Merge pull request #259 from singularitti/master

Add `is_`, `as_`, `isreal`, `real`, `isintegerpoly` & `asintegerpoly`

Author: jverzani

docs/src/reference.md

@@ -25,6 +25,10 @@ chop
 chop!
 truncate
 truncate!
+isreal
+real
+isintegral
+ismonic
 ```
 
 ## Arithmetic

src/common.jl

@@ -15,7 +15,9 @@ export fromroots,
        fit,
        integrate,
        derivative,
-       variable
+       variable,
+       isintegral,
+       ismonic
 
 """
     fromroots(::AbstractVector{<:Number}; var=:x)
@@ -298,6 +300,64 @@ function Base.iszero(p::AbstractPolynomial)
     return all(iszero.(coeffs(p))) && p[0] == 0
 end
 
+# See discussions in https://github.com/JuliaMath/Polynomials.jl/issues/258
+"""
+    all(pred, poly::AbstractPolynomial)
+
+Test whether all coefficients of an `AbstractPolynomial` satisfy predicate `pred`.
+
+You can implement `isreal`, etc., to a `Polynomial` by using `all`.
+"""
+Base.all(pred, poly::AbstractPolynomial) = all(pred, poly[:])
+"""
+    any(pred, poly::AbstractPolynomial)
+
+Test whether any coefficient of an `AbstractPolynomial` satisfies predicate `pred`.
+"""
+Base.any(pred, poly::AbstractPolynomial) = any(pred, poly[:])
+"""
+    map(fn, p::AbstractPolynomial)
+
+Transform coefficients of `p` by applying a function (or other callables) `fn` to each of them.
+
+You can implement `real`, etc., to a `Polynomial` by using `map`.
+"""
+Base.map(fn, p::P) where {P<:AbstractPolynomial} = ⟒(P)(map(fn, coeffs(p)), p.var)
+
+"""
+    isreal(p::AbstractPolynomial)
+
+Determine whether a polynomial is a real polynomial, i.e., having only real numbers as coefficients.
+
+See also: [`real`](@ref)
+"""
+Base.isreal(p::AbstractPolynomial) = all(isreal, p)
+"""
+    real(p::AbstractPolynomial)
+
+Construct a real polynomial from the real parts of the coefficients of `p`.
+
+See also: [`isreal`](@ref)
+
+!!! note
+    This could cause losing terms in `p`. This method is usually called on polynomials like `p = Polynomial([1, 2 + 0im, 3.0, 4.0 + 0.0im])` where you want to chop the imaginary parts of the coefficients of `p`.
+"""
+Base.real(p::AbstractPolynomial) = map(real, p)
+
+"""
+    isintegral(p::AbstractPolynomial)
+
+Determine whether a polynomial is an integer polynomial, i.e., having only integers as coefficients.
+"""
+isintegral(p::AbstractPolynomial) = all(isinteger, p)
+
+"""
+    ismonic(p::AbstractPolynomial)
+
+Determine whether a polynomial is a monic polynomial, i.e., its leading coefficient is one.
+"""
+ismonic(p::AbstractPolynomial) = isone(p[end])
+
 """
     coeffs(::AbstractPolynomial)
 

test/Poly.jl

@@ -421,8 +421,50 @@ fit(Poly, xx,yy,2)
 ## Issue with overflow and polyder Issue #159
 @test !iszero(polyder(Poly(BigInt[0, 1])^100, 100))
 
+@testset "`all` and `any`" begin
+    @test all(x -> x > 1, Polynomial([2 // 1, 3, Int8(4), 5.0]))
+    @test any(x -> x > 1, Polynomial([2 // 1, 3, Int8(4), 5.0]))
+    @test any(isnan, Polynomial([2 // 1, NaN, Int8(4), 5.0]))
+    @test any(!isfinite, Polynomial([2 // 1, NaN, Int8(4), 5.0]))
+    @test any(isinf, Polynomial([2 // 1, Inf64, Int8(4), 5.0]))
+    @test any(iszero, Polynomial([1, 0, 2.0, 3 // 1]))
+end
+
+@testset "`map`" begin
+    @test map(sqrt, Polynomial([1, 2, 3, 4.0])) == Polynomial([√1, √2, √3, √4])
+    @test map(x -> x + 1, Polynomial([1, 2, 3, 4.0])) == Polynomial([2, 3, 4.0, 5 // 1])
+    @test map(zero, Polynomial([1, 2, 3, 4.0])) == Polynomial(0)
+    @test map(one, Polynomial([1, 2, 3, 4.0])) == Polynomial([1, 1, 1, 1])
+    @test map(float, Polynomial([1, 2, 3, 4])) == Polynomial([1.0, 2.0, 3.0, 4.0])
+end
 
+@testset "`isreal` and `real`" begin
+    x = Polynomial([1 // 2, 2 + 0im, 3.0, 4.0 + 0.0im])
+    y = Polynomial([1 // 2, 2 + 0im, 3.0, 4.0 + 0.1im])
+    @test isreal(x) === true
+    @test isequal(x, real(x)) === true
+    @test eltype(real(x)) === Float64
+    @test real(x) == Polynomial([1 // 2, 2, 3, 4.0])
+    @test isreal(y) === false
+    @test real(y) == real(x)
+end
 
+@testset "`isintegral`" begin
+    x = Polynomial([1 // 1, Int8(2) + 0im, 3.0, Int16(4) + 0im])
+    y = Polynomial([1 // 2, Int8(2) + 0im, 3.0, Int16(4) + 0im])
+    @test isintegral(x) === true
+    @test isintegral(y) === false
+    @test convert(Polynomial{Int}, x) == Polynomial([1, 2, 3, 4])
+    @test_throws InexactError convert(Polynomial{Int}, y)
+end
+
+@testset "`ismonic`" begin
+    @test !ismonic(Polynomial([1, 2, 3, 4]))
+    @test ismonic(Polynomial([2, 3, 4, 1 // 1]))
+    @test ismonic(Polynomial([2, 3, 4, 1.0]))
+    @test !ismonic(zero(Polynomial))
+    @test ismonic(one(Polynomial))
+end
 
 
 @testset "Pade" begin