irreducible decomposition 中文意思是什麼
irreducible decomposition
解釋
不可約分解- irreducible : adj. 1. 不能降低[削減]的。2. 【醫學】難回復的，難復位的。3. 【數學】不能化簡的，不能約的，既約的。n. -bility ,-bly adv.
- decomposition : n. 1. 分解，分析，溶解，還原（作用）。2. 腐朽，解體。
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In the end, when the domain is finite, b is a meet - irreducible element or 6 has an irredundant finite meet - decomposition, a sufficient and necessary condition that the solution set is nonempty is given and the number of distinct minimal solutions is formulated
最後，當論域為有限集， b為交既約元或有不可約有限交分解時，給出了方程inf _ （ i j ） （ a _ j ， x _ j ） = b解集非空的充要條件以及極大元的個數公式。 -
In order to determine the solution set of the equation, by the means of meet - irreducible element and irredundant finite meet - decomposition, we first obtain the maximal solutions to the simple equation in the case that b has an irredundant finite meet - decomposition, and then consider the relation between the equation and the equation, based on this, we obtain the maximal solutions to the equation in the case that each element of the matrix b has an irredundant finite meet - decomposition and so determine its solution set completely
為了確定方程的解集，本文利用交既約元與不可縮短的有限交分解等工具，同樣地先求出簡單形式的型矩陣方程的所有極大解，然後討論方程與方程之間的關系，在此基礎上，在b的每個元素均有不可縮短的有限交分解的情況下，求出了方程的所有極大解，從而完全確定了方程的解集 -
In the case of infinite domains, it is proven that there exists a maximal solution x " of a @ x = b such that x * x for every solution x of a @ x = b if the solution set of a @ x = b is unempty and b has an irredundant completely meet - irreducible decomposition. it is also identified that there exists a maximal solution x * of a @ x = b such that x * x for every solution x of a @ x = b if the solution set of a @ x = bis unempty and every component of b is dual - compact and has an irredundant finite - decomposition. in the end, a necssary and sufficient condition that there exists a maximal solution x * of a @ x = bsuch that x * x for every solution x of a @ x = b is given when the solution set of a @ x = b is unempty
當論域為無限集時，證明了如果方程a @ x = b有解且b有不可約完全交既分解，則對方程a @ x = b的每一個解至少存在一個大於等於它的極大解；進一步證明了如果方程a @ x = b有解且b的每一個分量為對偶緊元並有不可約有限交分解，則對方程a @ x = b的每一個解存在一個大於等於它的極大解；最後給出了對方程a @ x = b的每一個解存在一個大於等於它的極大解的一個充要條件及[ 0 ， 1 ]格上方程a @ x = b的解集中存在極大解的一個充要條件。 -
Application of irreducible decomposition of polynomials over algebraic extension fields in cryptography
代數擴張域上的多項式分解在密碼學中的應用
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