## 4 Badges

5 years, 225 days

## resolution of the equation of degree 3...

Maple 2021

restart:
eq := a*x^3 + b*x^2 + c*x + d;
s := x1 + x2 + x3 = -b/a;
sp := x1*x2 + x1*x3 + x2*x3 = c/a;
p := x1*x2*x3 = -d/a;
sol:=solve({eq, p, s, sp}, {x1, x2, x3},explicit);
a := 1;
b := -5;
c := 6;
d := -1;
sol;

why is not successfull ?   Thank you.

## How to built a pentagon...

Maple 2021

restart;
with(plots);
with(plottools);
Vdot := proc (U, V)local i: add(U[i]*V[i], i = 1 .. 2) end proc:
dist := proc (M, N) sqrt(Vdot(expand(M-N), expand(M-N))) end proc:
ngon := n -> local i; [seq([cos(2*Pi*i/n), sin(2*Pi*i/n)], i = 1 .. n)]:
theta := (2*Pi)/5;
poly := [seq([cos(k*theta), sin(k*theta)], k = 1 .. 5), datatype = float];
Ii := [0, 1/2]:
H := [-1/4, 0]:
r := dist(Ii, H):
theta := (2*Pi)/5:
p1 := pointplot([seq([cos(k*theta), sin(k*theta)], k = 0 .. 5)], symbol = solidcircle, color = red, symbolsize = 10):
p2 := textplot([seq([cos(k*theta), sin(k*theta), cat("M", k)], k = 0 .. 4)], align = ["above", "right"]):
cir1 := circle([0, 0], 1/2, color = green,dashdot:):
cir2 := circle([-1/4, 0], r, color = black):
cir3:=circle([0,0],1,color=red):
display([p1, p2, cir1, cir2, cir3,polygonplot(poly, thickness = 5, color = blue, transparency = 0.95)], axes = normal);
Why this error , Thank you.

## Difficulty with concatenation and indexi...

Maple 2021

Why this error message ?
with(geometry);
vartheta := (2*Pi)/17;
x || k := cos(k*theta);
y || k := sin(k*theta);
xk := cos(k theta): yk := sin(k theta)
.M||k:=(point,x||k,y||k);
with(plots):
Points := pointplot([seq(M || k, k = 1 .. 16)], symbol = solidcircle, color = red, symbolsize = 10):
Error, (in plots:-pointplot) cannot convert data to an Array of datatype float[8]; Thank you for your answer..

## Count Fridays 13 of a year...

Maple 2021

How to adapt this program C to Maple ? Thank you.

Sub Les_Vendredi_13()
Dim Annee As Integer
Dim Mois As Byte
Dim Cellule As String
Dim Compteur As Byte
Cellule = "B2"
Compteur = 1
Columns("B:B")
.ClearContents For Annee = 1949 To 2009
For Mois = 1 To 12 If Weekday(Mois & "/13/" & Annee) = 6
Then Range(Cellule).Offset(Compteur, 0) = "13-" & Format(Mois, "00") & "-" & Annee Compteur = Compteur + 1 End
If Next Mois Next Annee Range(Cellule).Offset(Compteur, 0) = "Nbre = " & Compteur - 1
End Sub

## Pell Fermat equation...

Maple 2021

I try to sove the equation x^2-10*y^2=9 with tne procedure :
genpellsolve := proc(D::posint, N::integer)
local t, u, L1, L2, sols, x, y;
if type(sqrt(D), integer) then error "D must be a nonsquare integer"; end
if; t, u := pellsolve(D); if 0 < N then L1 := 0;
L2 := floor(sqrt(1/2*N*(t - 1)/D)); elif N < 0 then L1 := ceil(sqrt(-N/D));
L2 := floor(sqrt(-1/2*N*(t + 1)/D)); else return {[0, 0]}; end if;
sols := {}; for y from L1 to L2 do x := sqrt(N + D*y^2);
if type(x, integer) then sols := sols union {[x, y]};
if (x^2 + D*y^2) mod N <> 0 or (2*x*y) mod N <> 0 then sols := sols union {[-x, y]};
end if;
end if;
end do;  return sols;
end proc:
This procedudure fails; I don't see why. Thank you for your help.

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