Filters








14,068 Hits in 16.0 sec

Polar varieties and computation of one point in each connected component of a smooth real algebraic set

Mohab Safey El Din, Éric Schost
<span title="">2003</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/p5cu7ybzmnd3jpp7pphgogfzpi" style="color: black;">Proceedings of the 2003 international symposium on Symbolic and algebraic computation - ISSAC &#39;03</a> </i> &nbsp;
Suppose that V is smooth and equidimensional; then we show that computing suitable sections of the polar varieties associated to generic projections of V gives at least one point in each connected component  ...  Its arithmetic complexity is polynomial in the complexity of evaluation of the input system, an intrinsic algebraic quantity and a combinatorial quantity.  ...  INTRODUCTION Let V be a smooth and equidimensional complex algebraic variety. This paper is devoted to design an algorithm computing at least one point in each connected component of V ∩ R n .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/860854.860901">doi:10.1145/860854.860901</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/issac/DinS03.html">dblp:conf/issac/DinS03</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/cckfwq5sjjebboyhu7ispue4i4">fatcat:cckfwq5sjjebboyhu7ispue4i4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170808155825/http://www.csd.uwo.ca/faculty/eschost/publications/p32-safey.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/fc/09/fc0903bbacaa50362b6b64fbffc5c28acd3204c5.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/860854.860901"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

A Gröbner free alternative to solving and a geometric analogue to Cook's thesis

Marc Giusti
<span title="">2009</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/p5cu7ybzmnd3jpp7pphgogfzpi" style="color: black;">Proceedings of the 2009 international symposium on Symbolic and algebraic computation - ISSAC &#39;09</a> </i> &nbsp;
To characterize the set of real solutions of a system of polynomial equations it is a rst step to nd at least one point in each connected component.  ...  To characterize the set of real solutions of a system of polynomial equations it is a rst step to nd at least one point in each connected component. sucient to solve quadratic equations in one or two variables  ...  Each walk W yields a procedure R W which exhibits at least one real algebraic point in each connected component of V R .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1576702.1576703">doi:10.1145/1576702.1576703</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/issac/Giusti09.html">dblp:conf/issac/Giusti09</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/5tyxsfitzzcohg5zti65preqwi">fatcat:5tyxsfitzzcohg5zti65preqwi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20151009225638/http://issac2009.kias.re.kr/giusti.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/5b/6a/5b6ac5c6e875efb24b341977216fc534261d8a60.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1576702.1576703"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

On the intrinsic complexity of point finding in real singular hypersurfaces

Bernd Bank, Marc Giusti, Joos Heintz, Luis Miguel Pardo
<span title="">2009</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/5xfy4fcdxvcvdiybp6iqbffqc4" style="color: black;">Information Processing Letters</a> </i> &nbsp;
In previous work we designed an efficient procedure that finds an algebraic sample point for each connected component of a smooth real complete intersection variety.  ...  In the present paper we introduce a natural construction that allows to tackle the case of a non-smooth real hypersurface by means of a reduction to a smooth complete intersection.  ...  in order to find for each connected component of the real trace of S i,k a sample point.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.ipl.2009.07.014">doi:10.1016/j.ipl.2009.07.014</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/myjbeuezlfbkpajeiksmlpsgdy">fatcat:myjbeuezlfbkpajeiksmlpsgdy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20110401125713/http://www.lix.polytechnique.fr/~giusti/publications/infproclet.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/df/ed/dfedba3d9fd859723084456a8efbeaaa031f3b0e.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.ipl.2009.07.014"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Smooth Points on Semi-algebraic Sets [article]

Katherine Harris and Jonathan D. Hauenstein and Agnes Szanto
<span title="2020-07-15">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In this paper, we present a simple algorithm based on computing the critical points of some well-chosen function that guarantees the computation of smooth points in each connected compact component of  ...  Many algorithms for determining properties of real algebraic or semi-algebraic sets rely upon the ability to compute smooth points.  ...  Acknowledgments The authors thank Mohab Safey El Din and Elias Tsigaridas for many discussions regarding real algebraic geometry.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2002.04707v2">arXiv:2002.04707v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lydrjafrtnfedojvjns7tyccw4">fatcat:lydrjafrtnfedojvjns7tyccw4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200718014459/https://arxiv.org/pdf/2002.04707v2.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2002.04707v2" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Polar Varieties, Real Equation Solving, and Data Structures: The Hypersurface Case

