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  • Let us consider 

    Statistics:-Mode(Binomial(n, p));
                            floor((1 + n) p)
    

    Up to Wiki, the output is not correct. Simply no words.

    The copy paste and snip tool used to work.  I can no longer use either to paste in mapleprimes.

    There seems to be a bug in determining the folowing integral analytically:

    integrate(-(3/2*(exp(-(1/4)*x)*x-sqrt(Pi)*erf((1/2)*sqrt(x))*sqrt(x)))/(sqrt(x)*sqrt(Pi)*erf((1/2)*sqrt(x))), x = 0..1)

    Maple gives as a result

    3/2

    However, numerically integrating it

    integrate(-(3/2*(exp(-(1/4)*x)*x-sqrt(Pi)*erf((1/2)*sqrt(x))*sqrt(x)))/(sqrt(x)*sqrt(Pi)*erf((1/2)*sqrt(x))), x=0..1,numeric)

    gives

    0.1195461293

    In fact, integrating it from a to b,

    integrate(-(3/2*(exp(-(1/4)*x)*x-sqrt(Pi)*erf((1/2)*sqrt(x))*sqrt(x)))/(sqrt(x)*sqrt(Pi)*erf((1/2)*sqrt(x))), x=a..b)

    gives

    -3/2 a + 3/2 b

    suggesting that Maple thinks the integrand is just 3/2. If one plots it, then it becomes obvious that this is not the case.


     

    with(Statistics):````

    X := Statistics:-RandomVariable(Normal(0, 1)):

    PDF(sin(X), t)

    piecewise(t <= -1, 0, t < 1, 2^(1/2)*exp(-(1/2)*arcsin(t)^2)/(Pi^(1/2)*(-t^2+1)^(1/2)), 1 <= t, 0)

    (1)

    int(%, t = -1 .. 1)

    2*erf((1/4)*Pi*2^(1/2))

    (2)

    evalf(%)

    1.767540069

    (3)

    ``


    There were recently submitted a dozen Maple bugs by me and others. Maplesoft have brought no responses. They keep strategic silence. True merit is not afraid of criticism.

    Download Bug_in_Statistics_PDF.mw


     

    I found a strange bug in int.
    For some functions f(x), Maple is able to compute the antiderivative (correctly) but refuses to compute the definite integral.
    Or, computes the integral over 0..1  and  0..2  but refuses to compute over 1..2.

    int(exp(x^3), x);  #ok

    -(1/3)*(-1)^(2/3)*((2/3)*x*(-1)^(1/3)*Pi*3^(1/2)/(GAMMA(2/3)*(-x^3)^(1/3))-x*(-1)^(1/3)*GAMMA(1/3, -x^3)/(-x^3)^(1/3))

    (1)

    int(exp(x^3), x=1..2); #?

    int(exp(x^3), x = 1 .. 2)

    (2)

    int(exp(x^3), x=1..2, method=FTOC); #??

    int(exp(x^3), x = 1 .. 2, method = FTOC)

    (3)

    int(exp(x^3), x=0..2); #?

    int(exp(x^3), x = 0 .. 2)

    (4)

    int(exp(-x^3), x);  #ok

    (3/4)*x*exp(-(1/2)*x^3)*WhittakerM(1/6, 2/3, x^3)/(x^3)^(1/6)+exp(-(1/2)*x^3)*WhittakerM(7/6, 2/3, x^3)/(x^2*(x^3)^(1/6))

    (5)

    int(exp(-x^3), x=0..2);  #ok

    (3/4)*2^(1/2)*exp(-4)*WhittakerM(1/6, 2/3, 8)+(1/8)*2^(1/2)*exp(-4)*WhittakerM(7/6, 2/3, 8)

    (6)

    int(exp(-x^3), x=0..1);  #ok

    (3/4)*exp(-1/2)*WhittakerM(1/6, 2/3, 1)+exp(-1/2)*WhittakerM(7/6, 2/3, 1)

    (7)

    int(exp(-x^3), x=1 .. 2);  #???

    int(exp(-x^3), x = 1 .. 2)

    (8)


     

    Download !strange-bug-int.mw

    Let us consider 

    restart; J := int(cos(a*x)^2/(x^2-1), x = -infinity .. infinity, CPV);
    -(1/4)*Pi*sin(2*a)*csgn(I*a)-(1/4)*Pi*sin(2*a)*csgn(I/a)

    This result is not true for a=I:

    eval(J, a = I);
                                   0
    

    In this case the integral under consideration diverges because of 

    cos(I*x)^2;
                                    
                                cosh(x) ^2
    

     

    On some platforms, my editor of choice has become the aptly named Sublime Text. Unfortunately, it does not seem to have built in syntax highlighting for the Maple programming language and so I set out to write some.  In the end, I wrote enough highlighting to keep me sane when looking at Maple source, but it could use a lot more work.  So in case anyone is interested I've put what I have in a Github repository: SublimeTextMaple

    If you use Sublime Text, please download it and add your own enhacements and share in turn.

    I find it hard to believe when I enter the search term Maple 6 Maple 7 maple 8 etc.. old versions search prior to Maple 10 it only brings up a maximum of 4 pages.  I know there are more applications of old.  

    Are all applications still there and the search just not bringing them up?

