diff --git a/generaldegreeHypersurfaces.tex b/generaldegreeHypersurfaces.tex index 287eae8..330c388 100644 --- a/generaldegreeHypersurfaces.tex +++ b/generaldegreeHypersurfaces.tex @@ -770,7 +770,7 @@ DOI: 10.1515/crll.1986.367.103 \appendix \section{SageMath code} -We have written a SageMath function allowing us to define the Delta Complex associated to the complement of a projective Fermat hypersurface of degree $d$ in $\PP^n$. +We have written a SageMath function allowing us to define the $\Delta$-complex associated to the complement of a projective Fermat hypersurface of degree $d$ in $\PP^n$. The code for the function is: \begin{python} @@ -839,5 +839,15 @@ Running the code above we get: Delta_Complex = DeltaComplex_hypersurface(4,6) -> Delta complex with 5 vertices and 2802 simplices \end{python} + +Once we have gotten the $\Delta$-complex, we can compute the fundamental group or the cohomology of the space, for example. +\begin{python} +Dc = SimplicialSet(Delta_Complex) +dc_punto = Dc.set_base_point(Dc.all_n_simplices(0)[0]) +dc_punto.fundamental_group() + -> Finitely presented group < e0 | e0^6 > +dc_punto.cohomology() + -> {0: 0, 1: 0, 2: C6, 3: 0, 4: Z^520 x C6} +\end{python} \end{example} \end{document}