x/2 seems completely wrong as a CDF. In other cases Maple correctly writes the CDF as a piecewise-constant function clipped to 0..1:

with(Statistics):

dd := Distribution(ProbabilityFunction = 1/2, Support = 1 .. 2);

PDF(dd, x); # OK
                   (1/2)*Dirac(x-1)+(1/2)*Dirac(x-2)

CDF(dd, x);
                                (1/2)*x

Also CDF seems to have issues with DiscreteValueMap specified using a list, a table or piecewise():

dd := Distribution(ProbabilityFunction = 1/2, DiscreteValueMap = (n -> [1, 2][n]), Support = 1 .. 2);

PDF(dd, x); # OK
                    (1/2)*Dirac(x-1)+(1/2)*Dirac(x-2)

CDF(dd, x); # indeterminate
  int((1/2)*Dirac(0)*Dirac(_t-1)+(1/2)*Dirac(0)*Dirac(_t-2), _t = -infinity .. x)

with(Statistics):

CDF(Binomial(2, 1/2), x); # wrong
               piecewise(x < 0, 0, 2 <= x, 1, 1)

CDF(Binomial(2, p), x); # also wrong
     piecewise(x < 0, 0, 2 <= x, 1, p = 0, 1, p = 1, 0, 1)

Maple can actually generate PDFs for discrete distributions:

bpdf := unapply(PDF(Binomial(2, 1/2), x), x);
          x -> (1/4)*Dirac(x)+(1/2)*Dirac(x-1)+(1/4)*Dirac(x-2)

int(bpdf(t), t = -infinity .. x); # correct CDF
         (1/4)*Heaviside(x)+(1/2)*Heaviside(x-1)+(1/4)*Heaviside(x-2)

But then functions of random variables do not seem to work :

bdist := Distribution(PDF = bpdf, Support = -infinity .. infinity);

CDF(bdist, x); # OK
           piecewise(x < 0, 0, x = 0, undefined, x < 1, 1/4, x = 1, undefined, x < 2, 3/4, x = 2,
           undefined, 2 < x, 1)

CDF(add(RandomVariable(bdist), i = 1 .. 2), x); # indeterminate
          int((1/16)*Dirac(_t)^2+(1/4)*Dirac(0)*Dirac(_t-1)+(3/8)*Dirac(0)*Dirac(_t-2)+(1/4)*Dirac(0)*
          Dirac(_t-3)+(1/16)*Dirac(0)*Dirac(_t-4), _t = -infinity .. x)

It's a bit disappointing that Maple generates PDFs in terms of the delta function but doesn't support them properly, because that could be an easy and natural way to define mixed distributions.

There was a spam button that allowed a user with enough points to delete spam. It appears to have gone away, now we can just flag stuff as spam.

i have system of ode, which has three unkonwn function,x(t),y(t),z(t), and i need differentiation of theses function with respect to " t " , how can i use numeric solution to have these parameters? tnx for help in advance

 

Download question.mw

Hello everyone!

I have several problems with listcontplot.

First of all, when I plot spectrogram of my test signal I get correct result. I use colorscheme = ["#00007F", "Blue", "#007FFF", "Aqua", "#7FFF7F", "Yellow", "coral", "Red"] as colormap. But I can't understand how to set option coloring in listcontplot correctly to obtain same result, because coloring works as Gradient from ColorTools.

Secondly, I use subs to change plot ranges. My apprach consist in several steps:

plot( listdensityplot(...) );
temp := plottools:-getdata(%, 'rangesonly');
subs(temp[1] = NewX0 .. NewX1, temp[2] = NewY0 .. NewY1, listdensityplot(...) );

Is it possible to simplify this solution?

P.S. My test programm with test data.

Maple_s_test.mw

Test.txt

My Spectrograms:

Hi,

With exam period coming closer and closer I am getting worried that this (see picture) might happen again with my document. The document is completed "deconstructed" all the way through, it contains it unreadable form when exported as PDF and when opened from another device.

Does anybody know what has gone wrong and what to do?

Thankyou,

Emma

Apologies for possible double post, it seemingly locked up upon trying to post the first time. 

So before I get as far as to ask for how to get a certain PDE system solved and plotted, I tried to fiddle a little bit around with linear algebra. 

• First, the file SystemGoesWrong.mw . I have issues with declaring (same result if I remove the with(VectorCalculus)); as far as I can see, EQ0 and EQ00 should be the same, except that I have summed the vector in one of them. And the first that "works", is wrong: it returns a scaling of a vector. How come?
• But then I copy everything from the heading and down into a worksheet where I was already fighting some linear algebra things (can someone please explain?): SystemDeclaresBut.mw 
  Then EQ0 and EQ00 declare just fine! What is the issue?
• How do I get Maple to list the equations in "compact" form with vector-valued functions so that I can read and debug?  The actual PDE system I want to solve (numerically, of course), looks as follows: DE4Maple.pdf 
  That was also the reason why I tried to declare procedures (coordinate-wise maximum ...), but I guess that questions on how to extract a solution and plot it in a particular way will be its own posting after I have learned how to declare it.

