algebraic set in a sentence
1) An irreducible algebraic set is also called a "variety".
algebraic collocations
2) The definition of the regular maps apply also to algebraic sets .
3) An irreducible affine algebraic set is also called an affine variety.
algebraic set example sentences
4) Thus the subset __FORMULA__ of A2 is an algebraic set .5) The "projective varieties" are the projective algebraic sets whose defining ideal is prime.
6) Thus its elements are called the "irreducible components" of the algebraic set .
7) The affine varieties is a subcategory of the category of the algebraic sets .
8) Every projective algebraic set may be uniquely decomposed into a finite union of projective varieties.
9) Any algebraic set is a finite union of irreducible algebraic sets and this decomposition is unique.
10) Any algebraic set is a finite union of irreducible algebraic sets and this decomposition is unique.
11) Contrarily to the preceding ones, this section concerns only varieties and not algebraic sets .
12) It follows that the best implementations allow to compute almost routinely with algebraic sets of degree more than 100.
13) Generalizing this result, Hilbert's Nullstellensatz provides a fundamental correspondence between ideals of polynomial rings and algebraic sets .
14) If the condition of generating a prime ideal is removed, such a set is called a projective algebraic set .
15) Affine varieties can be given a natural topology by declaring the closed sets to be precisely the affine algebraic sets .
example sentences with algebraic set
16) The "V" stands for "variety" (a specific type of algebraic set to be defined below).17) For an algebraic set defined on the field of the complex numbers, the regular functions are smooth and even analytic.
18) An algebraic set being a finite union of algebraic varieties, its dimension is the maximum of the dimensions of its components.
19) An algebraic set is called "irreducible" if it cannot be written as the union of two smaller algebraic sets.
20) An algebraic set is called "irreducible" if it cannot be written as the union of two smaller algebraic sets .
21) For various reasons we may not always want to work with the entire ideal corresponding to an algebraic set "U".
22) The degree of the ideal and of its associated algebraic set is the number of points of this finite intersection, counted with multiplicity.
23) It is also equal to number of hyperplanes in general position which are needed to have an intersection with the algebraic set , which is a finite number of points.
24) For any affine algebraic set "V", the coordinate ring or structure ring of "V" is the quotient of the polynomial ring by this ideal.
25) A nonempty affine algebraic set "V" is called irreducible if it cannot be written as the union of two proper algebraic subsets.
26) A subset "V" of __FORMULA__ is called an affine algebraic set if "V" = "Z"("S") for some "S".
27) Using the Nullstellensatz and related results, mathematicians have established a strong correspondence between questions on algebraic sets and questions of ring theory.
28) The projective Zariski topology is defined for projective algebraic sets just as the affine one is defined for affine algebraic sets, by taking the subspace topology.
How to use algebraic set in a sentence
29) The projective Zariski topology is defined for projective algebraic sets just as the affine one is defined for affine algebraic sets , by taking the subspace topology.30) It is equal to the maximal length of the chains __FORMULA__ of sub-varieties of the given algebraic set (the length of such a chain is the number of "__FORMULA__").
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