close #213; update tests; fix bug in isconstant for SparsePolynomials

Author: jverzani

src/polynomials/Polynomial.jl

@@ -82,27 +82,38 @@ julia> p.(0:3)
 
 
 function Base.:+(p1::Polynomial{T}, p2::Polynomial{S}) where {T, S}
-
-    #isconstant(p1) && return p2 + p1[0] #  factor of 2  slower with this check
-    #isconstant(p2) && return p1 + p2[0]
-    p1.var != p2.var && error("Polynomials must have same variable")
-
     n1, n2 = length(p1), length(p2)
-    c = [p1[i] + p2[i] for i = 0:max(n1, n2)]
-    return Polynomial(c, p1.var)
+    if n1 > 1 && n2 > 1
+       p1.var != p2.var && error("Polynomials must have same variable")
+       c = [p1[i] + p2[i] for i = 0:max(n1, n2)]
+       return Polynomial(c, p1.var)
+    elseif n1 <= 1
+       c = copy(p2.coeffs )
+       c[1] += p1[0]
+       return Polynomial(c, p2.var)
+    else 
+       c = copy(p1.coeffs )
+       c[1] += p2[0]
+       return Polynomial(c, p1.var)
+    end
 end
 
 
 function Base.:*(p1::Polynomial{T}, p2::Polynomial{S}) where {T,S}
 
-    #isconstant(p1) && return p2 * p1[0] # no real effect
-    #isconstant(p2) && return p1 * p2[0]
-    p1.var != p2.var && error("Polynomials must have same variable")
-    n,m = length(p1)-1, length(p2)-1 # not degree, so pNULL works
-    R = promote_type(T, S)
-    c = zeros(R, m + n + 1)
-    for i in 0:n, j in 0:m
-        @inbounds c[i + j + 1] += p1[i] * p2[j]
+    n, m = length(p1)-1, length(p2)-1 # not degree, so pNULL works
+    if n > 0 && m > 0
+        p1.var != p2.var && error("Polynomials must have same variable")
+        R = promote_type(T, S)
+        c = zeros(R, m + n + 1)
+        for i in 0:n, j in 0:m
+            @inbounds c[i + j + 1] += p1[i] * p2[j]
+        end
+        return Polynomial(c, p1.var)
+    elseif n <= 0
+        return Polynomial(copy(p2.coeffs) * p1[0], p2.var)
+    else
+        return Polynomial(copy(p1.coeffs) * p2[0], p1.var)
     end
-    return Polynomial(c, p1.var)
+
 end

src/polynomials/SparsePolynomial.jl

@@ -92,7 +92,7 @@ end
 degree(p::SparsePolynomial) = isempty(p.coeffs) ? -1 : maximum(keys(p.coeffs))
 function isconstant(p::SparsePolynomial)
     n = length(keys(p.coeffs))
-    (n > 1 || iszero(p[0])) && return false
+    (n > 1 || (n==1 && iszero(p[0]))) && return false
     return true
 end
 
@@ -188,7 +188,7 @@ function Base.:+(p1::SparsePolynomial{T}, p2::SparsePolynomial{S}) where {T, S}
 
     isconstant(p1) && return p2 + p1[0]
     isconstant(p2) && return p1 + p2[0]
-    
+
     p1.var != p2.var && error("SparsePolynomials must have same variable")
 
     R = promote_type(T,S)

test/StandardBasis.jl

@@ -55,7 +55,7 @@ end
 end
 
 @testset "Other Construction" begin
-    for P in (ImmutablePolynomial{10}, Polynomial)
+    for P in (ImmutablePolynomial{10}, Polynomial, SparsePolynomial, LaurentPolynomial)
 
         # Leading 0s
         p = P([1, 2, 0, 0])
@@ -77,11 +77,11 @@ end
 
         pNULL = P(Int[])
         @test iszero(pNULL)
-        @test degree(pNULL) == -1
+        P != LaurentPolynomial && @test degree(pNULL) == -1
 
         p0 = P([0])
         @test iszero(p0)
-        @test degree(p0) == -1
+        P != LaurentPolynomial && @test degree(p0) == -1
 
         # variable(), P() to generate `x` in given basis
         @test degree(variable(P)) == 1
@@ -91,7 +91,7 @@ end
         @test variable(P, :y) == P(:y)
 
         # test degree, isconstant
-        @test degree(zero(P)) ==  -1
+        P != LaurentPolynomial &&  @test degree(zero(P)) ==  -1
         @test degree(one(P)) == 0
         @test degree(P(1))  ==  0
         @test degree(P([1]))  ==  0
@@ -506,7 +506,7 @@ end
     end
 
     # issue 206 with mixed variable types and promotion
-    for P in (ImmutablePolynomial,)
+    for P in Ps
         λ = P([0,1],:λ)
         A = [1 λ; λ^2 λ^3]
         @test A ==  diagm(0 => [1, λ^3], 1=>[λ], -1=>[λ^2])