Opened 8 years ago

# ffsolve.lib gives run time errors and wrong solutions

Reported by: Owned by: ryutaroh@… hannes major 4-1-0 and higher singular-libs 4-0-0 ffsolve

### Description

Consider the Hermitian curve y2 = x3 + 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
```

### comment:1 Changed 8 years ago by Oleksandr

Owner: changed from somebody to hannes

document the limitation

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