## asfn

Mr. alireza seraj

## 272 Reputation

15 years, 143 days

MS in physics.

## explain...

i want to convert "f=0" to a polynomial in terms of "zin", like:

a*zin^2+b*zin+c=0

so then how can i get it's coefficients?

## ok...

for example if u have:

f := -x^2+6*x+4;

what "x" maximize "f"?

and if we have just plot of f, can we get such "x" that maximize "f"?

## ok...

for example if u have:

f := -x^2+6*x+4;

what "x" maximize "f"?

and if we have just plot of f, can we get such "x" that maximize "f"?

## thanks alot, but ... my code...

thanks alot, but ...
my code is here. paste and run it.

with(LinearAlgebra); with(Student[Calculus1]);
d1 := [seq(0.1e-5*i, i = .1 .. 2, .1)]; w := Array(1 .. 20); h := Array(1 .. 20);
N := 10; theta1 := 0; n1 := 1.5; n2 := 3.5; d2 := 0.5e-6; c := 0.3e9;
theta2 := arcsin(n1*sin(theta1)/n2);
`#mover(mi("n1"),mi("~"))` := n1*cos(theta1);
`#mover(mi("n2"),mi("~"))` := n2*cos(theta2);
phi2 := 2*Pi*`#mover(mi("n2"),mi("~"))`*d2*nu/c;
for j to 20 do
Lambda := d1[j]+d2;
`#mover(mi("n"),mo("&uminus0;"))` := (n1*d1[j]+n2*d2)/Lambda;
`&nu;b` := c/(`#mover(mi("n"),mo("&uminus0;"))`*(2*Lambda));
phi1 := 2*Pi*`#mover(mi("n1"),mi("~"))`*d1[j]*nu/c;
M1 := `<|>`(`<,>`((`#mover(mi("n2"),mi("~"))`+`#mover(mi("n1"),mi("~"))`)*exp(-I*phi1), (`#mover(mi("n2"),mi("~"))`-`#mover(mi("n1"),mi("~"))`)*exp(-I*phi1)), `<,>`((`#mover(mi("n2"),mi("~"))`-`#mover(mi("n1"),mi("~"))`)*exp(I*phi1), (`#mover(mi("n2"),mi("~"))`+`#mover(mi("n1"),mi("~"))`)*exp(I*phi1)))/(2*`#mover(mi("n2"),mi("~"))`);
M2 := `<|>`(`<,>`((`#mover(mi("n2"),mi("~"))`+`#mover(mi("n1"),mi("~"))`)*exp(-I*phi2), (`#mover(mi("n1"),mi("~"))`-`#mover(mi("n2"),mi("~"))`)*exp(-I*phi2)), `<,>`((`#mover(mi("n1"),mi("~"))`-`#mover(mi("n2"),mi("~"))`)*exp(I*phi2), (`#mover(mi("n2"),mi("~"))`+`#mover(mi("n1"),mi("~"))`)*exp(I*phi2)))/(2*`#mover(mi("n1"),mi("~"))`);
Mcell := `.`(M2, M1);
h[j] := abs(Re(Mcell[2, 2]));
L := Roots(h[j]-1, nu = 1 .. 2*`&nu;b`, numeric);
w[j] := L[2]-L[1]
end do:
---------------------------------------------

and after that, run this:

---------------------------------------------

d1 := [1.*10^(-7), 2.*10^(-7), 3.*10^(-7), 4.*10^(-7), 5.*10^(-7), 6.*10^(-7), 7.*10^(-7), 8.*10^(-7), 9.*10^(-7), 0.10e-5, 0.11e-5, 0.12e-5, 0.13e-5, 0.14e-5, 0.15e-5, 0.16e-5, 0.17e-5, 0.18e-5, 0.19e-5, 0.20e-5];
d2 := 0.5e-6;
d := d1/d2;
f := CurveFitting:-PolynomialInterpolation(d,w, x);

---------------------------------------------
the error still exists.

