diff --git a/src/Initialization/init_SymEngine.jl b/src/Initialization/init_SymEngine.jl
index 3485773471..328039d01a 100644
--- a/src/Initialization/init_SymEngine.jl
+++ b/src/Initialization/init_SymEngine.jl
@@ -69,6 +69,21 @@ julia> free_symbols(:(x1 + x2 <= 2*x4 + 6), HalfSpace)
 """
 function free_symbols(::Expr, ::Type{<:LazySet}) end  # COV_EXCL_LINE
 
+# parse `a` and `b` from `a1 x1 + ... + an xn + K [cmp] 0` for [cmp] in {<, <=, =, >, >=}
+function _parse_linear_expression(linexpr::Basic, vars::Vector{Basic}, N)
+    if isempty(vars)
+        vars = SymEngine.free_symbols(linexpr)
+    end
+    b = SymEngine.subs(linexpr, [vi => zero(N) for vi in vars]...)
+    a = convert(Basic, linexpr - b)
+
+    # convert to correct numeric type
+    a = convert(Vector{N}, diff.(a, vars))
+    b = convert(N, b)
+
+    return a, b
+end
+
 # Note: this convenience function is not used anywhere
 function _free_symbols(expr::Expr)
     if _is_hyperplane(expr)
diff --git a/src/Interfaces/AbstractPolyhedron.jl b/src/Interfaces/AbstractPolyhedron.jl
index 1f1100f9f2..3e75a73137 100644
--- a/src/Interfaces/AbstractPolyhedron.jl
+++ b/src/Interfaces/AbstractPolyhedron.jl
@@ -75,11 +75,10 @@ function _linear_map_hrep_helper(M::AbstractMatrix, P::LazySet,
     return HPolyhedron(constraints)
 end
 
-# internal function; defined here due to dependency SymEngine and submodules
-function _is_halfspace() end
-
-# internal function; defined here due to dependency SymEngine and submodules
-function _is_hyperplane() end
+# internal functions; defined here due to dependency SymEngine and submodules
+function _is_halfspace end
+function _is_hyperplane end
+function _parse_linear_expression end
 
 # To account for the compilation order, other functions are defined in the file
 # AbstractPolyhedron_functions.jl
diff --git a/src/Sets/HalfSpace/convert.jl b/src/Sets/HalfSpace/convert.jl
index 7c5ce7ad71..92d353f0bc 100644
--- a/src/Sets/HalfSpace/convert.jl
+++ b/src/Sets/HalfSpace/convert.jl
@@ -7,6 +7,7 @@ end
 function load_SymEngine_convert_HalfSpace()
     return quote
         using .SymEngine: Basic
+        using ..LazySets: _parse_linear_expression
 
         """
             convert(::Type{HalfSpace{N}}, expr::Expr; vars=nothing) where {N}
@@ -53,31 +54,18 @@ function load_SymEngine_convert_HalfSpace()
         ```
         """
         function convert(::Type{HalfSpace{N}}, expr::Expr; vars::Vector{Basic}=Basic[]) where {N}
-            @assert _is_halfspace(expr) "the expression :(expr) does not correspond to a half-space"
-
-            # check sense of the inequality, assuming < or <= by default
-            got_geq = expr.args[1] in [:(>=), :(>)]
-
-            # get sides of the inequality
-            lhs, rhs = convert(Basic, expr.args[2]), convert(Basic, expr.args[3])
-
-            # a1 x1 + ... + an xn + K [cmp] 0 for cmp in <, <=, >, >=
-            eq = lhs - rhs
-            if isempty(vars)
-                vars = SymEngine.free_symbols(eq)
-            end
-            K = SymEngine.subs(eq, [vi => zero(N) for vi in vars]...)
-            a = convert(Basic, eq - K)
-
-            # convert to numeric types
-            K = convert(N, K)
-            a = convert(Vector{N}, diff.(a, vars))
-
-            if got_geq
-                return HalfSpace(-a, K)
-            else
-                return HalfSpace(a, -K)
-            end
+            @assert _is_halfspace(expr) "the expression $expr does not correspond to a half-space"
+
+            # convert to SymEngine expressions
+            linexpr, cmp = _parse_halfspace(expr)
+
+            # check sense of the inequality, assuming < or <= by default (checked before)
+            got_geq = cmp ∈ (:(>=), :(>))
+
+            # `a1 x1 + ... + an xn + b [cmp] 0` for [cmp] ∈ {<, <=, >, >=}
+            a, b = _parse_linear_expression(linexpr, vars, N)
+
+            return got_geq ? HalfSpace(-a, b) : HalfSpace(a, -b)
         end
 
