The quotient q of the division with remainder v=qw + r of the valuation ring elements v and w, where the remainder will have valuation less than that of w; if the valuation of v is greater than or equal than that of w, this simply returns the quotient v/w, if the valuation of w exceeds that of v it returns 0.
Given an element v of a valuation ring V, return the valuation (associated with V) of v.
Given two elements v, w of a valuation ring V with associated valuation φ, return a quotient and remainder q and r in V such that v=qw + r and 0≤φ(r)<φ(w). If φ(v)<φ(w) this simply returns q=0 and r=v, and if φ(v)≥φ(w) then it returns q=v/w and r=0.
This function returns a greatest common divisor of two elements v, w in a valuation ring V. This will return um, where m=min(φ(v), φ(w)) is the minimum of the valuations of v and w m=min(φ(v), φ(w)) and u is the uniformizing element of V (with valuation φ(u)=1).
This function returns a greatest common divisor z∈V of two elements v, w in a valuation ring V as well as multipliers x, y∈V such that xv + yw=z. The principal return value will be z=um, where m=min(φ(v), φ(w)) is the minimum of the valuations of v and w m=min(φ(v), φ(w)) and u is the uniformizing element of V (with valuation φ(u)=1).[Next][Prev] [_____] [Left] [Up] [Index] [Root]