Task: Modular arithmetic





Java: public class ModularArithmetic {
    private interface Ring<T> {
        Ring<T> plus(Ring<T> rhs);

        Ring<T> times(Ring<T> rhs);

        int value();

        Ring<T> one();

        default Ring<T> pow(int p) {
            if (p < 0) {
                throw new IllegalArgumentException("p must be zero or greater");
            }

            int pp = p;
            Ring<T> pwr = this.one();
            while (pp-- > 0) {
                pwr = pwr.times(this);
            }
            return pwr;
        }
    }

    private static class ModInt implements Ring<ModInt> {
        private int value;
        private int modulo;

        private ModInt(int value, int modulo) {
            this.value = value;
            this.modulo = modulo;
        }

        @Override
        public Ring<ModInt> plus(Ring<ModInt> other) {
            if (!(other instanceof ModInt)) {
                throw new IllegalArgumentException("Cannot add an unknown ring.");
            }
            ModInt rhs = (ModInt) other;
            if (modulo != rhs.modulo) {
                throw new IllegalArgumentException("Cannot add rings with different modulus");
            }
            return new ModInt((value + rhs.value) % modulo, modulo);
        }

        @Override
        public Ring<ModInt> times(Ring<ModInt> other) {
            if (!(other instanceof ModInt)) {
                throw new IllegalArgumentException("Cannot multiple an unknown ring.");
            }
            ModInt rhs = (ModInt) other;
            if (modulo != rhs.modulo) {
                throw new IllegalArgumentException("Cannot multiply rings with different modulus");
            }
            return new ModInt((value * rhs.value) % modulo, modulo);
        }

        @Override
        public int value() {
            return value;
        }

        @Override
        public Ring<ModInt> one() {
            return new ModInt(1, modulo);
        }

        @Override
        public String toString() {
            return String.format("ModInt(%d, %d)", value, modulo);
        }
    }

    private static <T> Ring<T> f(Ring<T> x) {
        return x.pow(100).plus(x).plus(x.one());
    }

    public static void main(String[] args) {
        ModInt x = new ModInt(10, 13);
        Ring<ModInt> y = f(x);
        System.out.print("x ^ 100 + x + 1 for x = ModInt(10, 13) is ");
        System.out.println(y);
        System.out.flush();
    }
}




VB: Option Base 1
Private Function mi_one(ByVal a As Variant) As Variant
    If IsArray(a) Then
        a(1) = 1
    Else
        a = 1
    End If
    mi_one = a
End Function

Private Function mi_add(ByVal a As Variant, b As Variant) As Variant
    If IsArray(a) Then
        If IsArray(b) Then
             If a(2) <> b(2) Then
                mi_add = CVErr(2019)
            Else
                a(1) = (a(1) + b(1)) Mod a(2)
                mi_add = a
            End If
        Else
            mi_add = CVErr(2018)
        End If
    Else
        If IsArray(b) Then
            mi_add = CVErr(2018)
        Else
           a = a + b
           mi_add = a
        End If
    End If
End Function

Private Function mi_mul(ByVal a As Variant, b As Variant) As Variant
    If IsArray(a) Then
        If IsArray(b) Then
            If a(2) <> b(2) Then
                mi_mul = CVErr(2019)
            Else
                a(1) = (a(1) * b(1)) Mod a(2)
                mi_mul = a
            End If
        Else
            mi_mul = CVErr(2018)
        End If
    Else
        If IsArray(b) Then
            mi_mul = CVErr(2018)
        Else
            a = a * b
            mi_mul = a
        End If
    End If
End Function
 
Private Function mi_power(x As Variant, p As Integer) As Variant
    res = mi_one(x)
    For i = 1 To p
        res = mi_mul(res, x)
    Next i
    mi_power = res
End Function
 
Private Function mi_print(m As Variant) As Variant
    If IsArray(m) Then
        s = "modint(" & m(1) & "," & m(2) & ")"
    Else
        s = CStr(m)
    End If
    mi_print = s
End Function
 
Private Function f(x As Variant) As Variant
    f = mi_add(mi_power(x, 100), mi_add(x, mi_one(x)))
End Function
 
Private Sub test(x As Variant)
    Debug.Print "x^100 + x + 1 for x == " & mi_print(x) & " is " & mi_print(f(x))
End Sub
Public Sub main()
    test 10
    test [{10,13}]
End Sub