Epsilon

Epsilon is a library of functions implemented in Maple and Java for polynomial elimination and decomposition with (geometric) applications. It has 8 modules and contains more than 70 functions, which allow one to triangularize systems of multivariate (differential) polynomials, decompose polynomial systems into triangular systems of various kinds (regular, normal, simple, irreducible, or with projection property), decompose algebraic varieties into irreducible or unmixed subvarieties, decompose polynomial ideals into primary components, factorize polynomials over algebraic extension fields, solve systems of polynomial equations and inequations, and handle and prove geometric theorems automatically.


References in zbMATH (referenced in 31 articles , 1 standard article )

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  1. Du, Daniel K.; Hou, Qing-Hu; Wang, Rong-Hua: Infinite orders and non-$D$-finite property of 3-dimensional lattice walks (2016)
  2. Sang, Bo; Niu, Chuanze: Solution of center-focus problem for a class of cubic systems (2016)
  3. Botana, Francisco; Hohenwarter, Markus; Janičić, Predrag; Kovács, Zoltán; Petrović, Ivan; Recio, Tomás; Weitzhofer, Simon: Automated theorem proving in GeoGebra: current achievements (2015)
  4. Chen, Zhenghong; Tang, Xiaoxian; Xia, Bican: Generic regular decompositions for parametric polynomial systems (2015)
  5. Pech, Pavel: Extension of Simson-Wallace theorem on skew quadrilaterals and further properties (2015)
  6. Alvandi, Parisa; Chen, Changbo; Marcus, Steffen; Maza, Marc Moreno; Schost, Éric; Vrbik, Paul: Doing algebraic geometry with the regularchains library (2014)
  7. Cheng, Jin-San; Gao, Xiao-Shan: Multiplicity-preserving triangular set decomposition of two polynomials (2014)
  8. Pech, Pavel: On a 3D extension of the Simson-Wallace theorem (2014)
  9. Liu, Y.P.; Liao, S.J.; Li, Z.B.: Symbolic computation of strongly nonlinear periodic oscillations (2013)
  10. Ayad, Ali; Fares, Ali; Ayyad, Youssef: An algorithm for solving zero-dimensional parametric systems of polynomial homogeneous equations (2012)
  11. Niu, Wei; Wang, Dongming: Algebraic analysis of stability and bifurcation of a self-assembling micelle system (2012)
  12. Ayad, A.: Complexity of solving parametric polynomial systems (2011)
  13. Boulier, François; Lefranc, Marc; Lemaire, François; Morant, Pierre-Emmanuel: Model reduction of chemical reaction systems using elimination (2011)
  14. Huang, Yanli; Wang, Dongming: Computing intersection and self-intersection loci of parametrized surfaces using regular systems and Gröbner bases (2011)
  15. Ida, Tetsuo; Kasem, Asem; Ghourabi, Fadoua; Takahashi, Hidekazu: Morley’s theorem revisited: origami construction and automated proof (2011)
  16. Ayad, Ali: On computing absolutely irreducible components of algebraic varieties with parameters (2010)
  17. Boulier, François; Lemaire, François: A normal form algorithm for regular differential chains (2010)
  18. Boulier, François; Lemaire, François; Moreno Maza, Marc: Computing differential characteristic sets by change of ordering (2010)
  19. Dalzotto, G.; Recio, T.: On protocols for the automated discovery of theorems in elementary geometry (2009)
  20. Fu, Haiming; Dai, Zhengde: New exact solutions for higher-order nonlinear Schrödinger equation (2009)

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