Roots of Elements

Roots of local ring and field elements can be found to some precision.

HasPRoot(L) : RngLoc -> BoolElt

HasPRoot(L) : FldLoc -> BoolElt

Decides whether L contains a p-th root of unity without actually constructing it.

SquareRoot(x) : RngLocElt -> RngLocElt

Sqrt(x) : RngLocElt -> RngLocElt

SquareRoot(x) : FldLocElt -> FldLocElt

Sqrt(x) : FldLocElt -> FldLocElt

    Precision: RngIntElt                Default: Precision(x)

Returns a square root of x. An error results if x is not a square. The result may have less precision than x. If Precision is not specified the precision of the element is used and if this is infinite the default precision of the ring or field is used to return the answer to.

IsSquare(x) : RngLocElt -> BoolElt

IsSquare(x) : FldLocElt -> BoolElt

Returns whether x is the square of an element in its parent and if it is returns a square root. The result may have less precision than x. The precision the answer is returned to is as for above when Precision isn't set.

Root(x, n) : RngLocElt, RngIntElt -> RngLocElt

Root(x, n) : FldLocElt, RngIntElt -> FldLocElt

    Precision: RngIntElt                Default: Precision(x)

Returns an nth root of x if one exists. An error results if x is not a nth power. The result may have less precision than x. If Precision is not specified the precision of the element is used and if this is infinite then the default precision of the ring or field is used to return the answer to.

IsPower(x, n) : RngLocElt, RngIntElt -> RngLocElt

IsPower(x, n) : FldLocElt, RngIntElt -> FldLocElt

Returns whether x is an nth power of some element belonging to its parent and if it is returns an nth root. The result may have less precision than x. The precision the answer is returned to is as for above when Precision isn't set.