fixup! Fix is_unit for MPolyRingElem

src/MPoly.jl

@@ -426,20 +426,23 @@ end
 iszero(x::MPolyRingElem{T}) where T <: RingElement = length(x) == 0
 
 function is_unit(f::T) where {T <: MPolyRingElem}
+  # for constant polynomials we delegate to the coefficient ring:
+  is_constant(f) && return is_unit(constant_coefficient(f))
+  # Here deg(f) > 0; over an integral domain, non-constant polynomials are never units:
+  is_domain_type(T) && return false
   # A polynomial over a commutative ring is a unit iff its
   # constant term is a unit and all other coefficients are nilpotent:
   # see e.g. <https://kconrad.math.uconn.edu/blurbs/ringtheory/polynomial-properties.pdf> for a proof.
-  !is_unit(constant_coefficient(f)) && return false
-  # for constant polynomials we are done now
-  is_constant(f) && return true
-  # over a domain, non-constant polynomials are never units
-  is_domain_type(T) && return false
-  # remains to check the non-constant non-zero terms have nilpotent coefficients
+  constant_term_is_unit = false
   for (c, expv) in zip(coefficients(f), exponent_vectors(f))
-    is_zero(expv) && continue # skip constant term
-    is_nilpotent(c) || return false
+    if is_zero(expv)
+      is_unit(c) || return false
+      constant_term_is_unit = true
+    else
+      is_nilpotent(c) || return false
+    end
   end
-  return true
+  return constant_term_is_unit
 end
 
 function content(a::MPolyRingElem{T}) where T <: RingElement