Adjusted the natrual definition to now handle sub.

This neded a subtraction that would work on natural numbers where
subtraction isn't closed. This will now handle it and filter to make
sure the answer is 1 or higher.

src/natural.rs

@@ -1,10 +1,7 @@
 // SPDX-License-Identifier: Apache-2.0
 // Sealed with Magistamp.
 
-use core::mem::size_of;
-use core::ops::{Add, Sub, Mul, Div, Rem};
-use core::ops::{AddAssign, SubAssign, MulAssign, DivAssign, RemAssign};
-use core::str::FromStr;
+use core::ops::{Add, AddAssign, Mul, MulAssign};
 
 use crate::number::Number;
 use crate::one::One;
@@ -18,15 +15,68 @@ use crate::one::One;
 /// u8, u16, u32, u64, u128, usize
 pub trait Natural: Number + One +
                    Add<Output=Self> + AddAssign +
-                   Sub<Output=Self> + SubAssign +
                    Mul<Output=Self> + MulAssign +
-                   Div<Output=Self> + DivAssign +
-                   Rem<Output=Self> + RemAssign
 {
+   /// Attempts to subtract a number from itself.
+   ///
+   /// Since subtraction isn't closed under this set (1 - 2 = -1) the trait
+   /// doesn't enforce that Sub and SubAssign are implemented. This function,
+   /// however, allows for subtraction and handles the case where the result is
+   /// no longer within the `Natural` numbers domain.
+   ///
+   /// # Arguments
+   /// `rhs`: The number to subtract.
+   ///
+   /// # Returns
+   /// `None` if the subtraction would fall below 1.  
+   /// `Some` if their is a valid result.
+   ///
+   /// # Examples
+   /// ```rust
+   /// use sigils::Natural;
+   ///
+   /// let x = 3u8 as Natural;
+   ///
+   /// assert_eq!(x.try_sub(2), Some(1));
+   /// assert_eq!(x.try_sub(7), None);
+   /// ```
+   fn try_sub(self, rhs: Self) -> Option<Self>;
+/*
+   ///
+   fn try_div(self, rhs: Self) -> Option<Self>;
+
+   ///
+   fn try_rem(self, rhs: Self) -> Option<Self>;
+
    /// Performs division and returns both the quotient and remainder.
    #[inline]
-   fn div_rem(self, rhs: Self) -> (Self, Self)
+   fn try_div_rem(self, rhs: Self) -> Option<(Self, Self)>
    {
-      (self / rhs, self % rhs)
+      Some((self.try_div(rhs)?, self.try_rem(rhs)?))
+   }
+*/
+}
+
+
+
+/// A macro to make implementing the `Natural` trait easier for all the
+/// base types in Rust.
+macro_rules! natural_trait_impl
+{
+   ($($varType:ty),*) =>
+   {
+      $(
+         impl Natural for $varType
+         {
+            #[inline]
+            fn try_sub(self, rhs: Self) -> Option<Self>
+            {
+               self.checked_sub(rhs).filter(|x| *x >= Self::one())
+            }
+         }
+      )*
    }
 }
+
+// Implement the Number trait for the types that are Numbers.
+natural_trait_impl!(u8, u16, u32, u64, u128, usize);