1 files changed, 41 insertions, 8 deletions

diff --git a/mdpoly/algebra.py b/mdpoly/algebra.py
index 46a82b6..ef3f7eb 100644
--- a/mdpoly/algebra.py
+++ b/mdpoly/algebra.py
@@ -8,7 +8,7 @@ from .types import Shape, MatrixIndex, PolyIndex
 from .representations import HasRepr
 
 from typing import Protocol, TypeVar, Any, runtime_checkable
-from functools import wraps, reduce
+from functools import wraps, reduce, cached_property
 from itertools import product
 from enum import Enum
 from abc import abstractmethod
@@ -158,6 +158,7 @@ def unary_operator(inner_type: AlgebraicStructure):
 class Add(Expr, HasRepr):
     """ Generic addition (no type check) """
 
+    @property
     def shape(self) -> Shape:
         """ See :py:meth:`mdpoly.abc.Expr.shape`. """
         if self.left.shape != self.right.shape:
@@ -189,6 +190,7 @@ class Add(Expr, HasRepr):
 class Sub(Expr, ReducibleExpr):
     """ Generic subtraction operator (no type check) """
 
+    @property
     def shape(self) -> Shape:
         """ See :py:meth:`mdpoly.abc.Expr.shape`. """
         if self.left.shape != self.right.shape:
@@ -207,6 +209,7 @@ class Sub(Expr, ReducibleExpr):
 class Mul(Expr, HasRepr):
     """ Generic multiplication operator (no type check). """
 
+    @property
     def shape(self) -> Shape:
         """ See :py:meth:`mdpoly.abc.Expr.shape`. """
         if self.left.shape != self.right.shape:
@@ -238,6 +241,7 @@ class Mul(Expr, HasRepr):
 class Exp(Expr, ReducibleExpr):
     """ Generic exponentiation (no type check). """
 
+    @property
     def shape(self) -> Shape:
         """ See :py:meth:`mdpoly.abc.Expr.shape`. """
         if self.left.shape != self.right.shape:
@@ -349,6 +353,7 @@ class PartialDiff(Expr, HasRepr, PolyRingAlgebra):
     def __init__(self, with_respect_to: Var):
         self.wrt = with_respect_to
 
+    @property
     def shape(self) -> Shape:
         """ See :py:meth:`mdpoly.abc.Expr.shape`. """
         return self.inner.shape
@@ -442,16 +447,16 @@ class MatrixAlgebra(AlgebraicStructure, Protocol):
 
     def transpose(self):
         """ Matrix transposition. """
-        raise NotImplementedError
+        return MatTranspose(self)
 
     @property
     def T(self):
         """ Shorthand for :py:meth:`mdpoly.algebra.MatrixAlgebra.transpose`. """
         return self.transpose()
 
-    def to_scalar(self, scalar_type: type):
-        """ Convert to a scalar expression. """
-        raise NotImplementedError
+    # def to_scalar(self, scalar_type: type):
+    #     """ Convert to a scalar expression. """
+    #     raise NotImplementedError
 
 
 @binary_operator(MatrixAlgebra, MatrixAlgebra)
@@ -466,7 +471,7 @@ class MatSub(Sub, MatrixAlgebra):
 
 @binary_operator(MatrixAlgebra, MatrixAlgebra)
 class MatElemMul(Mul, MatrixAlgebra):
-    """ Elementwise Matrix Multiplication """
+    """ Elementwise Matrix Multiplication. """
 
     def __repr__(self) -> str:
         return f"({self.left} .* {self.right})"
@@ -475,10 +480,38 @@ class MatElemMul(Mul, MatrixAlgebra):
 @binary_operator(MatrixAlgebra, MatrixAlgebra)
 class MatScalarMul(ReducibleExpr, MatrixAlgebra):
     """ Matrix-Scalar Multiplication. """
-    def reduce(self) -> Expr:
-        raise NotImplementedError
+
+    @property
+    def shape(self) -> Shape:
+        """ See :py:meth:`mdpoly.abc.Expr.shape`. """
+        if self.right.shape == Shape.scalar:
+            return self.left.shape
+
+        elif self.left.shape == Shape.scalar:
+            return self.right.shape
+
+        raise InvalidShape(f"Either {self.left} or {self.right} must be a scalar.")
+
+@binary_operator(MatrixAlgebra, MatrixAlgebra)
+class MatInnerProd(Expr, MatrixAlgebra):
+    """ Inner product. """
 
 
 @binary_operator(MatrixAlgebra, MatrixAlgebra)
 class MatMul(Expr, MatrixAlgebra):
     """ Matrix Multiplication. """
+
+    @property
+    def shape(self) -> Shape:
+        """ See :py:meth:`mdpoly.abc.Expr.shape`. """
+        ...
+
+    def __repr__(self) -> str:
+        return f"({self.left} @ {self.right})"
+
+
+@unary_operator(MatrixAlgebra)
+class MatTranspose(HasRepr, MatrixAlgebra):
+    """ Matrix transposition """
+
+    # def to_repr(self,