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Can I use Maple to solve equation like |a-b|+\sqrt{2b+c}+c^2-c+1/4=0 for a,b,c?

 

a,b,c are real numbers and I need to solve it in real domain.

I have the following characteristic equation by use of maple. How do I find a condition on x, that will return real eigenvalues and complex eigenvalues?

 

 

 

So here is the issue: I have a 50 by 50 tridiagonal matrix. The entries in the first row, first column are -i*x and the last row last column is -i*x; these are along the main diagonal, where i is complex and x is a variable. Everything in between these two entries is 0. Above and below the main diagonal the entries are -1. My issue is that I have to find a conditon on x that makes the eigenvalues real. I am completely new to maple and have no programming experience.. Can someone show me how to this?

Hi,

I got the Real and Imaginary of an expression J1 

assume(d,real):

Gamma:=0.04:tau:=10*Pi:j:=0:

J1:=(exp((1-I*d)*Gamma*tau)-1)/((1-I*d));

J1mod:=simplify((Re(J1))^2+(Im(J1))^2): (I works here this amont is real)

################

but when I change the expression  for J1 to be

J1:=((2*e^(-2^(-j-1)*(1-I*d))-e^(-2^(-j)*(1-I*d))-1)*exp((1-I*d)*Gamma*tau)-1)/((1-I*d)):

J1mod:=simplify((Re(J1))^2+(Im(J1))^2): 

J1mod here is complex(I dont know why? it doesnt separate the real and the im )

Any comments will help

Thanks

Hi,

I need you help to understand this problem.

 

Let alpha=0.1.;

When I do :  (-0.2)^alpha I get a complex number.

 

I must find a real number.

What's the problem

Thanks for your idea.

 

Hi all.

I try to get the real part from the complex expression. But it turns out to not be the simplest result:

A:=I*sin(k*Pi*(x-h*cos(theta))/a)*sin(l*Pi*(y-h*sin(theta))/b)*exp(-I*k[0]*h)*sin(k*Pi*x/a)*sin(l*Pi*y/b)

convert(exp(-I*k[0]*h), sin);

simplify(Re(A));

Maple results in:

Re(sin(k*Pi*(-x+h*cos(theta))/a)*sin(l*Pi*(-y+h*sin(theta))/b)*exp(-I*k[0]*h)*sin(k*Pi*x/a)*sin(l*Pi*y/b))

while the simplified result should be:

sin(k*Pi*(x-h*cos(theta))/a)*sin(l*Pi*(y-h*sin(theta))/b)*sin(k*Pi*x/a)*sin(l*Pi*y/b)*sin(k[0]*h)

 

I wander how to get the simplifyed result in maple. Thanks

If we a complex number in Maple, like for example:

I*b+a+x+I*y+I^2*c

 

How can we make maple rewrite it like this?

a+x-c+I*(y+b)

 

I tried using the comands Re(%) and Im(%) but Re just gives the whole expression again and Im gives 0.

I have a characteristic equation. some times It has polar roots . sometimes It has real roots and sometimes both of them.

I want to extract real roots and extract polar roots if they are.

for instance:

q:=m3*r^3+m2*r^2+m1*r+m0:

rot:=solve(q=0,r);

I want to know how can I use if in this part ?

Hello guys

I have a question:

I have an equation like below. Always it has different order for example :

T1:=q3*(r^6)+q2*(r^4)+q1*(r^2)+q0:
solve(T1=0,r):
and sometimes:

T2:=q5*(r^4)+q6*(r^2)+q7:
solve(T2=0,r):
q0,q1,q2,q3,q4,q5,q6 and q7 are constants.

We know that for T1 It has two real answer and for T2 we have any real answer.

How can I specify generally the real answers for all of them?

I want to use these real answer for another equation.

Thanks

Greetings to all!

Recently I encouter the following issue:

Maple (version 17) coudn't recognize that 20.0 equals with 20 and with 20.00. Believe me, this is very annoying!

Do I miss something? Is there any command that do the trick?

 

Thank you!

Giorgos K.

 

 

To motivate some ideas in my research, I've been looking at the expected number of real roots of random polynomials (and their derivatives).  In doing so I have noticed an issue/bug with fsolve and RootFinding[Isolate].  One of the polynomials I came upon was

f(x) = -32829/50000-(9277/50000)*x-(37251/20000)*x^2-(6101/6250)*x^3-(47777/20000)*x^4+(291213/50000)*x^5.

