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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.
limit((x^2-1)*sin(1/(x-1)), x = infinity, complex);
infinity-infinity*I
MultiSeries:-limit((x^2-1)*sin(1/(x-1)), x = infinity, complex);
infinity

whereas the same outputs are expected. The help http://www.maplesoft.com/support/help/Maple/view.aspx?path=infinity&term=infinity does not shed light on the problem. Here are few pearls:

  • infinity is used to denote a mathematical infinity, and hence it is usually used as a symbol by itself or as -infinity.
  • The quantities infinity, -infinity, infinity*I, -infinity*I, infinity + y*I, -infinity + y*I, x + infinity*I and x - infinity*I, where x and y are finite, are all considered to be distinct in Maple. However, all 2-component complex numerics in which both components are infinity are considered to be the same (representing the single point at the "north pole" of the Riemann sphere).
  • The type cx_infinity can be used to recognize this "north pole" infinity.

The command

plots:-implicitplot(evalc(argument((1+x+I*y)/(1-x-I*y))) <= (1/4)*Pi, x = -5 .. 5, y = -5 .. 5, crossingrefine = 1, gridrefine = 2, rational = true, filled, signchange = true, resolution = 1000);

produces an incorrect result

in view of

evalf(argument((1-4+4*I)/(1+4-4*I)));
                          2.889038378

There is a workaround 

plots:-inequal(evalc(argument((1+x+I*y)/(1-x-I*y))) <= (1/4)*Pi, x = -5 .. 5, y = -5 .. 5);

 

The command 

restart; st := time(): FunctionAdvisor(EllipticE); time()-st;

produces the result on my comp in 805.484 s. Too much time.

The command

J := int(sin(x)/(x*(1-2*a*cos(x)+a^2)), x = 0 .. infinity)assuming a::real,a^2 <>0;

outputs 

(infinity*I)*signum(a^3*(Sum(a^_k1, _k1 = 0 .. infinity))-a^2*(Sum(a^_k1, _k1 = 0 .. infinity))-a*(Sum(a^(-_k1), _k1 = 0 .. infinity))+a^2+Sum(a^(-_k1), _k1 = 0 .. infinity)+a)

which is wrong in view of 

evalf(eval(J, a = 1/2));
                       Float(undefined) I

The correct answer is Pi/(4*a)*(abs((1+a)/(1-a))-1) according to G&R 3.792.6. Numeric calculations confirm it.

The following three commands 

plots:-implicitplot(3*cos(x) = tan(y)^3, x = -Pi .. Pi, y = -(1/2)*Pi-1 .. (1/2)*Pi+1, thickness = 3, crossingrefine = 1, rational = true, signchange = true, resolution = 1000, gridrefine = 2);
plots:-implicitplot(3*cos(x) = tan(y)^3, x = -Pi .. Pi, y = -(1/2)*Pi-1 .. (1/2)*Pi+1, thickness = 3, crossingrefine = 1, rational = true, signchange = false, resolution = 1000, gridrefine = 2);
plots:-implicitplot(3*cos(x) = tan(y)^3, x = -Pi .. Pi, y = -(1/2)*Pi-1 .. (1/2)*Pi+1, thickness = 3, crossingrefine = 1, rational = true, resolution = 1000, gridrefine = 2);

produce the same incorrect plot 

It is clear the sraight lines given by y=Pi/2 and y=-Pi/2 are superfluous. It should be noticed that the Mmma's ContourPlot command without any options produces a correct plot.

Up to http://www.maplesoft.com/support/help/Maple/view.aspx?path=solve&term=solve

• 

If the solve command does not find any solutions, then if the second argument is a name or set of names, then the empty sequence (NULL) is returned; if the second argument is a list, then the empty list is returned. This means that there are no solutions, or the solve command cannot find the solutions. In the second case, a warning is issued, and the global variable_SolutionsMayBeLost is set to true.

