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These are questions asked by sand15


I'm surprised by the result of the procedure VectorCalculus:-Curvature which is always a positive scalar quantity:
For instance
c := VectorCalculus:-Curvature(<x, sin(x)>, x):
plot(c, x=0..2*Pi) 
# c >=0 for all x in [0, 2*Pi]

In the help pages it's written that the (signed) curvature for a function y(x) is y''/(1+y' 2)(3/2).

y := sin(x):
c := diff(y, x$2) / (1+diff(y,x)^2)^(3/2):
plot(c,  x=0..2*Pi) 
# c < 0 if x in (0, Pi)  and  c > 0 if x in (Pi, 2*Pi)

Could you please help me to understand this?

Thank in advance


Does anyone know how the command PLOT(POLYGONS(...)) fills  polygons?
I'm interested in polygons that are not simple, that is polygons for which 2 different sides without common vertex do not intersect.

Thanks in advance


Is it possible to change programmatically the permissions of a file without using ssystem?
Such as in ssystem("chmod +x MyFile") for instance



In statistics a  "degree of freedom" is a strictly positive integer.

The three distributions ChiSquare, StudentT and FRatio from package Statistics have degrees of freedom as parameters. Nevertheless they accept any strictly positive real values for them.
(one can verify that their "Conditions" attribute is of the form [0 < n] instead of [n::posint]).

I think this ought to be corrected in future versions


I seeking for informations on the Statistics:-ChiSquareSuitableModelTest procedure:

  1. Once you have choose the number of bins, what strategy does this procedure use to define the bins (equal width, equal probability, other one?).
  2. It seems the procedure accepts any value for this number of bins and that its correct use then is under the sole responsability of the user. Am I right?

In the book below (but I'm sure this can also be found on the web) there is a detailed discussion concerning "good practices" in using the Chi-Square goodness of fit test: does anyone known is something comparable is used in ChiSquareSuitableModelTest ?

Statistical methods in experimental physics, W.T.Eadie, D. Drijard, F.F.James, M. Roos, B. Sadoulet
North-Holland 1971
Paragraph 11.2.3 "choosing optimal bin size"

Thanks in advance

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