i used
"with(Statistics):"
and then "ScatterPlot" for two lists.
now i prefer to join(a perfect fit of) these curve-like dots by a line.

after calculation of hz[i] and x[i],
if we have :
hhz := piecewise(x < x[1], hz[1], x[1] < x and x < x[2], hz[2], x[2] < x and x < x[3], hz[3], x[3] < x and x < x[4], hz[4], x[4] < x and x < x[5], hz[5], x[5] < x and x < x[6], hz[6], x[6] < x and x < x[7], hz[7], x[7] < x and x < x[8], hz[8], x[8] < x and x < x[9], hz[9], x[9] < x and x < x[10], hz[10]);
is there any way to SUMMARIZE hhz in writing?

something like this
for i to 10
.
(calculation of Ai)
(calculation of Bi)
.
hi=Ai*cos(c*x)+Bi*sin(d*x)
end
plot(? hi)
what should i apply instead of ? or like that?

how can i get absolute value of width of the first peak at y=1 or y=-1(whichever is the first)? pls help me.

this was a piece of a program that i had to extract the plot expression to display shape of it and explain my scope for u!

i have many codes containing a shape like that (periodic).

how can i get the absolute value of the width of the first peak in "y=1" (or "-1 ,if u could shift the peaks under y axis by abs to above it. i dont know why abs doesn't work.")?

i want to draw a plot of the first widths of many charts like that, versus something else. i only want to know the value of the width.

with defining a constant below to be used in spacing;

`νb` := 6.00*10^13; and :

`evalf/constant/νB` := proc () options operator, arrow; `νb` end proc:

if u plot :

plot([abs(.9999999996*cos(1.166666667*10^(-14)*Pi*x)*cos(5.000000000*10^(-15)*Pi*x)-1.380952380*sin(1.166666667*10^(-14)*Pi*x)*sin(5.000000000*10^(-15)*Pi*x)), 1], nu = 0 .. 6*`νb`, tickmarks = [spacing(`νB`), default]);

you can see a periodic plot that cross "y=1" in some points.

i cant obtain these intersection points and assign them, especially the first(not "x=0") and the second one.

also the "abs" isn't work! why?