 Let us consider 

solve({x > -Pi, (tan(x)-tan(x)^2)^2-cos(x+4*tan(x)) = -1, x < Pi}, [x]);
                               []

We see the command omits the solution x=0 without any warning. It should be noticed that Mathematica solves it, outputting

{{x -> 0}, {x -> 0}}

and the warning

Solve::incs: Warning: Solve was unable to prove that the solution set found is complete.

One may draw a conclusion on her/his own.

 

Quite accidentally I discovered incorrect calculation of the simple definite integral:

int(1/(x^4+4), x=0..1);  

evalf(%);

                            1/8*ln(2)-1/16*ln(5)+1/32*Pi+1/8*arctan(1/3)   # This is incorrect result

                                                   0.1244471178

Is this a known bug?

 

If  first we calculate corresponding indefinite integral, and then by the formula of Newton - Leibniz, that everything is correct:

F:=int(1/(x^4+4), x):

eval(F, x=1)-eval(F, x=0);

evalf(%);

                                             1/16*ln(5)+1/8*arctan(2)

                                                     0.2389834593

 

 

I am currently working on an adaptive question in Maple TA 2016 and it seems that there is a bug in the drop - down list functionality: 

After I click "Verify" in a section, the answer disappears even though I choose it to be displayed. The window simply goes back to showing (Click for List) instead of keeping the answer, see the screenshot below.

 

Perhaps I am doing something wrong, though I have used Lists extensively in the previous version and never had that problem ..

 

Thanks for your  help!

Elisabeth

 

 

Hello All,

(I also sent this fact to Maplesoft Support).

Since I updayed to 2016.1 the F1 key does bring a menu witch send to..F5 only.

No way to have a "full" Help Menu.(See the attached file)

I guess a silly bug jumped in :)

Kind regards,

 

Jean-Michel

 

Hello there! Maple 2016.1 sometimes gets crasy about parsing input strings. I managed to capture this behaviour in the attached file. It looks like below. I am not sure what exactly triggers it. It just starts happening all of a sudden. What might be the cause...? 

 

"1 Pi"

Error, incorrect syntax in parse: `;` unexpected (near 4th character of parsed string)

"1 Pi"

 

"Pi/(2)"

Error, invalid semantics "&pi;"

"Pi/2"

 

"1"

Error, incorrect syntax in parse: `;` unexpected (near 4th character of parsed string)

"1"

 

``

 

Download test.mw

This question is related to the recent post
http://www.mapleprimes.com/questions/211460-Series-Of-Bessel-Functions

1. Consider the following fast convergent series:

f:=n->(-1)^(n+1)*1/(n+exp(n));
S1:=Sum(f(n),n=1..infinity);
evalf(S1);
S2:=Sum(f(2*n-1)+f(2*n),n=1..infinity);
evalf(S2);

As expected, the sum of the series is obtained very fast (with any precision), same results for S1 and S2.


2. Now change the series to a very slowly convergent one:

f:=n->(-1)^(n+1)/sqrt(n+sqrt(n));

evalf(S1) is computed also extremely fast, because the acceleration algorithm works here perfectly.
But evalf(S2) demonstrates a bug:

Error, (in evalf/Sum1) invalid input: `evalf/Sum/infinite` expects its 2nd argument, ix, to be of type name, but received ...


3. Let us take another series:

f:=n->(-1)^(n+1)/sqrt(n+sqrt(n)*sin(n));

Now evalf(S1) does not evaluate numerically and evalf(S2) ==> same error.
Note that I do not know whether this series is convergent or not, but the same thing happens for the obviously convergent series

f:=n->(-1)^(n+1)/sqrt(n^(11/5)+n^2*sin(n));

(because it converges slowly (but absolutely) and the acceleration fails).
I would be interested to know a method to approximate (in Maple) the sum of such series.

Edit. Now I know that the mentioned series 

converges (but note that Leibniz' test cannot be used).

eulermac(1/(n*ln(n)^2),n=2..N,1);  #Error
Error, (in SumTools:-DefiniteSum:-ClosedForm) summand is singular in the interval of summation


eulermac(1/(n*ln(n)^2+1),n=2..N,1);  #nonsense

 

 

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