The contents of the first file:

Download SystemGoesWrong.mw

... and of the second:

Download SystemDeclaresBut.mw

Suppose that I make a simple plot, of a function f(x), such as  p1 := plot( 2*x+1,x=0..4,numpoints=9);

Then logically, the plot p1 contains a table with values (x, f(x)) which are plotted.

HOW can I extract that table of values from the plot p1, and write it to a data file (simple text file), so that I can process the data elsewhere (for example, for making a professional graph from them).

I had scripts who did this up to Maple 13 (or Maple V release 13, if that is the politically correct version), but they do not work anymore with more recent versions.

Many thanks !!

Malte.

first question:

Define a two point distribution:
f1(x):=piecewise(x = 0, 0.3, x = 0.1, 0.7, 0)

Dist1 := Distribution(PDF = f1)

R1 := RandomVariable(Dist1)

Mean(R1)

Why Mean(R1) gives 0? should be 0.07...

If I managed to define antother discrete point distribution say R2. Can I define R:=R1+R2 and then caculate Mean(R) or even plot PDF of R?

I solved a system of differential equations and want to declare an integral with variable upper limit ( T(x) ) from a function I got from the system ( r(x) ). I did so, but Maple doesn't recognise it as a function of one variable, because when I put this T(x) into a system, it gives me an error:

Error, (in dsolve/numeric/process_input) input system must be an ODE system, got independent variables {t, x}

Though there is no t in the system, t was an integration variable when I declared T(x).

Where is the mistake?

2.mw

In LPSolve, I have solutions returned in matrix form that contain elements that are negligible (values close to zero).

Is there a simple way to convert and reduce these values to zero in the matrix (rather than return the exact values)?

Thanks! 

Is there a way that I can obtain a plot of a set of points like {(2,4),(3,5),(4,7),(5,8),(6,11)} in the domain of the set of positive integers. And the codomain is also the set of positive integers?

And after that is it possible to obtain a polynomial interpolation for three of the points say (2,4),(3,5) and (4,7)?

Thanks a lot in advance.

Hello,
How to find the points indicated in the graph of the following function:
(1.25 * y-sqrt (abs (x))) ^ 2 + x ^ 2-1,

I have used the Taks: the Second Derivative Test. Without results, as I show below:

Heart_Critical_Points_and_the_Second_Derivative_Test.mw
 

Download Heart_Critical_Points_and_the_Second_Derivative_Test.mw

Hey. I can't seem to implement the following recursive (piecewise) function:

f:=n->piecewise(n=0,1,n>=1,sum(f(k),k=0..n-1))

This doesn't work..How do I make it work? :( 

Spawned from here.

1. series() shows some strange dependence on the session history, the first call breaking subsequent computations. Also, for F(x, y), the zeroth term is RootOf(F(0, _Z)), even though 1 is the only solution, but for G(x, y), RootOf(G(0, _Z)) is evaluated to 1, even though 1 is not the only solution:

F := (x, y) -> ln((1+x)*y)+exp(x^2*y^2)-x-cos(x):
G := (x, y) -> ln((1+x)*y)+exp(x^2+y-1)-x-cos(x):

series(RootOf(G(x, y), y), x = 0, 5);
                 1-(1/2)*x^2-(1/6)*x^3+(7/48)*x^4+O(x^5)

series(RootOf(G(x, y), y), x = 0, 6);
Error, (in series/RootOf) unable to compute series

forget(series);
series(RootOf(G(x, y), y), x = 0, 6);
           1-(1/2)*x^2-(1/6)*x^3+(7/48)*x^4-(1/60)*x^5+O(x^6)

series(RootOf(F(x, y), y), x = 0, 1);
                         RootOf(ln(_Z)) + O(x)

2. For some reason solve hangs the first time, then returns a result quickly, and apparently doesn't go along well with simplify, because the last output contains an escaped local variable ans. Besides, I'm not sure why solve generates a huge answer. Is it expanding something to a high order? I was expecting just RootOf(_Z+tan(_Z))+O(x).

ser := series(y+tan(y)+x, x = 0, 1);

iser := timelimit(30, solve(ser, y)): # appears to run indefinitely without timelimit
Error, (in ArrayTools:-NumElems) time expired

iser := solve(ser, y): # returns immediately

evalf(iser); # OK
                                             O(x)

evalf(simplify(iser)); # less OK
       .1250000000*(eval(RootOf(_Z+tan(_Z)), [RootOf = ans, tan(_Z) = sin(_Z)/cos(_Z)]))+O(x)

This is in Maple 2017.3.