ffsolve.lib gives run time errors and wrong solutions

[ryutaroh@…]

Consider the Hermitian curve y^{2 = x}3 + x over GF(4). It has eight points in GF(4)^{2. When one tries to find its zeros by ffsolve.lib, it gives run time errors or wrong answers I give three example codes:}

LIB "ffsolve.lib";

ring r=(2,a),(y,x),lp;
minpoly=a2+a+1;
r;
poly defeq = -y^2 + x^3 + x; // Hermitian curve over GF(4) with 8 points.
ffsolve(ideal(defeq)); // returns only 4 points

---

// Second example
LIB "ffsolve.lib";

ring r2=(2,a),(y,x),wp(3,2);
minpoly=a2+a+1;
r2;
poly defeq = -y^2 + x^3 + x; // Hermitian curve over GF(4)
simplesolver(ideal(defeq)); // returns the empty list
ffsolve(ideal(defeq)); // run time error

---

// Third example
LIB "ffsolve.lib";

ring r3=(4,a),(y,x),lp; // definition of a finite field without min-poly.
r3;
poly defeq = -y^2 + x^3 + x; // Hermitian curve over GF(4) with 8 points.
ffsolve(ideal(defeq)); // run time error

[Oleksandr]

document the limitation