diff -r 5e3c1874797d -r 1b3b1687b9ed src/direct_product.rs
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/direct_product.rs	Fri Dec 13 22:37:12 2024 -0500
@@ -0,0 +1,228 @@
+/*!
+Direct products of the form $A \times B$.
+
+TODO: This could be easily much more generic if `derive_more` could derive arithmetic
+operations on references.
+*/
+
+use core::ops::{Mul,MulAssign,Div,DivAssign,Add,AddAssign,Sub,SubAssign,Neg};
+use std::clone::Clone;
+use serde::{Serialize, Deserialize};
+use crate::types::{Num, Float};
+use crate::{maybe_lifetime, maybe_ref, impl_vectorspace_ops};
+use crate::euclidean::{Dot, Euclidean};
+
+#[derive(Debug,Clone,PartialEq,Eq,Serialize,Deserialize)]
+pub struct Pair<A, B> (pub A, pub B);
+
+impl<A, B> Pair<A,B> {
+    pub fn new(a : A, b : B) -> Pair<A,B> { Pair{ 0 : a, 1 : b } }
+}
+
+impl<A, B> From<(A,B)> for Pair<A,B> {
+    #[inline]
+    fn from((a, b) : (A, B)) -> Pair<A,B> { Pair{ 0 : a, 1 : b } }
+}
+
+macro_rules! impl_binop {
+    ($trait : ident, $fn : ident, $refl:ident, $refr:ident) => {
+        impl_binop!(@doit: $trait, $fn;
+                           maybe_lifetime!($refl, &'l Pair<A,B>),
+                               (maybe_lifetime!($refl, &'l A), maybe_lifetime!($refl, &'l B));
+                           maybe_lifetime!($refr, &'r Pair<Ai,Bi>),
+                               (maybe_lifetime!($refr, &'r Ai), maybe_lifetime!($refr, &'r Bi));
+                           $refl, $refr);
+    };
+
+    (@doit: $trait:ident, $fn:ident;
+            $self:ty, ($aself:ty, $bself:ty);
+            $in:ty, ($ain:ty, $bin:ty);
+            $refl:ident, $refr:ident) => {
+        impl<'l, 'r, A, B, Ai, Bi> $trait<$in>
+        for $self
+        where $aself: $trait<$ain>,
+              $bself: $trait<$bin> {
+            type Output = Pair<<$aself as $trait<$ain>>::Output,
+                                       <$bself as $trait<$bin>>::Output>;
+
+            #[inline]
+            fn $fn(self, y : $in) -> Self::Output {
+                Pair { 0 : maybe_ref!($refl, self.0).$fn(maybe_ref!($refr, y.0)),
+                               1 : maybe_ref!($refl, self.1).$fn(maybe_ref!($refr, y.1)) }
+            }
+        }
+    };
+}
+
+macro_rules! impl_assignop {
+    ($trait : ident, $fn : ident, $refr:ident) => {
+        impl_assignop!(@doit: $trait, $fn;
+                              maybe_lifetime!($refr, &'r Pair<Ai,Bi>),
+                                  (maybe_lifetime!($refr, &'r Ai), maybe_lifetime!($refr, &'r Bi));
+                              $refr);
+    };
+    (@doit: $trait:ident, $fn:ident;
+            $in:ty, ($ain:ty, $bin:ty);
+            $refr:ident) => {
+        impl<'r, A, B, Ai, Bi> $trait<$in>
+        for Pair<A,B>
+        where A: $trait<$ain>,
+              B: $trait<$bin> {
+            #[inline]
+            fn $fn(&mut self, y : $in) -> () {
+                self.0.$fn(maybe_ref!($refr, y.0));
+                self.1.$fn(maybe_ref!($refr, y.1));
+            }
+        }
+    }
+}
+
+macro_rules! impl_scalarop {
+    ($trait : ident, $fn : ident, $refl:ident) => {
+        impl_scalarop!(@doit: $trait, $fn;
+                              maybe_lifetime!($refl, &'l Pair<A,B>),
+                                  (maybe_lifetime!($refl, &'l A), maybe_lifetime!($refl, &'l B));
+                              $refl);
+    };
+    (@doit: $trait:ident, $fn:ident;
+            $self:ty, ($aself:ty, $bself:ty);
+            $refl:ident) => {
+        // Scalar as Rhs
+        impl<'l, F : Num, A, B> $trait<F>
+        for $self
+        where $aself: $trait<F>,
+              $bself: $trait<F> {
+            type Output = Pair<<$aself as $trait<F>>::Output,
+                                       <$bself as $trait<F>>::Output>;
+            #[inline]
+            fn $fn(self, a : F) -> Self::Output {
+                Pair{ 0 : maybe_ref!($refl, self.0).$fn(a),
