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Computing the Betti numbers of semi-algebraic sets defined by partly quadratic systems of polynomials

หน่วยงาน Nanyang Technological University, Singapore

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ชื่อเรื่อง : Computing the Betti numbers of semi-algebraic sets defined by partly quadratic systems of polynomials
นักวิจัย : Basu, Saugata , Pasechnik, Dmitrii V. , Roy, Marie-Françoise
คำค้น : DRNTU::Science::Mathematics::Geometry
หน่วยงาน : Nanyang Technological University, Singapore
ผู้ร่วมงาน : -
ปีพิมพ์ : 2552
อ้างอิง : Basu, S., Pasechnik, D. V., & Roy, M.-F. (2009). Computing the Betti numbers of semi-algebraic sets defined by partly quadratic systems of polynomials. Journal of algebra, 21(8), 2206-2229. , 0021-8693 , http://hdl.handle.net/10220/4599 , http://sfxna09.hosted.exlibrisgroup.com:3410/ntu/sfxlcl3?sid=metalib:ELSEVIER_SCOPUS&id=doi:&genre=&isbn=&issn=&date=2009&volume=321&issue=8&spage=2206&epage=2229&aulast=Basu&aufirst=%20S&auinit=&title=Journal%20of%20Algebra&atitle=Computing%20the%20Betti%20numbers%20of%20semi%2Dalgebraic%20sets%20defined%20by%20partly%20quadratic%20systems%20of%20polynomials , http://dx.doi.org/10.1016/j.jalgebra.2008.09.043
ที่มา : -
ความเชี่ยวชาญ : -
ความสัมพันธ์ : Journal of algebra
ขอบเขตของเนื้อหา : -
บทคัดย่อ/คำอธิบาย :

Let R be a real closed field, , with degY(Q)2, degX(Q)d, , , and with degX(P)d, , . Let SRℓ+k be a semi-algebraic set defined by a Boolean formula without negations, with atoms P=0, P0, P0, . We describe an algorithm for computing the Betti numbers of S generalizing a similar algorithm described in [S. Basu, Computing the top few Betti numbers of semi-algebraic sets defined by quadratic inequalities in polynomial time, Found. Comput. Math. 8 (1) (2008) 45–80]. The complexity of the algorithm is bounded by ((ℓ+1)(s+1)(m+1)(d+1))2O(m+k). The complexity of the algorithm interpolates between the doubly exponential time bounds for the known algorithms in the general case, and the polynomial complexity in case of semi-algebraic sets defined by few quadratic inequalities [S. Basu, Computing the top few Betti numbers of semi-algebraic sets defined by quadratic inequalities in polynomial time, Found. Comput. Math. 8 (1) (2008) 45–80]. Moreover, for fixed m and k this algorithm has polynomial time complexity in the remaining parameters.

บรรณานุกรม :
Basu, Saugata , Pasechnik, Dmitrii V. , Roy, Marie-Françoise . (2552). Computing the Betti numbers of semi-algebraic sets defined by partly quadratic systems of polynomials.
    กรุงเทพมหานคร : Nanyang Technological University, Singapore.
Basu, Saugata , Pasechnik, Dmitrii V. , Roy, Marie-Françoise . 2552. "Computing the Betti numbers of semi-algebraic sets defined by partly quadratic systems of polynomials".
    กรุงเทพมหานคร : Nanyang Technological University, Singapore.
Basu, Saugata , Pasechnik, Dmitrii V. , Roy, Marie-Françoise . "Computing the Betti numbers of semi-algebraic sets defined by partly quadratic systems of polynomials."
    กรุงเทพมหานคร : Nanyang Technological University, Singapore, 2552. Print.
Basu, Saugata , Pasechnik, Dmitrii V. , Roy, Marie-Françoise . Computing the Betti numbers of semi-algebraic sets defined by partly quadratic systems of polynomials. กรุงเทพมหานคร : Nanyang Technological University, Singapore; 2552.