Do Hilbert series function classify all or only some type or some form of ideals?

I've been instructed to create an animation showing the changing plots of a single square waveform using 5,10,20,40,80,160,320, and 640 terms in my Fourier series. This is my code right now:

with (plots):L := [seq(2^i, i = 0 .. 6)];

[1, 2, 4, 8, 16, 32, 64]

animate( plot, [2/((2*n-1)*Pi))*sin((2*n-1)*Pi*x], n=L);Error, `)` unexpected

It doesn't work. Can anyone explain what I'm doing wrong, or how to solve my question?

Hallo

Use DrawSubgroupLattice for G:=Symm(4) then

A:=DerivedSeries(G);

Drawing this Series there are red marked 30,29,21,1.

But why not 8 or 9 or 10 which are between 21 and 1?

Best regards

Kurt Ewald

How to create a long progression in maple (up to 100 000 000 000), where a member is a previous one plus a certain number. For example: 25, 50, 75, 100... and then divide the whole series (all the members) by a number. What command should one use?

I want to do a step by step computation for obtaining the coefficents of the sine fourier series expansion of f(x)=x over the interval [-L,L]. The steps are as follows:1-write the fourier expansion as: Sum(A[n]*sin(n*pi*x/L),n=1..N)2-multiply the series by: sin(m*pi*x/L)3-integrate the series over the interval [-L,L]3-using the orthogonality properties of the set {sin(n*pi*x/L} compute the A[n].I can't do these steps since I have problem with the series manipulations in maple!Can any one suggest a way from begining to the end?Thanks. :)Below shows what I did in Maple 17.

Help Please! :)As it is seen in the picture, I can not integrate the power series. In contrast, the differentiation works!what is wrong?

I have a table of data arranged in the following columns: Year, Jan, Feb, Mar,..,Dec in Excel or csv

I would like to import this data into a time series in Maple so I can plot the result.

What is the simplest way of doing this?

Hi

I need you to help me in writting procedure with input "r" ( order of derivative) and some coefficients seq(alpha[i],i=1..N). My code work very well, need only put all the element in procedure with output The Taylor series obtained in last line of my code and the order of error. I want the procedure return the coefficients beta used in the series and the order of Error and the coefficients beta[i]

May thinks.

Second_Question.mw

I will not modify my previous question: only I add this remark. I tried to write these lines of procedure. Add_display.mwI need only to add( if the procedure is true) these lines in my procedure. These lines gives the degree of error computed in the code, but when I put these lines in the codes, there is an error. Thanks for your help.

Degree := degree(Error,stepsize); if (showorder) then: print(cat(`This stencil is of order `,Degree)); fi: if (showerror) then: print(cat(`This leading order term in the error is `,Error)); fi: convert(D[r$n](f)(vars) = stencil,diff);

Hi all.

Assume that we have partitioned [0,a], into N equidistant subintervals and in each subinterval we have M sets of poly nomials of the following form:

where T_{m}(t)=t^{m}( namely Taylor Series) and t_{f} is a(final point)for Example with N=4, M=3 we have:

now we want to approximate a function, asy f(t), in this interval with following form:

How can we do this with maple????

how can we find the c_{i}'s?????

Thanks a lotMahmood Dadkhah

Ph.D Candidate

Applied Mathematics Department

Hi,

Maybe someone can give me a nice answer without Maple.

I am given a fourier series: ln|cosx|=Co - sum( (-1)^k/k * cos2kx,k=1..infinity) and am asked what this tells me about the chevychev series for ln(u).

Thanks

I open a discussion about convolution and Fourier coefficients in Fourier series.

I have a function defined by f(x)=0 if x in [-Pi,0[ and 1 if x in [0,Pi[, of course f 2*Pi periodic function.

My goal is compare the Fourier coefficients of f*f ( * convolution ) and The Fourier Coefficient of f.

Thanks for your help.

Maybe a good question.

Write f(x)=ln(abs(cos(x))) with infinite serie cosine(2*n*x).

Thank for your remark.

Hello,

I have this expression on image below and I would like to do multi taylor in these variables. The maple says that the expansion is not possible to do. Does somebody know where the problem could be ? Thank you very much for help.

Equation:

Taylor series:

how maple calculate exp(x) with e.g. 100000 decimal numbers

a divsion of the series x^k/k! with e.g. 1/25000!/25001 lasts longer than the exp(1.xx) calculation

is there a faster way to calculate exp(x) than with the x^k/k! series

thanks

Dear All;

Happy, to discuss with you these lines, and thank you to help me.

My goal is:

ode := D(y)(x) = f(x,y(x)); In this expression, is assumed to be a known function of the independant variable x and the function that we are trying to solve for y(x). The simplest numerical stencils to solve this equation will give us an approximation to y at some point x = X + h given some knowledge of y at x = X. All of these stencils are based on the Taylor series approximation for y(x) about x = X to linear order:eq1 := y(x) = series(y(x),x=X,3); eq2 := h = x - X;eq3 := subs(isolate(eq2,x),eq1); Now, we can remove the first derivative of y by making use of the differential equation:eq4 := subs(x=X,ode);eq5 := subs(eq4,eq3);

Now we must compute the same for y(x-h) and then make. How can I do this please

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