remove shape property, introduce accumulate function, reimplement derivative expression

1 files changed, 14 insertions, 13 deletions

diff --git a/polymatrix/expression/mixins/determinantexprmixin.py b/polymatrix/expression/mixins/determinantexprmixin.py
index 8fe2536..048b263 100644
--- a/polymatrix/expression/mixins/determinantexprmixin.py
+++ b/polymatrix/expression/mixins/determinantexprmixin.py
@@ -16,10 +16,10 @@ class DeterminantExprMixin(ExpressionBaseMixin):
     def underlying(self) -> ExpressionBaseMixin:
         ...
 
-    # overwrites abstract method of `ExpressionBaseMixin`
-    @property
-    def shape(self) -> tuple[int, int]:
-        return self.underlying.shape[0], 1
+    # # overwrites abstract method of `ExpressionBaseMixin`
+    # @property
+    # def shape(self) -> tuple[int, int]:
+    #     return self.underlying.shape[0], 1
 
     # overwrites abstract method of `ExpressionBaseMixin`
     def apply(
@@ -34,12 +34,12 @@ class DeterminantExprMixin(ExpressionBaseMixin):
         assert underlying.shape[0] == underlying.shape[1]
 
         inequality_terms = {}
-        auxillary_terms = []
+        auxillary_equations = {}
 
         index_start = state.n_param
         rel_index = 0
 
-        for row in range(self.shape[0]):
+        for row in range(underlying.shape[0]):
 
             current_inequality_terms = collections.defaultdict(float)
 
@@ -66,13 +66,15 @@ class DeterminantExprMixin(ExpressionBaseMixin):
                         new_monomial = monomial + (index_start + rel_index + inner_row,)
                         current_inequality_terms[new_monomial] -= value
 
+                # auxillary terms
+                # ---------------
+
                 auxillary_term = collections.defaultdict(float)
 
                 for inner_col in range(row):
 
                     # P@x in P@x-v
                     key = tuple(reversed(sorted((inner_row, inner_col))))
-                    # terms = underlying.get_poly(*key)
                     try:
                         underlying_terms = underlying.get_poly(*key)
                     except KeyError:
@@ -83,7 +85,6 @@ class DeterminantExprMixin(ExpressionBaseMixin):
                             auxillary_term[new_monomial] += value
                 
                 # -v in P@x-v
-                # terms = underlying.get_poly(row, inner_row)
                 try:
                     underlying_terms = underlying.get_poly(row, inner_row)
                 except KeyError:
@@ -92,23 +93,23 @@ class DeterminantExprMixin(ExpressionBaseMixin):
                     for monomial, value in underlying_terms.items():
                         auxillary_term[monomial] -= value
 
-                auxillary_terms.append(dict(auxillary_term))
+                x_variable = index_start + rel_index + inner_row
+                assert x_variable not in state.auxillary_equations
+                auxillary_equations[x_variable] = dict(auxillary_term)
 
             rel_index += row
             inequality_terms[row, 0] = dict(current_inequality_terms)
 
         state = state.register(rel_index)
 
-        # print(f'{auxillary_terms=}')
-
         poly_matrix = init_poly_matrix(
             terms=inequality_terms,
-            shape=self.shape,
+            shape=(underlying.shape[0], 1),
         )
 
         state = dataclasses.replace(
             state, 
-            auxillary_terms=state.auxillary_terms + tuple(auxillary_terms),
+            auxillary_equations=state.auxillary_equations | auxillary_equations,
             cached_polymatrix=state.cached_polymatrix | {self: poly_matrix},
         )