Hensel validation pseudocode

Latex/pseudocode.tex

@@ -391,10 +391,16 @@ Cherché: $g, h \in \mathbb{IK}[x,y]/(x^{k+1})$ tel que $g^*_{ij} \in g_{ij}, h^
       \varepsilon \delta_{ij} & \text{if } \delta_{ij} > 0\\
       \varepsilon \cdot \underset{\delta_{lm} > 0}{\min}\delta_{lm} & \text{if } \delta_{ij} = 0
 \end{cases}$\\
-4. for $t = 0,\dots,t_{max}$\\
-5. \qquad $e \leftarrow gh-f\mod x^{k+1}$ \\
-6. \qquad fastdivrem(se,g)\\
-7.
+4. for $i = 0,\dots,i_{max}$\\
+5. \qquad $e \leftarrow g_ih_i-f\mod x^{k+1}$ \\
+6. \qquad $q,r = $ fastdivrem(se,$h_i$)\\
+7. \qquad $g_{i+1} \leftarrow g_i + te +qg_i \mod x^{k+1}$\\
+8. \qquad $h_{i+1} \leftarrow h_i+r \mod x^{k+1}$\\
+9. \qquad if $radius(h_{i+1}) - radius(h_i) < \eta_h$ and $radius(g_{i+1}) - radius(g_i) < \eta_g$\\
+10.\qquad \qquad return $g_i,h_i$\\
+11.\qquad end if\\
+12. end for
+
 
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