x := (1+v/2*cos(u/2))*cos(u);
y := (1+v/2*cos(u/2))*sin(u);
z := v/2*sin(u/2);

I converted this comment into a question since it was unrelated to the question in which it was put.
That way also other MaplePrimes users can have a shot at this new question.
Preben Alsholm
 

Dear Preben Alsholm 

Hi;

Hope you to be healthy and have nice times,

I have another problem and if it doesn't consuming your valuable times, please guide me.

I have some Basis function,say W1(t),W2(t),W3(t),W4(t) which are orthonormal and i want to write a program that can approximate the integral of W(t)=[W1(t),W2(t),W3(t),W4(t)] again by Wi's, in other word
int(W(t')dt',t'=0..t)≈PW(t), where P is knows as integral operational matrix. the following is my attempt and unfortunately has no real solution!!!!

restart:
>              # Definition of 3th B-Spline
>
> piecewise(x>=0 and x<=1,1,0):
> h[1]:=unapply(%,x):
>
>             # Definition of 3th B-Spline
>
> h[2]:=simplify(int(h[1](x-t),t=0..1)):
> hh:=unapply(%,x):
>
>              #Definition of 3th B-Spline

int(hh(x-t),t=0..1): 
> simplify(%):
> N:=unapply(%,x):
>
> J:=1:     # Number of base function is 2^J+2
> phi:=linalg[matrix](2^J+2,1):
> for i from -2 to 2^J-1
> do
> N(2^J*x-i)*h[1](x): #for deleting out side of[0,1]
> simplify(%):
> phi[i+3,1]:=unapply(%,x):
> od:
>
> w[1]:=phi[1,1](x):
> w[1]/sqrt(int(w[1]^2,x=0..1)):
> W[1]:=unapply(%,x):     
>
> for i from 2 to 2^J+2
> do
> kk:=0:
> for j1 from 1 to i-1
> do
> aa[j1]:=int(phi[i,1](x)*w[j1],x=0..1):
> bb[j1]:=int(w[j1]^2,x=0..1):
> kk:=kk+aa[j1]/bb[j1]*w[j1]:
> od:
> w[i]:=simplify(phi[i,1](x)-kk):
> w[i]/sqrt(int(w[i]^2,x=0..1)):
> W[i]:=unapply(%,x):                 #Orthonormality process
>
>
> for j from 1 to 2^J+2 do
> for io from 1 to 2^J+2 do
> f[j]:=int(W[j](s),s=0..x);
> c[io][j]:=int(f[j](x)*W[io](x),x=0..1);
> od;
> od;

Best Wishes

I am new to Maple and I have difficulties simplifying expressions like the following: (exp(a+b)+exp(a+c))*exp(-a).

I would expect to see exp(b)+exp(c) but nothing happens when I use the simplify() function.

I googled but didn't find a solution.

Hi everyone,

At some point in my calculations, I want to do some simple manipulations wiht the use of the «clickable» features in M17.  For the moment, I can see directy how to do it by hand and I do it by copy-paste and use the mous to change it a little bit.  But I just cannot find a simple way to do it by simple click.

You will find in this attach question, the maipulations I want to do.  It is starting from equaiton (7).  Am I at the edge where it is simple by hand than with the features?

 Space_manipulation.mw

Thank you in advance.

--------------------------------------
Mario Lemelin

Maple 17.02 Ubuntu 13.10 - 64 bits
Maple 17 Win 7 -  64 bits
messagerie : mario.lemelin@cgocable.ca
téléphone :  (819) 376-0987

Hello,

I was wondering how (or what is the best way) to write a worksheet in which a change of formula is used when a certain value on the y-axis is reached.

So for example: if there is a mass-spring system with damping in it, I would like to change the value of the damping when the displacement/velocity/acceleration has reached a certain value.
So when I apply a force to the mass-spring system, and the acceleration for example is LOWER than 0.2 m/s^2 I use a value of X % damping, but when the value of the acceleration is HIGER than 0.2 m/s^2 I want to apply Y % damping. So in time the curve will increase (when low damping is used) and the curve will decrease (because high damping is used, because the y-value is higher than 0.2 m/s^2), and so on...

I hope somebody has a 'simple' idea. I know what I want to do, but I don't know how to put this down in a formula which I can write in Maple.

Greetings,
Frank

Hi, i need help. I'm currently working with Taylor and Maclaurin series in Maple. I can easily compute the sum by typing in fx : 

taylor( (e^x,x=0, 5) , and then I get the first 5 numbers of the series. But I would like Maple to write the series as a sum from n =0 to infinity fx.  I can't figure out how to do it. Can it be done? 

Thanks for helping.

Hi,

I want to compute a formula which is too complicated and it contains some variables. So I divide it into several parts. But it always turns out kernel connection has been lost. I looked maplesoft online help system and change the ConnectionType from 0 to 2. But it does not work. So how does this happen and how to solve?

I attach my maple file which appears error.
Thanks a lot!

Regards,

Yan

Dear guys. I want to solve this equation analytically:

diff(Q(t),t)^2 = ln(t)^(b) + b*ln(t)^(b-1)

I think it is impossible. So I assumed that diff(Q(t),t)^2 = diff(P(t),t) and now I can solve it for P(t) easily. I obtained:

P(t) = t*ln(t)^(b)

Now, I want to know that there is anyway to obtain Q(t) using the latter relation and  diff(Q(t),t)^2 = diff(P(t),t) ?

Also I have a function as V(P)=P^(-2). What can I say about the behaviour of V(Q)?

Thanks a lot.

