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polynomial.jl
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polynomial.jl
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using Polymake.SparseArrays
@testset "Polymake.Polynomial" begin
IntTypes = [Int32, Int64, UInt64, BigInt]
FloatTypes = [Float32, Float64, BigFloat]
RationalTypes = [Rational{I} for I in IntTypes]
for C in [Int64, Polymake.Integer, Polymake.Rational, Float64, Polymake.QuadraticExtension{Polymake.Rational}]
@test Polymake.Polynomial{C,Int64} <: Any
@test Polymake.Polynomial{C,Int64}([1, 2],[3 4 5; 6 7 8]) isa Any
@test Polymake.Polynomial{C,Int64}([1, 2],[3 4 5; 6 7 8]) isa Polymake.Polynomial
@test Polymake.Polynomial{C,Int64}([1, 2],[3 4 5; 6 7 8]) isa Polymake.Polynomial{Polymake.to_cxx_type(C),Polymake.to_cxx_type(Int64)}
end
jl_v = [1, 2]
jl_m = [3 4 5; 6 7 0]
@testset "Constructors/Converts" begin
for C in [Int64, Polymake.Integer, Polymake.Rational, Float64]
@test Polymake.Polynomial(C.(jl_v), jl_m) isa Polymake.Polynomial{Polymake.to_cxx_type(C),Polymake.to_cxx_type(Int64)}
@test Polymake.Polynomial{Float64}(C.(jl_v), jl_m) isa Polymake.Polynomial{Polymake.to_cxx_type(Float64),Polymake.to_cxx_type(Int64)}
@test Polymake.Polynomial{Polymake.Rational,Int64}(C.(jl_v), jl_m) isa Polymake.Polynomial{Polymake.Rational,Polymake.to_cxx_type(Int64)}
end
end
@testset "Low-level operations" begin
for (C,s) in [(Int64, "long"), (Polymake.Integer, "pm::Integer"), (Polymake.Rational, "pm::Rational"), (Float64, "double"), (Polymake.QuadraticExtension{Polymake.Rational}, "pm::QuadraticExtension<pm::Rational>")]
p = Polymake.Polynomial(C.(jl_v),jl_m)
@test Polymake.nvars(p) == size(jl_m)[2]
@test Polymake.nvars(p) isa Int
# the following line is only necessary if the tests are run with an active session of Polymake
# because variable names are global for the specific typing; ["x"] is its default value
Polymake.set_var_names(p,["x"])
@test string(p) == string("pm::Polynomial<", s, ", long>\n2*x_0^6*x_1^7 + x_0^3*x_1^4*x_2^5")
Polymake.set_var_names(p,["x", "y", "z"])
@test Polymake.get_var_names(p) == ["x", "y", "z"]
@test string(p) == string("pm::Polynomial<", s, ", long>\n2*x^6*y^7 + x^3*y^4*z^5")
@test Polymake.nvars(p) == size(jl_m, 2)
@test Polymake.coefficients_as_vector(p) isa Polymake.Vector
@test Polymake.coefficients_as_vector(p) isa Polymake.Vector{Polymake.to_cxx_type(C)}
v = Polymake.coefficients_as_vector(p)
perm1 = sortperm(jl_v)
perm2 = sortperm(v)
@test v[perm2] == jl_v[perm1]
@test Polymake.monomials_as_matrix(p) isa Polymake.SparseMatrix
@test Polymake.monomials_as_matrix(p) isa Polymake.SparseMatrix{Polymake.to_cxx_type(Int64)}
m = Polymake.monomials_as_matrix(p)
@test m[perm2, :] == jl_m[perm1, :]
end
end
@testset "Equality" begin
for C1 in [Int64, Polymake.Integer, Polymake.Rational, Float64, Polymake.QuadraticExtension{Polymake.Rational}], C2 in [Int64, Polymake.Integer, Polymake.Rational, Float64, Polymake.QuadraticExtension{Polymake.Rational}]
@test Polymake.Polynomial{C1}(jl_v,jl_m) == Polymake.Polynomial{C2}(jl_v,jl_m)
end
end
@testset "Arithmetic" begin
jl_v2 = [5, 6]
jl_m2 = [3 4 5; 6 7 8]
for C1 in [Int64, Polymake.Integer, Polymake.Rational, Float64, Polymake.QuadraticExtension{Polymake.Rational}]
p = Polymake.Polynomial{C1}(jl_v,jl_m)
for C2 in [Int64, Polymake.Integer, Polymake.Rational, Float64, Polymake.QuadraticExtension{Polymake.Rational}]
q = Polymake.Polynomial{C2}(jl_v2,jl_m2)
@test p + q isa Polymake.Polynomial{Polymake.to_cxx_type(promote_type(C1,C2))}
@test p + q == Polymake.Polynomial([6, 2, 6],[3 4 5; 6 7 0; 6 7 8])
@test p * q isa Polymake.Polynomial{Polymake.to_cxx_type(promote_type(C1,C2))}
@test p * q == Polymake.Polynomial([12, 6, 10, 5],[12 14 8; 9 11 13; 9 11 5; 6 8 10])
@test p - q isa Polymake.Polynomial{Polymake.to_cxx_type(promote_type(C1,C2))}
@test p - q == Polymake.Polynomial([-4, 2, -6],[3 4 5; 6 7 0; 6 7 8])
end
@test p^3 isa Polymake.Polynomial{Polymake.to_cxx_type(C1)}
@test p^3 == Polymake.Polynomial([8, 12, 6, 1],[18 21 0; 15 18 5; 12 15 10; 9 12 15])
# @test p/2 isa Polymake.Polynomial{Polymake.to_cxx_type(C1)}
# @test p/2 == Polymake.Polynomial{C1}(C1 <: Integer ? floor.(jl_v/2) : jl_v/2,jl_m)
@test -p isa Polymake.Polynomial{Polymake.to_cxx_type(C1)}
@test -p == Polymake.Polynomial(-jl_v,jl_m)
@test p + (-p) == 0
@test p + 8 isa Polymake.Polynomial{Polymake.to_cxx_type(C1)}
@test 8 + p isa Polymake.Polynomial{Polymake.to_cxx_type(C1)}
@test p + 8 == Polymake.Polynomial([jl_v; 8], [jl_m; 0 0 0])
@test 8 + p == Polymake.Polynomial([jl_v; 8], [jl_m; 0 0 0])
@test p - 7 isa Polymake.Polynomial{Polymake.to_cxx_type(C1)}
@test 7 - p isa Polymake.Polynomial{Polymake.to_cxx_type(C1)}
@test p - 7 == Polymake.Polynomial([jl_v; -7], [jl_m; 0 0 0])
@test 7 - p == Polymake.Polynomial([-jl_v; 7], [jl_m; 0 0 0])
@test p * 6 isa Polymake.Polynomial{Polymake.to_cxx_type(C1)}
@test 6 * p isa Polymake.Polynomial{Polymake.to_cxx_type(C1)}
@test p * 6 == Polymake.Polynomial(6jl_v, jl_m)
@test 6 * p == Polymake.Polynomial(6jl_v, jl_m)
@test 8 + p - p == 8
@test 8 == 8 + p - p
@test (5 * p) / 5 isa Polymake.Polynomial{Polymake.to_cxx_type(C1)}
@test (5 * p) / 5 == p
end
end
@testset "UniPolynomial" begin
c = Polymake.polytope.cube(3,1,0)
ehr = c.EHRHART_POLYNOMIAL
@test Polymake.monomials_as_vector(ehr) == [0, 1, 2, 3]
@test Polymake.coefficients_as_vector(ehr) == [1, 3, 3, 1]
end
end