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Subset of n-space defined by a finite sequence of polynomial equations and inequalities
mathematics, a basic semialgebraic set is a set defined by polynomial equalities and polynomial inequalities, and a semialgebraic set is a finite union of
Semialgebraic_set
Study of systems of inequalitites
them (in particular real polynomial mappings). Semialgebraic geometry is the study of semialgebraic sets, i.e. real-number solutions to algebraic inequalities
Real_algebraic_geometry
Quantifier elimination for semi-algebraic sets
widely used in computational algebraic geometry. A semialgebraic set in Rn is a finite union of sets defined by a finite number of polynomial equations
Tarski–Seidenberg_theorem
\{g_{i}\}} . For general semialgebraic sets, the most general result is Stengle's Positivstellensatz. For compact semialgebraic sets we have Schmüdgen's positivstellensatz
Positive_polynomial
Field in mathematics similar to the real numbers
of a semialgebraic set is a semialgebraic set, and that there is an algorithm that, given a quantifier-free formula defining a semialgebraic set, produces
Real_closed_field
Measure of a mathematical object studied in the field of algebraic geometry
real dimension of a set of real points, typically a semialgebraic set, is the dimension of its Zariski closure. For a semialgebraic set S, the real dimension
Dimension of an algebraic variety
Dimension_of_an_algebraic_variety
Mathematical space
geometry, a semialgebraic space is a space which is locally isomorphic to a semialgebraic set. Let U be an open subset of Rn for some n. A semialgebraic function
Semialgebraic_space
Convex optimization problem
convex semialgebraic set in the plane can be written as a feasible region of a SOCP. However, it is known that there exist convex semialgebraic sets of higher
Second-order_cone_programming
Realization of semialgebraic sets by points
combinatorics and algebraic geometry used to represent algebraic (or semialgebraic) varieties as realization spaces of oriented matroids. Informally it
Mnëv's_universality_theorem
and hence is not subanalytic. Semialgebraic set Edward Bierstone and Pierre D. Milman, Semianalytic and subanalytic sets, Inst. Hautes Études Sci. Publ
Subanalytic_set
Set of values which satisfy a given set of equations
solution sets are called algebraic sets if there are no inequalities. Over the reals, and with inequalities, there are called semialgebraic sets. More generally
Solution_set
Type of infinite structure
in place of polynomials.) In the case of RCF, the definable sets are the semialgebraic sets. Thus the study of o-minimal structures and theories generalises
O-minimal_theory
Quantified formulas with real-number variables
false. Equivalently, it is the problem of testing whether a given semialgebraic set is non-empty. This decision problem is NP-hard and lies in PSPACE
Existential theory of the reals
Existential_theory_of_the_reals
Theorem of real algebraic geometry
"positive-locus-theorem") characterizes polynomials that are positive on a semialgebraic set, which is defined by systems of inequalities of polynomials with real
Krivine–Stengle Positivstellensatz
Krivine–Stengle_Positivstellensatz
Stratifiability condition in mathematical topology
can be given Whitney stratifications, such as semialgebraic sets (due to René Thom) and subanalytic sets (due to Heisuke Hironaka). This has led to their
Whitney_conditions
Decomposing n-space into cells in which each of a set of polynomials has constant sign
geometry. Given a set S of polynomials in Rn, a cylindrical algebraic decomposition is a decomposition of Rn into connected semialgebraic sets called cells
Cylindrical algebraic decomposition
Cylindrical_algebraic_decomposition
Generalization of a semialgebraic set
mathematics, a piecewise algebraic space is a generalization of a semialgebraic set, introduced by Maxim Kontsevich and Yan Soibelman. The motivation
Piecewise_algebraic_space
calculus Semialgebraic geometry a part of algebraic geometry; more specifically a branch of real algebraic geometry that studies semialgebraic sets. Set-theoretic
Glossary of areas of mathematics
Glossary_of_areas_of_mathematics
Award for advancements in discrete mathematics
