What is the solution of these equations
$\begin{align}a1 - 2*b1*b3 - b2^2 - b4^2 - 2*b5*b6=0 \\ a2=0 \\ a3 - b3^2=0 \\ a4 - 2*b3*b4 - b6^2=0 \\ a5=0 \\ a6=0 \\ b1^2=0 \\ b1*b2=0 \\ b1*b4 + 1/2*b5^2=0 \\ b1*b5=0 \\ b1*b6 + b2*b5 + b4*b5=0 \\ b2^2*b5=0 \\ b2*b3=0 \\ b2*b4=0 \\ b2*b5^2=0 \\ b2*b6 + b3*b5 + b4*b6=0 \\ b3^2*b5=0 \\ b3*b4*b5=0 \\ b3*b6=0 \\ b4^2*b5=0 \\ b4^2*b6=0 \\ b4*b5^2=0 \\ b5^3=0 \\ b5^2*b6=0 \end{align}$
Now my question is for:
- $b3 \neq 0$ What I am getting directly from this equation is $b1=b2=b5=b6=0=a2=a5=a6$ and $a1=b4^2$ and $a4=2b3b4$.
Now in the solution of sage I am getting $b4=0$ as well. But why? I am trying for an hour and couldn't figure it out! I hope that there is some hidden equation which is not very clear but what is the general way to find it out. If we don't want to use any computational tool.
- Same case when $b6 \neq 0$. I can't find why $b2=0$. Please give me a way to figure this calculation out as well.