## how to calculate a permutation raised by a power i...

```example let P be a permutation: P: = Matrix ([[1,2,3], [4,5,6]])
calculate P ^ 4567 knowing that the order of P = 20```

## how to determine the matrix of a permutation by kn...

how to determine the matrix of a permutation by knowing the orbit in Maple?

## Difficult ODEsys...

Why doesn't Maple show a solution to the following odesys of second order and not show an error?

Differential Equations Trebuchet, Phase II_2020-06-05

 (1)

 (2)

 (3)

 (4)

 (5)

 (6)

 (7)

 (8)

 (9)

 (10)

 (11)

 (12)

## ‘csgn’ in an expression...

Hi,

I need taylor expasion of

A(w):=M/sqrt(M^2+2*w)-mup*sqrt(((mu*M^2+3*sigmap-2*w)-sqrt((mu*M^2+3*sigmap-2*w)^2-12*mu*sigmap*M^2))/(6*sigmap))

I used taylor(A,w,4), but I had a problem!

If I know that A(w) is a real function, how can I remove ‘csgn’ from the  ‘taylor(A,w,4)’ command:

Thanks.

12.mws

## affixe of the foot of the perpendicular from O to ...

restart; with(plots):with(LinearAlgebra):unprotect(O); alias(conj = conjugate); conj z = lambda*v+a; La droite D est représentée par son équation complexe Appelons H l'affixe h le pied de la perpendicukaire abaissée de O sur (D) Les vecteurs OH et V sont orthogonaux donc z = lambda v + a h*conj(v)+conj(h)*v = 0; Le point H appartient à la droite (D) donc : h = lambda*v+a; conj(h) = conj(a)+lambda*conj(v); (lambda*v+a)*conj(v)+(conj(a)+lambda*conj(v))*v = 0; solve(%, lambda); h := simplify(subs(lambda = %, lambda*v+a)); a := 3-I*4; v := -2/3+4*I; evalc(h); H := [Re(h), Im(h)]; Représentation graphique d'un cas particulier : f := proc (x) options operator, arrow; -3*x+5 end proc: a := 3: A := [a, f(a)]:O:=[0,0]: zo := [8/3+I*f(8/3)]; ze := [2+I^(eval(diff(f(x), x), x = 2))]; Zo := [8/3, f(8/3)]; Ze := [2, f(2)]; ex := -3*x+5; V := `

## The use of global variables in numerical ODE probl...

Good day sirs, I write a system of DAE but giving me this code "(The use of global variables in numerical ODE problems is deprecated, and will be removed in a future release. Use the 'parameters' argument instead (see ?dsolve,numeric,parameters)". The code is attached below.

Thanking you in anticipating for your help.

Help!!!!.mw

## Different output for function definition...

f := x -> exp(-x)*sin(x); intvx:= 0..3;
f := proc (x) options operator, arrow; exp(-x)*sin(x) end proc
intvx := 0 .. 3

And this one below ( i prefer this one ) , but got in worksheet now the one above
Probably a option issue ?

 f := x -> exp(-x)*sin(x); intvx:= 0..3;

## seq vs int in maple...

restart;

ii := 50;

seq(ii, ii = 0 .. 5);

evalf(int(ii, ii = 0 .. 5))

For sequence the syntax is correct i.e the output is 0,1,2,3,4,5. is ii inside sequence command takes the value 5 assigned it then changes when ii ranges from 0 to 5?

restart;

ii:=50:
seq(ii)

output: 50

restart;

ii:=50:

seq(seq(ii),ii=1..5)

obtained: 1,2,3,4,5

please explain how seq command works

## How to solve the following deq? Why the extra (t) ...

Trebuchet, Phase I, 2020-05-27 Ki restart; with(RealDomain); with(SolveTools); assume(h < r1); additionally(h < r2); [Im, Re, ^, arccos, arccosh, arccot, arccoth, arccsc, arccsch, arcsec, arcsech, arcsin, arcsinh, arctan, arctanh, cos, cosh, cot, coth, csc, csch, eval, exp, expand, limit, ln, log, sec, sech, signum, simplify, sin, sinh, solve, sqrt, surd, tan, tanh ] [AbstractRootOfSolution, Basis, CancelInverses, Combine, Complexity, Engine, GreaterComplexity, Identity, Inequality, Linear, Parametric, Polynomial, PolynomialSystem, RationalCoefficients, SemiAlgebraic, SortByComplexity] hz1 := g*(r3*m3*cos(phi1(t))-r1*m2*sin(phi2(t))/sin(phi2(t)-phi1(t)))/theta3; whattype(phi1(t)); whattype(phi2(t)); / r1 m2 sin(phi2(t)) \ g |r3 m3 cos(phi1(t)) + -----------------------| \ sin(-phi2(t) + phi1(t))/ hz1 := ------------------------------------------------ theta3 function function hz2 := phi1(t)+arcsin((h+r1*sin(phi1(t)))/r2); /h + r1 sin(phi1(t))\ hz2 := phi1(t) + arcsin|-------------------| \ r2 / subs(phi2 = hz2, hz1); / / | | 1 | | ------ |g |r3 m3 cos(phi1(t)) theta3 | | | | \ \ // /h + r1 sin(phi1(t))\\ \ \\ r1 m2 sin||phi1(t) + arcsin|-------------------||(t)| || \\ \ r2 // / || + ----------------------------------------------------------|| / / /h + r1 sin(phi1(t))\\ \|| sin|-|phi1(t) + arcsin|-------------------||(t) + phi1(t)||| \ \ \ r2 // /// deq := diff(phi1(t), t, t)-% = 0; / / / 2 \ | | | d | 1 | | deq := |---- phi1(t)| - ------ |g |r3 m3 cos(phi1(t)) | 2 | theta3 | | \ dt / | | \ \ / /h + r1 sin(phi1(t))\ \ \ r1 m2 sin|phi1(t)(t) + arcsin|-------------------|(t)| | \ \ r2 / / | + -----------------------------------------------------------| / /h + r1 sin(phi1(t))\ \| sin|-phi1(t)(t) - arcsin|-------------------|(t) + phi1(t)|| \ \ r2 / // \ | | | = 0 | | / ics := phi1(0) = -arcsin(h/r1), (D(phi1))(0) = 0; /h \ ics := phi1(0) = -arcsin|--|, D(phi1)(0) = 0 \r1/ dsolve({deq, ics}, phi1(t)); dsolve(deq); deq_numeric := subs(r1 = 8, r2 = 8, r3 = 1, h = 5, m2 = 1, m3 = 20, theta3 = 20, deq); / | / d / d \\ 1 | |--- |--- phi1(t)|| - -- g |20 cos(phi1(t)) \ dt \ dt // 20 | | \ / /5 \ \ \ 8 sin|phi1(t)(t) + arcsin|- + sin(phi1(t))|(t)| | \ \8 / / | + --------------------------------------------------------| = 0 / /5 \ \| sin|-phi1(t)(t) - arcsin|- + sin(phi1(t))|(t) + phi1(t)|| \ \8 / // ics_numeric := phi1(0) = 0, (D(phi1))(0) = -.63; ics_numeric := phi1(0) = 0, D(phi1)(0) = -0.63 hz1 := dsolve({ics, deq_numeric}, phi1(t), numeric); Error, (in dsolve/numeric/process_input) unknown arcsin(5/8+sin(phi1(t))) present in ODE system is not a specified dependent variable or evaluatable procedure sin(-phi1(t)-arcsin((h+r1*sin(phi1(t)))/r2)); / /h + r1 sin(phi1(t))\\ -sin|phi1(t) + arcsin|-------------------|| \ \ r2 //

## Integrating the exponential integral....

Hello everyone,

first, I'd like to mention that I am relatively new to Maple and am therefore thankful for any advice you might have!

I am trying to integrate the term (k_1^2 * r) from a to infinity, see the picture below as well as the attached file. Maple seems to have some issues with that. However, if I break the integral down into more manageable parts it suddenly works! Why is that? How can I get Maple to solve this immeadiately?  I suspect the culprit lies in the term that contains (-Ei(-B*r)*r^(-1)) where Ei is the exponential integral as defined in Maple. The resulting  hypergeometric function seems suspicious.

The problem is that I have to evaluate 21 integrals of this type (k_x*k_y*r) and breaking them down manually becomes pretty cumbersome, especially as the number of terms in the expanded expressions increases. Is there a way to automate this procedure? I guess I would need to extract individual terms and automatically plug them into the integral expression. That should the last resort, however.

The specific problem (everything included for context, weird stuff happens after equation 15):

Maple_Problem.mw

As for the variables: E, t, and R are real positive numbers. a and B are already assumed as real and positive. A_0, C_0, A_2, and C_2 are real numbers (could be negative, I do not know yet since they must be determined later on). a_0 is definitely real, but it may be negative. r is the polar coordinate, so it is also real and positive, but adding this assumption did not yield a better result.

Thank you for your help!

## How to find an eqution of a line in complex...

conj := conjugate; d := a*x+b*y-c = 0; z := x+I*y; evalc(z+conj(z)); evalc(z-conj(z)); d := expand((1/2)*a*(z+conj(z))+b*(z-conj(z))/(2*I))-c; is(d = z(a-I*b)+conj(z)*(a+I*b)-2*c); varpi = a+I*b; is(d = z*conj(varpi)+conj(z)*varpi-2*c); How to perform calculations correctly ? Thank you.

## Solve equation with sin,cos ,ln and tan...

How to get the inflection points for this function.?

fprime_expr:=x^sin(x)*(cos(x)*ln(x)+sin(x)/x);

i tried symbolic and numeric , but no answer

for X:= solve( fprime_expr =0, x);

## Why does this piecewise function regularly return ...

Hello,

While working for an assignment I had to use a piecewise function which gives a result based on a randomly generated value. The following is a much simpler version of what I've been working on, but it gives the same error.

A random value is uniformly distributed between 0 and 100. The piecewise returns a 1 if the value is between 0 and 50 and it returns 2 if the value is between 50 and 100. As far as I understand this function should only ever give 1 or 2, never something else. However when I loop this a few times Maple regularly returns a 0, which doesn't make sense to me. I've printed the values that return a 0 but none of these should break the piecewise. Can someone please explain to me what's going wrong here and how to fix it?

My code:

restart; randir := piecewise(0 <= r1() and r1() < 50, 1, 50 <= r1() and r1() < 100, 2);
for i to 1000 do r1 := rand(0. .. 100.0); if randir = 0 then print(fail[i], r1()) end if end do;

I've included a failure check to see when and at what values it returns a 0, and as you can see it happens very often.

## How to plot with string values?...

I'm trying to create a graph using a matrix that has numbers and text values, how can I specify that some values of the matrix are strings and others are numbers? I'd like to create something like this