| ชื่อเรื่อง | : | Bounding the Betti numbers and computing the Euler–Poincaré characteristic of semi-algebraic sets defined by partly quadratic systems of polynomials |
| นักวิจัย | : | Basu, Saugata , Pasechnik, Dmitrii V. , Roy, Marie-Françoise |
| คำค้น | : | DRNTU::Science::Mathematics::Algebra |
| หน่วยงาน | : | Nanyang Technological University, Singapore |
| ผู้ร่วมงาน | : | - |
| ปีพิมพ์ | : | 2553 |
| อ้างอิง | : | Basu, S., Pasechnik, D. V., & Roy, M.- F. Bounding the Betti numbers and computing the Euler–Poincaré characteristic of semi-algebraic sets defined by partly quadratic systems of polynomials. Journal of the European Mathematical Society, 12(2), 529-553. , 1435-9855 , http://hdl.handle.net/10220/9277 , http://dx.doi.org/10.4171/JEMS/208 |
| ที่มา | : | - |
| ความเชี่ยวชาญ | : | - |
| ความสัมพันธ์ | : | Journal of the European mathematical society |
| ขอบเขตของเนื้อหา | : | - |
| บทคัดย่อ/คำอธิบาย | : | Let R be a real closed field, Q ⊂ R[Y1 , . . . , Yl, X1 , . . . , Xk], with degY(Q) ≤ 2, degX(Q) ≤ d, Q ∈ Q, #(Q) = m, and P ⊂ R[X1, . . . , Xk] with degX(P) ≤ d, P ∈ P, #(P) = s, and S ⊂ Rl+k a semi-algebraic set defined by a Boolean formula without negations, with atoms P = 0, P ≥ 0, P ≤ 0, P ∈ P ∪ Q. We prove that the sum of the Betti numbers of S is bounded by l2 (O(s + l + m)ld)k+2m. This is a common generalization of previous results in [4] and [3] on bounding the Betti numbers of closed semi-algebraic sets defined by polynomials of degree d and 2, respectively. We also describe an algorithm for computing the Euler–Poincaré characteristic of such sets, e generalizing similar algorithms described in [4, 9]. The complexity of the algorithm is bounded by (lsmd)O(m(m+k)). |
| บรรณานุกรม | : |
Basu, Saugata , Pasechnik, Dmitrii V. , Roy, Marie-Françoise . (2553). Bounding the Betti numbers and computing the Euler–Poincaré characteristic of semi-algebraic sets defined by partly quadratic systems of polynomials.
กรุงเทพมหานคร : Nanyang Technological University, Singapore. Basu, Saugata , Pasechnik, Dmitrii V. , Roy, Marie-Françoise . 2553. "Bounding the Betti numbers and computing the Euler–Poincaré characteristic of semi-algebraic sets defined by partly quadratic systems of polynomials".
กรุงเทพมหานคร : Nanyang Technological University, Singapore. Basu, Saugata , Pasechnik, Dmitrii V. , Roy, Marie-Françoise . "Bounding the Betti numbers and computing the Euler–Poincaré characteristic of semi-algebraic sets defined by partly quadratic systems of polynomials."
กรุงเทพมหานคร : Nanyang Technological University, Singapore, 2553. Print. Basu, Saugata , Pasechnik, Dmitrii V. , Roy, Marie-Françoise . Bounding the Betti numbers and computing the Euler–Poincaré characteristic of semi-algebraic sets defined by partly quadratic systems of polynomials. กรุงเทพมหานคร : Nanyang Technological University, Singapore; 2553.
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