add factor for Laurent polynomials (#1149)

src/Generic.jl

@@ -43,7 +43,8 @@ import ..AbstractAlgebra: add!, addeq!, addmul!, base_ring, canonical_unit,
                           content, data, deflate, deflation, degree, degrees,
                           degrees_range, denominator, derivative, div,
                           divexact, divides, divrem, domain, elem_type,
-                          evaluate, exp, exponent_vectors, expressify, factor,
+                          evaluate, exp, exponent_vectors, expressify,
+                          factor, factor_squarefree,
                           gen, gens, get_field, identity_matrix, inflate,
                           integral, inv, isconstant, isdomain_type,
                           isexact_type, isgen, ismonomial, isreduced_form,

src/generic/LaurentMPoly.jl

@@ -189,6 +189,28 @@ function divrem(a::LaurentMPolyWrap, b::LaurentMPolyWrap)
     error("divrem not implemented for LaurentMPoly")
 end
 
+function factor(a::LaurentMPolyWrap)
+   R = parent(a)
+   ap, ad = _normalize(a)
+   f = factor(ap)
+   d = Dict{typeof(a), Int}()
+   for (p, e) in f
+      d[LaurentMPolyWrap(R, p)] = e
+   end
+   return Fac(LaurentMPolyWrap(R, unit(f), ad), d)
+end
+
+function factor_squarefree(a::LaurentMPolyWrap)
+   R = parent(a)
+   ap, ad = _normalize(a)
+   f = factor_squarefree(ap)
+   d = Dict{typeof(a), Int}()
+   for (p, e) in f
+      d[LaurentMPolyWrap(R, p)] = e
+   end
+   return Fac(LaurentMPolyWrap(R, unit(f), ad), d)
+end
+
 ###############################################################################
 #
 #   Canonicalisation

src/generic/LaurentPoly.jl

@@ -165,6 +165,10 @@ function _remove_gen(a::LaurentPolyWrap)
          return i, (i == 0 ? a.poly : shift_right(a.poly, i))
       end
    end
+   # we need something finite on zero input
+   if iszero(a.poly)
+      return (0, a.poly)
+   end
    return remove(a.poly, gen(parent(a.poly)))
 end
 
@@ -255,6 +259,28 @@ function lcm(p::LaurentPolyWrap{T}, q::LaurentPolyWrap{T}) where T
    return LaurentPolyWrap(parent(p), lcm(p.poly, q.poly), 0)
 end
 
+function factor(a::LaurentPolyWrap)
+   R = parent(a)
+   va, ua = _remove_gen(a)
+   f = factor(ua)
+   d = Dict{typeof(a), Int}()
+   for (p, e) in f
+      d[LaurentPolyWrap(R, p, 0)] = e
+   end
+   return Fac(LaurentPolyWrap(R, unit(f), a.mindeg + va), d)
+end
+
+function factor_squarefree(a::LaurentPolyWrap)
+   R = parent(a)
+   va, ua = _remove_gen(a)
+   f = factor_squarefree(ua)
+   d = Dict{typeof(a), Int}()
+   for (p, e) in f
+      d[LaurentPolyWrap(R, p, 0)] = e
+   end
+   return Fac(LaurentPolyWrap(R, unit(f), a.mindeg + va), d)
+end
+
 ###############################################################################
 #
 #   Ad hoc binary operators