         # type-less default half-space conversion
diff --git a/src/Sets/HalfSpace/init_SymEngine.jl b/src/Sets/HalfSpace/init_SymEngine.jl
index 30402768f6..d4b84c73ac 100644
--- a/src/Sets/HalfSpace/init_SymEngine.jl
+++ b/src/Sets/HalfSpace/init_SymEngine.jl
@@ -1,9 +1,15 @@
 import .SymEngine: free_symbols
 
+function _parse_halfspace(expr::Expr)
+    lhs = convert(SymEngine.Basic, expr.args[2])
+    rhs = convert(SymEngine.Basic, expr.args[3])
+    cmp = expr.args[1]
+    return (lhs - rhs, cmp)
+end
+
 function free_symbols(expr::Expr, ::Type{<:HalfSpace})
-    # get sides of the inequality
-    lhs, rhs = convert(SymEngine.Basic, expr.args[2]), convert(SymEngine.Basic, expr.args[3])
-    return SymEngine.free_symbols(lhs - rhs)
+    linexpr, _ = _parse_halfspace(expr)
+    return SymEngine.free_symbols(linexpr)
 end
 
 eval(load_SymEngine_ishalfspace())
diff --git a/src/Sets/HalfSpace/ishalfspace.jl b/src/Sets/HalfSpace/ishalfspace.jl
index 34502a0592..25ad2ddc8c 100644
--- a/src/Sets/HalfSpace/ishalfspace.jl
+++ b/src/Sets/HalfSpace/ishalfspace.jl
@@ -1,7 +1,5 @@
 function load_SymEngine_ishalfspace()
     return quote
-        using .SymEngine: Basic
-        import .SymEngine: free_symbols
         using ..LazySets: _is_linearcombination
 
         """
@@ -45,23 +43,22 @@ function load_SymEngine_ishalfspace()
         ```
         """
         function _is_halfspace(expr::Expr)::Bool
-
-            # check that there are three arguments
-            # these are the comparison symbol, the left hand side and the right hand side
+            # check that there are three arguments:
+            # the comparison symbol, the left-hand side and the right-hand side
             if (length(expr.args) != 3) || !(expr.head == :call)
                 return false
             end
 
+            # convert to SymEngine expression
+            linexpr, cmp = _parse_halfspace(expr)
+
             # check that this is an inequality
-            if !(expr.args[1] in [:(<=), :(<), :(>=), :(>)])
+            if cmp ∉ [:(<=), :(<), :(>=), :(>)]
                 return false
             end
 
-            # convert to symengine expressions
-            lhs, rhs = convert(Basic, expr.args[2]), convert(Basic, expr.args[3])
-
             # check if the expression defines a half-space
-            return _is_linearcombination(lhs) && _is_linearcombination(rhs)
+            return _is_linearcombination(linexpr)
         end
     end
 end  # load_SymEngine_ishalfspace
diff --git a/src/Sets/Hyperplane/convert.jl b/src/Sets/Hyperplane/convert.jl
index b81658db09..c954a136fb 100644
--- a/src/Sets/Hyperplane/convert.jl
+++ b/src/Sets/Hyperplane/convert.jl
@@ -1,6 +1,7 @@
 function load_SymEngine_convert_Hyperplane()
     return quote
         using .SymEngine: Basic
+        using ..LazySets: _parse_linear_expression
 
         """
             convert(::Type{Hyperplane{N}}, expr::Expr; vars=nothing) where {N}
@@ -41,28 +42,15 @@ function load_SymEngine_convert_Hyperplane()
         ```
         """
         function convert(::Type{Hyperplane{N}}, expr::Expr; vars::Vector{Basic}=Basic[]) where {N}
-            @assert _is_hyperplane(expr) "the expression :(expr) does not correspond to a Hyperplane"
+            @assert _is_hyperplane(expr) "the expression $expr does not correspond to a Hyperplane"
 
