diff -r c4e394a9c84c -r 402d717bb5c0 src/direct_product.rs
--- a/src/direct_product.rs	Mon Sep 01 13:51:03 2025 -0500
+++ b/src/direct_product.rs	Mon Sep 01 20:55:34 2025 -0500
@@ -6,9 +6,7 @@
 */
 
 use crate::euclidean::Euclidean;
-use crate::instance::{
-    ClosedSpace, Decomposition, DecompositionMut, Instance, InstanceMut, MyCow, Ownable,
-};
+use crate::instance::{Decomposition, DecompositionMut, Instance, InstanceMut, MyCow, Ownable};
 use crate::linops::{VectorSpace, AXPY};
 use crate::loc::Loc;
 use crate::mapping::Space;
@@ -289,22 +287,24 @@
 where
     A: Euclidean<F>,
     B: Euclidean<F>,
-    //Pair<A, B>: Euclidean<F>,
-    Self: Sized
-        + Mul<F, Output = <Self as VectorSpace>::Owned>
-        + MulAssign<F>
-        + Div<F, Output = <Self as VectorSpace>::Owned>
-        + DivAssign<F>
-        + Add<Self, Output = <Self as VectorSpace>::Owned>
-        + Sub<Self, Output = <Self as VectorSpace>::Owned>
-        + for<'b> Add<&'b Self, Output = <Self as VectorSpace>::Owned>
-        + for<'b> Sub<&'b Self, Output = <Self as VectorSpace>::Owned>
-        + AddAssign<Self>
-        + for<'b> AddAssign<&'b Self>
-        + SubAssign<Self>
-        + for<'b> SubAssign<&'b Self>
-        + Neg<Output = <Self as VectorSpace>::Owned>,
+    // //Pair<A, B>: Euclidean<F>,
+    // Self: Sized
+    //     + Mul<F, Output = Self::OwnedEuclidean>
+    //     + MulAssign<F>
+    //     + Div<F, Output = Self::OwnedEuclidean>
+    //     + DivAssign<F>
+    //     + Add<Self, Output = Self::OwnedEuclidean>
+    //     + Sub<Self, Output = Self::OwnedEuclidean>
+    //     + for<'b> Add<&'b Self, Output = Self::OwnedEuclidean>
+    //     + for<'b> Sub<&'b Self, Output = Self::OwnedEuclidean>
+    //     + AddAssign<Self>
+    //     + for<'b> AddAssign<&'b Self>
+    //     + SubAssign<Self>
+    //     + for<'b> SubAssign<&'b Self>
+    //     + Neg<Output = Self::OwnedEuclidean>,
 {
+    type OwnedEuclidean = Pair<A::OwnedEuclidean, B::OwnedEuclidean>;
+
     fn dot<I: Instance<Self>>(&self, other: I) -> F {
         other.eval_decompose(|Pair(u, v)| self.0.dot(u) + self.1.dot(v))
     }
@@ -318,16 +318,14 @@
     }
 }
 
-impl<F, A, B, O, P> VectorSpace for Pair<A, B>
+impl<F, A, B> VectorSpace for Pair<A, B>
 where
-    A: VectorSpace<Field = F, Owned = O, OwnedVariant = O>,
-    B: VectorSpace<Field = F, Owned = P, OwnedVariant = P>,
-    O: ClosedSpace + AXPY<A, Field = F, Owned = O, OwnedVariant = O>,
-    P: ClosedSpace + AXPY<B, Field = F, Owned = P, OwnedVariant = P>,
+    A: VectorSpace<Field = F>,
+    B: VectorSpace<Field = F>,
     F: Num,
 {
     type Field = F;
-    type Owned = Pair<O, P>;
+    type Owned = Pair<A::Owned, B::Owned>;
 
     /// Return a similar zero as `self`.
     fn similar_origin(&self) -> Self::Owned {
@@ -347,8 +345,8 @@
     A: AXPY<U, Field = F>,
     B: AXPY<V, Field = F>,
     F: Num,
-    Self: MulAssign<F> + DivAssign<F>,
-    Pair<A, B>: MulAssign<F> + DivAssign<F>,
+    // Self: MulAssign<F> + DivAssign<F>,
+    // Pair<A, B>: MulAssign<F> + DivAssign<F>,
 {
     fn axpy<I: Instance<Pair<U, V>>>(&mut self, α: F, x: I, β: F) {
         x.eval_decompose(|Pair(u, v)| {
@@ -383,6 +381,7 @@
 pub struct PairDecomposition<D, Q>(D, Q);
 
 impl<A: Space, B: Space> Space for Pair<A, B> {
+    type OwnedSpace = Pair<A::OwnedSpace, B::OwnedSpace>;
     type Decomp = PairDecomposition<A::Decomp, B::Decomp>;
 }