Fe b 20 08 GALOIS GROUPS OF SCHUBERT PROBLEMS VIA HOMOTOPY COMPUTATION
نویسنده
چکیده
Numerical homotopy continuation of solutions to polynomial equations is the foundation for numerical algebraic geometry, whose development has been driven by applications of mathematics. We use numerical homotopy continuation to investigate the problem in pure mathematics of determining Galois groups in the Schubert calculus. For example, we show by direct computation that the Galois group of the Schubert problem of 3-planes in C meeting 15 fixed 5-planes non-trivially is the full symmetric group S6006.
منابع مشابه
1 2 Ju n 20 08 GALOIS GROUPS OF SCHUBERT PROBLEMS VIA HOMOTOPY COMPUTATION
Numerical homotopy continuation of solutions to polynomial equations is the foundation for numerical algebraic geometry, whose development has been driven by applications of mathematics. We use numerical homotopy continuation to investigate the problem in pure mathematics of determining Galois groups in the Schubert calculus. For example, we show by direct computation that the Galois group of t...
متن کامل0 71 0 . 46 07 v 1 [ m at h . A G ] 2 5 O ct 2 00 7 GALOIS GROUPS OF SCHUBERT PROBLEMS VIA HOMOTOPY COMPUTATION
Numerical homotopy continuation of solutions to polynomial equations is the foundation for numerical algebraic geometry, whose development has been driven by applications of mathematics. We use numerical homotopy continuation to investigate the problem in pure mathematics of determining Galois groups in the Schubert calculus. For example, we show by direct computation that the Galois group of t...
متن کاملGalois groups of Schubert problems via homotopy computation
Numerical homotopy continuation of solutions to polynomial equations is the foundation for numerical algebraic geometry, whose development has been driven by applications of mathematics. We use numerical homotopy continuation to investigate the problem in pure mathematics of determining Galois groups in the Schubert calculus. For example, we show by direct computation that the Galois group of t...
متن کاملGenerating A Mathematical Web Service Client With xfy
We have developed a probabilistic method that uses numerical polynomial homotopy continuation to compute Galois groups of Schubert problems. Our implementation of the method produced answers to the questions considered inaccessible by other techniques. The problem of computing all solutions of a system of polynomial equations may be solved using numerical polynomial homotopy continuation [10]. ...
متن کاملDouble Transitivity of Galois Groups in Schubert Calculus of Grassmannians
We investigate double transitivity of Galois groups in the classical Schubert calculus on Grassmannians. We show that all Schubert problems on Grassmannians of 2and 3-planes have doubly transitive Galois groups, as do all Schubert problems involving only special Schubert conditions. We use these results to give a new proof that Schubert problems on Grassmannians of 2-planes have Galois groups t...
متن کامل