Items tagged with root

Dear all,

I have the following problem: Maple does not simplify the denominator in the following example:

which gives

16*a^8*B/((dz*L*sqrt(s)*sqrt(s+c)*sqrt(L^2*s*(s+c)*dz^2+4*a^2)+L^2*s*(s+c)*dz^2+2*a^2)^2*(-dz*L*sqrt(s)*sqrt(s+c)*sqrt(L^2*s*(s+c)*dz^2+4*a^2)+L^2*s*(s+c)*dz^2+2*a^2)^2)

However, the result should be B. If only the denomiator is expanded it works: 

gives

16*a^8

which equals the nominator except for the B...

How can I use simplify in order to yield the desired result? 

Thanks a lot!

 

 

 

Table_1_for_example_1.mw

I am try to find root by using fsolve. But I am not get solution.

Please help me to solve this problem?

I have been attached the program above.

Thank You.

Best Regards.

Velmurugan G

 

 

 

hi.please help me for gain result with out root of form....

thanks

root_of.mw

digite := 20; -1; L := 20*R; -1; varepsilon := solve(tan(sigma*L/(2*R))+tanh(sigma*L/(2*R)), sigma)

(1/10)*RootOf(tan(_Z)+tanh(_Z))

(1)

``


Download root_of.mw

hello.

i have two problem in maple file, that is attached..

one of them is RootOf...note that i suppose that [varepsilon := -2.3650203724313] for i can going on following calculation

and second is  Float(undefined) in calculation integral

please help me

thanks

(m=1_n=6)2.mw

Hello,how can i find the roots of this equation? "5lambda.tan(lambda)-1" and lambda=0..10

hi.how convert root of to explicit form.

w is a imaginary..

thanks

123.mw

restart; w := (1/2)*(2*d-5+I*sqrt(4*d-9))/(d-2)

(1/2)*(2*d-5+I*(4*d-9)^(1/2))/(d-2)

(1)

with(LinearAlgebra):

{Q1 = RootOf((2*I)*(4*d-9)^(1/2)*_Z*d-((2*d-5+I*(4*d-9)^(1/2))/(d-2).(d*(I*(4*d-9)^(1/2)+1)*_Z/((d-2)*b)))*b*d+2*((2*d-5+I*(4*d-9)^(1/2))/(d-2).(d*(I*(4*d-9)^(1/2)+1)*_Z/((d-2)*b)))*b-2*d*_Z), Q2 = -(1/2)*d*(I*(4*d-9)^(1/2)+1)*RootOf((2*I)*(4*d-9)^(1/2)*_Z*d-((2*d-5+I*(4*d-9)^(1/2))/(d-2).(d*(I*(4*d-9)^(1/2)+1)*_Z/((d-2)*b)))*b*d+2*((2*d-5+I*(4*d-9)^(1/2))/(d-2).(d*(I*(4*d-9)^(1/2)+1)*_Z/((d-2)*b)))*b-2*d*_Z)/((d-2)*b)}

(2)

``

 

Download 123.mw

I have problem to get real answer in a simple equation. maple just give me complex answer.

how i can get parametric real answer? Ihave trid this two way but not applicaple.

with(RealDomain); assume(T::real)

My code is:
Qz := 7.39833755306637215940309264474*10^7*sqrt(1/T)*(T-297.2)/T-16242.7935852035929839431551189*sqrt(1/T)/T;

q := (.6096*(299.2-T))/(sqrt(1.60000000000000000000000000000*10^(-9)-r^2)-0.346410161513775458705489268300e-4);

with(RealDomain); assume(T::real);

e := simplify(solve({0 = q-Qz}, {T}))

and the result like:

e := {T = 1/RootOf(-609600000000000000000000000000000000000000000000000000000+(879515018020273730453559011332895956000000000000000000000000000*sqrt(-625000000*r^2+1)-761682348615485390130551939524898425387968750740910059296172487)*Z^5+(-2959335021226548863761237057896000000000000000000000000000000*sqrt(-625000000*r^2+1)+2562859306691152293409465394507279449380503585614734443742000)*_Z^3+182392320000000000000000000000000000000000000000000000000000*_Z^2)^2}

dose anyone hase any opinion?

Dear friends

It seems that Maple takes a long time to evaluate the square roots of numbers.

See the simple code below.

st := time();

for i to 1000 do for j to 1000 do

a[i, j] := evalf(abs(i-j+1)^0.3-abs(i-j)^0.3):

end: end:

time()-st

I run it, then after a few seconds I run it again and again  to see the consuming time: once the running time is 77 seconds, then is 57 seconds, again is 73 seconds ...

Two questions:

1- Why the time is so differnt?

2- Why a simple code is being done at about a minute? Based on the number of operations, I think it should be done at less than a second. It just involves finding two million real third roots each of them less than 100 operations (if Newton method for finding roots is applied it probably needs less than 20 operations). I was thinking that a computer may do one billion operations per second. 

Since I need to report my numerical results in a scientific paper, it is important for me to know what's going on.

