Truncated normal forms for solving polynomial systems: Generalized and efficient algorithms

Bates, 2013, vol. 25 Batselier, 2014, A fast recursive orthogonalization scheme for the Macaulay matrix, J. Comput. Appl. Math., 267, 20, 10.1016/j.cam.2014.01.035 Cattani, 2005, Solving Polynomial Equations: Foundations, Algorithms, and Applications Corless, 1997, A reordered Schur factorization method for zero-dimensional polynomial systems with multiple roots, 133 Cox, 1992 Cox, 2006, vol. 185 Dreesen, 2012, Back to the roots: polynomial system solving, linear algebra, systems theory, IFAC Proc. Vol., 45, 1203, 10.3182/20120711-3-BE-2027.00217 Elkadi, 2007, Introduction à la résolution des systèmes polynomiaux, vol. 59 Emiris, 1999, Matrices in elimination theory, J. Symb. Comput., 28, 3, 10.1006/jsco.1998.0266 Faugère, 2010, FGb: a library for computing Gröbner bases, vol. 6327, 84 Joswig, 2009, polymake and lattice polytopes, 491 Möller, 2001, Multivariate polynomial system solving using intersections of eigenspaces, J. Symb. Comput., 32, 513, 10.1006/jsco.2001.0476 Mourrain, 1999, A new criterion for normal form algorithms, 430 Mourrain, 2007, Pythagore's dilemma, symbolic-numeric computation, and the border basis method, 223 Mourrain, 2009, Subdivision methods for solving polynomial equations, J. Symb. Comput., 44, 292, 10.1016/j.jsc.2008.04.016 Mourrain, 2005, Generalized normal forms and polynomial system solving, 253 Mourrain, 2008, Stable normal forms for polynomial system solving, Theor. Comput. Sci., 409, 229, 10.1016/j.tcs.2008.09.004 Nakatsukasa, 2015, Computing the common zeros of two bivariate functions via Bézout resultants, Numer. Math., 129, 181, 10.1007/s00211-014-0635-z Sorber, 2014, Numerical solution of bivariate and polyanalytic polynomial systems, SIAM J. Numer. Anal., 52, 1551, 10.1137/130932387 Stetter, 1996, Matrix eigenproblems are at the heart of polynomial system solving, ACM SIGSAM Bull., 30, 22, 10.1145/242961.242966 Sturmfels, 2002, Solving Systems of Polynomial Equations, vol. 97 Szegő, 1967 Telen, 2018, Solving polynomial systems via truncated normal forms, SIAM J. Matrix Anal. Appl., 39, 1421, 10.1137/17M1162433 Telen, 2018, A stabilized normal form algorithm for generic systems of polynomial equations, J. Comput. Appl. Math., 342, 119, 10.1016/j.cam.2018.04.021 Townsend, 2013, An extension of Chebfun to two dimensions, SIAM J. Sci. Comput., 35, 10.1137/130908002 Trefethen, 2013, vol. 128 Trefethen, 1997, vol. 50 Verschelde, 1999, Algorithm 795: PHCpack: a general-purpose solver for polynomial systems by homotopy continuation, ACM Trans. Math. Softw., 25, 251, 10.1145/317275.317286