Sparse resultants and straight-line programs
We prove that the sparse resultant, redefined by D'Andrea and Sombra and by Esterov as a power of the classical sparse resultant, can be evaluated in a number of steps which is polynomial in its degree, its number of variables and the size of the exponents of the monomials in the Laurent polyno...
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todo:paper_07477171_v87_n_p14_Jeronimo2023-10-03T15:39:01Z Sparse resultants and straight-line programs Jeronimo, G. Sabia, J. Algorithms Sparse resultants Straight-line programs We prove that the sparse resultant, redefined by D'Andrea and Sombra and by Esterov as a power of the classical sparse resultant, can be evaluated in a number of steps which is polynomial in its degree, its number of variables and the size of the exponents of the monomials in the Laurent polynomials involved in its definition. Moreover, we design a probabilistic algorithm of this order of complexity to compute a straight-line program that evaluates it within this number of steps. © 2017 Elsevier Ltd Fil:Jeronimo, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Sabia, J. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_07477171_v87_n_p14_Jeronimo |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
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R-134 |
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Algorithms Sparse resultants Straight-line programs |
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Algorithms Sparse resultants Straight-line programs Jeronimo, G. Sabia, J. Sparse resultants and straight-line programs |
| topic_facet |
Algorithms Sparse resultants Straight-line programs |
| description |
We prove that the sparse resultant, redefined by D'Andrea and Sombra and by Esterov as a power of the classical sparse resultant, can be evaluated in a number of steps which is polynomial in its degree, its number of variables and the size of the exponents of the monomials in the Laurent polynomials involved in its definition. Moreover, we design a probabilistic algorithm of this order of complexity to compute a straight-line program that evaluates it within this number of steps. © 2017 Elsevier Ltd |
| format |
JOUR |
| author |
Jeronimo, G. Sabia, J. |
| author_facet |
Jeronimo, G. Sabia, J. |
| author_sort |
Jeronimo, G. |
| title |
Sparse resultants and straight-line programs |
| title_short |
Sparse resultants and straight-line programs |
| title_full |
Sparse resultants and straight-line programs |
| title_fullStr |
Sparse resultants and straight-line programs |
| title_full_unstemmed |
Sparse resultants and straight-line programs |
| title_sort |
sparse resultants and straight-line programs |
| url |
http://hdl.handle.net/20.500.12110/paper_07477171_v87_n_p14_Jeronimo |
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AT jeronimog sparseresultantsandstraightlineprograms AT sabiaj sparseresultantsandstraightlineprograms |
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