\begin{thebibliography}{10}

\bibitem{ABM}
Maria~Emilia Alonso, Jean Brachat, and Bernard Mourrain.
\newblock {Stable Deformation of Zero-Dimensional Quotient Algebras}.
\newblock Technical report, 2009.

\bibitem{ACL2014}
Maria~Emilia Alonso, Thierry Coquand, and Henri Lombardi.
\newblock {Revisiting Zariski main theorem from a constructive point of view.}
\newblock {\em {J. Algebra}}, 406:46--68, 2014.

\bibitem{AL2010}
Maria~Emilia Alonso and Henri Lombardi.
\newblock Local {B}\'ezout theorem.
\newblock {\em J. Symbolic Comput.}, 45(10):975--985, 2010.

\bibitem{ArBook}
V.I. Arnold, S.M. Gusein-Zade, and A.N. Varchenko.
\newblock {\em {Singularities of differentiable maps, Volume 1. Classification
  of critical points, caustics and wave fronts. Transl. from the Russian by Ian
  Porteous, edited by V. I. Arnold.}}
\newblock Boston, MA: Birkh\"auser, reprint of the 1985 hardback edition, 2012.

\bibitem{Bi67}
Errett Bishop.
\newblock {\em Foundations of constructive analysis}.
\newblock McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1967.

\bibitem{Bra}
Jean Brachat.
\newblock {\em {Sch\'emas de {H}ilbert et {D}\'ecomposition de tenseurs}}.
\newblock PhD thesis, 2011.

\bibitem{SmLe97}
B.~de~Smit and H.~W. Lenstra.
\newblock {Finite complete intersection algebras and the completeness radical.}
\newblock {\em J. Algebra}, 196(2):520--531, 1997.

\bibitem{Eis2012}
Michael Eisermann.
\newblock The fundamental theorem of algebra made effective: an elementary
  real-algebraic proof via {S}turm chains.
\newblock {\em Amer. Math. Monthly}, 119(9):715--752, 2012.

\bibitem{GH}
Phillip Griffiths and Joseph Harris.
\newblock {\em Principles of algebraic geometry}.
\newblock Wiley Classics Library. John Wiley \& Sons, Inc., New York, 1994.
\newblock Reprint of the 1978 original.

\bibitem{CACM}
Henri Lombardi and Claude Quitt\'e.
\newblock {\em {Commutative Algebra. Constructive Methods}}.
\newblock {Algebra and Applications, Vol. 20. Berlin, New-York: Springer},
  2015.

\bibitem{Mou99}
Bernard Mourrain.
\newblock {A new criterion for normal form algorithms.}
\newblock In {\em {Applied algebra, algebraic algorithms and error correcting
  codes. 13th international symposium, AAECC-13, Honolulu, HI, USA, November
  15--19, 1999. Proceedings}}, pages 430--443. Berlin: Springer, 1999.

\bibitem{Ost73}
A.~M. Ostrowski.
\newblock {\em Solution of equations in {E}uclidean and {B}anach spaces}.
\newblock Academic Press [A Subsidiary of Harcourt Brace Jovanovich,
  Publishers], New York-London, 1973.
\newblock Third edition of {{\i}t Solution of equations and systems of
  equations}, Pure and Applied Mathematics, Vol. 9.

\bibitem{lq15}
Claude Quitt\'e and Henri Lombardi.
\newblock Le théorème de de {S}mit et {L}enstra, démonstration
  élémentaire. http://arxiv.org/abs/1508.05589.
\newblock 2015.

\bibitem{Ric00}
Fred Richman.
\newblock The fundamental theorem of algebra: a constructive development
  without choice.
\newblock {\em Pacific J. Math.}, 196(1):213--230, 2000.

\end{thebibliography}