    Let us consider 

    maximize(int(exp(-x^4), x = k .. 3*k), location);

    Error, (in maximize) invalid input: iscont expects its 1st argument, f, to be of type algebraic, but received x = k .. 3*k
    whereas the expected output is 

    [(2*((1/40)*GAMMA(1/4, (1/80)*ln(3))*5^(1/4)*ln(3)^(3/4)-(1/40)*GAMMA(1/4, (81/80)*ln(3))*5^(1/4)*ln(3)^(3/4)))*5^(3/4)*(1/ln(3))^(3/4), [k = (1/10)*10^(3/4)*ln(3)^(1/4)]]

    as Mma 11 produces. The following 

    RealDomain:-solve(diff(int(exp(-x^4), x = k .. 3*k), k));
      -(1/10)*5^(3/4)*ln(3)^(1/4), (1/10)*5^(3/4)*ln(3)^(1/4)

    is not a workaround because of 

    int(exp(-x^4), x = (1/10)*5^(3/4)*ln(3)^(1/4) .. (3/10)*5^(3/4)*ln(3)^(1/4));
      FAIL

     

    Let us consider 

    MultiSeries:-series(Psi((2*x+1)/(2*x))-Psi((x+1)/(2*x)), x = 0);
    
    x-(1/2)*x^2+(1/4)*x^4-(1/2)*x^6 +O(x^7)
    

    The above result contradicts 

    MultiSeries:-limit(diff(Psi((2*x+1)/(2*x))-Psi((x+1)/(2*x)), x), x = 0);
                               undefined
    MultiSeries:-limit((Psi((2*x+1)/(2*x))-Psi((x+1)/(2*x)))/x, x = 0, right);
                                   1
    MultiSeries:-limit((Psi((2*x+1)/(2*x))-Psi((x+1)/(2*x)))/x, x = 0, left);
                               undefined
    plot((Psi((2*x+1)/(2*x))-Psi((x+1)/(2*x)))/x, x = -0.1e-1 .. 0.1e-2, discont, y = -5 .. 5);
    

    Correct computatiton for

    for reasonable expressions f(x,y), g(x,y) would be very useful in double integrals.

    For the moment this is not possible. Too many bugs:

    int(Heaviside(1-x^2-y^2), x=-infinity..infinity, y=-infinity..infinity); #should be Pi
                               undefined
    int(Heaviside(1-x^2-y^2), x=-1..1, y=-1..1); #should be Pi
                                   0
    int(Heaviside(y-x^2), x=-1..1, y=-1..1); #should be 4/3
                                   -2

    int(Heaviside(y-x^2), y=-1..1, x=-1..1); #This one is OK!
                                  4/3

     

     

     

     

    restart; with(Statistics):
    X := RandomVariable(Normal(0, 1)): Y := RandomVariable(Uniform(-2, 2)):
    Probability(X*Y < 0);

    crashes my comp in approximately 600 s. Mma produces 1/2 on my comp in 0.078125 s.

    Let us consider

    with(Statistics):
    X1 := RandomVariable(Normal(0, 1)):
    X2 := RandomVariable(Normal(0, 1)):
    X3 := RandomVariable(Uniform(0, 1)): 
    X4 := RandomVariable(Uniform(0, 1)):
    Z := max(X1, X2, X3, X4); CDF(Z, t);
    
    int((1/2)*(_t0*Heaviside(_t0-1)-_t0*Heaviside(_t0)-Heaviside(1-_t0)*Heaviside(-_t0)+Heaviside(-_t0)+Heaviside(1-_t0)-1)*(1+erf((1/2)*_t0*2^(1/2)))*(2^(1/2)*Heaviside(_t0-1)*exp(-(1/2)*_t0^2)*_t0-2^(1/2)*Heaviside(_t0)*exp(-(1/2)*_t0^2)*_t0-2^(1/2)*Heaviside(-_t0)*Heaviside(1-_t0)*exp(-(1/2)*_t0^2)-Pi^(1/2)*undefined*erf((1/2)*_t0*2^(1/2))*Dirac(_t0)-Pi^(1/2)*undefined*erf((1/2)*_t0*2^(1/2))*Dirac(_t0-1)+2^(1/2)*Heaviside(-_t0)*exp(-(1/2)*_t0^2)+2^(1/2)*Heaviside(1-_t0)*exp(-(1/2)*_t0^2)-Pi^(1/2)*undefined*Dirac(_t0)-Pi^(1/2)*undefined*Dirac(_t0-1)+Pi^(1/2)*Heaviside(_t0-1)*erf((1/2)*_t0*2^(1/2))-Pi^(1/2)*Heaviside(_t0)*erf((1/2)*_t0*2^(1/2))-exp(-(1/2)*_t0^2)*2^(1/2)+Pi^(1/2)*Heaviside(_t0-1)-Pi^(1/2)*Heaviside(_t0))/Pi^(1/2), _t0 = -infinity .. t)

    whereas Mma 11 produces the correct piecewise expression (see that here screen15.11.16.docx).

    Edit. Mma output.

    Let us consider 

    J := int(x^n/sqrt(1+x^n), x = 0 .. 1) assuming n > 0;
    
    2*(2^(1/2)-hypergeom([1/2, 1/n], [(n+1)/n], -1))/(2+n)
    
    limit(J,n=infinity);
    FAIL
    MultiSeries:-limit(J,n=infinity);
    FAIL

    Mma 11 finds the limit is zero. Hope one feels the difference.

    Hi MaplePrimes,

    This YouTube video has a nice puzzle. 

    It is titled "Can you solve the locker riddle". 
    My first blush was to consider modular arithmatic
    https://www.youtube.com/watch?v=c18GjbnZXMw

    Here is a maple page -
    divisors_excercise.mw

    divisors_excercise.pdf

    Have a very fine rest of the day.

    Regards,
    Matt

     

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