Create partial order of MonomialIndex wrt degree of monomial

1 files changed, 17 insertions, 1 deletions

diff --git a/polymatrix/polymatrix/typing.py b/polymatrix/polymatrix/typing.py
index 91544d1..50f3f52 100644
--- a/polymatrix/polymatrix/typing.py
+++ b/polymatrix/polymatrix/typing.py
@@ -13,7 +13,9 @@ class VariableIndex(NamedTuple):
     """
     Index for a variable raised to an integral power.
 
-    `VariableIndex` has a total order with respect to the variable index.
+    `VariableIndex` has a partial order with respect to the variable index. For
+    example if :math:`x` had index 0, :math:`y` has index 1, then :math:`y
+    \succeq x`, the exponent does not matter so :math:`y \succeq x^2`.
     """
     variable: int # index in ExpressionState object
     power: int
@@ -34,8 +36,22 @@ class VariableIndex(NamedTuple):
 class MonomialIndex(tuple[VariableIndex]):
     """
     Index for a monomial, i.e. a product of `VariableIndex`.
+
+    `MonomialIndex` has a partial order with respect to the degree.
     """
 
+    @property
+    def degree(self) -> int:
+        """ Degree of the monomial """
+        if MonomialIndex.is_constant(self):
+            return 0
+
+        return sum(v.power for v in self)
+
+    def __lt__(self, other):
+        """ Monomial indices can be sorted with respect to the exponent value. """
+        return self.degree < other.degree
+
     @staticmethod
     def empty() -> MonomialIndex:
         """ Get an empty monomial index. """