here is my complete codes without any errors. you can paste it in maple, it will work. look at the plot. it has some surfaces in maximum height of plot at z=1. i want color this surface in a distinct color from other potions of the plot :
with(LinearAlgebra); with(plots); N := 10; n1 := 1.5; n2 := 3.4; n3 := 3.5; d1 := 0.16e-6; d2 := d1; d3 := d1; c := 0.3e9; theta2 := arcsin(n1*sin(theta1)/n2); theta3 := arcsin(n2*sin(theta2)/n3); `#mover(mi("n1"),mi("~"))` := n1*cos(theta1); `#mover(mi("n2"),mi("~"))` := n2*cos(theta2); `#mover(mi("n3"),mi("~"))` := n3*cos(theta3); Lambda := d1+d2+d3; `#mover(mi("n"),mo("&uminus0;"))` := (n1*d1+n2*d2+n3*d3)/Lambda; `νb` := c/(`#mover(mi("n"),mo("&uminus0;"))`*(2*Lambda)); `evalf/constant/νB` := proc () options operator, arrow; `νb` end proc; phi1 := 2*Pi*n1*d1*nu*cos(theta1)/c; phi2 := 2*Pi*n1*d1*nu*cos(theta2)/c; phi3 := 2*Pi*n1*d1*nu*cos(theta3)/c; M111 := (`#mover(mi("n2"),mi("~"))`+`#mover(mi("n1"),mi("~"))`)*exp(-I*phi1); M112 := (`#mover(mi("n2"),mi("~"))`-`#mover(mi("n1"),mi("~"))`)*exp(I*phi1); M121 := (`#mover(mi("n2"),mi("~"))`-`#mover(mi("n1"),mi("~"))`)*exp(-I*phi1); M122 := (`#mover(mi("n2"),mi("~"))`+`#mover(mi("n1"),mi("~"))`)*exp(I*phi1); M211 := (`#mover(mi("n3"),mi("~"))`+`#mover(mi("n2"),mi("~"))`)*exp(-I*phi2); M212 := (`#mover(mi("n3"),mi("~"))`-`#mover(mi("n2"),mi("~"))`)*exp(I*phi2); M221 := (`#mover(mi("n3"),mi("~"))`-`#mover(mi("n2"),mi("~"))`)*exp(-I*phi2); M222 := (`#mover(mi("n3"),mi("~"))`+`#mover(mi("n2"),mi("~"))`)*exp(I*phi2); M311 := (`#mover(mi("n1"),mi("~"))`+n3)*exp(-I*phi3); M312 := (`#mover(mi("n1"),mi("~"))`-n3)*exp(I*phi3); M321 := (`#mover(mi("n1"),mi("~"))`-n3)*exp(-I*phi3); M322 := (`#mover(mi("n1"),mi("~"))`+n3)*exp(I*phi3); M1 := (Matrix(2, 2, {(1, 1) = M111, (1, 2) = M112, (2, 1) = M121, (2, 2) = M122}))/(2*`#mover(mi("n2"),mi("~"))`); M2 := (Matrix(2, 2, {(1, 1) = M211, (1, 2) = M212, (2, 1) = M221, (2, 2) = M222}))/(2*`#mover(mi("n3"),mi("~"))`); M3 := (Matrix(2, 2, {(1, 1) = M311, (1, 2) = M312, (2, 1) = M321, (2, 2) = M322}))/(2*`#mover(mi("n1"),mi("~"))`); Mcell := `.`(`.`(M3, M2), M1); t := 1/Mcell[2, 2]; r := t*Mcell[1, 2]; h := abs(Re(Mcell[2, 2])); R := abs(r)^2; `ϕ` := arccos(Re(Mcell[2, 2])); `ϕi` := arccosh(abs(Re(Mcell[2, 2]))); `ψN1` := sin(N*`ϕ`)/sin(`ϕ`); `ψN2` := sinh(N*`ϕi`)/sinh(`ϕi`); RN1 := `ψN1`^2*R/(1-R+`ψN1`^2*R); RN2 := `ψN2`^2*R/(1-R+`ψN2`^2*R); f := piecewise(h <= 1, RN1, RN2); implicitplot3d(z-f, nu = 0 .. 6*`νb`, theta1 = 0 .. (1/2)*Pi, z = 0 .. 1, tickmarks = [default, [seq((1/18)*i*Pi = (10*i)^`𝔬`, i = 1 .. 9)], default], resolution = 10000, labels = ["ν", "θ", "R"])

f is a func of teta1 & nu.

the shape has some surfaces z=1 in Upmost. and i want to show that surface in different color because i want to show it in a distinct way.

RN1 := psi;N1`^2*R/(1-R+psi;N1`^2*R);

RN2 := psi;N2`^2*R/(1-R+psi;N2`^2*R)

f := piecewise(h <= 1, RN1, RN2);

implicitplot3d(z-f, nu = 0 .. constant`, theta1 = 0 .. (1/2)*Pi, z = 0 .. 1, tickmarks = [default, [seq((1/18)*i*Pi = (10*i)^`𝔬`, i = 1 .. 9)], default], resolution = 10000, labels = ["ν", "θ", "R"])

i dont want to combine 2 plot!

i just want to color some portion of one plot,

ie. if i have a stair shape, color one surface of it (that is for example in z=3) in diff color than other potions of my shape.

i mean in a 3d shape how can i clear maple to color a surface of the shape in a color different from the color of other sections of the shape?

i have win XP and permanent copy of maple11.

i think java is not suitable for making setup.

once it was occured previously , when i removed & setup Win XP again the problem solved.

---the second half of my prog is: (M1 & M2 are unimodular matrices)

M:=M2.M1: t:=1/M[2,2]: R:=|t.M[1,2]|^2: h:=|Re(1/t)|:

phi:= arccos(Re(1/t)): Phi:=arccosh(|Re(1/t)|):

psi1:=sin(N*phi)/sin(phi): psi2:=sinh(N*Phi)/sinh(Phi):

---"all of above assignments are functions of 'nu' (or x).

---for example i want if h<=1 then plot psi1 else psi2, i have to use a proc & implicitplot like:

k:=proc(nu,y) if h<=1 then (y-psi1) else (y-psi2) end if end proc:

implicit plot(k,0..10^14,0..10^14);

---but it doesn't work !! i think the k proc doesn't recognize psi1 or psi2 !?!