B. Bank, M. Giusti, J. Heintz, G.M. Mbakop
<span title="">1997</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/hhnp3o4qcjfyfd4gpifcdou6ui" style="color: black;">Journal of Complexity</a> </i> &nbsp;
Our main result concerns the problem of finding at least one representative point for each connected component of a real compact and smooth hypersurface.  ...  One feature of central importance of this algorithm is the use of a problem-adapted data type represented by the data structures arithmetic network and straight-line program (arithmetic circuit).  ...  Since is a real component of the set is not empty and contained in . The polar variety is contained in the algebraic set . that is contained in the Zariski closure of as well.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1006/jcom.1997.0432">doi:10.1006/jcom.1997.0432</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ue62lbipkbdbziqqfnzaffh5j4">fatcat:ue62lbipkbdbziqqfnzaffh5j4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190415074332/https://core.ac.uk/download/pdf/82748066.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/c2/cb/c2cbb0481bf272a21d18df789d9bbc903c2bff31.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1006/jcom.1997.0432"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Properness Defects of Projections and Computation of at Least One Point in Each Connected Component of a Real Algebraic Set

Mohab Safey El Din, �ric Schost
<span title="2004-07-14">2004</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/cu3ouk4pmzhsroy4l5k2c35xtu" style="color: black;">Discrete &amp; Computational Geometry</a> </i> &nbsp;
Computing at least one point in each connected component of a real algebraic set is a basic subroutine to decide emptiness of semi-algebraic sets, which is a fundamental algorithmic problem in effective  ...  We show how studying the set of non-properness of a linear projection enables us to detect the connected components of a real algebraic set without critical points for .  ...  Main Algorithm We now describe our main algorithm, which computes at least one point in each connected component of a real algebraic variety.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00454-004-1107-5">doi:10.1007/s00454-004-1107-5</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/wpizqm665ralbi6zsympyke3ie">fatcat:wpizqm665ralbi6zsympyke3ie</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190503101359/https://link.springer.com/content/pdf/10.1007%2Fs00454-004-1107-5.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/82/91/8291b3dbcf88116e1ea1b1bdf2db8e01f751d157.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00454-004-1107-5"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Probabilistic Algorithms for Geometric Elimination

Guillermo Matera
<span title="1999-07-01">1999</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/lnpibodwo5cpnp3qbzbnlmdepu" style="color: black;">Applicable Algebra in Engineering, Communication and Computing</a> </i> &nbsp;
ACKNOWLEDGEMENT The authors thank the referees for their careful reading of the manuscript. Their comments helped us to correct several misleading errors. (Received November 25, 2003.)  ...  Then, the real affine dual polar variety W-^(S R ) is non-empty and contains at least one point of each connected component of SR. Proof.  ...  Suppose that 5R is smooth. Then "sufficiently generic" real dual polar varieties of 5R contain for each connected component of 5R at least one representative point.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s002000050115">doi:10.1007/s002000050115</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/dazmppdajnahnlt6q6zyk557fy">fatcat:dazmppdajnahnlt6q6zyk557fy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170814005154/http://dml.cz/bitstream/handle/10338.dmlcz/135615/Kybernetika_40-2004-5_2.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/53/69/53696c1433c5c99ede17b86304ff8c5a10f9bcfb.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s002000050115"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Polar Varieties Revisited [chapter]