graphs. Nikolai E. Mnev for Mnev's universality theorem, that every semialgebraic set is equivalent to the space of realizations of an oriented matroid
Fulkerson_Prize
Ellipsoid most closely containing, or contained in, an n-dimensional convex object
Didier; Lagoa, Constantino M. (2017). "Simple approximations of semialgebraic sets and their applications to control". Automatica. 78: 110–118. arXiv:1509
John_ellipsoid
Topological space that locally resembles Euclidean space
spaces, including algebraic varieties, analytic varieties, semialgebraic sets, and subanalytic sets. CW-complexes A CW complex is a topological space formed
Manifold
Area of mathematical logic
varieties and of the definable relations on real-closed fields as semialgebraic sets In the 1960s, the introduction of the ultraproduct construction led
Model_theory
Shape that can be represented as a linear matrix inequality
spectrahedral shadows. Every spectrahedral shadow is a convex set that is also semialgebraic, but the converse (conjectured to be true until 2017) is false
Spectrahedron
Model of computational complexity
degree d {\displaystyle d} . Geometrically, the space is divided into semialgebraic sets (a generalization of a hyperplane). These decision tree models, defined
Decision_tree_model
American mathematician (1958–2025)
2001 (with Claus Scheiderer) "The moment problem for non-compact semialgebraic sets.", Adv. Geom, vol.1, 71-88 2001 (with Bruce Reznick) "A new bound
Victoria_Powers
Brief description on Macbeath Regions
Arijit; Jartoux, Bruno; Mustafa, Nabil (2019). "Shallow Packings, Semialgebraic Set Systems, MacBeath Regions, and Polynomial Partitioning". Discrete
Macbeath_region
1998 non-fiction book
in this area is the use of the number of connected components of a semialgebraic set to provide a lower bound on the time complexity of an associated computational
Complexity and Real Computation
Complexity_and_Real_Computation
dévissage can be applied to stratified structures such as semialgebraic or semianalytic sets, and which excludes some pathological spaces that do not correspond
Tame_topology
Possible distances in a bar-joint system
l_{p}}^{d}(G,\delta _{G})} is the projection of the Cayley-Menger semialgebraic set, with fixed ( G , δ ) {\displaystyle (G,\delta )} or ( G , [ δ G l
Cayley_configuration_space
rapid-decay. semianalytic The notion of semianalytic is an analog of semialgebraic. semicontinuous A semicontinuous function. separable A topological space
Glossary of real and complex analysis
Glossary_of_real_and_complex_analysis
exponentials of polynomials. Although they are generally neither algebraic nor semialgebraic, they retain a number of structural features familiar from real algebraic
Exponential_polynomial
Economical computational problem
surfaces it lies (with polynomial surfaces, the cells are also known as semialgebraic sets). For each cell, we either find a market-clearing price-vector (i
Market equilibrium computation
Market_equilibrium_computation
Branch of mathematics
algebra is the part of algebra which is relevant to real algebraic (and semialgebraic) geometry. It is mostly concerned with the study of ordered fields and
Global_optimization
Numerical optimization process
pp. 73–85. Parrilo, P., (2000) Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization. Ph.D. thesis, California
Sum-of-squares_optimization
Theorem in mathematics
field k (or an o-minimal structure). Precisely, the theorem holds for a semialgebraic (or definable) map between open subsets of k n {\displaystyle k^{n}}
Inverse_function_theorem
Mathematical field
every definable subset of R n {\displaystyle \mathbb {R} ^{n}} is semialgebraic. The ⟨ + , × , exp , < ⟩ {\displaystyle \langle +,\times ,\exp ,<\rangle
Transseries
Mathematical ring
of global sections of affine real closed spaces (a generalization of semialgebraic spaces) and in this context they were invented by Niels Schwartz in
Real_closed_ring
SEMIALGEBRAIC SET
SEMIALGEBRAIC SET
Male
Greek
(Σήθος) Greek form of Egyptian Sutekh, possibly SETHOS means "one who dazzles." In mythology, this is the name of an ancient evil god of Chaos, storms, and the desert, who slew Osiris.Â
Surname or Lastname
English
English : habitational name from a place in Shropshire, so named from Welsh mynydd ‘hill’ + Old English tūn ‘enclosure’, ‘settlement’.
