# A Modular Method for Computing the Splitting Field of a Polynomial

Abstract : We provide a modular method for computing the splitting field $K_f$ of an integral polynomial $f$ by suitable use of the byproduct of computation of its Galois group $G_f$ by $p$-adic Stauduhar’s method. This method uses the knowledge of $G_f$ with its action on the roots of $f$ over a $p$-adic number field, and it reduces the computation of $K_f$ to solving systems of linear equations modulo some powers of $p$ and Hensel liftings. We provide a careful treatment on reducing computational difficulty. We examine the ability/practicality of the method by experiments on a real computer and study its complexity.
Keywords :
Document type :
Conference papers
Domain :

Cited literature [20 references]

https://hal.archives-ouvertes.fr/hal-01337040
Contributor : Lip6 Publications <>
Submitted on : Wednesday, November 23, 2016 - 4:46:46 PM
Last modification on : Thursday, March 21, 2019 - 1:20:53 PM
Document(s) archivé(s) le : Monday, March 20, 2017 - 11:50:50 PM

### File

final_RenaultYokoyama_3.pdf
Files produced by the author(s)

### Identifiers

• HAL Id : hal-01337040, version 1

### Citation

Guénaël Renault, Kazuhiro Yokoyama. A Modular Method for Computing the Splitting Field of a Polynomial. Algorithmic Number Theory Symposium, Jul 2006, Berlin, Germany. pp.124-140. ⟨hal-01337040⟩

Record views
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5201376080513, "perplexity": 1969.3891938797476}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578529606.64/warc/CC-MAIN-20190420100901-20190420122901-00123.warc.gz"}