Ragni Piene
<span title="">2015</span> <i title="Springer International Publishing"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
I will take a look at three applications: finding points on real components focal loci and caustics of reflection The work on polars and reciprocal polars of real projective and affine algebraic varieties  ...  Today I will survey the classical theory of polar varieties and the less classical of reciprocal polar varieties.  ...  How to find a way of determining a point on each connected component?  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-319-15081-9_8">doi:10.1007/978-3-319-15081-9_8</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/o3rw7f25f5gvldkhcg5qz5b7me">fatcat:o3rw7f25f5gvldkhcg5qz5b7me</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20160527044113/http://www.ricam.oeaw.ac.at/specsem/specsem2013/workshop3/slides/piene.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/20/ad/20ad2f39a1d44f0c61da70fc594a777bd3a7ff78.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-319-15081-9_8"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Algorithms of Intrinsic Complexity for Point Searching in Compact Real Singular Hypersurfaces

Bernd Bank, Marc Giusti, Joos Heintz, Lutz Lehmann, Luis Miguel Pardo
<span title="2012-01-04">2012</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2joypbq7ubehha6yu7ylkxkoqa" style="color: black;">Foundations of Computational Mathematics</a> </i> &nbsp;
We are going to decide whether this equation has a non-singular real solution and, if this is the case, we exibit one for each generically smooth connected component of {F = 0} R .  ...  In the case that the real variety defined by F is smooth, there exist already algorithms of intrinsic  ...  Therefore, a set of algebraic sample points for the connected components of V R gives rise to a set of algebraic sample points for the generically smooth connected components of {F = 0} R .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10208-011-9112-6">doi:10.1007/s10208-011-9112-6</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/x3ecohcci5en3mroqrlvfxwonm">fatcat:x3ecohcci5en3mroqrlvfxwonm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20140501201156/http://www2.mathematik.hu-berlin.de:80/publ/pre/2011/P-11-19.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/f3/04/f304f349aaccc2a3211a371486a16ff728b5a9b1.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10208-011-9112-6"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

On the isotopic meshing of an algebraic implicit surface

Daouda Niang Diatta, Bernard Mourrain, Olivier Ruatta
<span title="">2012</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ezljl2d3lzga5efenbxdvvfcpa" style="color: black;">Journal of symbolic computation</a> </i> &nbsp;
We present a new and complete algorithm for computing the topology of an algebraic surface S given by a square free polynomial in Q[X , Y , Z ].  ...  We extend the work in Diatta et al. (2008) , on the topology of non-reduced algebraic space curves, and apply it to the polar curve or apparent contour of the surface S.  ...  component is a stratum), • S 2 the set of the connected components of S − P (each connected component is a stratum)  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.jsc.2011.09.010">doi:10.1016/j.jsc.2011.09.010</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/elh2gme7dja5lmaedn3m7vkxge">fatcat:elh2gme7dja5lmaedn3m7vkxge</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190313034954/https://core.ac.uk/download/pdf/82453129.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/4d/10/4d1017a667091164efdefb273a7de125082e29dc.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.jsc.2011.09.010"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Point searching in real singularcomplete intersection varieties: algorithms of intrinsic complexity

Bernd Bank, Marc Giusti, Joos Heintz
<span title="2013-10-31">2013</span> <i title="American Mathematical Society (AMS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/5bz4zmidbngqxk6yv4msbkm54u" style="color: black;">Mathematics of Computation</a> </i> &nbsp;
. , X n be indeterminates over Q and let X := (X 1 , .  ...  a smooth real trace S R algebraic sample points for each connected component of S R .  ...  In case that S R is smooth and a is real ((n − p − i + 1) × (n + 1)) -matrix, the real dual polar variety W K(a) (S R ) contains at least one point of each connected component of S R , whereas the classic  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1090/s0025-5718-2013-02766-4">doi:10.1090/s0025-5718-2013-02766-4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/bclh3lk3rfhm5p6eihbdelryia">fatcat:bclh3lk3rfhm5p6eihbdelryia</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170923023203/http://webdoc.sub.gwdg.de/ebook/serien/e/preprint_HUB/P-11-18.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/57/ee/57eec42e87863ecfb15afe224c1f28e858f0c284.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1090/s0025-5718-2013-02766-4"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

