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matrix3 S = 3@S;
float a = -S.xx;
float b = -2 * S.xy;  // assuming S is symmetric; otherwise adjust using S[0][1] and S[1][0]
float c = -S.yy;

float t1, t2;
int numRoots = solvequadratic(a, b, c, t1, t2);

if (numRoots == 2)
{
    vector v1 = set(t1, 1, 0);  // First asymptotic direction
    vector v2 = set(t2, 1, 0);  // Second asymptotic direction
    
    // Normalize the vectors
    v1 = normalize(v1);
    v2 = normalize(v2);
    
    // Process the directions v1 and v2 as needed.
    
    v@a1dir=v1;
}