Add determinant (#86)

Closes #58 #78

Author: PBrdng

src/MultivariatePolynomials.jl

@@ -5,10 +5,10 @@ module MultivariatePolynomials
 #using DocStringExtensions
 
 using Compat
-import Compat.LinearAlgebra: dot, norm
+import Compat.LinearAlgebra: dot, norm, det
 
 # The ' operator lowers to `transpose()` in v0.6 and to
-# `adjoint()` in v0.7+. 
+# `adjoint()` in v0.7+.
 # TOOD: remove this switch when dropping v0.6 support
 @static if VERSION <= v"0.7.0-DEV.3351"
     import Base: transpose
@@ -91,5 +91,6 @@ include("comparison.jl")
 include("substitution.jl")
 include("differentiation.jl")
 include("division.jl")
+include("det.jl")
 
 end # module

src/det.jl

@@ -0,0 +1,8 @@
+function det(M::Matrix{<:AbstractPolynomialLike})
+    m = size(M)[1]
+    if m > 2
+        return sum((-1)^(i-1) * M[i,1] *  det(M[1:end .!= i, 2:end]) for i in 1:m)
+    else
+        return M[1,1] * M[2,2] - M[2,1] * M[1,2]
+    end
+end

test/commutativetests.jl

@@ -4,6 +4,7 @@ include("monomial.jl")
 include("term.jl")
 include("monovec.jl")
 include("polynomial.jl")
+include("det.jl")
 
 include("rational.jl")
 

test/det.jl

@@ -0,0 +1,7 @@
+@testset "Det" begin
+    Mod.@polyvar x y
+
+    @test det([x 1; y 1]) == x - y
+    @test det([x 1; x 1]) == 0
+    @test det([x 1 1 1; x y 1 2; 0 0 0 1; x 0 y 0]) == -x*y^2 + 2*x*y - x
+end