A common spreadsheet computation is to take values in column A in a spreadsheet and multiply by values in column B, e.g. A1*B1=C1; A2*B2=C2.  How do I do this in a Maple matrix?

I am trying to reduce a tensor expression: ω_iω_jU_i,j 

For which I have tried the following

Question 1. Am I using the continuity condition correctly? How do I use this condition correctly? If I change the index for the expression, substitution does not work correctly. 

Question 2. How do I expand the red_eq term in terms of the basis to give out the full expression? 

Question 3. I would like to eventually replace U by (A-Amean) in the current expression. How do I implement this? 

Download term8.mwterm8.mw

I am running into what looks like an interference between the Physics package and linear algebra, specifically when using the . (dot operator) to stand for matrix-vector multiplication:

I have a column vector and a matrix and need to evaluate the product matrix.vector. Usually this works fine and gives me the column vector with the result, just as expected. In this particular case (having with(Physics[Vectors]) at the top of the sheet) I get an error message:

Error, (in Typesetting:-delayDotProduct) invalid input: Physics:-Vectors:-`.` expects its 1st argument, a, to be of type Or({algebraic, procedure}, `=`), but received Matrix(3, 3, ...)

The Matrix it complains about is in fact the one I am sending it. It was created from a Physics:-Vectors object using the Component function (so it should be a regular Maple Matrix). In fact, the Matrix is the result of a LinearAlgebra:-MatrixInverse operation.

The weird thing is: This works when I am using 1-d input in Worksheet mode (which I am usually doing). In this case I am creating a sheet in Document mode using 2-d input as it is a sheet I will use in some teaching activity later this year, so I want it to look more polished. I can replace the dot with the relevant MatrixVectorMultiply function and it will work, but that is a kludge I don't think  should be necessary.

Anybody ever seen this? BTW, I am doing this on Maple 15 using the version of Physics that came with it.

Thanks,

Mac Dude

with(Groebner):
with(LinearAlgebra):
T := lexdeg([x1,x2,x3],[e1,e2,e3]);
hello1 := proc(xx,yy)
return MatrixMatrixMultiply(xx,yy);
end proc:
hello2 := proc(xx,yy)
return xx+yy- MatrixMatrixMultiply(xx,yy);
end proc:
m1 := Matrix(3, 3, {(1, 1) = -.737663975994461+0.*I, (1, 2) = -.588973463383001+0.*I, (1, 3) = .330094104689369+0.*I, (2, 1) = -.588012653178741+0.*I, (2, 2) = .320157823261769+0.*I, (2, 3) = -.742792089286083+0.*I, (3, 1) = -.331802619371428+0.*I, (3, 2) = .742030476217061+0.*I, (3, 3) = .582492741708719+0.*I});
m2 := Matrix(3, 3, {(1, 1) = -.742269137704830+0.*I, (1, 2) = -.590598631673326+0.*I, (1, 3) = .316590877121441+0.*I, (2, 1) = -.593533033362923+0.*I, (2, 2) = .360143915024171+0.*I, (2, 3) = -.719732518911068+0.*I, (3, 1) = -.311054762892221+0.*I, (3, 2) = .722142379823161+0.*I, (3, 3) = .617863510611693+0.*I});
m3 := Matrix(3, 3, {(1, 1) = -.751491355856820+0.*I, (1, 2) = -.574908634018322+0.*I, (1, 3) = .323636840615627+0.*I, (2, 1) = -.575794245520782+0.*I, (2, 2) = .332066412772496+0.*I, (2, 3) = -.747123071744916+0.*I, (3, 1) = -.322058579916187+0.*I, (3, 2) = .747804760642505+0.*I, (3, 3) = .580574121936877+0.*I});
AA := hello1(m1, m2);
BB := hello2(m1, m2);
GB := Basis([e1- AA,e2- BB],T):
NormalForm(m3, GB, T);

A := `<|>`(`<,>`(1, 2,3), `<,>`(2, 3, 0), `<,>`(2, 0, 0));
v, EigenVector1:= Eigenvectors(A);
FirstEigenValue := v[1];
SecondEigenValue:= v[2];
ThirdEigenValue:= v[3];
NewMatrix3 := Matrix([[x1, x2, x3],
[x2, x3,0],
[x2,0 , 0]]);
Hello :=solve([MatrixMatrixMultiply(NewMatrix3,Matrix([[EigenVector1[1][1]],[ EigenVector1[2][1]],[ EigenVector1[3][1]]]))[1][1] = FirstEigenValue* Matrix([[EigenVector1[1][1]],[ TestPredictedProj1[2][1]],[ EigenVector1[3][1]]])[1][1],
MatrixMatrixMultiply(NewMatrix3,Matrix([[EigenVector1[1][2]],[ EigenVector1[2][2]],[ EigenVector1[3][2]]]))[2][1] = SecondEigenValue* Matrix([[EigenVector1[1][2]],[ EigenVector1[2][2]],[ EigenVector1[3][2]]])[1][1],
MatrixMatrixMultiply(NewMatrix3,Matrix([[EigenVector1[1][3]],[ EigenVector1[2][3]],[ EigenVector1[3][3]]]))[3][1] = ThirdEigenValue* Matrix([[EigenVector1[1][3]],[ EigenVector1[2][3]],[ EigenVector1[3][3]]])[1][1]
], [x1,x2,x3]);

i am confused at right hand side

 FirstEigenValue* Matrix([[EigenVector1[1][1]],[ TestPredictedProj1[2][1]],[ EigenVector1[3][1]]])[1][1]

there are three values, i do not know use which value in each equation

actually, my expectation is simple, just find back the original matrix from eigenvector and eigenvalue