Subsections

• Generic Functions on Elements
• Generic Predicates
• Other Functions

+ a : FldLocElt -> FldLocElt

- a : FldLocElt -> FldLocElt

a + b : FldLocElt, FldLocElt -> FldLocElt

a - b : FldLocElt, FldLocElt -> FldLocElt

a * b : FldLocElt, FldLocElt -> FldLocElt

a / b : FldLocElt, FldLocElt -> FldLocElt

a ^ k : FldLocElt, RngIntElt -> FldLocElt

Parent(r) : RngElt -> Rng

IsOne(a) : FldLocElt -> BoolElt

IsZero(a) : FldLocElt -> BoolElt

IsMinusOne(a) : FldLocElt -> BoolElt

IsUnit(a) : FldLocElt -> BoolElt

a eq b : FldLocElt, FldLocElt -> BoolElt

a ne b : FldLocElt, FldLocElt -> BoolElt

a in F : FldLocElt, FldLoc -> BoolElt

a notin F : FldLocElt, FldLoc -> BoolElt

Given a p-adic ring or field R, this procedure changes the default precision on elements created in R to n.

Given an element a in a p-adic ring or field, return the absolute precision to which a is stored. This is the largest number s such that the coefficient of p^(s - 1) of a is stored.

Given an element a in a p-adic ring or field, return the relative precision to which a is stored. This is the number of coefficients of a, starting from the first non-zero coefficient, and equals the difference of the absolute precision and the valuation of a.

Given an element a in a p-adic ring or field, return the valuation of a, which is the smallest integer v such that the coefficient of p^v in the p-adic expansion of a is known and non-zero. If such v does not exist (which happens only if all known coefficients are zero), an error results (the valuation is infinite).

The square root of the non-zero element a from the local ring or field R, i.e., an element y of R such that y^2 = a. An error results if f is not a square.

The n-th root of the non-zero element f from the local ring or field R, i.e., an element y of R such that y^n = a. An error results if no such root exists in R.

The p-adic logarithm of an element of a p-adic ring or field element. Note that log(p)=0.

The p-adic exponential of an element of a p-adic ring or field element.