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These are replies submitted by vv

@Mariusz Iwaniuk 
It should be added that this is valid in general only for x>0 [not a bilateral expansion]



simplify(gg(x0) - alpha);

The mathematical definition of a PRNG is clear. But deciding whether a computer-based PRNG is acceptable or not is practically impossible. All we can do is to choose arbitrarily (more or less) some criteria. The main criterion seems to be "usefulness".

The Pyton code must be converted to Maple by hand. This cannot be done automatically. Actually it is probably easier to start directly from the algorithm.

The main concern is that Maple has a very solid Groebner package. Are you sure the Python code has something better or not implemented in Maple? It would be useful to present a few examples obtained with your code.

@Melvin Brown 

For the animation you have spacestep = 1/50, timestep = .1
but in the plots there are the default values.
If you use the same values, the results will agree. I don't know how the error estimates are implemented; I think that the differences should not be so big, unless the method is not stable.


But is it possible to reproduce the worksheet from scratch (without setting manually the labels or by copy+paste)?


It seems that the worksheet has some strange output data.
After removing the output and re-executing, everything is OK.

Parameters in a procedure cannot be assigned like this
( P := convert(P, list);   etc)

@Carl Love 

I think you meant "expression" instead of "statement" for arrow operators.

For example,
f := () -> local i; i:=7;
is not correct (but enclosing (i:=7) is ok).

Note that 
f:=proc() local i; i:=7 end;
is correct too.

You must provide epsfunc for a concrete answer.


Actually omega should be >0, otherwise you do not have an inner product.

@Carl Love 

Should be Joachimsthal.


Edit. Actually, the OP proves partly another (easier) result due to Joachimsthal:

Let [a*cos(t[i]), b*sin(t[i])], i=1..4, be four distinct points on the ellipse x^2/a^2+y^2/b^2=1.
These points are concyclic iff t[1]+t[2]+t[3]+t[4] is a multiple of 2*Pi.

Anyway, the OP does not seem to be very interested in his post.



A more unpleasant fact is that Maple is not able to compute e.g.

evalf[20](Int(LegendreP(-1/2 + y*I, 3)*exp(-y), y=0..infinity));

The integrand is "nice" but the user will have to chop the interval.




You still have typos: Mylib <> MyLib, Mylib <> MyMat. Why don't you use copy+paste?

Please open the attached file and execute it using the (!!!) icon.


description "My Package";
option package;
export E1,E2;
E1 := "first export":
E2 := "second export"
end module;



LibLocation:="C:/temp/MyLib.mla":  # dir with write access

LibraryTools:-Create(LibLocation); # if the library is new; if exists ==> error (to be ignored)

LibraryTools:-Save(MyMat, LibLocation);


restart;  # check




libname:=LibLocation, libname:


[E1, E2]


E1, E2;

"first export", "second export"



[["MyMat.m", [2019, 11, 8, 9, 34, 55], 41984, 115]]




Download libex.mw

@Rouben Rostamian  

And also:


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