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Froberg R. — An Introduction to Grobner Bases
Froberg R. — An Introduction to Grobner Bases

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Название: An Introduction to Grobner Bases

Автор: Froberg R.

Аннотация:

When talking to students in mathematics at the beginner's level, one often gets the questions: How is it possible to do research in mathematics? Isn't all mathematics already explored? It is rather hard to be able to explain that the converse is true, that the research and knowledge increases at greater speed every decade. One reason for the difficulty to discuss this is of course that the level of abstraction of mathematics has constantly increased. This is true for most parts of mathematics, in particular for commutative algebra and (especially for) algebraic geometry. Since the 1960s there is however also a trend in the opposite direction in these fields. Interest in constructiveness and concrete calculations is also now increasing. One important reason for this is the growth in the capability of computers. It has become possible to carry out calculations that one could only dream of earlier. It is also possible to perform experiments on a large scale.


Язык: en

Рубрика: Математика/

Серия: Сделано в холле

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1998

Количество страниц: 177

Добавлена в каталог: 04.06.2011

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$a\cdot b$      17
$A^{n}$      55
$P^{n}(k)$      117
$\mathbb{C}$      1
$\mathbb{C}[x_{1},...,x_{n}]_{(x_{1},...,x_{n})}$      142
$\mathbb{Q}$      3
$\mathbb{R}$      3
$\mathbb{Z}$      1
$\mathbb{Z}_{n}$      6
$\mathfrak{a}^{*}$      102
$\mathfrak{B}(a)$      119
$\mathfrak{B}(X)$      119
$\mathfrak{o}(S)$      62
$\oplus$      33
$\prec$      45
$\prec_{g}$      46
$\sqrt{A}$      18
$\times$      33
a(a)      108
a(V)      121
a+b      17
a:b      17
ACC      52
Admissible ordering      45
Affine algebraic set      62
Algebraic set      61
Algebraically closed      15
Ascending chain condition      52
Associated graded ring      125
Associated prime      74
Associated to      74
Basis for a vector space      32
Belong to      74
Bijective      26
Block ordering      45
Buchberger’s Algorithm      59
Characteristic      9
Commutative ring      2
Compatible      45
Cone of an ideal      123
Content of a polynomial      23
Coset      25
DCC      65
Deglex      45
Degree of a polynomial      8
Degree ordering      46
Degree reverse lexicographical      45
Degrevlex      45
Dehomogenization of a polynomial      107
Dehomogenization of an ideal      108
Dickson’s Lemma      47
Differential algebra      147
Dimension of a projective set      133
Dimension of an algebra      132
Dimension of an algebraic set      133
Dimension of vector space      32
Direct product      33
Direct sum      33
Elementary symmetric polynomial      93
Elimination      95
Embedded component      74
Equivalence relation      20
Euclidean ring      16
Extension field      6
Factor ring      25
Field      5
Finitely generated ideal      11
Formal power series      127
Fraction field      21
Free module      55
Fundamental theorem of algebra      15
Gaussian integers      17
GCD      13
Good extension      112
Grading of an ordering      46
Groebner basis      51
H(A)      107
h(f)      105
H(V)      121
Hilbert polynomial      131
Hilbert series      129
Hilbert’s basis theorem      51
Hilbert’s Nullstellensatz      66
Homogeneous algebra      100
Homogeneous component      99 100
Homogeneous polynomial      99
Homogenization of a polynomial      105
Homogenization of an ideal      107
Homomorphism of rings      26
i(x)      62
Ideal      10
Im      26
Image      26
Injective      26
Integral domain      5
Irreducible algebraic set      64
Irreducible ideal      71
Irreducible polynomial      14
Irreducible projective set      120
Isolated component      74
Isomorphism of rings      26
Ker      26
Kernel      26
l(a)      48
lc      48
LCM      15
Leading coefficient      48
Leading monomial      48
Leading term      48
Lex      45
Lexicographical      45
Linearly independent      31
LM      48
Local ring      142
lt      48
M(A)      123
m(f)      123
Maximal ideal      30
Maximum condition      52
mdeg      37
MODULO      25
Monic      14
Monomial      37 45
Monomial ideal      37
Monomial ordering      45
Multigrading      37
Multiplicity of a solution      80
NF      53
Nilpotent      72
Noetherian      52
Noncommutative polynomial ring      142
Normal form      53
Polynomial ring      8
Primary decomposition      73
Primary ideal      72
Prime ideal      29
Principal ideal      11
Product ordering      45
Projective closure      121
Projective set      119
Projective space      117
Q(R)      22
Radical ideal      18
Radical of an ideal      18
Reduced Groebner basis      53
rem      50
Ring      1
R[[X]]      127
S-polynomial      57
Sagbi basis      147
Socle      129
Squarefree      41
Standard basis      142
Subfield      6
Submodule      55
subspace      32
Supp      48
Support      48
Surjective      26
Symmetric polynomial      92
Syzygy      55
Tangent cone      125
Term      45
Two-sided ideal      143
Unique factorization domain      23
Unit element      2
Variety      62
Vector space      31
Zero-dimensional system      80
Zerodivisor      9
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