From 290f814d9803aee04eb26ee5b4a76a021825caa2 Mon Sep 17 00:00:00 2001
From: Nao Pross <np@0hm.ch>
Date: Tue, 19 Mar 2024 00:17:03 +0100
Subject: Implement matrix product

---
 mdpoly/operations/mul.py       | 25 ++++++++++++++++++++++---
 mdpoly/operations/transpose.py |  2 +-
 2 files changed, 23 insertions(+), 4 deletions(-)

diff --git a/mdpoly/operations/mul.py b/mdpoly/operations/mul.py
index 1c5a629..04796a2 100644
--- a/mdpoly/operations/mul.py
+++ b/mdpoly/operations/mul.py
@@ -6,11 +6,13 @@ from itertools import product
 from dataclasses import dataclass
 from dataclassabc import dataclassabc
 
+from ..abc import Expr
 from ..index import Shape
 from ..errors import AlgebraicError, InvalidShape
 from ..index import MatrixIndex, PolyIndex
 
 from . import BinaryOp, Reducible
+from .transpose import MatTranspose
 
 if TYPE_CHECKING:
     from ..abc import ReprT
@@ -107,7 +109,8 @@ class MatMul(BinaryOp):
         """ See :py:meth:`mdpoly.abc.Expr.shape`. """
         if not self.left.shape.rows == self.right.shape.cols:
             raise AlgebraicError("Cannot perform matrix multiplication between "
-                                 f"{self.left} and {self.right} (shapes {self.left.shape} and {self.right.shape})")
+                                 f"{self.left} and {self.right} (shapes {self.left.shape} "
+                                 f"and {self.right.shape})")
 
         return Shape(self.left.shape.rows, self.right.shape.cols)
 
@@ -121,8 +124,21 @@ class MatMul(BinaryOp):
         # Compute matrix product
         for row in range(self.left.shape.rows):
             for col in range(self.right.shape.cols):
-                for i in range(self.left.shape.cols):
-                    raise NotImplementedError
+                # Entry of result
+                entry = MatrixIndex(row, col)
+
+                for k in range(self.left.shape.cols):
+                    lentry = MatrixIndex(row, k)
+                    rentry = MatrixIndex(k, col)
+
+                    # Product of polynomials at lentry and rentry
+                    for lterm, rterm in product(lrepr.terms(lentry), rrepr.terms(rentry)):
+                        # Compute index of product
+                        term = PolyIndex.product(lterm, rterm)
+                        # Compute product
+                        p = r.at(entry, term)
+                        p += lrepr.at(lentry, term) * rrepr.at(rentry, term)
+                        r.set(entry, term, p)
 
         return r, state
 
@@ -148,6 +164,9 @@ class MatDotProd(BinaryOp, Reducible):
 
         return Shape.scalar()
 
+    def reduce(self) -> Expr:
+        return MatMul(MatTranspose(self.left), self.right)
+
 
 # ┏━┓┏━┓╻  ╻ ╻┏┓╻┏━┓┏┳┓╻┏━┓╻     ┏━┓┏━┓┏━┓╺┳┓╻ ╻┏━╸╺┳╸
 # ┣━┛┃ ┃┃  ┗┳┛┃┗┫┃ ┃┃┃┃┃┣━┫┃     ┣━┛┣┳┛┃ ┃ ┃┃┃ ┃┃   ┃ 
diff --git a/mdpoly/operations/transpose.py b/mdpoly/operations/transpose.py
index 0e4228b..c67c9d2 100644
--- a/mdpoly/operations/transpose.py
+++ b/mdpoly/operations/transpose.py
@@ -3,7 +3,7 @@ from typing import TYPE_CHECKING
 
 from dataclasses import dataclass
 
-from ..expressions import UnaryOp
+from . import UnaryOp
 
 if TYPE_CHECKING:
     from ..index import Shape
-- 
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