## simplifying a complex symbolic expression...

Hi everyone, I want to simplify a complex symbolic expression and then separate it to the real and imaginary part in maple. The expression is as below:

Ec := (Ems+I*Eml)*(1+((Ems+I*Eml)/Ef-1)*Zeta*phi/((Ems+I*Eml)/Ef+Zeta))/(1-((Ems+I*Eml)/Ef-1)*phi/((Ems+I*Eml)/Ef+Zeta));

All the constants are positive. Can anyone help?

## Computing a limit by maple....

I want to compute a limit via maple and that it will show me the way how to compute the limit.

The limit is:

\lim_{epsilon ->0, t\in [0,1]} 1/(exp((-1+(1-4*epsilon)^(0.5))/(2*epsilon))-exp((-1-(1-4*epsilon)^(0.5))/(2*epsilon)))*[exp((-1+(1-4*epsilon)^(0.5))/(2*epsilon)*t)-exp((-1-(1-4*epsilon)^(0.5))/(2*epsilon)*t)]/(exp(1-t)-exp(1-t/(epsilon)))

According to my book it should converge to 1.

I tried manually but got stuck.

## seq for sparse rtables...

seq(x) in the help page:  When x is a sparse Matrix, Vector or rtable, only the nonzero entries are scanned.
Is the statement correct/complete?

V := Vector(6, [11,22,0,44], storage=sparse):
entries(V);
seq(V);


[11], [22], [44]
11, 22, 44, 0, 0, 0

## how to find back the system which solution is maxw...

how to find back the system which solution is maxwell equations?

as maxwell equations is an invariant,

if solution is maxwell which is invariant, how to find back the system which solve it, the solution is maxwell?

will there a multiple systems which solution is maxwell equations?

if can not find, how to enumerate all combinations of systems to search maxwell equations?

## Fourier Transform Amplitude spectrum...

How can I plot this fourier transform as a amplitude spectrum?

F(w)=(10/w)*exp(-7iw)*sin(4*w)

I ploted |f(w)| vs w. But it is not the answer. |F(w)|=(10/w)*sin(4*w)

## How to display an Array filled with 0?...

Hi,

I'm stuck on this problem to which a careful reading of the help pages would probably give an answer:

Why is the return of Array(-1..1, [1$3]) of a different type than the one of Array(-1..1, [0$3]) ?

 > restart:
 > B := Array(-1..1,[1$3]); lprint(B);  Array(-1 .. 1, {-1 = 1, 0 = 1, 1 = 1})  > B := Array(-1..1,[0$3]); lprint(B)
 Array(-1 .. 1, {})
 > seq(B[n], n=-1..1)
 (1)
 >

## How to use a previous result (output) on a definit...

Hello

I am definitely missing something on how Maple deals with functions and outputs.  I need to define a new function using an output of a previous calculation but I didn't figure out how to do it.

aux := rsolve({y(0) = y0, y(n) = 4*y(n-1)*(1-y(n-1))}, y(n));
solucao := (n,y0)-> aux;
solucao(3,1/2);

Neither n nor y0 are replaced for the given values.  What am I missing?

Many thanks

Ed

## Calculate limit with symbolic tool ?...

Hi

I am trying to compute a limit to demonstrate the link between the binomial and Poisson distribution. (lambda = np)

ComplémentCalculSymbolique.mw

## Calculate Variance with symbolic calcul ?...

Hi,

I try to symbolically calculate the variance of the binomial distribution (np(1-p)), but the result is not simplified

ComplémentCalculSymbolique.mw

## fsolve(complex equation) and parallel programing...

Hi everybody
I have some problems with fsolve(complex equation). It results some answers (I expect answers in the range 10e6 to 10e11) but substitution them into the main equation leads to numbers of order 10e-8 to 10e8. I know fsolve solves equation numerically, so 10e-8 t0 10e-6 is acceptable, but what about 10e7? How can I handle this problem? I have an Array of this kind of equations to solve and then analyze answers.
How can I increase the speed of calculations? I try to do some parallelization (thanks dohashi for posts about parallel programming) but I couldn't do. I upload the code below.

Thanks.

