## different answers to same command...

Why do I get different answers for the same command?

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## convert(arctan(y, x), abs) is wrong...

```convert(arctan(y, x), abs);
/ y + I x \
-I ln|---------|
\|y + I x|/
```

The output has x and y swapped. Further, for complex x and y it's wrong even if x and y are swapped back, because Maple's definition of arctan has sqrt(x^2+y^2) in the denominator, which isn't the same as abs(x+I*y).

## Maybe an issue with the NegativeBinomial distribut...

Hello everybody

I'm using discrete distributions from the Statistics package and I found a rather strange result.

In short the theoritical values of some statistics of a NegativeBinomial(1, P) Random Variable (P being the probability of success equal to 1e-4) are correctly computed, but their empirical estimators computed from a sample of this RV are roughly wrong.

For NegativeBinomial(1, P) is similar to Geometric(P) I asked Maple to compute the theoritical values of some statistics of Geometric(P) and next to assess their empirical values from a sample of Geometric(P).
Some discrepancies still remain but they can be explained by statistical fluctuations.

Could you please look to the attached file (an error on my part is still possible) and help me to fix this ?

PS : the histogram of Sample(NegativeBinomial(K, P), AnySizeYouWant) is obviously wrong (it should look like a decreasing exponential)

## signum(0,abs(zero),0) gives 1...

```signum(0, abs(x), 0);
signum(0, |x|, 0)

signum(0, abs(tan(Pi/5)-sqrt(5-2*sqrt(5))), 0);
1
```

The second one should give 0 or return unevaluated.

## MapleSim Probe Windows do not appear...

I have recently reinstalled the MapleSim 6.4 but the probe windows do not appeaar anymore.

The image below shows that there are 3 probes (none are disabled) and when I run the simulation nothing happens.,

## problem in dsolve...

hi..i have a problem with dsolve.

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## Solve PDE with piecewise condition...

Hi Maple folks!

I am trying to solve the following PDE in maple:

pde:= diff(c(x,t),t)+c(x,t)*diff(c(x,t),x)=0

bc:=c(x,0)=piecewise(x < 0, 0, x > 0, 1)

I tried the following:

pdsolve({pde,bc}, c(x, 0))

But it gives no solution, i also tried a numeric solution, but i couldn't make it work. Please help.

Thanks! :)

## Extract terms from matrix using markers...

I have written a Maple code which extracts terms in a matrix into two new matrices dependent on certain markers. I am running into problems with this particular code as it requires enormous amounts of RAM when going to large matrix sizes (32GB+); and will take 4-5 days to complete for larger matrix sizes, or simply crashes.

Each matrix element is an algebraic expression containing A and B and the markers hh and ss. The example in the attached Maple file (3 x 3 matrix) is a minimal working example and the actual expressions are much longer and the matrices much larger (5000 x 5000 or larger). I utilise the symmetry of the matrix to ease the process, and use the tril command of MTM to extract only the lower triangular matrix; as this is all that is needed for the next stage (I have yet to test how efficient this command is, but use it for now).

The two markers hh and ss are targeted and if found in an expression that term will be extracted accordingly. The matrix elements are expanded and a procedure run over the matrix and will extract terms with hh into one matrix and terms with ss into another matrix. I think the map(expand,...) part is what causes the memory issue; but I believe this needs to be done to correctly extract terms.

Any help or tips are greatly appreciated on how to increase efficiency and improve this method.

Sub_matrix_extraction.mw

-Yeti

## timelimit has side effects...

```aa := tan(Pi/11)^2;
bb := RootOf(_Z^5-55*_Z^4+330*_Z^3-462*_Z^2+165*_Z-11, index = 1); # bb = aa
ee := (exp(-Pi-I*Pi*aa/bb))^(1+I);

seq((proc() try timelimit(k, signum(Re(ee)-1/k)) catch: lprint(lastexception) end try end proc)(),
k = 1..10);

`shake/shake`, "time expired"
`expand/sin`, "time expired"
`evalr/tan`, "time expired"
sdmp:-mul, "time expired"
1, 1, 1, 1, 1, 1
```

An explanation: aa/bb=1, so, as we know from here, ee=exp(-2*Pi), and ee is tricky to evaluate numerically. Normally signum(Re(ee)-1/5) just seems to hang indefinitely, which is not the worst thing it could do. But after one of the timelimit interrupts (or after clicking "Interrupt the current operation"), something breaks, and Maple starts returning wrong values.

This is in Maple 2017.2, system="X86 64 WINDOWS", wordsize=64.

Also, is there any way to clear the cached values so that this computation can be repeated without doing restart?

## Can Maple solve any (numerical) system of polynomi...

Hi, I have a system of 15 polynomial equations (of 15 variables) of 2nd degree. Meaning, every monomial has at most mulplications of 2 different variables or a single variable squared.

I tried to solve them in Maple but it's been 2 hours and Maple is still thinking.. I don't have any indication if Maple is just stuck or it should return a solution at some point.

Below I wrote the Maple commands that I tried to run (sorry but I'm new here so I didn't know how to write them nicely). I also wrote one of the solutions that I'm expecting to get (15 values for the 15 variables). and you can see that by typing eq7 for example I got -2.5=-2.5 (and the same for the rest of the equations) which means that the values are correct.