Surname or Lastname
English and Scottish
English and Scottish : habitational name from any of the numerous and widespread places so called. The majority of these are named with Old English middel ‘middle’ + tūn ‘enclosure’, ‘settlement’; a smaller group, with examples in Cumbria, Kent, Northamptonshire, Northumbria, Nottinghamshire, and Staffordshire, have as their first element Old English mylen ‘mill’.
Surname or Lastname
English and Irish
English and Irish : variant of Mayhew.Variant of French Mailhot.A William Mayo born in Wiltshire, England, c. 1684 was a surveyor who settled in VA about 1623 and helped survey the VA-NC boundary and found Richmond and Petersburg, VA. [newpara]The Mayo Clinic in Rochester, MN, was founded by William Worrall Mayo (1819–1911), who immigrated to the U.S. from England, in 1845, and his sons, all gifted and innovative physicians and surgeons.
Surname or Lastname
English
English : habitational name from a place in North Yorkshire, so named from Old English setl ‘seat’, ‘dwelling’.
Male
Italian
Italian form of Roman Latin Septimus, SETTIMIO means "seventh."
Male
Greek
(Σήθι) Greek form of Egyptian Seti, SETHI means "of Seth."Â
Surname or Lastname
English
English : occupational name for a stone- or bricklayer, from Middle English setter ‘one who lays stones or bricks in building’ (agent derivative of setten ‘to set’).English : occupational name from Old French saietier ‘silk weaver’ (an agent derivative of sayete, a kind of silk).English : from an agent derivative of Middle English setten ‘to place (decoration, on a garment or metal surface)’, probably an occupational name for an embroiderer.German : unexplained.Norwegian : unexplained.
Surname or Lastname
English
English : topographic name for someone who lived in the center of a village, from Middle English midde ‘mid’ + toun ‘village’, ‘town’.English : habitational name from places in Lancashire, Worcestershire, and West Yorkshire, so named in Old English as ‘farmstead at a river confluence’, from (ge)m̄ðe ‘river confluence’ + tūn ‘farmstead’, ‘settlement’.
Surname or Lastname
English
English : habitational name from places called Merton in London, Devon, Norfolk, and Oxfordshire, named in Old English with mere ‘lake’, ‘pool’ + tūn ‘enclosure’, ‘settlement’. Compare Marton, Martin 2.
Female
Japanese
(節å) Japanese name SETSUKO means "temperate child."
Surname or Lastname
English and Scottish
English and Scottish : habitational name from any of the places so called. In over thirty instances from many different areas, the name is from Old English midel ‘middle’ + tūn ‘enclosure’, ‘settlement’. However, Middleton on the Hill near Leominster in Herefordshire appears in Domesday Book as Miceltune, the first element clearly being Old English micel ‘large’, ‘great’. Middleton Baggot and Middleton Priors in Shropshire have early spellings that suggest gem̄ðhyll (from gem̄ð ‘confluence’ + hyll ‘hill’) + tūn as the origin.A Scottish family of this name derives it from lands at Middleto(u)n near Kincardine. The Scottish physician Peter Middleton practiced in New York City after 1752 and was one of the founders of the medical school at King's College (now Columbia University) in 1767. One of the earliest of the Charleston, SC, Middleton family of prominent legislators was Arthur Middleton, born in Charleston in 1681.
Surname or Lastname
Scottish and English
Scottish and English : topographic name for someone who lived near a mill, Middle English mille, milne (Old English myl(e)n, from Latin molina, a derivative of molere ‘to grind’). It was usually in effect an occupational name for a worker at a mill or for the miller himself. The mill, whether powered by water, wind, or (occasionally) animals, was an important center in every medieval settlement; it was normally operated by an agent of the local landowner, and individual peasants were compelled to come to him to have their grain ground into flour, a proportion of the ground grain being kept by the miller by way of payment.English : from a short form of a personal name, probably female, as for example Millicent.
