On Computing Galois Groups and Its Application To Solvability by Radicals
This thesis presents a polynomial time algorithm for the basic question of Galois theory, checking the solvability by radicals of a monic irreducible polynomial over the integers. It also presents polynomial time algorithms for factoring polynomials over algebraic number fields, for computing block...
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2023
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| Online Access: | https://hdl.handle.net/1721.1/149566 |
| _version_ | 1811095351492345856 |
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| author | Laudau, Susan Eva |
| author2 | Miller, Gary L. |
| author_facet | Miller, Gary L. Laudau, Susan Eva |
| author_sort | Laudau, Susan Eva |
| collection | MIT |
| description | This thesis presents a polynomial time algorithm for the basic question of Galois theory, checking the solvability by radicals of a monic irreducible polynomial over the integers. It also presents polynomial time algorithms for factoring polynomials over algebraic number fields, for computing blocks of imprimitivity of roots of a polynomial under the transitive action of the Galois group on the roots of the polynomial, and for computing intersections algebraic number fields. |
| first_indexed | 2024-09-23T16:15:42Z |
| id | mit-1721.1/149566 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T16:15:42Z |
| publishDate | 2023 |
| record_format | dspace |
| spelling | mit-1721.1/1495662023-03-30T03:06:22Z On Computing Galois Groups and Its Application To Solvability by Radicals Laudau, Susan Eva Miller, Gary L. This thesis presents a polynomial time algorithm for the basic question of Galois theory, checking the solvability by radicals of a monic irreducible polynomial over the integers. It also presents polynomial time algorithms for factoring polynomials over algebraic number fields, for computing blocks of imprimitivity of roots of a polynomial under the transitive action of the Galois group on the roots of the polynomial, and for computing intersections algebraic number fields. 2023-03-29T15:07:18Z 2023-03-29T15:07:18Z 1983-03 https://hdl.handle.net/1721.1/149566 9510369 MIT-LCS-TR-288 application/pdf |
| spellingShingle | Laudau, Susan Eva On Computing Galois Groups and Its Application To Solvability by Radicals |
| title | On Computing Galois Groups and Its Application To Solvability by Radicals |
| title_full | On Computing Galois Groups and Its Application To Solvability by Radicals |
| title_fullStr | On Computing Galois Groups and Its Application To Solvability by Radicals |
| title_full_unstemmed | On Computing Galois Groups and Its Application To Solvability by Radicals |
| title_short | On Computing Galois Groups and Its Application To Solvability by Radicals |
| title_sort | on computing galois groups and its application to solvability by radicals |
| url | https://hdl.handle.net/1721.1/149566 |
| work_keys_str_mv | AT laudaususaneva oncomputinggaloisgroupsanditsapplicationtosolvabilitybyradicals |