𝐑 𝟑 de k- Vektör İçin R(x1,x2,…,xk) S(3) Cisminin Üreteçleri

Abstract

k- bilinmeyenli reel kaysayılı tüm G- invaryant rasyonel fonksiyonların kümesi 𝑅(x1,x2,…,xk) 𝐺 ile gösterilir. Üç boyutlu ℝ3 Öklid uzayında benzerlik dönüşümleri grubu G = S(3) olmak üzere, bu çalışmada ℝ3 de verilen ve k vektörden oluşan 𝐴 = {𝑥1, 𝑥2 ,… , 𝑥𝑘} kümesinin rasyonel S(3)-invaryantlarını tam olarak belirleyebilmek için G grubuna göre invaryant rasyonel fonksiyonlar cismi olan R(x1,x2,…,xk) G cisminin üreteç kümesi ifade edilmiştir. Böylece A kümesinin herhangi bir S(3) invaryantı bu üreteç kümenin elemanlarının bir fonksiyonu olarak ifade edilebilecektir. 

Keywords

• G-invariant foksiyonlar
• benzerlik dönüşümü
• üreteç invaryantlar
• S(3)-invaryant rasyonel fonksiyonlar

The generators of the field R(x1,x2,…,xk) S(3) for k- vectors given in 𝑅 3

Abstract

The field of the G-invariant rational functions with k- variables 𝑥1, 𝑥2,… , 𝑥𝑘 is denoted by𝑅(x1,x2,…,xk)𝐺. In this paper the generator set of the field of G-invariant rational functions denoted by R(x1,x2,…,xk)G is obtained to determine completely all S(3)-invariants of the set 𝐴 = {𝑥1 , 𝑥2 ,…, 𝑥𝑘} consisted of k- vector variables in ℝ3 where G = S(3) which is the similarity transformations' group in 3 dimensional Euclidean space ℝ3. So any S(3)-invariant of the set A can be stated by the functions of the generator set of the field R(x1,x2,…,xk) G.

Keywords

• similarity transformation
• generator invariants
• S(3)-invariant rational functions
• G- invariant functions

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