## thanks alot, but ... my code...

thanks alot, but ...
my code is here. paste and run it.

with(LinearAlgebra); with(Student[Calculus1]);
d1 := [seq(0.1e-5*i, i = .1 .. 2, .1)]; w := Array(1 .. 20); h := Array(1 .. 20);
N := 10; theta1 := 0; n1 := 1.5; n2 := 3.5; d2 := 0.5e-6; c := 0.3e9;
theta2 := arcsin(n1*sin(theta1)/n2);
`#mover(mi("n1"),mi("~"))` := n1*cos(theta1);
`#mover(mi("n2"),mi("~"))` := n2*cos(theta2);
phi2 := 2*Pi*`#mover(mi("n2"),mi("~"))`*d2*nu/c;
for j to 20 do
Lambda := d1[j]+d2;
`#mover(mi("n"),mo("&uminus0;"))` := (n1*d1[j]+n2*d2)/Lambda;
`&nu;b` := c/(`#mover(mi("n"),mo("&uminus0;"))`*(2*Lambda));
phi1 := 2*Pi*`#mover(mi("n1"),mi("~"))`*d1[j]*nu/c;
M1 := `<|>`(`<,>`((`#mover(mi("n2"),mi("~"))`+`#mover(mi("n1"),mi("~"))`)*exp(-I*phi1), (`#mover(mi("n2"),mi("~"))`-`#mover(mi("n1"),mi("~"))`)*exp(-I*phi1)), `<,>`((`#mover(mi("n2"),mi("~"))`-`#mover(mi("n1"),mi("~"))`)*exp(I*phi1), (`#mover(mi("n2"),mi("~"))`+`#mover(mi("n1"),mi("~"))`)*exp(I*phi1)))/(2*`#mover(mi("n2"),mi("~"))`);
M2 := `<|>`(`<,>`((`#mover(mi("n2"),mi("~"))`+`#mover(mi("n1"),mi("~"))`)*exp(-I*phi2), (`#mover(mi("n1"),mi("~"))`-`#mover(mi("n2"),mi("~"))`)*exp(-I*phi2)), `<,>`((`#mover(mi("n1"),mi("~"))`-`#mover(mi("n2"),mi("~"))`)*exp(I*phi2), (`#mover(mi("n2"),mi("~"))`+`#mover(mi("n1"),mi("~"))`)*exp(I*phi2)))/(2*`#mover(mi("n1"),mi("~"))`);
Mcell := `.`(M2, M1);
h[j] := abs(Re(Mcell[2, 2]));
L := Roots(h[j]-1, nu = 1 .. 2*`&nu;b`, numeric);
w[j] := L[2]-L[1]
end do:
---------------------------------------------

and after that, run this:

---------------------------------------------

d1 := [1.*10^(-7), 2.*10^(-7), 3.*10^(-7), 4.*10^(-7), 5.*10^(-7), 6.*10^(-7), 7.*10^(-7), 8.*10^(-7), 9.*10^(-7), 0.10e-5, 0.11e-5, 0.12e-5, 0.13e-5, 0.14e-5, 0.15e-5, 0.16e-5, 0.17e-5, 0.18e-5, 0.19e-5, 0.20e-5];
d2 := 0.5e-6;
d := d1/d2;
f := CurveFitting:-PolynomialInterpolation(d,w, x);

---------------------------------------------
the error still exists.

## thank u veru much!...

thank u veru much!

## thank u veru much!...

thank u veru much!

## thanks for your guide. i...

i wanted to if possible color the surface for example in blue and the other in red to show good contrast to understand even tiny slope from z=1.

## thanks for your guide. i...

i wanted to if possible color the surface for example in blue and the other in red to show good contrast to understand even tiny slope from z=1.

## thanks very much!...

thanks very much!

## thanks very much!...

thanks very much!

## thank you, Robert.  ...

thank you, Robert.

## thank you, Robert.  ...

thank you, Robert.

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