The system of diophantine equations $$\{x^2-y^2+z^2-u^2+q^2-t^2=0,\,xy+zt-uq=0 \}$$ is given. Do the formulas
$$x:=(j(p^2-4ps+3s^2)-(p-s)(3p^2-4ps+s^2))k^2+2(j-2(p-s))(p-s)kn+(j-p+s)n^2, $$
$$y:=(p-s)(4j(p-s)-3p^2+4ps-s^2)k^2+2(p-s)(j-2(p-s))kn-(p-s)n^2, $$
$$z:=(j(p^2-4ps+3s^2)+s(3p^2-4ps+s^2))k^2+2(p-s)(2s+j)kn+(j+s)n^2, $$
$$t:=(j(p+s)-3p^2+4ps-s^2)(p-s)k^2+2[jp-2(p-s)(p-s)]kn+(j-p+s)n^2, $$
$$q:=(j(5p^2-8ps+3s^2)-(p-s)(3p^2-4ps+s^2))k^2+2(j(2p-s)-2(p-s)(p-s))kn+(j-p+s)n^2, $$
$$u:=(j(p^2-4ps+3s^2)+(2s-p)(3p^2-4ps+s^2))k^2+2(p-s)(j+2(2s-p))kn+(j+2s-p)n^2,
$$ where $p:=a^2-3b^2,\,s=2ab-4b^2,\, j:=3b^2-4ab+a^2,$ produce all its solutions?