Some fixes for Polynomials with non-Real types

I was sad to find that my Polynomials-with-modular-arithmetic example
had broken at some point. These were the couple of changes I needed
to get that working again.

Author: Keno

src/Polynomials.jl

@@ -69,7 +69,7 @@ immutable Poly{T<:Number}
             return new(zeros(T,1), @compat Symbol(var))
         else
             # determine the last nonzero element and truncate a accordingly
-            a_last = max(1,findlast(a))
+            a_last = max(1,findlast(x->x!=zero(T), a))
             new(a[1:a_last], @compat Symbol(var))
         end
     end
@@ -356,7 +356,7 @@ function polyval{T,S}(p::Poly{T}, x::S)
     if lenp == 0
         return zero(R) * x
     else
-        y = convert(R, p[end]) + 0*x
+        y = convert(R, p[end]) + zero(T)*x
         for i = (endof(p)-1):-1:0
             y = p[i] + x*y
         end

src/show.jl

@@ -15,6 +15,21 @@ function printexponent(io,var,i)
 end
 
 function printterm{T}(io::IO,p::Poly{T},j,first)
+    pj = p[j]
+    if pj == zero(T)
+        return false
+    end
+    first || print(io, " + ")
+    if pj != one(T) || j == 0
+        print(io, '(')
+        show(io,pj)
+        print(io, ") ")
+    end
+    printexponent(io,p.var,j)
+    true
+end
+
+function printterm{T<:Real}(io::IO,p::Poly{T},j,first)
     pj = p[j]
     if pj == zero(T)
         return false

test/runtests.jl

@@ -184,7 +184,6 @@ p1 = Poly([4,5,6])
 p1[0:1] = [7,8]
 @test all(p1[0:end] .== [7,8,6])
 
-
 ## conjugate of poly (issue #59)
 as = [im, 1, 2]
 bs = [1, 1, 2]
@@ -202,3 +201,22 @@ types = [Int, UInt8, Float64]
 for t in types
   @test t == eltype(Poly{t})
 end
+
+## Polynomials with non-Real type
+import Base: +, *, -
+immutable Mod2 <: Number
+  v::Bool
+end
++(x::Mod2,y::Mod2) = Mod2(x.v$y.v)
+*(x::Mod2,y::Mod2) = Mod2(x.v&y.v)
+-(x::Mod2,y::Mod2) = x+y
+-(x::Mod2) = x
+Base.one(::Type{Mod2}) = Mod2(true)
+Base.zero(::Type{Mod2}) = Mod2(false)
+Base.convert(::Type{Mod2},x) = Mod2(convert(Bool,x))
+Base.convert(::Type{Bool},x::Mod2) = x.v
+
+# Test that none of this throws
+p = Poly([Mod2(true),Mod2(false)])
+repr(p)
+p(Mod2(false))