Basic functions

deg(x)

Return the degree of x. The default value of deg(x) is 0. (More precisely, it is LinearCombinations.Zero(), which behaves like 0.)

See also deg(::AbstractTensor), LinearCombinations.Zero.

Examples

The degree of a GradedString (created with the gr"" string macro) is its length.

julia> using LinearCombinations.TestHelpers: GradedString, @gr_str

julia> deg(*)
LinearCombinations.Zero()

julia> gr"xy" |> deg
2

julia> gr"xy" * gr"z" |> deg
3

julia> Base.Fix1(*, gr"xy") |> deg
2

julia> Base.Fix1(*, gr"xy") ∘ Base.Fix1(*, gr"z") |> deg
3

julia> deg(LinearCombinations.diff)
-1

has_char2(::Type{R}) where R -> Bool
has_char2(x::R) where R -> Bool

Return true if the ring R is known to have characteristic 2 and false otherwise.

By default, has_char2 returns false for all arguments. Changing it to true for a ring R avoids (possibly expensive) sign computations.

See also is_domain.

is_domain(::Type{R}) where R -> Bool

Return true if the ring R is known to be integral domain and false otherwise. An integral domain is a commutative ring without zero divisors.

By default, is_domain returns true only for subtypes of Real and Complex. If is_domain(R) == true, then sometimes more efficient algorithms can be chosen.

See also has_char2.

LinearCombinations.withsign(k, x)

Return a value representing (-1)^k*x. The default definition is

withsign(k, x) = has_char2(x) || iseven(k) ? x : -x

Additional methods may be needed to support more exotic coefficient types.