-            # get sides of the inequality
-            lhs = convert(Basic, expr.args[1])
+            # convert to SymEngine expression
+            linexpr = _parse_hyperplane(expr)
 
-            # treats the 4 in :(2*x1 = 4)
-            rhs = :args in fieldnames(typeof(expr.args[2])) ? convert(Basic, expr.args[2].args[2]) :
-                  convert(Basic, expr.args[2])
+            # a1 x1 + ... + an xn + b = 0
+            a, b = _parse_linear_expression(linexpr, vars, N)
 
-            # a1 x1 + ... + an xn + K = 0
-            eq = lhs - rhs
-            if isempty(vars)
-                vars = SymEngine.free_symbols(eq)
-            end
-            K = SymEngine.subs(eq, [vi => zero(N) for vi in vars]...)
-            a = convert(Basic, eq - K)
-
-            # convert to numeric types
-            K = convert(N, K)
-            a = convert(Vector{N}, diff.(a, vars))
-
-            return Hyperplane(a, -K)
+            return Hyperplane(a, -b)
         end
 
         # type-less default Hyperplane conversion
diff --git a/src/Sets/Hyperplane/init_SymEngine.jl b/src/Sets/Hyperplane/init_SymEngine.jl
index c0926b6506..61d9d0aa59 100644
--- a/src/Sets/Hyperplane/init_SymEngine.jl
+++ b/src/Sets/Hyperplane/init_SymEngine.jl
@@ -1,14 +1,16 @@
 import .SymEngine: free_symbols
 
-function free_symbols(expr::Expr, ::Type{<:Hyperplane})
-    # get sides of the equality
+function _parse_hyperplane(expr::Expr)
     lhs = convert(SymEngine.Basic, expr.args[1])
-
-    # treats the 4 in :(2*x1 = 4)
     rhs = :args in fieldnames(typeof(expr.args[2])) ?
           convert(SymEngine.Basic, expr.args[2].args[2]) :
           convert(SymEngine.Basic, expr.args[2])
-    return SymEngine.free_symbols(lhs - rhs)
+    return lhs - rhs
+end
+
+function free_symbols(expr::Expr, ::Type{<:Hyperplane})
+    linexpr = _parse_hyperplane(expr)
+    return SymEngine.free_symbols(linexpr)
 end
 
 eval(load_SymEngine_ishyperplanar())
diff --git a/src/Sets/Hyperplane/is_hyperplanar.jl b/src/Sets/Hyperplane/is_hyperplanar.jl
index 758474fa1b..ab8577c1b8 100644
--- a/src/Sets/Hyperplane/is_hyperplanar.jl
+++ b/src/Sets/Hyperplane/is_hyperplanar.jl
@@ -4,7 +4,6 @@ end
 
 function load_SymEngine_ishyperplanar()
     return quote
-        using .SymEngine: Basic
         using ..LazySets: _is_linearcombination
 
         """
@@ -48,25 +47,17 @@ function load_SymEngine_ishyperplanar()
         ```
         """
         function _is_hyperplane(expr::Expr)::Bool
-
-            # check that there are three arguments
-            # these are the comparison symbol, the left hand side and the right hand side
+            # check that the head is `=` and there are two arguments:
+            # the left-hand side and the right-hand side
             if (length(expr.args) != 2) || !(expr.head == :(=))
                 return false
             end
 
-            # convert to symengine expressions
-            lhs = convert(Basic, expr.args[1])
-
-            if :args in fieldnames(typeof(expr.args[2]))
-                # treats the 4 in :(2*x1 = 4)
-                rhs = convert(Basic, expr.args[2].args[2])
-            else
-                rhs = convert(Basic, expr.args[2])
-            end
+            # convert to SymEngine expression
+            linexpr = _parse_hyperplane(expr)
 
             # check if the expression defines a hyperplane
-            return _is_linearcombination(lhs) && _is_linearcombination(rhs)
+            return _is_linearcombination(linexpr)
         end
     end
 end  # load_SymEngine_ishyperplanar