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mmcdara

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9 years, 54 days
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These are questions asked by mmcdara

How can I force Maple to rewrite express...

mmcdara 7891 Maple 2015
sum
January 25 2020
2 4

Hi,

Is it possible to force Maple to simplify these Sum(s) ?
SimplifySum.mw
 

> 

s := Sum(a*X[n]+b, n=1..N);
simplify(s);
value(s);  # part of the job done  but...


IWouldLikeToHave = a*Sum(X[n], n=1..N) + b*N; # or +N*b, it doesn't matter

Sum(a*X[n]+b, n = 1 .. N)

  

Sum(a*X[n]+b, n = 1 .. N)

  

N*b+sum(a*X[n], n = 1 .. N)

  

IWouldLikeToHave = a*(Sum(X[n], n = 1 .. N))+N*b

 (1)
> 

s := Sum(X[n]+Y[n], n=1..N);
(expand@value)(s);


IWouldLikeToHave = Sum(X[n], n=1..N) + Sum(Y[n], n=1..N);

Sum(X[n]+Y[n], n = 1 .. N)

  

sum(X[n]+Y[n], n = 1 .. N)

  

IWouldLikeToHave = Sum(X[n], n = 1 .. N)+Sum(Y[n], n = 1 .. N)

 (2)
> 

 

 

 

Thanks in advance

 

How can I define (and sample) a mixture...

mmcdara 7891 Maple 2015
distribution sample statistics
January 16 2020
2 3

Hi, 

I can't find a unique way to define a mixture of two random variables that enables at the same time to compute its PDF and generate a sample.
In the attached file you will find two methods :

  1. the first one is the most formal and only CAS are supposed to be able to allow its implementation:
     it enables computing the PDF and the CDF (trivial) but fails to generate a sample.
    (PS : in a first attempt I had defined only the PDF, which should have been enough for method=envelope does work... ... at my opinion)
     
  2. the second method is the one one would use in non CAS languages (for instance Matlab, R, ...). It enables generating a sample (of course) but fails to compute the PDF (which is not very surprising).

So my question: does anyone here would have some suggestions to make one these two methods capable to compute both the PDF (eventually the CDF) and generate samples ?

PS: still have this kind of problems (tomleslie suggested months ago that using interface(rtablesize=10) could help but it's not the case here)
Maple Worksheet - Error
Failed to load the worksheet /maplenet/convert/Mixture_of_random_variables.mw .
 

Download Mixture_of_random_variables.mw

 

Can anyone explain me how 'infinity' is ...

mmcdara 7891 Maple 2015
infinity eval limit
January 14 2020
2 2

Hi 

I got, a bit by mistake, a weird result that seems to come from the way "Maple" manipulates infinity (please have a look at the results below)
I couldn't find a correct explanation to these results in the help pages dedicated to infinity or evaluation.

Could anyone explain me why, in some circumstances, 'infinity' seems to be a name (for instance infinity*Pi; does not return  infinity but infiniy/Pi).
Thanks in advance

 

> 

restart:
> 

with(Statistics):
> 

f := PDF(Cauchy(0, 1), x)

1/(Pi*(x^2+1))

 (1)
> 

m := int(x*f, x=-infinity..+infinity);

undefined

 (2)
> 

p := int(x*f, x);

(1/2)*ln(x^2+1)/Pi

 (3)
> 

# Naive "proof" : eval(..., infinity) seems to consider infinity as a name (consistent with
# the first line in help(infinity) without any particular property.
# This seems to be confirmed by the value of p1 and p2 : I expected to get infinity instead
# of infinity/Pi.

p1 := eval(p, x=-infinity);
p2 := eval(p, x=+infinity);
p2 - p1;

infinity/Pi

  

infinity/Pi

  

0

 (4)
> 

# Correct "proof" :

a := limit(p, x=-infinity);
b := limit(p, x=+infinity);
b-a

infinity

  

infinity

  

undefined

 (5)
> 

# Does Maple treat 'infinity' as a number ?

infinity         - infinity;
infinity*2       - infinity*2;
infinity*(1/3)   - infinity*(1/3);
infinity*0.333   - infinity*0.333;
infinity*sqrt(2) - infinity*sqrt(2);
infinity/Pi      - infinity/Pi;

undefined

  

undefined

  

undefined

  

Float(undefined)

  

0

  

0

 (6)
> 

limit(sqrt(2)/x, x=0) - limit(sqrt(2)/y, y=0);
limit(Pi/x, x=0)      - limit(Pi/y, y=0);

undefined

  

undefined

 (7)
> 

 


 

Download Infinity.mw

How can I have a pretty display of a pie...

mmcdara 7891 Maple 2015
layout piecewise documenttools
January 10 2020
2 2

Hi,

How can I force the command InsertContent(Worksheet(Group(Input( T )))) to display the variable eq as it appears in label (2) ?

(a screen capture of the output of InsertContent(Worksheet(Group(Input( T )))) is given after the Maple code)

> 

restart:
> 

interface(version)

`Standard Worksheet Interface, Maple 2015.2, Mac OS X, December 21 2015 Build ID 1097895`

 (1)
> 

with(DocumentTools):
> 

with(DocumentTools[Layout]):
> 

eq := piecewise(t < 1, sin(t), cos(t));

C := Cell( Textfield(style=TwoDimOutput,Equation(eq)) ):
T := Table(Column(), widthmode=percentage, width=40, Row(C)):
InsertContent(Worksheet(Group(Input( T )))):

eq := piecewise(t < 1, sin(t), cos(t))

 (2)
> 

 



Download Layout.mw

Is it possible to create variables of so...

mmcdara 7891
type
January 08 2020
3 3

Hi, 

It seems to me that variables (maybe I should have use 'names' instead) become "typed" only once they have been instanciated with ':=' ?

But is it possible in Maple  to do something like that
"I declare that variable V will be of type T even if I do not explicitely instanciate it?"

... or is it here one of the distinction between a "typed CAS" and a "non typed" CAS ?

Thanks in advance

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