Return the element of the local field L described by r where r may be
anything which is coercible into the quotient representation of L.
Return the generator of the local field L. The only valid input for i
is 1.
Return a generator for the inertial subfield of the local field L.
Return an element of the local field L of valuation 1.
a * b : RngLocAElt, RngLocAElt -> RngLocAElt
a + b : RngLocAElt, RngLocAElt -> RngLocAElt
a - b : RngLocAElt, RngLocAElt -> RngLocAElt
- a : RngLocAElt -> RngLocAElt
a ^ n : RngLocAElt, RngIntElt -> RngLocAElt
a / b : RngLocAElt, RngLocAElt -> RngLocAElt
Return whether the local field elements a and b are considered equal.
IsMinusOne(a) : RngLocAElt -> BoolElt
Return whether the local field element a is known to be 1 or -1 to the
precision of the field.
Return whether the local field element a is not known to be non zero.
Return whether the local field element a is known to be zero.
The valuation of the element a in a local field.
The relative precision of the element a in a local field.
Return the coefficients of powers of the generator of the parent of a in a.
The representation matrix of the element a of a local field.
Norm(a, F) : RngLocAElt, Rng -> RngElt
Trace(a) : RngLocAElt -> RngElt
Trace(a, F) : RngLocAElt, Rng -> RngElt
MinimalPolynomial(a) : RngLocAElt -> RngUPolElt
MinimalPolynomial(a, F) : RngLocAElt -> RngUPolElt
Return the norm, trace or minimal polynomial of a. If a coefficient field
F of the parent L of a is given then the norm, trace or minimal polynomial
will be that of a as an element of L represented as an extension of F.
Continuing from the first example we have :
> UniformizingElement(L);
a^2 + (6 + O(7^50))*a + 3 + O(7^50)
> InertialElement(L);
a + O(7^50)
> Valuation(UniformizingElement(L));
1
> Valuation(InertialElement(L));
0
> Eltseq(UniformizingElement(L));
[ 3 + O(7^50), 6 + O(7^50), 1 + O(7^50) ]
V2.28, 13 July 2023