+                              1 : maybe_ref!($refl, self.1).$fn(a)}
+            }
+        }
+    }
+}
+
+// Not used due to compiler overflow
+#[allow(unused_macros)]
+macro_rules! impl_scalarlhs_op {
+    ($trait:ident, $fn:ident, $refr:ident, $field:ty) => {
+        impl_scalarlhs_op!(@doit: $trait, $fn, 
+                                  maybe_lifetime!($refr, &'r Pair<Ai,Bi>),
+                                  (maybe_lifetime!($refr, &'r Ai), maybe_lifetime!($refr, &'r Bi));
+                                  $refr, $field);
+    };
+    (@doit: $trait:ident, $fn:ident, 
+            $in:ty, ($ain:ty, $bin:ty);
+            $refr:ident, $field:ty) => {
+        impl<'r, Ai, Bi> $trait<$in>
+        for $field
+        where $field : $trait<$ain>
+                     + $trait<$bin> {
+            type Output = Pair<<$field as $trait<$ain>>::Output,
+                                       <$field as $trait<$bin>>::Output>;
+            #[inline]
+            fn $fn(self, x : $in) -> Self::Output {
+                Pair{ 0 : self.$fn(maybe_ref!($refr, x.0)),
+                              1 : self.$fn(maybe_ref!($refr, x.1))}
+            }
+        }
+    };
+}
+
+macro_rules! impl_scalar_assignop {
+    ($trait : ident, $fn : ident) => {
+        impl<'r, F : Num, A, B> $trait<F>
+        for Pair<A,B>
+        where A: $trait<F>, B: $trait<F> {
+            #[inline]
+            fn $fn(&mut self, a : F) -> () {
+                self.0.$fn(a);
+                self.1.$fn(a);
+            }
+        }
+    }
+}
+
+macro_rules! impl_unaryop {
+    ($trait:ident, $fn:ident, $refl:ident) => {
+        impl_unaryop!(@doit: $trait, $fn;
+                             maybe_lifetime!($refl, &'l Pair<A,B>),
+                                 (maybe_lifetime!($refl, &'l A), maybe_lifetime!($refl, &'l B));
+                             $refl);
+    };
+    (@doit: $trait:ident, $fn:ident;
+            $self:ty, ($aself:ty, $bself:ty);
+            $refl : ident) => {
+        impl<'l, A, B> $trait
+        for $self
+        where $aself: $trait,
+              $bself: $trait {
+            type Output = Pair<<$aself as $trait>::Output,
+                                       <$bself as $trait>::Output>;
+            #[inline]
+            fn $fn(self) -> Self::Output {
+                Pair{ 0 : maybe_ref!($refl, self.0).$fn(),
+                              1 : maybe_ref!($refl, self.1).$fn()}
+            }
+        }
+    }
+}
+
+
+impl_vectorspace_ops!(impl_binop, impl_assignop, impl_scalarop, impl_scalarlhs_op,
+                      impl_scalar_assignop, impl_unaryop);
+
+
+impl<A, B, U, V, F> Dot<Pair<U, V>, F> for Pair<A, B>
+where
+    A : Dot<U, F>,
+    B : Dot<V, F>,
+    F : Num
+{
+
+    fn dot(&self, Pair(ref u, ref v) : &Pair<U, V>) -> F {
+        self.0.dot(u) + self.1.dot(v)
+    }
+}
+
+impl<A, B, F> Euclidean<F>  for Pair<A, B>
+where
+    A : Euclidean<F>,
+    B : Euclidean<F>,
+    F : Float
+{
+    type Output = Pair<<A as Euclidean<F>>::Output, <B as Euclidean<F>>::Output>;
+
+    fn similar_origin(&self) -> <Self as Euclidean<F>>::Output {
+        Pair(self.0.similar_origin(), self.1.similar_origin())
+    }
+
+    fn dist2_squared(&self, Pair(ref u, ref v) : &Self) -> F {
+        self.0.dist2_squared(u) + self.1.dist2_squared(v)
+    }
+}
+
+use crate::linops::AXPY;
+
+impl<F, A, B, U, V> AXPY<F, Pair<U, V>> for Pair<A, B>
+where
+    A : AXPY<F, U>,
+    B : AXPY<F, V>,
+    F : Num
+{
+    fn axpy(&mut self, α : F, x : &Pair<U, V>, β : F) {
+        self.0.axpy(α, &x.0, β);
+        self.1.axpy(α, &x.1, β);
+    }
+
+    fn copy_from(&mut self, x : &Pair<U, V>,) {
+        self.0.copy_from(&x.0);
+        self.1.copy_from(&x.1);
+    }
+
+    fn scale_from(&mut self, α : F, x : &Pair<U, V>) {
+        self.0.scale_from(α, &x.0);
+        self.1.scale_from(α, &x.1);
+    }
+}
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