I am newcommer in Maple. I am using Maple 2019. Just a simple question;

solve(x^2-3*x+4=0, x);

gives

1.50000000000000 + (9.09238836013723*10^(-59))*I, 1.50000000000000 - (9.09238836013723*10^(-59))*I

instead I need to show in the forms of radiacal. I have also the problem in dsolve command;

dsolve(2*diff(y(x),x$2)+3*diff(y(x),x)+4*y(x),y(x));

with the result

y(x) = (2.73949338633639*10^(-116) + (2.73949338633639*10^(-116))*I)*_C1 + (1. + (2.73949338633639*10^(-116))*I)*_C2

Thanks indeed in advance

Sayed

Considering the follwoing expr:

A(x):=mue+(mun/gama)+(u0^2)-mud*x-mue*exp(x)-(mun/gama)*exp(gama*x)-(u0^2)*(1-2*x/u0^2)^(1/2);

where 

mue:=1/(1+alpha+beta);
mun:=alpha/(1+alpha+beta);
mud:=beta/(1+alpha+beta);
u0:=(mue+mun*gama)^(-1/2);
 and assuming the values of alpha and beta lie between 0.1..0.6 and gama=15 ro 20.

How do I determine those values of (alpha,beta,gama) satisfying conditions [(3), (4)], [(3), (5)] or [(3),(6)]?

conditions:

A(x[m] <> 0) = 0:

where x_m is an extreme point of A(x) (other than x=0),

d*A(x)/dx, x = x[m] < 0:

d*A(x)/dx, x = x[m] > 0:

d*A(x)/dx, x = x[m] = 0:

Can anyone please help me out with the following integration

                      f(x) = tanh(x)/sqrt(x^2+1)

limits x_initial =1, x_final =100

Thanks

Hi, 

Does it exist a way to get all the types a variable verifies?
For instance
x:=4;
type(x, t); # true for t in {positive, posint, algebraic, ...}

Thanks in advance

Hi,
How do I simplify the following polynomial:

 -(729 beta (1/2 (-1/9 (-5/27 beta-1/9) lambda^6-1/9 (1/9 beta^2 TT+(10/9 TE+2/3 TT) beta-1/9 TE) lambda^4+5/27 (2/5 TT (3/2 TT+TE) beta+TE (TE-2/5 TT)) beta lambda^2-1/9 TE beta^2 TT (-TT+TE)) p1(m,t)^2+(beta TT-1/3 lambda^2)^2 (-1/3 lambda^2+TE)^3 ((p2(m,t))/(lambda^2-3 TE)+3/2 ((lambda^2+TE) p1(m,t)^2)/((lambda^2-3 TE)^3))))/((3 beta TT-lambda^2)^3 (3 TE-lambda^2)^2),

as follows:

-3*beta*p2(m,t)/(lambda^2-3*beta*TT)+3*beta^2*(5*lambda^2-3*beta*TT)*p1(m,t)^2/(2*(lambda^2-3*beta*TT)^3)
?