Probabilistic Algorithm for Computing the Dimension of Real Algebraic Sets

Ivan Bannwarth, Mohab Safey El Din
<span title="">2015</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/p5cu7ybzmnd3jpp7pphgogfzpi" style="color: black;">Proceedings of the 2015 ACM on International Symposium on Symbolic and Algebraic Computation - ISSAC &#39;15</a> </i> &nbsp;
Our algorithm takes advantage of genericity properties of polar varieties to avoid computationally difficult steps of quantifier elimination. We also report on a first implementation.  ...  . , Xn] be a polynomial of degree D. We consider the problem of computing the real dimension of the real algebraic set defined by f = 0. Such a problem can be reduced to quantifier elimination.  ...  RAGlib is used for deciding the emptiness of real algebraic sets and computing sample points in each of their connected components. It implements algorithms that essentially run in time D O(n) .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/2755996.2756670">doi:10.1145/2755996.2756670</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/issac/BannwarthD15.html">dblp:conf/issac/BannwarthD15</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/irpkhvbzfrfwtj3rosasixqsia">fatcat:irpkhvbzfrfwtj3rosasixqsia</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170830103746/https://hal.archives-ouvertes.fr/hal-01152751/document" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/9c/16/9c1640a969d7921044504f3094451c8216f9ee90.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/2755996.2756670"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

Polar Varieties, Real Equation Solving and Data-Structures: The hypersurface case [article]

B. Bank, M. Giusti, J. Heintz, G.M. Mbakop
<span title="1996-09-06">1996</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Our main result concerns the problem of finding at least one representative point for each connected component of a real compact and smooth hypersurface.  ...  under consideration, we are able to find for each connected component of the hypersurface a representative point (this point will be given in a suitable encoding).  ...  N codifies for each connected component of V at least one representative point.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/alg-geom/9609004v1">arXiv:alg-geom/9609004v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qlbc77lk6fdr3a5oaave4gsi6a">fatcat:qlbc77lk6fdr3a5oaave4gsi6a</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20171006125259/https://core.ac.uk/download/pdf/2258172.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/85/a0/85a08a2f6332506b03a9af3ac583b05fd4d207bf.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/alg-geom/9609004v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Polar Varieties and Efficient Real Equation Solving: The Hypersurface Case [article]

B. Bank, M. Giusti, J. Heintz, R. Mandel, G. M. Mbakop
<span title="1996-09-06">1996</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Our main result concerns the problem of finding one representative point for each connected component of a real bounded smooth hypersurface.  ...  Replacing the affine degree of the equation system by a suitably defined real degree of certain polar varieties associated to the input equation, which describes the hypersurface under consideration, and  ...  Definition 1 The component C j is called a real component of W if the real variety C j ∩ IR n contains a smooth point of C j .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/alg-geom/9609003v1">arXiv:alg-geom/9609003v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/owc2qixnqjd4lcbb5dels23nl4">fatcat:owc2qixnqjd4lcbb5dels23nl4</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-alg-geom9609003/alg-geom9609003.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> File Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/61/69/6169ef7a86a08a08bc14d61c7f0be19c28d821ad.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/alg-geom/9609003v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Intrinsic complexity estimates in polynomial optimization [article]

Bernd Bank, Marc Giusti, Joos Heintz, Mohab Safey El Din (LIP6, INRIA Paris-Rocquencourt)
<span title="2014-02-10">2014</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
It is known that point searching in basic semialgebraic sets and the search for globally minimal points in polynomial optimization tasks can be carried out using (s d)^O(n) arithmetic operations, where  ...  We associate to each of these problems an intrinsic system degree which becomes in worst case of order (n d)^O(n) and which measures the intrinsic complexity of the task under consideration.  ...  In case that S is closed and that any point of S R is (F 1 , . . . , F p ) -regular, the i th dual polar variety associated with a contains at least one point of each connected component of S R and is  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1304.5214v2">arXiv:1304.5214v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/i2bekejbkveflk62enc4mbc2pq">fatcat:i2bekejbkveflk62enc4mbc2pq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200914153138/https://arxiv.org/pdf/1304.5214v2.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/10/71/10713f6c0de1be8ee947ed732fce3dc7357416ee.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1304.5214v2" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>
&laquo; Previous Showing results 1 &mdash; 15 out of 14,068 results