Types
The package defines a number of types for the high level interface.
Basic
These types directly map to corresponding Arb types.
Arblib.Mag — TypeMag <: RealArblib.Arf — TypeArf <: AbstractFloatArblib.Acf — TypeAcf <: AbstractFloatComplex arbitrary precision floating point number type.
The internal representation of the real and imaginary parts are the same as for Arf. It is a wrapper of the type acf in Flint.
See also AcfRef for handling pointers to acf objects and Acb for a complex number type with rigorous error tracking.
The Acf type only implements very basic functionalities. For most purposes it is better to use the Acb type, this is true even in situations where the rigorous error tracking done by Acb is not needed.
Arblib.Arb — TypeArb <: AbstractFloatArblib.Acb — TypeAcb <: NumberArblib.ArbVector — TypeArbVector <: DenseVector{Arb}
ArbVector(n::Integer; prec::Integer = DEFAULT_PRECISION[])
ArbVector(v::ArbVectorLike; shallow::Bool = false, prec::Integer = precision(v))
ArbVector(v::AbstractVector; prec::Integer = _precision(v))The constructor with n::Integer returns a vector with n elements filled with zeros. The other two constructors returns a copy of the given vector. If shallow = true then the returned vector shares the underlying data with the input, mutating one of them mutates both.
See also ArbRefVector.
Arblib.AcbVector — TypeAcbVector <: DenseVector{Acb}
AcbVector(n::Integer; prec::Integer = DEFAULT_PRECISION[])
AcbVector(v::AcbVectorLike; shallow::Bool = false, prec::Integer = precision(v))
AcbVector(v::AbstractVector; prec::Integer = _precision(v))The constructor with n::Integer returns a vector with n elements filled with zeros. The other two constructors returns a copy of the given vector. If shallow = true then the returned vector shares the underlying data with the input, mutating one of them mutates both.
See also AcbRefVector.
Arblib.ArbPoly — TypeArbPolyArblib.AcbPoly — TypeAcbPolyArblib.ArbMatrix — TypeArbMatrix <: DenseMatrix{Arb}
ArbMatrix(r::Integer, c::Integer; prec::Integer = DEFAULT_PRECISION[])
ArbMatrix(A::ArbMatrixLike; shallow::Bool = false, prec::Integer = precision(v))
ArbMatrix(A::AbstractMatrix; prec::Integer = _precision(v))
ArbMatrix(v::AbstractVector; prec::Integer = _precision(v))The constructor with r::Integer, c::Integer returns a r × c filled with zeros. The other three constructors returns a copy of the given matrix or vector. If shallow = true then the returned matrix shares the underlying data with the input, mutating one of them mutates both.
See also ArbRefMatrix.
Arblib.AcbMatrix — TypeAcbMatrix <: DenseMatrix{Acb}
AcbMatrix(r::Integer, c::Integer; prec::Integer = DEFAULT_PRECISION[])
AcbMatrix(A::AcbMatrixLike; shallow::Bool = false, prec::Integer = precision(v))
AcbMatrix(A::AbstractMatrix; prec::Integer = _precision(v))
AcbMatrix(v::AbstractVector; prec::Integer = _precision(v))The constructor with r::Integer, c::Integer returns a r × c filled with zeros. The other three constructors returns a copy of the given matrix or vector. If shallow = true then the returned matrix shares the underlying data with the input, mutating one of them mutates both.
See also AcbRefMatrix.
Series
The package defines two series types, which are wrapper for the polynomial types with a specified degree.
Arblib.ArbSeries — TypeArbSeries <: NumberArblib.AcbSeries — TypeAcbSeries <: NumberRef
In addition to these there are a number of Ref types, which allow for non-allocating access in a number of cases.
Arblib.MagRef — TypeMagRef <: RealArblib.ArfRef — TypeArfRef <: AbstractFloatArblib.AcfRef — TypeAcfRef <: NumberType handling references to Acf objects.
There are currently no types from which AcfRef can be natively constructed. It can as of now only be constructed from a raw point to an acf_struct.
Arblib.ArbRef — TypeArbRef <: AbstractFloatArblib.AcbRef — TypeAcbRef <: NumberArblib.ArbRefVector — TypeArbRefVector <: DenseMatrix{ArbRef}Similar to ArbVector but indexing elements returns an ArbRef referencing the corresponding element instead of an Arb copy of the element. The constructors are the same as for ArbVector
Arblib.AcbRefVector — TypeAcbRefVector <: DenseMatrix{AcbRef}Similar to AcbVector but indexing elements returns an AcbRef referencing the corresponding element instead of an Acb copy of the element. The constructors are the same as for AcbVector
Arblib.ArbRefMatrix — TypeArbRefMatrix <: DenseMatrix{ArbRef}Similar to ArbMatrix but indexing elements returns an ArbRef referencing the corresponding element instead of an Arb copy of the element. The constructors are the same as for ArbMatrix
Arblib.AcbRefMatrix — TypeAcbRefMatrix <: DenseMatrix{AcbRef}Similar to AcbMatrix but indexing elements returns an AcbRef referencing the corresponding element instead of an Acb copy of the element. The constructors are the same as for `AcbMatrix
Correspondence between types
We have the following table for the correspondence with between the Low level wrapper types and the high level interface types.
| Arb | Wrapper | High level | Ref |
|---|---|---|---|
mag_t | mag_struct | Mag | MagRef |
arf_t | arf_struct | Arf | ArfRef |
acf_t | acf_struct | Acf | AcfRef |
arb_t | arb_struct | Arb | ArbRef |
acb_t | acb_struct | Acb | AcbRef |
arb_t* | arb_vec_struct | ArbVector | ArbRefVector |
acb_t* | acb_vec_struct | AcbVector | AcbRefVector |
arb_poly_t | arb_poly_struct | ArbPoly or ArbSeries | |
acb_poly_t | acb_poly_struct | AcbPoly or AcbSeries | |
arb_mat_t | arb_mat_struct | ArbMatrix | ArbRefMatrix |
acb_mat_t | acb_mat_struct | AcbMatrix | AcbRefMatrix |