Good day.

Reading through the Fuzzy C-Means routine (attached) written by the one-and-only Carl Love, I was wondering if anybody can tell me how to specify which points in the data belong most strongly to the assigned cluster. 

In the attached routine, there are 2 cases considered; two and three clusters. 

It would be interesting to obtain a list of all points that are assigned to each respective cluster.

Thanks for reading!

Fuzzy_clusters.mw

I have question how start histogram from 0? I have vector with probablity which start from 0.

I generate samples from my probablity:

pr=values of probablity

X:=RandomVariable(ProbablityTable(pr)):

A=Sample(X,1000):

Q=Histogram(A, binwidth=1,range=0..10):

...

I try to use bindwidth=-1 but it's impossible. 

How start histogram from 0 for vectors in maple15?

Hello I am trying to compute the following expression;

(x^2r+y^2+z^2) gamma^{0} partial_{x} (-xy(1-r)) gamma^{2} partial_{y} \Psi

in which r = sqrt(1-K(x^2+y^2+z^2)), K is a constant, the gamma's are the Dirac gamma matrices and \Psi is the wave function. Essentially I would like to have partial_{x} operate on the expression to the right of it and apply product rule where there will be three terms with the last one being partia_{x} partial_{y} \Psi where it evaluates on everything expect the partial and the wavefunction, combining into the term partial_{x} partial_{y} \Psi, and if the partials are the same they combine into a single second order derivative with respect to the given variable. I have done this calculation by hand but seeing that there is an extensive amount of terms I would like to automate it using Maple. I have tried using the D() calling sequence but it doesn't quite give me what I am looking for. Is there anything documentation which will give me what I am looking for?

Hello

I have used Groebner[UnivariatePolynomial] extensively on my procedures and I wonder whether there is an improvement in speed and memory use in Maple 2020 in relation to the version I am currently using, that is, Maple 2017.  

Many thanks.

Ed

restart;
with(LinearAlgebra):
with(VariationalCalculus):
# Energie cinetique/potentiel
T := 0.5*m*(diff(r(t),t)^2+r(t)^2*diff(theta(t),t)^2)+(1/6)*m[0]*l^2*diff(theta(t),t)^2;
Ve := 0.5*k*(r(t)-r[o])^2;
Vg := -m*g*r(t)*cos(theta(t)) - 0.5*m[o]*g*l*cos(theta(t));
# Lagrangien
L := T - (Ve + Vg);
E := EulerLagrange(L,t,[theta(t),r(t)]);
EQ1:=simplify(E[1]);
EQ2:=simplify(E[2]);
dsolve({EQ1,EQ2,D(theta)(0)=0,D(r)(0)=0,theta(0)=0,r(0)=10},{r(t),theta(t)});
dsolve({EQ1,EQ2},{r(t),theta(t)});

Hello ! 

I'm currently trying to learn some advanced mechanics with the Lagrangian method. I'm ok with the physics part. I can solve small problems by hand but when I try it on maple, it won't work.

The equations I'm using have no mistakes, I'm following a book step by step. 

What I'm stuck with is to get a formula of theta and r that are only function of time (t) to then be able to plot it. And I need dsolve to work to get that.

Got a problem related to values written to a library. One of the values somehow gets lost, and I wonder if I did the definition correct.

The specific problem is, that I have defined a table with an index. The value of mytable["hello"] seems to be missing when reading the library.

TestLibrary.mw

Hello,

I am trying to solve the 6 coupled differential equation. The 6 equations have 6 functions to be solved for with 12 boundary condition. I know for a fact that the solution to this equation exists in the form of nice polynomials.

I tried to solve without constraint. The maple solves the equations for only 4 functions and other 2 have value in form of integrals.

With the equations contraints the maple gets disconnected from the kernel after 4-5 hours of evluating.

Any idea to solves this issue ?? I have attached the workbook.

Thanks.

Mota

     Dear Sir/Madam,

I have faced a problem while using Maple 18. The  warning is the following

Warning, The use of global variables in numerical ODE problems is deprecated, and will be removed in a future release. Use the 'parameters' argument instead (see ?dsolve,numeric,parameters)

This is the code

restart;
with(plots);
beta := 0.2e-1; delta := .5; PI := 10000; mu := 0.16e-1; tau := 0.3e-1; rho := 0.4e-1; epsilon := 0.4e-1; sigma[1] := 0.1e-2; sigma[2] := 0.2e-2; eta := 0.6e-1;
sys := {diff(e(t), t) = beta*(sigma[1]*i(t)+sigma[2]*e(t))*s(t)-(delta+mu)*e(t), diff(i(t), t) = tau*delta*e(t)-(epsilon+rho+mu)*i*t, diff(r(t), t) = (1-tau)*delta*e(t)+epsilon*i(t)-(mu+eta)*r(t), diff(s(t), t) = PI+eta*r(t)-beta*(sigma[1]*i(t)+sigma[2]*e(t))*s(t)-mu*s(t), e(0) = 148, i(0) = 74, r(0) = 14, s(0) = 4110};
p1 := dsolve(sys, numeric, method = rkf45, output = procedurelist);
Warning, The use of global variables in numerical ODE problems is deprecated, and will be removed in a future release. Use the 'parameters' argument instead (see ?dsolve,numeric,parameters)
Error, (in dsolve/numeric) i(t) and i cannot both appear in the given ODE
p2o := odeplot(p1, [t, s(t)], 0 .. 4, numpoints = 100, labels = ["Time (months)", " Infected  "], labeldirections = [horizontal, vertical], style = line, color = red, axes = boxed);
Error, (in plots/odeplot) input is not a valid dsolve/numeric solution

plots[display](p2o);

Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/nnn.mw .

