On polynomial ideals, their complexity, and applications:
Abstract: "A polynomial ideal membership problem is a (w+1)-tuple P = (f, g₁, g₂, ..., g[subscript w]) where f and g[subscript i] are multivariate polynomials over some ring, and the problem is to determine whether f is in the ideal generated by the g[subscript i]. For polynomials over the inte...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
München
1995
|
| Schriftenreihe: | Technische Universität <München>: TUM-I
9520 |
| Schlagworte: | |
| Zusammenfassung: | Abstract: "A polynomial ideal membership problem is a (w+1)-tuple P = (f, g₁, g₂, ..., g[subscript w]) where f and g[subscript i] are multivariate polynomials over some ring, and the problem is to determine whether f is in the ideal generated by the g[subscript i]. For polynomials over the integers or rationals, it is known that this problem is exponential space complete. We discuss complexity results known for a number of problems related to polynomial ideals, like the word problem for commutative semigroups, a quantitative version of Hilbert's Nullstellensatz, and the reachability and other problems for (reversible) Petri nets." |
| Beschreibung: | Literaturverz. S. 13 - 15 |
| Beschreibung: | 15 S. graph. Darst. |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV010841162 | ||
| 003 | DE-604 | ||
| 005 | 20040416 | ||
| 007 | t | ||
| 008 | 960701s1995 gw d||| t||| 00||| ger d | ||
| 016 | 7 | |a 947783989 |2 DE-101 | |
| 035 | |a (OCoLC)36404478 | ||
| 035 | |a (DE-599)BVBBV010841162 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a ger | |
| 044 | |a gw |c DE | ||
| 049 | |a DE-12 |a DE-91G | ||
| 088 | |a TUM I 9520 | ||
| 100 | 1 | |a Mayr, Ernst W. |d 1950- |e Verfasser |0 (DE-588)109817923 |4 aut | |
| 245 | 1 | 0 | |a On polynomial ideals, their complexity, and applications |c Ernst W. Mayr |
| 264 | 1 | |a München |c 1995 | |
| 300 | |a 15 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Technische Universität <München>: TUM-I |v 9520 | |
| 500 | |a Literaturverz. S. 13 - 15 | ||
| 520 | 3 | |a Abstract: "A polynomial ideal membership problem is a (w+1)-tuple P = (f, g₁, g₂, ..., g[subscript w]) where f and g[subscript i] are multivariate polynomials over some ring, and the problem is to determine whether f is in the ideal generated by the g[subscript i]. For polynomials over the integers or rationals, it is known that this problem is exponential space complete. We discuss complexity results known for a number of problems related to polynomial ideals, like the word problem for commutative semigroups, a quantitative version of Hilbert's Nullstellensatz, and the reachability and other problems for (reversible) Petri nets." | |
| 650 | 4 | |a Informatik | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Computational complexity | |
| 650 | 4 | |a Computer science |x Mathematics | |
| 650 | 4 | |a Ideals (Algebra) | |
| 650 | 4 | |a Polynomial rings | |
| 830 | 0 | |a Technische Universität <München>: TUM-I |v 9520 |w (DE-604)BV006185376 |9 9520 | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-007246850 | ||
Datensatz im Suchindex
| _version_ | 1804125328857104384 |
|---|---|
| any_adam_object | |
| author | Mayr, Ernst W. 1950- |
| author_GND | (DE-588)109817923 |
| author_facet | Mayr, Ernst W. 1950- |
| author_role | aut |
| author_sort | Mayr, Ernst W. 1950- |
| author_variant | e w m ew ewm |
| building | Verbundindex |
| bvnumber | BV010841162 |
| ctrlnum | (OCoLC)36404478 (DE-599)BVBBV010841162 |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01841nam a2200397 cb4500</leader><controlfield tag="001">BV010841162</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20040416 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">960701s1995 gw d||| t||| 00||| ger d</controlfield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">947783989</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)36404478</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV010841162</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">ger</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">gw</subfield><subfield code="c">DE</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-12</subfield><subfield code="a">DE-91G</subfield></datafield><datafield tag="088" ind1=" " ind2=" "><subfield code="a">TUM I 9520</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Mayr, Ernst W.