It is worthy of noting that I use Maple 18 on a Lenovo Laptop with Corei3 1.90 GHz with 64 bit operating system and 4 Gb RAM.

In advance, I appreciate for helping me to reveal the secrets.

Thank you all

 

Nonzero complex numbers a, b, and c are such that every pair of the polynomials ( in x )
a*x^11+b*x^4+c, b*x^11+c*x^4+a, c*x^11+a*x^4+b has a common root. How to prove or disprove with Maple that all the three polynomials have a common root? I am aware of the resultant command in Maple.

Dear all;

I need you help for solving this problem, and thanks in advantage for your help.

I have a polynom like  P =x^6-4*x^3+x-2;  and i would like to find an approximate value of the roots in some interval [a,b] =[-2,2] using sturm sequence.

The method is based on:

1) first construct the sturm sequence:

For given polynom P =x^6-4*x^3+x-2;

Let S0=P;

S1=diff(p,x);

let   s:=quo(S0,S1,x);
       S2:=-rem(S0,S1,x);

.... S[k+1-rem(S[k-1],S[k]);

 

S[k] is the sturm sequence.

2) let f(a)= number of change of sign in the sturm sequence and f(b) the same . so f(b)-f(a) give the number of roots in the interval [a,b].

3) If f(b)-f(a) =0 so there are no roots

and if f(a)-f(b)=1 one can find the root

4) if f(a) -f(b) >2  :

given toterance tol=0.001; for example

if the abs(a-b)<2*epsilon we display a message that there are k roots at (b+a)/2

with our error tolerance

5) otherwise if c=(b+a)/2 is not a root of P_k(x)  for any k, ( where p_k is an element of the sturm sequence ) 

we divide the interval into equal halves [a,c] and [x,b] and we run step 2 on each interval

else if c is a root of one of these p_k(x) add any time account to c so that c lies close the middle of [a,b] and not a root

6) Give all the roots ( approximate the rrots with small error epsilon).

 

I kindly  appreciate your help

 

 

 

Dear Friends:

I am currently working on a calculation for phase velocity of acoustic waves and don’t get along.  

My equation has the following form:

equ := tan( (31 / 20000) * sqrt( -9610000/c^2 + 1) / Pi) / tan((961/1260000) * sqrt( -39690000/c^2 + 1)/ P i) = -(1191640000/63)*sqrt(-9610000/c^2 + 1)*sqrt (-39690000/c^2 + 1)/ (c^2*(19220000/c^2 - 1)^2)

Using ‘sol = solve(equ,c)’ returns

sol := 96100* RootOf(1 + (400000000 * Pi^2 * RootOf(40320000000000000000 * Pi^4 * tan(_Z)*_Z^4256000000000000 * Pi^3 * csgn(_Z) * _Z^3 * tan((1/157500) * sqrt(24806250000 * Pi^2 * _Z^2 - 45167) / Pi) * sqrt(24806250000 * Pi^2 * _Z^2 - 45167) -96868800000000 * Pi^2 * tan(_Z) * _Z^2 + 615040000 * Pi * csgn(_Z) * _Z * tan((1/157500) * sqrt(24806250000 * Pi^2 * _Z^2 - 45167) / Pi ) * sqrt(24806250000 * Pi^2 * _Z^2 - 45167)+58181823 * tan(_Z))^2 - 961)* _Z^2)

c should be in a range of 13,000.

Two questions:

1) How can I deal with _Z?

2) Any suggestion how I can calculate ‘c’? Maybe numerical?

I am relative new in maple…

Many thanks!

Alex

How to find (i. e. to evaluate) the positive root of the polynomial equation

mul(x+j, j = 0 .. 2015)=1?

The command

RootFinding:-NextZero(x-> mul(x+j, j = 0 .. 2015)-1 , 0);

outputs

                              FAIL
The same with Digits:=100.

solve.mw

Hi all, I want to determine the roots of this figure that attached here. But the function has 5 parameters so the code doesn't work for it! Help me.

I have another question: The code that attached, determine the roots on horizontal axis, how could I find the values of root on vertical axis?In this figure I want to know the value of F(0) that cut the vertical axis?

Regards

 

``

``

``

plot(KummerM(1/2-(1/4)*sqrt(2*Nu), 1, sqrt(2*Nu)), Nu = 0 .. 120)

 

``

j := 1

"for i from 0 to 100000 do  Nu[i]= i/(1000); end do;    for i from 0 to 100000 do  if (KummerM(1/(2)-1/(4)*sqrt(2*Nu[i]),1,sqrt(2*Nu[i]))=0)  x[j]=Nu[i]; j= j+1;  end do if ;  end;   I know the answers for   x    are: 3.6568,  22.3047,  56.9605,  107.6203,  174.2820,  256.9450,  355.6088,  470.2730...     I    can    solve    only    one    of    them:           "

evalf(solve(KummerM(1/2-(1/4)*sqrt(2*Nu), 1, sqrt(2*Nu)) = 0))

3.656793458

(1)

PLEASE*HELP*ME

 

Download loop.mw

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 ?

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