Algorithm 795: PHCpack: a general-purpose solver for polynomial systems by homotopy continuation
ACM Transactions on Mathematical Software (TOMS)
Numerical Decomposition of the Solution Sets of Polynomial Systems into Irreducible Components
SIAM Journal on Numerical Analysis
Numerical Polynomial Algebra
Computing the multiplicity structure in solving polynomial systems
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Numerical local rings and local solution of nonlinear systems
Proceedings of the 2007 international workshop on Symbolic-numeric computation
Computing the multiplicity structure from geometric involutive form
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
A Singular Introduction to Commutative Algebra
A Singular Introduction to Commutative Algebra
Computing the multiplicity structure of an isolated singular solution: Case of breadth one
Journal of Symbolic Computation
Border basis representation of a general quotient algebra
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
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A symbolic-numeric method for calculating an H-basis for the ideal of a positive dimensional complex affine algebraic variety, possibly defined numerically, is given. H-bases for ideals I in I, introduced by Macaulay and later studied by Möller and Sauer, are an analog of Gröbner bases with respect to a global degree ordering: f is an element of I of total degree n if and only f is a C-linear combination of polynomials of total degree n or less which are monomial multiples of members of the H-basis. The method uses the interplay of local and global duality. Applications include factoring multivariable polynomials, analyzing singular curves, finding equations for the union of varieties, and, most importantly, finding equations for components of reducible varieties given numerically.