intersections := proc(P, Q, T)
local R, W, w, t, a, b, sol, buff, v;
sol := NULL;
if T = Y then W := X; else
W := Y; end if;
R := resultant(P, Q, T);
print(`Résultant :`); print(R);
w := fsolve(R, W); t := NULL;
for v in [w] do t := t, fsolve(subs(W = v, P), T); end do;
for a in {w} do for b in {t} do if T = Y then
buff := abs(subs(X = a, Y = b, P)) + abs(subs(X = a, Y = b, Q));
printf(`X=%a,   Y=%a   --->  %a\\n`, a, b, buff); if buff < 1/100000000 then sol := sol, [a, b]; end if;
else buff := abs(subs(X = b, Y = a, P)) + abs(subs(X = b, Y = a, Q));
printf(`X=%a,   Y=%a   --->  %a\\n `, a, b, buff); if buff < 1/100000000 then sol := sol, [b, a]; end if; end if; end do; end do; printf(`Nombre de solutions :  %a\\n`, nops({sol})); print({sol}); end proc:
intersections(X^2 + Y^2 - 1, X - Y, X);
X=-.7071067812,   Y=-.7071067812   --->  0.\n 
I do not wish to find \n in the answer

restart;
with(geometry);
with(plots);
Bl := color = black;
y0 := x -> -ln(1 - exp(-x));
y0 := proc (x) options operator, arrow; -ln(1-exp(-x)) end proc

y1 := x -> -ln(-1 + exp(-x));
y1 := proc (x) options operator, arrow; -ln(-1+exp(-x)) end proc

y2 := x -> -ln(1 + exp(-x));
y2 := proc (x) options operator, arrow; -ln(1+exp(-x)) end proc

p := plot(y0(x), x = 0.02 .. 4, scaling = constrained, color = blue);
p1 := plot(y2(x), x = -4 .. 4, scaling = constrained, color = green);
p2 := plot(y1(x), x = -4 .. 0, scaling = constrained, color = red);
display({p, p1, p2}, view = [-4 .. 4, -4 .. 5]);
Calculate its area; Thank you.

On donne un cercle fixe de diamètre AB, un point M variable sur ce cercle et on construit un carré de sens direct AMNP; Trouver les lieux des points N et P.
restart;
with(plots);
r := 1;
A := [-r, 0];
B := [r, 0];
M := [r*cos(theta), r*sin(theta)];
N := [r*cos(theta) - r*sin(theta), r*sin(theta) + r*cos(theta)];
P := [-r*cos(theta) - r*sin(theta), r*cos(theta) - r*sin(theta)];
c1 := `~`[plottools]*circle([0, 0], r, color = blue);
plot1 := plot(c1, color = blue);
plot2 := animate([N[1], N[2], theta = 0 .. 2*Pi], color = red, thickness = 2);
plot3 := animate([P[1], P[2], theta = 0 .. 2*Pi], color = green, thickness = 2);
display(plot1, plot2, plot3);
Would you like to improve this code so it works. Thank you.
 

restart;
_local(D, O);
with(Student:-MultivariateCalculus);
A := [0, 0, 0];
B := [a, 0, 0];
C := [a, b, 0];
D := [0, b, 0];
S := [0, 0, h];
O := [x, y, z];
lineSC := Line(S, C);
lineSD := Line(S, D);
H := Projection(A, lineSC);
K := Projection(A, lineSD);
OH := H - O;
OK := K - O;
OC := C - O;
M := Matrix([OH, OK, OC]);
O := eval(O, %);
simplify(Distance(O, H));
                               O

Error, invalid input: eval received Matrix(3, 3, {(1, 1) = -x+h^2*a/(a^2+b^2+h^2), (1, 2) = -y+h^2*b/(a^2+b^2+h^2), (1, 3) = -z+h*(a^2+b^2)/(a^2+b^2+h^2), (2, 1) = -x, (2, 2) = -y+h^2*b/(b^2+h^2), (2, 3) = -z+h*b^2/(b^2+h^2), (3, 1) = -x+a, (3, 2) = -y+b, (3, 3) = -z}), which is not valid for its 2nd argument, eqns
How to correct this error ? Thank you.

eq1 := x = (a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)/((-a + b + c)*(a + b - c)*(a - b + c)*(a + b + c));
eq2 := y = (-a^2 + b^2 + c^2)*(a^2 + b^2 - c^2)/((-a + b + c)*(a + b - c)*(a - b + c)*(a + b + c));
eq3 := z = (-a^2 + b^2 + c^2)*(a^2 - b^2 + c^2)/((-a + b + c)*(a + b - c)*(a - b + c)*(a + b + c));
sol := solve({eq1, eq2, eq3, x + y + z = 1}, {a, b, c}, explicit);
No resolution. To find the Cartesian coordinates from barycentric coordinates;