I know there is an algorithm for solving any system of numerical polynomial equations of any degree. I don't know if Maple implemented it.

Anyone knows if Maple is able to solve the equations below? and if not, is there any other way that can be done to solve them?

Thanks

David

Here's the commands for Maple (including one of the solutions I'm expecting to get).

The variables are: r11, r12, r13, r21, r22, r23, r31, r32, r33, t1, t2, t3, s1, s2, s3

eq1:=r11^2+r21^2+r31^2 = 1;
eq2:=r12^2+r22^2+r32^2 = 1;
eq3:=r13^2+r23^2+r33^2 = 1;
eq4:=r11*r12+r21*r22+r31*r32 = 0;
eq5:=r11*r13+r21*r23+r31*r33 = 0;
eq6:=r12*r13+r22*r23+r32*r33 = 0;
eq7:=-30*r13-.79382581863774e-1*s1*r11-.95259098236529e-1*s1*r12+.992282273297173*s1*r13 = -.83717247687439e-1*t1;
eq8:=-30*r13+.79382581863774e-1*s2*r11+.95259098236529e-1*s2*r12+.992282273297173*s2*r13 = .76364294519742e-1*t2;
eq9:=-30*r13-.86165283952334e-1*s3*r11+.103398340742801*s3*r12+.990900765451843*s3*r13 = -.81460429387834e-1*t3;
eq10:=-30*r23-.79382581863774e-1*s1*r21-.95259098236529e-1*s1*r22+.992282273297173*s1*r23 = -.107930827800543*t1;
eq11:=-30*r23+.79382581863774e-1*s2*r21+.95259098236529e-1*s2*r22+.992282273297173*s2*r23 = .60269029165473e-1*t2;
eq12:=-30*r23-.86165283952334e-1*s3*r21+.103398340742801*s3*r22+.990900765451843*s3*r23 = .105021268850622*t3;
eq13:=-30*r33-.79382581863774e-1*s1*r31-.95259098236529e-1*s1*r32+.992282273297173*s1*r33 = .990627255252918*t1-30;
eq14:=-30*r33+.79382581863774e-1*s2*r31+.95259098236529e-1*s2*r32+.992282273297173*s2*r33 = .995256820446840*t2-30;
eq15:=-30*r33-.86165283952334e-1*s3*r31+.103398340742801*s3*r32+.990900765451843*s3*r33 = .991128009660183*t3-30;

r11 := 1;
r12 := 0;
r13 := 0;
x := .523598775598299;
r21 := 0;
r22 := cos(x);
r23 := -sin(x);
r31 := 0;
r32 := sin(x);
r33 := cos(x);
t1 := 29.862424638395044;
t2 := 32.737813080348531;
t3 := 30.689747387623886;
s1 := 31.493054789905649;
s2 := 31.493054789905628;
s3 := 29.014005238849720;
eq1;
eq2;
eq3;
eq4;
eq5;
eq6;
eq7;
eq8;
eq9;
eq10;
eq11;
eq12;
eq13;
eq14;
eq15;

unassign('r11', 'r12', 'r13', 'r21', 'r22', 'r23', 'r31', 'r32', 'r33', 't1', 't2', 't3', 's1', 's2', 's3');
solve({eq1, eq10, eq11, eq12, eq13, eq14, eq15, eq2, eq3, eq4, eq5, eq6, eq7, eq8, eq9}, {r11, r12, r13, r21, r22, r23, r31, r32, r33, s1, s2, s3, t1, t2, t3});

## problem to solve scheme...

how to resolve this error... ??

## dummy index summation in maple?...

I did dummy indices implication using add command as below. is it OK or there are mistakes?

Is there another way to imply dummy index summation in maple instead of using add command?

any suggestion???

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 (1.1)

## Can Maple determine the value of DthetaZero such t...

ODE:= -2 sin(1/2 theta(t)) cos(1/2 theta(t)) (diff(theta(t),t)^2-9.8000 sin(theta(t))-(150+4 sin(1/2 theta(t))^2) (diff(theta(t),t,t)=0:

ICS:=  theta(0) = Pi/6, D(theta)(0) = DthetaZero:

## How do I make DocumentTools behave as in the help ...

When I use functions from the DocumentTools to display information in a Maple document, they display a weird bracked along the left hand side of the display. I would like them to display in the same way they do in the help pages. I have attached a document showing the results I get when I repeat some of the examples from the help pages.

display-problems.mw

## DEtools/DEplot/CheckDE) derivatives must be given ...

subs can not make diff(1, t) = 0

sys := simplify(subs(diff(1,t)=0,subs(c(t)=1,[ode1a,ode3a])));
sys := [diff(a(t), t) = 1.342398800*10^5*a(t)+89591*b(t)+44647, 44647*a(t)+44902*b(t)+44859];

DEplot(sys, [a(t), b(t)], t = 0 .. 16, a = -16 .. 16, b = -16 .. 16, color = magnitude, title = `Stable Limit Cycles`, arrows = curve, dirfield = 800, axes = none);
Error, (in DEtools/DEplot/CheckDE) derivatives must be given explicitly

why can not plot?

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