A new approach for automatic theorem proving in real geometry:
Abstract: "We present a new method for proving geometric theorems in the real plane or higher dimension. The method is derived from elimination set ideas for quantifier elimination in linear and quadratic formulas over the reals. In contrast to other approaches, our method can also prove theore...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Passau
1996
|
| Schriftenreihe: | Universität <Passau> / Fakultät für Mathematik und Informatik: MIP
1996,11 |
| Schlagworte: | |
| Zusammenfassung: | Abstract: "We present a new method for proving geometric theorems in the real plane or higher dimension. The method is derived from elimination set ideas for quantifier elimination in linear and quadratic formulas over the reals. In contrast to other approaches, our method can also prove theorems whose complex analogues fail. After specification of independent variables, non-degeneracy conditions are generated automatically. Moreover, when trying to prove conjectures that do -- apart from non-degeneracy conditions -- not hold in the claimed generality, missing premises are found automatically. We demonstrate the applicability of our method to non-trivial examples. In particular, we can treat a variety of examples for which quantifier elimination by partial CAD fails." |
| Beschreibung: | 22, 4 S. graph. Darst. |
Internformat
MARC
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| 100 | 1 | |a Dolzmann, Andreas |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a A new approach for automatic theorem proving in real geometry |c A. Dolzmann ; Th. Sturm |
| 264 | 1 | |a Passau |c 1996 | |
| 300 | |a 22, 4 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Universität <Passau> / Fakultät für Mathematik und Informatik: MIP |v 1996,11 | |
| 520 | 3 | |a Abstract: "We present a new method for proving geometric theorems in the real plane or higher dimension. The method is derived from elimination set ideas for quantifier elimination in linear and quadratic formulas over the reals. In contrast to other approaches, our method can also prove theorems whose complex analogues fail. After specification of independent variables, non-degeneracy conditions are generated automatically. Moreover, when trying to prove conjectures that do -- apart from non-degeneracy conditions -- not hold in the claimed generality, missing premises are found automatically. We demonstrate the applicability of our method to non-trivial examples. In particular, we can treat a variety of examples for which quantifier elimination by partial CAD fails." | |
| 650 | 4 | |a Automatic theorem proving | |
| 650 | 4 | |a Geometry | |
| 650 | 0 | 7 | |a Theoretische Informatik |0 (DE-588)4196735-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Informatik |0 (DE-588)4026894-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mathematik |0 (DE-588)4037944-9 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Informatik |0 (DE-588)4026894-9 |D s |
| 689 | 0 | 2 | |a Mathematik |0 (DE-588)4037944-9 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Sturm, Thomas |e Verfasser |4 aut | |
| 810 | 2 | |a Fakultät für Mathematik und Informatik: MIP |t Universität <Passau> |v 1996,11 |w (DE-604)BV000905393 |9 1996,11 | |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-007221106 | |
Datensatz im Suchindex
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| author | Dolzmann, Andreas Sturm, Thomas |
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| building | Verbundindex |
| bvnumber | BV010808802 |
| classification_rvk | SS 5600 |
| ctrlnum | (OCoLC)38179119 (DE-599)BVBBV010808802 |
| discipline | Informatik |
| format | Book |
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| id | DE-604.BV010808802 |
| illustrated | Illustrated |
| indexdate | 2025-01-10T17:04:59Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007221106 |
| oclc_num | 38179119 |
| open_access_boolean | |
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| owner_facet | DE-154 DE-739 DE-12 DE-91G DE-BY-TUM DE-384 DE-634 |
| physical | 22, 4 S. graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| record_format | marc |
| series2 | Universität <Passau> / Fakultät für Mathematik und Informatik: MIP |
| spelling | Dolzmann, Andreas Verfasser aut A new approach for automatic theorem proving in real geometry A. Dolzmann ; Th. Sturm Passau 1996 22, 4 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Universität <Passau> / Fakultät für Mathematik und Informatik: MIP 1996,11 Abstract: "We present a new method for proving geometric theorems in the real plane or higher dimension. The method is derived from elimination set ideas for quantifier elimination in linear and quadratic formulas over the reals. In contrast to other approaches, our method can also prove theorems whose complex analogues fail. After specification of independent variables, non-degeneracy conditions are generated automatically. Moreover, when trying to prove conjectures that do -- apart from non-degeneracy conditions -- not hold in the claimed generality, missing premises are found automatically. We demonstrate the applicability of our method to non-trivial examples. In particular, we can treat a variety of examples for which quantifier elimination by partial CAD fails." Automatic theorem proving Geometry Theoretische Informatik (DE-588)4196735-5 gnd rswk-swf Informatik (DE-588)4026894-9 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Theoretische Informatik (DE-588)4196735-5 s Informatik (DE-588)4026894-9 s Mathematik (DE-588)4037944-9 s DE-604 Sturm, Thomas Verfasser aut Fakultät für Mathematik und Informatik: MIP Universität <Passau> 1996,11 (DE-604)BV000905393 1996,11 |
| spellingShingle | Dolzmann, Andreas Sturm, Thomas A new approach for automatic theorem proving in real geometry Automatic theorem proving Geometry Theoretische Informatik (DE-588)4196735-5 gnd Informatik (DE-588)4026894-9 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4196735-5 (DE-588)4026894-9 (DE-588)4037944-9 |
| title | A new approach for automatic theorem proving in real geometry |
| title_auth | A new approach for automatic theorem proving in real geometry |
| title_exact_search | A new approach for automatic theorem proving in real geometry |
| title_full | A new approach for automatic theorem proving in real geometry A. Dolzmann ; Th. Sturm |
| title_fullStr | A new approach for automatic theorem proving in real geometry A. Dolzmann ; Th. Sturm |
| title_full_unstemmed | A new approach for automatic theorem proving in real geometry A. Dolzmann ; Th. Sturm |
| title_short | A new approach for automatic theorem proving in real geometry |
| title_sort | a new approach for automatic theorem proving in real geometry |
| topic | Automatic theorem proving Geometry Theoretische Informatik (DE-588)4196735-5 gnd Informatik (DE-588)4026894-9 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Automatic theorem proving Geometry Theoretische Informatik Informatik Mathematik |
| volume_link | (DE-604)BV000905393 |
| work_keys_str_mv | AT dolzmannandreas anewapproachforautomatictheoremprovinginrealgeometry AT sturmthomas anewapproachforautomatictheoremprovinginrealgeometry |