</subfield><subfield code="d">1950-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)109817923</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">On polynomial ideals, their complexity, and applications</subfield><subfield code="c">Ernst W. Mayr</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">München</subfield><subfield code="c">1995</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">15 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Technische Universität <München>: TUM-I</subfield><subfield code="v">9520</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Literaturverz. S. 13 - 15</subfield></datafield><datafield tag="520" ind1="3" ind2=" "><subfield code="a">Abstract: "A polynomial ideal membership problem is a (w+1)-tuple P = (f, g₁, g₂, ..., g[subscript w]) where f and g[subscript i] are multivariate polynomials over some ring, and the problem is to determine whether f is in the ideal generated by the g[subscript i]. For polynomials over the integers or rationals, it is known that this problem is exponential space complete. We discuss complexity results known for a number of problems related to polynomial ideals, like the word problem for commutative semigroups, a quantitative version of Hilbert's Nullstellensatz, and the reachability and other problems for (reversible) Petri nets."</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Informatik</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Computational complexity</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Computer science</subfield><subfield code="x">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Ideals (Algebra)</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Polynomial rings</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Technische Universität <München>: TUM-I</subfield><subfield code="v">9520</subfield><subfield code="w">(DE-604)BV006185376</subfield><subfield code="9">9520</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-007246850</subfield></datafield></record></collection> |
| id | DE-604.BV010841162 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:59:49Z |
| institution | BVB |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007246850 |
| oclc_num | 36404478 |
| open_access_boolean | |
| owner | DE-12 DE-91G DE-BY-TUM |
| owner_facet | DE-12 DE-91G DE-BY-TUM |
| physical | 15 S. graph. Darst. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| record_format | marc |
| series | Technische Universität <München>: TUM-I |
| series2 | Technische Universität <München>: TUM-I |
| spelling | Mayr, Ernst W. 1950- Verfasser (DE-588)109817923 aut On polynomial ideals, their complexity, and applications Ernst W. Mayr München 1995 15 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Technische Universität <München>: TUM-I 9520 Literaturverz. S. 13 - 15 Abstract: "A polynomial ideal membership problem is a (w+1)-tuple P = (f, g₁, g₂, ..., g[subscript w]) where f and g[subscript i] are multivariate polynomials over some ring, and the problem is to determine whether f is in the ideal generated by the g[subscript i]. For polynomials over the integers or rationals, it is known that this problem is exponential space complete. We discuss complexity results known for a number of problems related to polynomial ideals, like the word problem for commutative semigroups, a quantitative version of Hilbert's Nullstellensatz, and the reachability and other problems for (reversible) Petri nets." Informatik Mathematik Computational complexity Computer science Mathematics Ideals (Algebra) Polynomial rings Technische Universität <München>: TUM-I 9520 (DE-604)BV006185376 9520 |
| spellingShingle | Mayr, Ernst W. 1950- On polynomial ideals, their complexity, and applications Technische Universität <München>: TUM-I Informatik Mathematik Computational complexity Computer science Mathematics Ideals (Algebra) Polynomial rings |
| title | On polynomial ideals, their complexity, and applications |
| title_auth | On polynomial ideals, their complexity, and applications |
| title_exact_search | On polynomial ideals, their complexity, and applications |
| title_full | On polynomial ideals, their complexity, and applications Ernst W. Mayr |
| title_fullStr | On polynomial ideals, their complexity, and applications Ernst W. Mayr |
| title_full_unstemmed | On polynomial ideals, their complexity, and applications Ernst W. Mayr |
| title_short | On polynomial ideals, their complexity, and applications |
| title_sort | on polynomial ideals their complexity and applications |
| topic | Informatik Mathematik Computational complexity Computer science Mathematics Ideals (Algebra) Polynomial rings |
| topic_facet | Informatik Mathematik Computational complexity Computer science Mathematics Ideals (Algebra) Polynomial rings |
| volume_link | (DE-604)BV006185376 |
| work_keys_str_mv | AT mayrernstw onpolynomialidealstheircomplexityandapplications |