Schoof's algorithm: Difference between revisions

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m Removed dead link, which is superseded by the updated links below.
 
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: <math>
(x^3+Ax+B)((x^3+Ax+B)^{\frac{q^{2}-1}{2}}-\theta(x))^2
</math>
 
Line 88:
 
: <math>
X(x)\equiv (x^3+Ax+B)\left(\frac{(x^3+Ax+B)^{\frac{q^{2}-1}{2}}-\theta(x)}{x^{q^2}-x_{\bar{q}}}\right)^2\bmod \psi_l(x).
</math>
Here, it seems not right, we throw away <math>x^{q^{2}}-x_{\bar{q}}</math>?
 
Now if <math>X \equiv x^{q} _ {\bar{t}}\bmod \psi_l(x)</math> for onesome <math>\bar{t}\in [0,(l-1)/2]</math>, then <math>\bar{t}</math> satisfies
 
: <math>