

0 3

Given this equation: (chi^2*(xi^2-1)^2+1-Omega^2)*(xi^2-Omega^2)-xi^2 = 0

chi^2=1/1200; I want to plot xi vs Omega. Can anyone help me out?

Spring pendulum and second order nonlinear equatio...

Asked by: andhaga 10

October 25 2014

0 1

Hi!

I am quite new to Maple and have a problem I've been struggling with all day.

I have a spring pendulum and have to develop the equation of motion in the y-direction. The pendulum consist of a mass at the end of a elastic, unbendable and massless rod.

Please find my Maple-worksheet attached below.

How do I solve the differential equation 2.9 for y(t)? As far as I can see the problem is that I have to differentiate y(t), which is not designated as a function, with respect to y (?)

I would really appriciate if somebody could help me.

Thank you in advance!

Isolating Expressions...

Asked by: styrr 15

October 25 2014

2 7

Hi there,

I'm doing my first steps with Maple and am a little confused with a problem:
I want to solve something like

and expect the result to be z=-m*a. However I get empty brackets as result.
I tried to dig a little and I find that maple has problems isolating x1+x2+x3+x4

Error, (in isolate) x1*a+x2*a+x3*a+x4*a does not contain x1+x2+x3+x4

When I isolate it myself Maple even tells me they wouldn't be the same

false

I even reduced the problem to x1*a+x2*a and Maple still has problems with that. As this is a really simple problem I strongly assume the issue lies with the user. Can anyone help me there?

Thanks

Adding animations in a word (pdf) document and als...

Asked by: Fairouz 5

October 25 2014

1 4

Dear

I need to add animations in a word(.pdf) docuement or a pwerpoint presentation. I Saved my image as .gif and inserted it in my doc but it is an image (no animation)

Thanks

Fairouz

Second order differential equation...

Asked by: andhaga 10

October 25 2014

2 3

Hi!

I am new to Maple and have a problem I've been struggling with all day.

I have a pendulum and need to find a equation of motion in the y-direction. Please find my code in the picture below.

I can see that my problem starts at Eqy where the differentiation deletes one of the right-hand-side parts because I don't have any function y(t), and Maple thinks y(t) a constant (?)
Can somebody please tell me what I'm doing wrong?

Thank you in advance!

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