The pattern recognition of simplify falls short for this expression and must first be converted into a recognizable form for simplify via collect.
That seems like a good explanation to me.

@salim-barzani 
determinant_-_conjugate_vraag_mprimes_29-11-2025.mw

This is working in a worksheet 

Download vraag_mprimes-_how_to_find_paramters_21-11-2021.mw

This is the secant method as a procedure for not singular elliptic curves.
I did some examples, but th eprocedure code is not yet fully functional...
Example 1 is single point and example 2 is doubling example 1 

fxy := y^2 - 2*y + 14 = 2*x^3 + 11*x^2 - 29*x - 17:
P := [3, 7];

# Test met jouw kromme
fxy := y^2 - 2*y + 14 = 2*x^3 + 11*x^2 - 29*x - 17:
P := [3, 7];

printf("=== TEST 1: POINT DOUBLING 2P ===\n");
P2 := EllipticCurveSecantMethod(fxy, x, y, P, P, -10..10, -10..15, 
                               steps = true, showplot = true);
printf("2P = (%a, %a)\n", P2[1], P2[2])

Use : m > 1 and not 3m (m= 1... n )  

Found k  with 2 ai's , but the solution to this is the interesting part

From the Maple Programming Guide, section "5.3 Constructors":
?object,ModuleCopy:

it was rather easy with ai to come up with this animation , but now the details ...:-)

restart;
with(PDEtools);
with(LinearAlgebra);
with(SolveTools);
_local(gamma);
K := 2*k[i]*exp((-(alpha*l[i]^3 + (-k[i]^2 - b - c)*l[i] - a)*k[i]*Int(1/g(_z1), _z1 = 0 .. t) + 2*(k[i]*(y + z)*l[i] + x*k[i] + eta[i])*beta)/(2*beta))/(1 + exp((-(alpha*l[i]^3 + (-k[i]^2 - b - c)*l[i] - a)*k[i]*Int(1/g(_z1), _z1 = 0 .. t) + 2*(k[i]*(y + z)*l[i] + x*k[i] + eta[i])*beta)/(2*beta)));
K1 := eval(K, i = 1);
Fig1params := {a = 1, alpha = 1, b = 1, beta = 1, c = 1, y = 1, z = 1, eta[1] = 1, k[1] = 1, l[1] = -2, r[1] = 1};
test := value(eval(K1, {g = (t -> cos(t)), i = 1}));
unum := eval(test, Fig1params);
ux := eval(unum, t = 0);
printf("=== CONTROLE ===\n");
printf("test = ");
print(test);
printf("unum = ");
print(unum);
printf("ux = ");
print(ux);
plot(ux, x = -10 .. 10, numpoints = 300, title = "ux plot");
plot3d(unum, t = -10 .. 10, x = -10 .. 10, shading = ZHUE, grid = [50, 50], lightmodel = light4, style = surfacecontour, title = "unum 3D plot");
=================================================================
restart;
with(plots);
K := 2*k[i]*exp((-(alpha*l[i]^3 + (-k[i]^2 - b - c)*l[i] - a)*k[i]*Int(1/g(_z1), _z1 = 0 .. t) + 2*(k[i]*(y + z)*l[i] + x*k[i] + eta[i])*beta)/(2*beta))/(1 + exp((-(alpha*l[i]^3 + (-k[i]^2 - b - c)*l[i] - a)*k[i]*Int(1/g(_z1), _z1 = 0 .. t) + 2*(k[i]*(y + z)*l[i] + x*k[i] + eta[i])*beta)/(2*beta)));
K1 := eval(K, i = 1);
Fig1params := {a = 1, alpha = 1, b = 1, beta = 1, c = 1, y = 1, z = 1, eta[1] = 1, k[1] = 1, l[1] = -2, r[1] = 1};
K1_num := (x_val, t_val, g_func) -> eval(eval(K1, {g = g_func, t = t_val, x = x_val, Int(1/g(_z1), _z1 = 0 .. t) = evalf(Int(1/g_func(s), s = 0 .. t_val))}), Fig1params);
ux_num := x -> K1_num(x, 0, cos);
printf("=== TEST EENVOUDIGE PUNTEN ===\n");
for i from -2 to 2 do
    result := ux_num(i);
    printf("ux_num(%d) = %a\n", i, result);
end do;
plot(ux_num(x), x = -10 .. 10, numpoints = 300, title = "2D Plot: ux_num(x)");
plot3d(K1_num(x, t, cos), x = -10 .. 10, t = -5 .. 5, shading = ZHUE, grid = [30, 30], title = "3D Plot: K1_num(x,t,cos)");

generalized hyperbolic distribution
Generalized Hyperbolic Distributions - Jim Killingsworth
GENERALIZED_HYPERBOLIC_DISTRIBUTIONmprimes7-10-2025.mw

We can use the max­i­mum like­li­hood method to fit a gen­er­al­ized hy­per­bol­ic dis­tri­b­u­tion to a giv­en set of data
Let me try   for stock exchance in Amsterdam (AEX) ?, no i  take first the example data his­tor­i­cal stock prices of Mi­crosoft Cor­po­ra­tion

GH_Distribution_Plot := proc(mu, delta, alpha, lambda, {beta := 0, xmin := -10, xmax := 10})

normal_form_abnd_limit_cycle_of_thi_sjerk_system_mprimes_28-9-2025.mw

restart;
f := 419*x^2 + 116*x*y - 426*x*z + 78*y^2 - 142*y*z + 133*z^2 - 1604*x - 682*y + 1086*z + 2306;
df_dx := diff(f, x);
df_dy := diff(f, y);
df_dz := diff(f, z);
centrum := solve({df_dx = 0, df_dy = 0, df_dz = 0}, {x, y, z});
                      "maple.ini in user"

             df_dx := 838 x + 116 y - 426 z - 1604

              df_dy := 116 x + 156 y - 142 z - 682

             df_dz := -426 x - 142 y + 266 z + 1086

               centrum := {x = 7, y = 11, z = 13}

It is a quadratic surface, with this point : centrum ? : point symmetry around centrum, needs more info.

eqt1 := u(x, y, 0, t) = 4*alpha*(-lambda[1]*t*(lambda[1]^2 - 3*lambda[2]^2)*alpha + (b*lambda[1] + ((r[1] + r[2])*c)/2 + a)*t + beta*(y*lambda[1] + x))*lambda[2]^2*beta/(lambda[2]^2*t^2*(lambda[1]^2 + lambda[2]^2)^3*alpha^3 + 3*t*lambda[2]^2*alpha^2*(2*(b*t + beta*y)*lambda[2]^4/3 + t*c*(r[2] - r[1])*lambda[2]^3*I/3 + 2*lambda[1]*((((r[1] + r[2])*c)/2 + a)*t + x*beta)*lambda[2]^2 - lambda[1]^2*t*c*(r[2] - r[1])*lambda[2]*I - (2*lambda[1]^3*((b*lambda[1] + ((r[1] + r[2])*c)/2 + a)*t + beta*(y*lambda[1] + x)))/3) + lambda[2]^2*((b*t + beta*y)^2*lambda[2]^2 + t*c*(b*t + beta*y)*(r[2] - r[1])*lambda[2]*I + ((b*lambda[1] + c*r[2] + a)*t + beta*(y*lambda[1] + x))*((b*lambda[1] + c*r[1] + a)*t + beta*(y*lambda[1] + x)))*alpha + beta^2)

Can this function be used now ?

@salim-barzani 
interaktietermen_procedure_21-9-2025.mw