restart;
solve({l*(2*l^2*lambda^4*sigma*w*a[2]+l^2*lambda^2*mu*w*b[1]+6*l*lambda^2*m*sigma*a[0]^2-6*l*lambda^2*m*b[1]^2+6*l*m*mu^2*a[0]^2-l*lambda^2*rho*sigma*a[0]-l*mu^2*rho*a[0]+4*lambda^2*sigma*w*a[0]+4*mu^2*w*a[0]) = 0, l*(2*l^2*lambda^3*sigma*w*a[1]+6*l^2*lambda^2*mu*w*b[2]+2*l^2*lambda*mu^2*w*a[1]+12*l*lambda^2*m*sigma*a[0]*a[1]-12*l*lambda^2*m*b[1]*b[2]-l*lambda^2*rho*sigma*a[1]+12*l*m*mu^2*a[0]*a[1]-l*mu^2*rho*a[1]+4*lambda^2*sigma*w*a[1]+4*mu^2*w*a[1]) = 0, l*(5*l^2*lambda^3*sigma*w*b[2]-3*l^2*lambda^2*mu*sigma*w*a[1]-7*l^2*lambda*mu^2*w*b[2]-3*l^2*mu^3*w*a[1]+12*l*lambda^2*m*sigma*a[0]*b[2]+12*l*lambda^2*m*sigma*a[1]*b[1]-l*lambda^2*rho*sigma*b[2]+24*l*lambda*m*mu*b[1]*b[2]+12*l*m*mu^2*a[0]*b[2]+12*l*m*mu^2*a[1]*b[1]-l*mu^2*rho*b[2]+4*lambda^2*sigma*w*b[2]+4*mu^2*w*b[2]) = 0, l*(8*l^2*lambda^3*sigma*w*a[2]+6*l^2*lambda*mu^2*w*a[2]+12*l*lambda^2*m*sigma*a[0]*a[2]+6*l*lambda^2*m*sigma*a[1]^2+l^2*lambda*mu*w*b[1]-6*l*lambda^2*m*b[2]^2-l*lambda^2*rho*sigma*a[2]+12*l*m*mu^2*a[0]*a[2]+6*l*m*mu^2*a[1]^2-6*l*lambda*m*b[1]^2-l*mu^2*rho*a[2]+4*lambda^2*sigma*w*a[2]+4*mu^2*w*a[2]) = 0, -l*(4*l^2*lambda^3*mu*sigma*w*a[2]-l^2*lambda^3*sigma*w*b[1]+l^2*lambda*mu^2*w*b[1]-12*l*lambda^2*m*sigma*a[0]*b[1]+l*lambda^2*rho*sigma*b[1]-12*l*lambda*m*mu*b[1]^2-12*l*m*mu^2*a[0]*b[1]+l*mu^2*rho*b[1]-4*lambda^2*sigma*w*b[1]-4*mu^2*w*b[1]) = 0, 6*l^2*(l*lambda^2*sigma*w*a[2]+lambda^2*m*sigma*a[2]^2+l*mu^2*w*a[2]+m*mu^2*a[2]^2-lambda*m*b[2]^2) = 0, 2*l^2*(l*lambda^2*sigma*w*a[1]+6*lambda^2*m*sigma*a[1]*a[2]+3*l*lambda*mu*w*b[2]+l*mu^2*w*a[1]+6*m*mu^2*a[1]*a[2]-6*lambda*m*b[1]*b[2]) = 0, -2*l^2*(5*l*lambda^2*mu*sigma*w*a[2]-l*lambda^2*sigma*w*b[1]+5*l*mu^3*w*a[2]-6*lambda^2*m*sigma*a[1]*b[2]-6*lambda^2*m*sigma*a[2]*b[1]-l*mu^2*w*b[1]-6*lambda*m*mu*b[2]^2-6*m*mu^2*a[1]*b[2]-6*m*mu^2*a[2]*b[1]) = 0, 6*l^2*b[2]*(l*w+2*m*a[2]) = 0}, {a[0], a[1], a[2], b[1], b[2]});
Warning, solutions may have been lost
{a[0] = 0, a[1] = 0, a[2] = 0, b[1] = 0, b[2] = 0}, 

   /       l rho - 4 w                                        \ 
  { a[0] = -----------, a[1] = 0, a[2] = 0, b[1] = 0, b[2] = 0 }
   \          6 l m                                           / 
 

Problems with incomplete worksheet.

I have saved a .mw worksheet, which i cannot open in Maple, and i get an error code:
"There were problems during the loading process. Your worksheet may be incomplete"

I have attached a link, where a user is helped with the same problem, but i cannot understand the solution there has been given:

https://www.mapleprimes.com/questions/125503-Incomplete-Worksheet

I have attached the worksheets, and would be so gratefull for any help:

Beregningsdokument.mw
Beregningsdokument_2.mw

Best regards

Henrik Jorgensen

I am trying to work through an example in a textbook, but its a few years old and uses maple 2015. I am currently using the 2018 edition of maple. The code is an example of how to generate the points on an elliptic curve given a specific input. 
Here is the example code from the textbook:

epoints := proc(ec, x, ub, p)
    local ecurve, z, pct, k, i;
    pct := 0;
    for k from 0 to p-1 while pct <= ub do
        z := subs(x=k, ec) mod p;
        if z = 0 then
           pct := pct+1;
           ecurve[pct] := [k,z];
        fi:
        if z &^ ((p-1)/2) mod p = 1 then
           z := z &^ ((p+1)/4) mod p;
           ecurve[pct+1] := [k,z];
           ecurve[pct+2] := [k, -z mod p];
           pct := pct+2;
        fi:
    od:
    if pct > ub then
       pct := ub:
    fi:
    seq(ecurve[i], i=1..pct):
end:

Here is my code, written to work with Maple 2018:

ecpoints := proc (ec, x, ub, p) local ecurve, z, pct, k, i;
      pct := 0; for k from 0 to p-1 while pct <= ub
         do z := `mod`(subs(x = k, ec), p);
         if z = 0 then pct := pct+1;
            ecurve[pct] := [k, z] end if;
         if `mod`(z^((1/2)*p-1/2), p) = 1 then
            z := `mod`(z^((1/4)*p+1/4), p) = 1;
           ecurve[pct+1] := [k, z];
           ecurve[pct+2] := [k, `mod`(-z, p)];
           pct := pct+2 end if
   end do;
   if ub < pct then pct := ub end if;

   seq(ecurve[i], i = 1 .. pct)
end proc

The problem is with the output. The output should be [0, 5], [0, 14], [2, 4], [2, 15], [3, 6], [3, 13], [4, 6], [4, 13], [6, 0], [10, 16], [10, 3], [12, 6], [12, 13], [14, 16], [14, 3], [18, 17], [18, 2].
What I get is [0, 5 = 1], [0, 14 = 18], [2, 4 = 1], [2, 15 = 18], [3, 6 = 1], [3, 13 = 18], [4, 6 = 1], [4, 13 = 18], [6, 0], [10, 16 = 1], [10, 3 = 18], [12, 6 = 1], [12, 13 = 18], [14, 16 = 1], [14, 3 = 18], [18, 17 = 1], [18, 2 = 18]. 
Any hints on what I could be doing wrong here or what is going on?