We know that f(x) has at least 1 real root and, in fact, graphing shows that f(x) has exactly 1 real root (~1.018).  However, fsolve(f) and Isolate(f) both return no real roots.  On the other hand, Isolate(f,method=RC) correctly returns the root near 1.018.  I know that fsolve's details page says "It may not return all roots for exceptionally ill-conditioned polynomials", though this system does not seem especially ill-conditioned.  Moreover, Isolate's help page says confidently "All significant digits returned by the program are correct, and unlike purely numerical methods no roots are ever lost, although repeated roots are discarded" which is clearly not the case here.  It also seems interesting that the RealSolving package used by Isolate(f,method=RS) (default method) misses the root while the RegularChains package used by Isolate(f,method=RC) correctly finds the root.

 All-in-all, I am not sure what to make of this.  Is this an issue which has been fixed in more recent incarnations of fsolve or Isolate?  Is this a persistent problem?  Is there a theoretical reason why the root is being missed, particularly for Isolate?

Any help or insight would be greatly appreciated.

Hi everyone,

I have a maple program that generates a polynomial g(y)=(80y^8 + 68y^6 + 12y^4 -4y^2 -1). This polynomial has two real roots (irrational roots), call them +/- y*. My code does a sequential calculation, and often sI am left with a higher order polynomial in y that has the form h(y)= p(y)*g(y), where p(y) is also a polynomial in y. This polynomial h(y)=p(y)*g(y) is not in factored form (i.e. it would look like expand(p(y)*g(y)). Is there a way to instruct maple to recoginize that +/-y* is also a root h(y)=p(y)*g(y)? So far I've tried things like applyrule([g(y*)=0],h(y*)), but nothing seems to work (I suspect because Maple cannot recgonize that g(y) is a factor of h(y)). I am not interested in computing this numerically. I am just trying to find a way to instruct Maple to recognize symbolically that h(y*) =0.

Thanks a million for anyone who has any idea.

Best,

 

Justin

I am using Maple 15 to numerically solve a system of differential algebraic euqations (DAE) with given initial conditions, and I've tried rfk45_dae and rosenbrock_dae solver, but both solver responded in error like this

 

Error, (in dsolve/numeric) cannot numerically solve complex DAE initial value problems, the system must be converted to a real system

 

I don't understand what is a real system, and how could i convert it to a real system.

 

Hello,

• Is there a simple way to find the domain for the real solutions of f(x)?

• And is there a way to let maple get the part of f(x) with the sqrt?
   (not by typing it by hand as I dit below)

• Is there a way to write the summary of the found domains in one line?

Thanks for your help. 





restart:
# How to find the Domain for real solutions for x?
f(x):=(x-1+sqrt(x^2-3*x+2))/(x-1);
discont_for_x=discont(f(x),x);
# x<>+1 (because the de denom=0 is not allowed)
denom(f(x))=0;
x={solve(denom(f(x))=0,x)};
# x<=1 union  2<=x (because the part under the sqrt must be >=0 to give Real solutions)
sqrt(x^2-3*x+2);
0<=x^2-3*x+2;
x=solve(0<=x^2-3*x+2,x);




Hi, the title isn't great as I didn't know how to describe this really. I need to solve the following equation for b:

y = (1-exp(-x*b))/(1-exp(-50*b))

When I put a value for y in, this is fine and fsolve gives me a numeric real solution. However, even when using RealDomain, it does not give me a real solution if I leave y as it is, and instead gives a 'RootOf' solution, which I don't really understand. This is the same whether using solve or isolate:

b=-(1/50)RootOf(_Zx-50ln(-y+ye^(_Z)+1))

I have the values of x and y for multiple data points and can put them in an nx1 matrix. Is there a way to replace x and y with matrices (with real numbers in) and solve for each set of points for b (ie there would be n values of b)? Obviously I could go through and put in each value of x and y but this would take ages, so was just wondering if there's a quick way to do this.

I have tried by simply putting matrices instead of the letter but get the error:

Error, invalid input: exp expects its 1st argument, x, to be of type algebraic, but received Vector(50, {(1) = -50*b, (2) = -49*b,...

Thanks for your time

James

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