Task: Balanced ternary
Python: class BalancedTernary:
    

    str2dig = {'+': 1, '-': -1, '0': 0} 
    dig2str = {1: '+', -1: '-', 0: '0'} 
    table = ((0, -1), (1, -1), (-1, 0), (0, 0), (1, 0), (-1, 1), (0, 1)) 

    def __init__(self, inp):
        if isinstance(inp, str):
            self.digits = [BalancedTernary.str2dig[c] for c in reversed(inp)]
        elif isinstance(inp, int):
            self.digits = self._int2ternary(inp)
        elif isinstance(inp, BalancedTernary):
            self.digits = list(inp.digits)
        elif isinstance(inp, list):
            if all(d in (0, 1, -1) for d in inp):
                self.digits = list(inp)
            else:
                raise ValueError("BalancedTernary: Wrong input digits.")
        else:
            raise TypeError("BalancedTernary: Wrong constructor input.")

    @staticmethod
    def _int2ternary(n):
        if n == 0: return []
        if (n % 3) == 0: return [0] + BalancedTernary._int2ternary(n // 3)
        if (n % 3) == 1: return [1] + BalancedTernary._int2ternary(n // 3)
        if (n % 3) == 2: return [-1] + BalancedTernary._int2ternary((n + 1) // 3)

    def to_int(self):
        return reduce(lambda y,x: x + 3 * y, reversed(self.digits), 0)

    def __repr__(self):
        if not self.digits: return "0"
        return "".join(BalancedTernary.dig2str[d] for d in reversed(self.digits))

    @staticmethod
    def _neg(digs):
        return [-d for d in digs]

    def __neg__(self):
        return BalancedTernary(BalancedTernary._neg(self.digits))

    @staticmethod
    def _add(a, b, c=0):
        if not (a and b):
            if c == 0:
                return a or b
            else:
                return BalancedTernary._add([c], a or b)
        else:
            (d, c) = BalancedTernary.table[3 + (a[0] if a else 0) + (b[0] if b else 0) + c]
            res = BalancedTernary._add(a[1:], b[1:], c)
            
            if res or d != 0:
                return [d] + res
            else:
                return res

    def __add__(self, b):
        return BalancedTernary(BalancedTernary._add(self.digits, b.digits))

    def __sub__(self, b):
        return self + (-b)

    @staticmethod
    def _mul(a, b):
        if not (a and b):
            return []
        else:
            if   a[0] == -1: x = BalancedTernary._neg(b)
            elif a[0] ==  0: x = []
            elif a[0] ==  1: x = b
            else: assert False
            y = [0] + BalancedTernary._mul(a[1:], b)
            return BalancedTernary._add(x, y)

    def __mul__(self, b):
        return BalancedTernary(BalancedTernary._mul(self.digits, b.digits))


def main():
    a = BalancedTernary("+-0++0+")
    print "a:", a.to_int(), a

    b = BalancedTernary(-436)
    print "b:", b.to_int(), b

    c = BalancedTernary("+-++-")
    print "c:", c.to_int(), c

    r = a * (b - c)
    print "a * (b - c):", r.to_int(), r

main()

VB: Imports System.Text

Module Module1
    Sub Main()
        Dim a As New BalancedTernary("+-0++0+")
        Console.WriteLine("a: {0} = {1}", a, a.ToLong)
        Dim b As New BalancedTernary(-436)
        Console.WriteLine("b: {0} = {1}", b, b.ToLong)
        Dim c As New BalancedTernary("+-++-")
        Console.WriteLine("c: {0} = {1}", c, c.ToLong)
        Dim d = a * (b - c)
        Console.WriteLine("a * (b - c): {0} = {1}", d, d.ToLong)
    End Sub

    Class BalancedTernary
        Private Enum BalancedTernaryDigit
            MINUS = -1
            ZERO = 0
            PLUS = 1
        End Enum

        Private ReadOnly value() As BalancedTernaryDigit

        
        Public Sub New()
            ReDim value(-1)
        End Sub

        
        Public Sub New(str As String)
            ReDim value(str.Length - 1)
            For i = 1 To str.Length
                If str(i - 1) = "-" Then
                    value(i - 1) = BalancedTernaryDigit.MINUS
                ElseIf str(i - 1) = "0" Then
                    value(i - 1) = BalancedTernaryDigit.ZERO
                ElseIf str(i - 1) = "+" Then
                    value(i - 1) = BalancedTernaryDigit.PLUS
                Else
                    Throw New ArgumentException("Unknown Digit: " + str(i - 1))
                End If
            Next
            Array.Reverse(value)
        End Sub

