Characteristic Set
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High Quality Content by WIKIPEDIA articles! The mathematical concept of a characteristic set was discovered in the late forties by J.F. Ritt. Besides Gröbner basis method, it provides an alternative algorithmic way for solving multivariate polynomial equations or differential equations. In the late seventies, the Chinese mathematician Wen-Tsun Wu specialized it with modifications to commutative algebra. He demonstrated its power for mechanical theorem proving.For an ideal I in the ring k[x1,...,xn] over a field k, a (Ritt) characteristic set C of I is composed of a set of polynomials in I, wh...
High Quality Content by WIKIPEDIA articles! The mathematical concept of a characteristic set was discovered in the late forties by J.F. Ritt. Besides Gröbner basis method, it provides an alternative algorithmic way for solving multivariate polynomial equations or differential equations. In the late seventies, the Chinese mathematician Wen-Tsun Wu specialized it with modifications to commutative algebra. He demonstrated its power for mechanical theorem proving.For an ideal I in the ring k[x1,...,xn] over a field k, a (Ritt) characteristic set C of I is composed of a set of polynomials in I, which is in triangular shape: polynomials in C have distinct main variables. (See the formal definition below.) Given a characteristic set C of I, one can decide if a polynomial f is zero modulo I. That is, membership test is checkable for I, provided a characteristic set of I.
