add ordering.jl (#190)

* add ordering.jl

* remove paragraph indentation

Author: sumiya11

docs/src/types.md

@@ -59,6 +59,7 @@ nterms
 coefficients
 coefficient(p::AbstractPolynomialLike, m::AbstractMonomialLike, vars)
 monomials
+ordering
 mindegree
 maxdegree
 extdegree

src/MultivariatePolynomials.jl

@@ -69,6 +69,7 @@ include("monomial.jl")
 include("term.jl")
 include("polynomial.jl")
 include("monovec.jl")
+include("ordering.jl")
 
 include("rational.jl")
 

src/ordering.jl

@@ -0,0 +1,26 @@
+export MonomialOrdering
+export GradedLex
+export ordering
+
+"""
+    AbstractOrdering
+
+Abstract type for a monomial ordering.
+"""
+abstract type AbstractOrdering end
+
+"""
+    GradedLex
+
+Graded lexicographical monomial ordering.
+Compares total monomial degree first, then breaks ties lexicographically.
+Currently, a default option for all `AbstractPolynomialLike{T}`.
+"""
+struct GradedLex <: AbstractOrdering end
+
+"""
+    ordering(p::AbstractPolynomialLike)
+
+Returns the ordering of polynomial `p`.
+"""
+ordering(::AbstractPolynomialLike) = GradedLex()

test/monomial.jl

@@ -38,6 +38,7 @@ end
     @test one(x^2) isa AbstractMonomial
     @test (@inferred one(typeof(x^2))) == 1
     @test one(typeof(x^2)) isa AbstractMonomial
+    @test ordering(x) === GradedLex()
 
     Mod.@polyvar y[1:7]
     m = y[1] * y[3] * y[5] * y[7]

test/polynomial.jl

@@ -144,6 +144,7 @@ const MP = MultivariatePolynomials
         f = 4*x*y^2*z + 4*z^2 - 5*x^3 + 7*x^2*z^2
         @test coefficients(f) == [7, 4, -5, 4]
         @test monomials(f) == monovec([x^2*z^2, x*y^2*z, x^3, z^2])
+        @test ordering(f) === GradedLex()
     end
 
     @testset "Convertion" begin