Hello

Moving from Mathematica to Maple and back these couple of days is driving me insane.  I get stuck trying to translate very simple things for not knowing each command belongs to each software.  Therefore I do apologize for another silly question. 

Given the list of indexed variables

varA := [A[1, 0], A[1, 1], A[1, 2], A[1, 3], A[1, 4], A[1, 5], A[1, 6], A[1, 7], A[1, 8], A[1, 9], A[2, 0], A[2, 1], A[2, 2], A[2, 3], A[2, 4], A[2, 5], A[2, 6], A[2, 7], A[2, 8], A[2, 9], A[3, 0], A[3, 1], A[3, 2], A[3, 3], A[3, 4], A[3, 5], A[3, 6], A[3, 7], A[3, 8], A[3, 9]]

how to apply the following substitution 

varA/. {Subscript[A, m_, 2] -> Subscript[B, m, 3], 
  Subscript[A, m_, 3] -> Subscript[B, m, 2], 
  Subscript[A, m_, 5] -> Subscript[B, m, 6], 
  Subscript[A, m_, 6] -> Subscript[B, m, 5], 
  Subscript[A, m_, 7] -> Subscript[B, m, 9], 
  Subscript[A, m_, 9] -> Subscript[B, m, 7]}

After trying a couple of commands such as map, subs, etc. I decide to try fromMma but no avail.  

Many thanks for the patience and help.

Ed

I want to solve the following system of PDEs with Maple: 

In fact, I want to determine q1,n1,p1,nn1,qn1,pn1 as a functions of pphi1 (assume  ne1(X,T)=(alpha/(2))*pphi1(X,T))

(mu, nu, beta, lambda, TE , alpha and TT are constant, but q1,n1,p1,nn1,qn1,pn1 depend on (X,T))

How do I do that?             

                   
> diff(q1(X, T), X)-lambda*(diff(n1(X, T), X)) = 0;

diff(pphi1(X, T), X)+TE*(diff(p1(X, T), X))-lambda*(diff(q1(X, T), X)) = 0;

-lambda*(diff(p1(X, T), X))+3*(diff(q1(X, T), X)) = 0;

-lambda*(diff(nn1(X, T), X))+diff(qn1(X, T), X) = 0;

-lambda*(diff(qn1(X, T), X))+beta*TT*(diff(pn1(X, T), X))-beta*(diff(pphi1(X, T), X)) = 0;

-lambda*(diff(pn1(X, T), X))+3*(diff(qn1(X, T), X)) = 0;

-mu*ne1(X, T)-nu*nn1(X, T)+n1(X, T) = 0;

Dear All, 

I am trying to solve the following differential equation, which is a kind of Spherical Harmonics. Can anyone please help me out how to solve this?

((D@@2)(y))(r)+(D(y))(r)/r-sin(y(r))*cos(y(r))/r^2+sin(y(r))^2/r-sin(y(r))-sin(2*y(r)) = 0

Thanks 

Hello every one:

I am trying to plat the graph of a function (which has been defined in my code). I use the plat 3D operator but it doesn't give me the correct plot . I even increase the digites and numpoints but appearently it gave me less precise plot . 

The problem of plots is as follows :

First I defined the function V and  asking maple to compute the values of V at some random points, spacially at (0,0) , (0,2*Pi) and (2*Pi,0) . It gave me 0 which means Maple computes the values correctly because it can be mathematically proved  that this function has the value 0 on all the board of a triangle with vertices (0,0) , (0,2*Pi) and (2*Pi,0) . 

As you can see in my code maple doesn't show the correct value (0)  for the boundary points even at (0,0) ! 

I don't know how shoud I fix this problem.You can find my code in attached .Thanks in advanced for your help. Maple_question.mw 

Could some Maple expert please explain this strange behavior of int? Using Maple 2020 on windows 10

Same integrand. But in one case exp(arcsin(x)) and in another exp(1)^arcsin(x). Why one worked and not the other?

Here is the code

restart;
integrand1 := (x^3*exp(arcsin(x)))/sqrt(1 - x^2);
integrand2 := (x^3*exp(1)^arcsin(x))/sqrt(1 - x^2);
simplify(integrand1-integrand2);
int(integrand1,x);
int(integrand2,x)

Download bug.mw

I have a simple little physics scenario that I'd like to nicely pretty print showing the relationships between KE = elastic PE to find velocity when the object returns back to x=0.

This resolves to:

It would be nice to have all the individual terms reduce like how this works in Mathematica:

FullSimplify[Solve[1/2*m*v^2 == 1/2*F*x, v], {F > 0, x > 0, m > 1}]

Any tips on how to get all the square roots to reduce?

bessel.mwHow would I tell maple to stop using a function class to abrievate the work.  I'm trying to have it show the actual derivative instead of it giving me a Bessel function

I want to see the series solution in other words