# Introduction to numerical algebraic geometry

@inproceedings{Sommese2005IntroductionTN, title={Introduction to numerical algebraic geometry}, author={Andrew J. Sommese and Jan Verschelde and Charles W. Wampler}, year={2005} }

In a 1996 paper, Andrew Sommese and Charles Wampler began developing a new area, “Numerical Algebraic Geometry”, which would bear the same relation to “Algebraic Geometry” that “Numerical Linear Algebra” bears to “Linear Algebra”.

## 67 Citations

### Numerical Algebraic Geometry for Macaulay2

- Mathematics, Computer ScienceArXiv
- 2009

A package to interlink the existing symbolic methods of Macaulay2 and the powerful engine of numerical approximate computations to exhibit performance competitive with the other homotopy continuation software.

### Computing Tropical Curves via Homotopy Continuation

- Computer Science, MathematicsExp. Math.
- 2016

This work exploits a connection between amoebas and tropical curves to devise a method for computing tropical curves using numerical algebraic geometry and gives an implementation that is used to compute Newton polygons of A-polynomials of knots.

### Nonlinear algebra in 3 D computer vision

- Mathematics
- 2020

I study computational algebraic geometry—an amusing, somewhat more broad name for this field is nonlinear algebra. This field is firmly anchored to its algorithmic techniques—traditionally, symbolic…

### General witness sets for numerical algebraic geometry

- MathematicsISSAC
- 2020

This work presents a general notion of witness set for subvarieties of a smooth complete complex algebraic variety using ideas from intersection theory, and introduces Schubert witness sets, which provide general witness sets for Grassmannians and flag manifolds.

### Numerical algorithms for detecting embedded components

- Mathematics, Computer ScienceJ. Symb. Comput.
- 2017

### Computing Puiseux series for algebraic surfaces

- Mathematics, Computer ScienceISSAC
- 2012

The preliminary methods produce exact representations for solution sets of the cyclic n-roots problem, for n = m2, corresponding to a result of Backelin.

### Signatures of algebraic curves via numerical algebraic geometry

- Mathematics, Computer ScienceJ. Symb. Comput.
- 2020

### Galois groups of Schubert problems via homotopy computation

- MathematicsMath. Comput.
- 2009

This work shows by direct computation that the Galois group of the Schubert problem of 3-planes in ℂ 8 meeting 15 fixed 5-planes non-trivially is the full symmetric group S 6006.

### Regularization and Matrix Computation in Numerical Polynomial Algebra

- Mathematics, Computer Science
- 2009

Regularization principles for reformulating the ill-posed algebraic problems, derive matrix computations arising in numerical polynomial algebra, as well as subspace strategies that substantially improve computational efficiency by reducing matrix sizes are developed.

## References

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Background: Polynomial Systems Homotopy Continuation Projective Spaces Probability One Polynomials of One Variable Other Methods Isolated Solutions: Coefficient-Parameter Homotopy Polynomial…

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- Mathematics, Computer ScienceISSAC '01
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A semi-numerical algorithm for computing all irreducible branches of a curve in C3 defined by polynomials with rational coefficients is proposed, based on some properties appearing after a generic change of coordinate.