Download nnn.mw

Hello all,   Hope everyone is safe

Does anyone know why a vector of floats as the variable for SignalPlot returnes the error:

Error:  (in SignalProcessing:-SignalPlot) unable to store  ' " " ' when datatype = float[8] 

Accel3  is vector variable reporting back as  "57850 element Vector[column]"

 SampleRate:=50000.0

When called by SignalPlot?   

SignalPlot(Accel3, samplerate = SampleRate)

I have successfully used SignalPlot without a problem before.

Regards,

Bill

Hello everyone. I want to know how I can extract terms with the lowest sum of the degree of x and of y in a multivariate polynomial (in x and y)?

For instance, if I've f(x) = 100x^2y^2 + 35x^2y + 45y, I want an output of 45y.

On the other hand, if I've g(x) = 13x^2y^2 + xy^2 + 2yx^2, I want an output of xy^2 + yx^2.

Maple Tutors allow for copying of MathML but I need LaTeX of it. Any help please?

If we have an equation for the generalized Bloch sphere i.e.,

\partial_{t}(u^{2} + v^{2} + w^{2}) = 0,

where u, v and w are functions of x and t and the initial conditions u=v=0, w=-1. Then how to plot this equation on maple?

This is an interesting exercise in setting up triple integrals in cylindrical and spherical coordinates to obtain a formula that is immediate without any calculation using the theorem of Pappus. The cylindrical integral is easy. The spherical one is hard, but Maple gives me the result off by a factor of minus one half for generic values of the two radii, but the correct result for concrete numbers! I cannot figure out what I am doing wrong. Any ideas?
http://www34.homepage.villanova.edu/robert.jantzen/courses/mat2500/handouts/torusvolume.mw

Hi,

I have an expression (functionx) that I want to convert it to a series of x with different powers. My only issue is that I cannot accept negative powers. For example, If I had functionx = cos(x) I want to convert it to 1 - 1/2*x^2 + 1/24*x^4, which can be done with a Taylor expansion.

Here the functionx is a bit complicated if I use Tylor expansion that means I only consider the approximation for a small range of x. Is there any other approximation I could use to convert functionx to a new function that has x to the power of positive values?

restart;
functionx:=(0.007334702136*x + 2.418028262*10^231*x^57 + 1.182475218*10^223*x^55 + 5.780663993*10^214*x^53 + 2.824838912*10^206*x^51 + 6.735888408*10^189*x^47 + 1.379783148*10^198*x^49 + 3.286285701*10^181*x^45 + 7.803772225*10^164*x^41 + 1.602116861*10^173*x^43 + 1.845464073*10^148*x^37 + 3.797245890*10^156*x^39 + 4.338988887*10^131*x^33 + 8.956080140*10^139*x^35 + 2.097852265*10^123*x^31 + 4.865844768*10^106*x^27 + 1.011819388*10^115*x^29 + 2.331704338*10^98*x^25 + 1.112530729*10^90*x^23 + 2.489476842*10^73*x^19 + 5.280116219*10^81*x^21 + 5.385068408*10^56*x^15 + 1.164024492*10^65*x^17 + 4.797076312*10^31*x^9 + 1.099976521*10^40*x^11 + 2.456776729*10^48*x^13 + 7.927675416*10^14*x^5 + 2.012154161*10^23*x^7 + 2.781719840*10^6*x^3)/(0.003667351068*x^2 + 695429.9599*x^4 + 4.737736934*10^(-11) + 4.169014245*10^229*x^58 + 1.070493332*10^213*x^54 + 2.111562890*10^221*x^56 + 5.432382523*10^204*x^52 + 1.403310085*10^188*x^48 + 2.759566295*10^196*x^50 + 7.144099350*10^179*x^46 + 1.858041006*10^163*x^42 + 3.641174684*10^171*x^44 + 9.493114726*10^154*x^40 + 4.856484403*10^146*x^38 + 1.276173202*10^130*x^34 + 2.487800039*10^138*x^36 + 6.555788327*10^121*x^32 + 3.372731292*10^113*x^30 + 1.737801703*10^105*x^28 + 8.968093608*10^96*x^26 + 4.635544704*10^88*x^24 + 1.244738421*10^72*x^20 + 2.400052827*10^80*x^22 + 9.166471012*10^38*x^12 + 1.754840521*10^47*x^14 + 3.365667755*10^55*x^16 + 6.466802735*10^63*x^18 + 1.321279236*10^14*x^6 + 2.515192701*10^22*x^8 + 4.797076312*10^30*x^10)^2:
plot(functionx, x=-0.001..0.001):

The reason that I look for an expression for functionx is:

I need to replace x with a series of sin and cos functions and then find specific coefficients that have that sin or cos. In the current form Maple cannot find the coefficients of sin and cos.

I hope it is clear. I have attached the main code.Expansion.mw

Regards,

Baharm31