        
        Public Sub New(l As Long)
            Dim value As New List(Of BalancedTernaryDigit)
            Dim sign = Math.Sign(l)
            l = Math.Abs(l)

            While l <> 0
                Dim remainder = CType(l Mod 3, Byte)
                If remainder = 0 OrElse remainder = 1 Then
                    value.Add(remainder)
                    l /= 3
                ElseIf remainder = 2 Then
                    value.Add(BalancedTernaryDigit.MINUS)
                    l = (l + 1) / 3
                End If
            End While

            Me.value = value.ToArray
            If sign < 0 Then
                Invert()
            End If
        End Sub

        
        Public Sub New(origin As BalancedTernary)
            ReDim value(origin.value.Length - 1)
            Array.Copy(origin.value, value, origin.value.Length)
        End Sub

        
        Private Sub New(value() As BalancedTernaryDigit)
            Dim endi = value.Length - 1
            While endi > 0 AndAlso value(endi) = BalancedTernaryDigit.ZERO
                endi -= 1
            End While
            ReDim Me.value(endi)
            Array.Copy(value, Me.value, endi + 1)
        End Sub

        
        Private Sub Invert()
            For i = 1 To value.Length
                value(i - 1) = CType(-CType(value(i - 1), Integer), BalancedTernaryDigit)
            Next
        End Sub

        
        Public Overrides Function ToString() As String
            Dim result As New StringBuilder
            Dim i = value.Length - 1
            While i >= 0
                If value(i) = BalancedTernaryDigit.MINUS Then
                    result.Append("-")
                ElseIf value(i) = BalancedTernaryDigit.ZERO Then
                    result.Append("0")
                ElseIf value(i) = BalancedTernaryDigit.PLUS Then
                    result.Append("+")
                End If

                i -= 1
            End While
            Return result.ToString
        End Function

        
        Public Function ToLong() As Long
            Dim result = 0L
            For i = 1 To value.Length
                result += value(i - 1) * Math.Pow(3.0, i - 1)
            Next
            Return result
        End Function

        
        Public Shared Operator -(origin As BalancedTernary) As BalancedTernary
            Dim result As New BalancedTernary(origin)
            result.Invert()
            Return result
        End Operator

        
        Private Shared carry = BalancedTernaryDigit.ZERO
        Private Shared Function Add(a As BalancedTernaryDigit, b As BalancedTernaryDigit) As BalancedTernaryDigit
            If a <> b Then
                carry = BalancedTernaryDigit.ZERO
                Return a + b
            Else
                carry = a
                Return -CType(b, Integer)
            End If
        End Function

        
        Public Shared Operator +(a As BalancedTernary, b As BalancedTernary) As BalancedTernary
            Dim maxLength = Math.Max(a.value.Length, b.value.Length)
            Dim resultValue(maxLength) As BalancedTernaryDigit
            For i = 1 To maxLength
                If i - 1 < a.value.Length Then
                    resultValue(i - 1) = Add(resultValue(i - 1), a.value(i - 1))
                    resultValue(i) = carry
                Else
                    carry = BalancedTernaryDigit.ZERO
                End If

                If i - 1 < b.value.Length Then
                    resultValue(i - 1) = Add(resultValue(i - 1), b.value(i - 1))
                    resultValue(i) = Add(resultValue(i), carry)
                End If
            Next
            Return New BalancedTernary(resultValue)
        End Operator

        
        Public Shared Operator -(a As BalancedTernary, b As BalancedTernary) As BalancedTernary
            Return a + (-b)
        End Operator

        
        Public Shared Operator *(a As BalancedTernary, b As BalancedTernary) As BalancedTernary
            Dim longValue = a.value
            Dim shortValue = b.value
            Dim result As New BalancedTernary

            If a.value.Length < b.value.Length Then
                longValue = b.value
                shortValue = a.value
            End If

            For i = 1 To shortValue.Length
                If shortValue(i - 1) <> BalancedTernaryDigit.ZERO Then
                    Dim temp(i + longValue.Length - 2) As BalancedTernaryDigit
                    For j = 1 To longValue.Length
                        temp(i + j - 2) = CType(shortValue(i - 1) * longValue(j - 1), BalancedTernaryDigit)
                    Next
                    result += New BalancedTernary(temp)
                End If
            Next

            Return result
        End Operator
    End Class

End Module