EQ1 := 1.780876811*10^90*(-(1.857495893*10^(-32)*I)*(-(.9215096529*(-1.077177489*10^(-57)*omega^2+1.251444314*10^(-43)-7.423792254*10^(-74)*omega^4))*(1.042248387*10^(-7)*omega-3.773917830*10^(-22)*omega^3)+1.022012860*10^(-43)-9.365146438*10^(-58)*omega^2+1.290731820*10^(-74)*omega^4+8.072440803*10^(-47)*omega^2*(7.038725244*10^(-13)-9.109383000*10^(-28)*omega^2))*exp(-.9800000000*I-4.717786244*10^(-17)*omega^2)-(1.857495893*10^(-32)*I)*((.9215096529*(5.411991727*10^(-58)*omega^2-1.370413754*10^(-43)+1.063387455*10^(-73)*omega^4))*(1.042248387*10^(-7)*omega-3.773917830*10^(-22)*omega^3)-1.119171234*10^(-43)+3.850718130*10^(-58)*omega^2+1.279097989*10^(-74)*omega^4+1.703871878*10^(-48)*omega^2*(5.154059190*10^(-14)+3.036461000*10^(-28)*omega^2)+8.072440803*10^(-47)*omega^2*(7.038725244*10^(-13)+9.109383000*10^(-28)*omega^2))*exp(.9800000000*I-4.717786244*10^(-17)*omega^2)+2.054040475*10^(-31)*((1.936145393*10^(-59)+1.043762907*10^(-58)*I)*omega^2+4.297601656*10^(-46)-1.690952584*10^(-44)*I+(-1.159596547*10^(-75)+1.164619044*10^(-74)*I)*omega^4)*exp(-4.717786244*10^(-17)*omega^2)*(1.042248387*10^(-7)*omega-3.773917830*10^(-22)*omega^3)+(2.799879047*10^(-71)*I)*(-6.704964363*10^(-12)-3.118737242*10^(-28)*omega^2)*omega*exp(.9800000000*I-1.090999486*10^(-14)*omega^2)-(2.799879047*10^(-71)*I)*(8.281232388*10^(-12)+2.177273887*10^(-28)*omega^2)*omega*exp(-.9800000000*I-1.090999486*10^(-14)*omega^2)+3.476335242*10^(-51)*((.1388433141*I)*(-2.893776471*10^(-25)-1.303697368*10^(-38)*omega^2+7.808106616*10^(-55)*omega^4)+4.959435112*10^(-25)-3.098806468*10^(-39)*omega^2-3.391707726*10^(-55)*omega^4-1.314961283*10^(-30)*(-2.854029409*10^(-11)+1.827522021*10^(-27)*omega^2)*omega^2)*exp(-4.717786244*10^(-17)*omega^2)-2.814230381*10^(-37)*(9.949004410*10^(-35)*(-6.832852706*10^(-13)-1.621609260*10^(-14)*I-(2.889900216*10^(-30)*I)*omega^2-(.9082907587*I)*(8.002616800*10^(-12)-1.954522389*10^(-30)*omega^2)-(.4487255373*I)*(9.612550267*10^(-12)+9.109383000*10^(-28)*omega^2)+4.081082866*10^(-29)*omega^2)*exp(-1.090999486*10^(-14)*omega^2)-1.995292057*10^(-54)*omega)*omega)/omega^2

Test_MaplePrime971127.mw

## Galton Board animation?...

Hi,

I’m looking for a MathApps or animation of  Galton Board ’s experiment ( statistics distributions). Any ldeas?

Thanks

## Multiplying Eigenvalues...

Question: Generate 8 random 3 by 3 matrices using the RandomMatrix command from the  LinearAlgebra package. As each matrix is generated use Eigenvalues to compute its eigenvalues. Then take the product of the eigenvalues, and check that for each matrix, this product is equal to the determinant of the matrix.

[Hint: The product will be complicated algebraically and you will need to apply first expand, then simplify to reduce the product of the eigenvalues to an integer. First try to do for a single matrix , then make a loop to do it 8 times.]

Attempt:
> with(LinearAlgebra):

for i from 1 to 8 do

M[i]:=RandomMatrix(3,3):

N[i]:=Eigenvalues(M[i]):

simplify(N[i]):
end do:

evalf(N[i].N[i]);
When I change the 8 from 1-7 I get a number, but once I change it to 8 I get "N 2(over)9"

can I get any suggestions

## map a list of functions expecting two input values...

Hi there. Thank you all in advanced.

The general question is how to pass a pair of values to a list of functions that expect that pair of values as input.
I already know this solution for passing a list of values to a list of functions that expect one value as input.

map(eval~,[f(x),g(x)],x=~[p,q,t])

Well f(x) and g(x) take every element of the list, but what if f(x) and g(x) expect two values. The concrete case is to pass p and q to iquo and irem. The following were my tries:

• map(eval~,[iquo(x),irem(x)],x=[p,q])
• map(eval~,[iquo(x),irem(x)],x=(p,q))
• map(eval~,[iquo(op(x)),irem(op(x))],x=[p,q])

I searched and found some partial related topics in the site but not quite with this approach.

## Using series/asympt for RootOf...

Hello,

How do I tell maple which branch to choose when calculating an asymptotic series of a RootOf expression. e.g.

restart;

sol:=RootOf((8*n-8)*_Z^6+(n^4+36*n^2-68*n+56)*_Z^5+(n^5+10*n^4+80*n^3-200*n^2+224*n-152)*_Z^4+(n^6+28*n^5+69*n^4-268*n^3+468*n^2-356*n+200)*_Z^3+(3*n^7+32*n^6+7*n^5-204*n^4+380*n^3-544*n^2+272*n-128)*_Z^2+(3*n^8+14*n^7-20*n^6-32*n^5+252*n^4-240*n^3+304*n^2-80*n+32)*_Z-n^9-12*n^8-44*n^7-40*n^6-4*n^5-128*n^4+48*n^3-64*n^2);

asympt(sol,n,2);

Now the series contains RootOf(_Z^6-_Z^5) which occurs in the denominator to order 1/n and thus blows up if 0 is chosen. I know that the solution must be greater zero and smaller than n/2.