Surname or Lastname
English
English : habitational name from Mitcham in Surrey, so named from Old English micel ‘big’ + hÄm ‘homestead’, ‘settlement’.
Surname or Lastname
English
English : habitational name from Milwich in Staffordshire, so named from Old English myln ‘mill’ + wīc ‘dairy farm’; ‘(trading) settlement’.
Male
English
Anglicized form of Hebrew Sheth, SETH means "buttocks." In the bible, this is the name of the third son of Adam and Eve. Compare with other forms of Seth.
Surname or Lastname
English
English : habitational name from a place in Kent named Meopham, from an Old English personal name MÄ“apa + Old English hÄm ‘homestead’, ‘settlement’.
Surname or Lastname
English
English : patronymic from Setter.
Male
Hindi/Indian
(सेठ) Hindi name derived from the Sanskrit word setu, SETH means "bridge." Compare with other forms of Seth.
Surname or Lastname
English
English : habitational name from places in Cheshire and East Yorkshire, so named from Old English mylen ‘mill’ + tūn ‘enclosure’, ‘settlement’.
SEMIALGEBRAIC SET
SEMIALGEBRAIC SET
Biblical
an exalting; high
Boy/Male
Hindu, Indian, Marathi
Another Name for the Moon
Boy/Male
Indian, Tamil
Ezhil - Beautiful; Inpan - Happiness
Surname or Lastname
English
English : probably from the Old English personal name Ecgwulf, meaning ‘sword wolf’.
Girl/Female
Muslim/Islamic
A handfull of sweet basil
Boy/Male
Indian
Luck
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Telugu
Credit; Marvellous
Boy/Male
Hindu, Indian
Dragged
Girl/Female
British, English, French
From Alsace
Boy/Male
Tamil
Bordering, Leader, Universal whole
SEMIALGEBRAIC SET
SEMIALGEBRAIC SET
SEMIALGEBRAIC SET
SEMIALGEBRAIC SET
SEMIALGEBRAIC SET
n.
A settled place of abode; residence; a right growing out of residence; legal residence or establishment of a person in a particular parish or town, which entitles him to maintenance if a pauper, and subjects the parish or town to his support.
n.
That which settles at the bottom of a liquid; lees; dregs; sediment.
n.
A colony newly established; a place or region newly settled; as, settlement in the West.
n.
Fractures or dislocations caused by settlement.
n.
One who settles, becomes fixed, established, etc.
a.
Having small bristles or setae.
n.
An instrument used to set or turn the teeth of a saw a little sidewise, that they may make a kerf somewhat wider than the thickness of the blade, to prevent friction; -- called also saw-wrest.
a.
Eager in appetite or desire of gratification; affected by keen hunger; ravenous; as, an eagle or a lion sharp-set.
n.
A setula.
n.
A small, short hair or bristle; a small seta.
n.
Especially, one who establishes himself in a new region or a colony; a colonist; a planter; as, the first settlers of New England.
n.
Matter that subsides; settlings; sediment; lees; dregs.
n.
That which settles, or is settled, established, or fixed.
n.
That which settles or finishes; hence, a blow, etc., which settles or decides a contest.
n.
The act or process of adjusting or determining; composure of doubts or differences; pacification; liquidation of accounts; arrangement; adjustment; as, settlement of a controversy, of accounts, etc.
pl.
of Setula
a.
Properly or firmly set.
n.
The act of peopling, or state of being peopled; act of planting, as a colony; colonization; occupation by settlers; as, the settlement of a new country.
n.
A vessel, as a tub, in which something, as pulverized ore suspended in a liquid, is allowed to settle.
n.
The act of one who, or that which, settles; the act of establishing one's self, of colonizing, subsiding, adjusting, etc.