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Make the Algebra and Module traits multigrading-capable #268

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00c35a0
Make Algebra trait generic over grading (multidegree support)
claude Jul 13, 2026
a6b6947
Make Module trait generic over grading (multidegree support)
claude Jul 13, 2026
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5 changes: 3 additions & 2 deletions ext/crates/algebra/Cargo.toml
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Original file line number Diff line number Diff line change
Expand Up @@ -15,6 +15,7 @@ bivec = { path = "../bivec" }
fp = { path = "../fp", default-features = false }
maybe-rayon = { path = "../maybe-rayon" }
once = { path = "../once" }
sseq = { path = "../sseq", default-features = false }

anyhow = "1.0.98"
auto_impl = "1.3.0"
Expand All @@ -36,8 +37,8 @@ rstest = "0.25.0"
[features]
default = ["odd-primes"]
cache-multiplication = []
concurrent = ["fp/concurrent", "maybe-rayon/concurrent"]
odd-primes = ["fp/odd-primes"]
concurrent = ["fp/concurrent", "maybe-rayon/concurrent", "sseq/concurrent"]
odd-primes = ["fp/odd-primes", "sseq/odd-primes"]

[[bench]]
name = "milnor"
Expand Down
22 changes: 14 additions & 8 deletions ext/crates/algebra/src/algebra/adem_algebra.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -12,6 +12,7 @@ use fp::{
use itertools::Itertools;
use once::OnceVec;
use rustc_hash::FxHashMap as HashMap;
use sseq::coordinates::MultiDegree;

#[cfg(doc)]
use crate::algebra::SteenrodAlgebra;
Expand Down Expand Up @@ -222,7 +223,8 @@ impl Algebra for AdemAlgebra {
.collect()
}

fn compute_basis(&self, max_degree: i32) {
fn compute_basis(&self, max_degree: impl Into<MultiDegree<1>>) {
let max_degree = i32::from(max_degree.into());
if self.generic {
self.generate_basis_generic(max_degree);
self.generate_basis_element_to_index_map(max_degree);
Expand All @@ -238,7 +240,8 @@ impl Algebra for AdemAlgebra {
}
}

fn dimension(&self, degree: i32) -> usize {
fn dimension(&self, degree: impl Into<MultiDegree<1>>) -> usize {
let degree = i32::from(degree.into());
if degree < 0 {
0
} else {
Expand All @@ -250,24 +253,27 @@ impl Algebra for AdemAlgebra {
&self,
result: FpSliceMut,
coeff: u32,
r_degree: i32,
r_degree: impl Into<MultiDegree<1>>,
r_index: usize,
s_degree: i32,
s_degree: impl Into<MultiDegree<1>>,
s_index: usize,
) {
self.multiply_inner(
result,
coeff,
r_degree,
i32::from(r_degree.into()),
r_index,
s_degree,
i32::from(s_degree.into()),
s_index,
i32::MAX,
);
}

fn basis_element_to_string(&self, degree: i32, idx: usize) -> String {
format!("{}", self.basis_element_from_index(degree, idx))
fn basis_element_to_string(&self, degree: impl Into<MultiDegree<1>>, idx: usize) -> String {
format!(
"{}",
self.basis_element_from_index(i32::from(degree.into()), idx)
)
}

fn basis_element_from_string(&self, mut elt: &str) -> Option<(i32, usize)> {
Expand Down
53 changes: 37 additions & 16 deletions ext/crates/algebra/src/algebra/algebra_trait.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -6,6 +6,7 @@ use fp::{
vector::{FpSlice, FpSliceMut},
};
use itertools::Itertools;
use sseq::coordinates::MultiDegree;

/// A graded algebra over $\mathbb{F}_p$.
///
Expand All @@ -20,8 +21,16 @@ use itertools::Itertools;
/// this function before performing other operations at that degree.
///
/// Algebras may have a distinguished set of generators; see [`GeneratedAlgebra`].
#[enum_dispatch]
pub trait Algebra: std::fmt::Display + Send + Sync + 'static {
///
/// # Grading
/// The trait is generic over the number of gradings `N` (defaulting to `1`, the singly-graded
/// case). Degrees are [`MultiDegree<N>`]; every degree *input* is taken as `impl Into<MultiDegree<N>>`
/// so callers in the singly-graded world keep passing bare `i32`s (via `From<i32> for
/// MultiDegree<1>`). `MultiDegree<2>` is a bidegree, used by `Ext` (see `ext::ext_algebra`).
///
/// `Algebra` cannot use `#[enum_dispatch]` because it is now generic; `SteenrodAlgebra` dispatches
/// it by hand (see `dispatch_steenrod!`).
pub trait Algebra<const N: usize = 1>: std::fmt::Display + Send + Sync + 'static {
/// A name for the algebra to use in serialization operations. This defaults to "" for algebras
/// that don't care about this problem.
fn prefix(&self) -> &str {
Expand Down Expand Up @@ -49,10 +58,10 @@ pub trait Algebra: std::fmt::Display + Send + Sync + 'static {
///
/// This function must be idempotent and cheap to call again with the
/// same argument.
fn compute_basis(&self, degree: i32);
fn compute_basis(&self, degree: impl Into<MultiDegree<N>>);

/// Returns the dimension of the algebra in degree `degree`.
fn dimension(&self, degree: i32) -> usize;
fn dimension(&self, degree: impl Into<MultiDegree<N>>) -> usize;

/// Computes the product `r * s` of two basis elements, and adds the
/// result to `result`.
Expand All @@ -62,9 +71,9 @@ pub trait Algebra: std::fmt::Display + Send + Sync + 'static {
&self,
result: FpSliceMut,
coeff: u32,
r_degree: i32,
r_degree: impl Into<MultiDegree<N>>,
r_idx: usize,
s_degree: i32,
s_degree: impl Into<MultiDegree<N>>,
s_idx: usize,
);

Expand All @@ -76,12 +85,14 @@ pub trait Algebra: std::fmt::Display + Send + Sync + 'static {
&self,
mut result: FpSliceMut,
coeff: u32,
r_degree: i32,
r_degree: impl Into<MultiDegree<N>>,
r_idx: usize,
s_degree: i32,
s_degree: impl Into<MultiDegree<N>>,
s: FpSlice,
) {
let p = self.prime();
let r_degree = r_degree.into();
let s_degree = s_degree.into();
for (i, v) in s.iter_nonzero() {
self.multiply_basis_elements(
result.copy(),
Expand All @@ -102,12 +113,14 @@ pub trait Algebra: std::fmt::Display + Send + Sync + 'static {
&self,
mut result: FpSliceMut,
coeff: u32,
r_degree: i32,
r_degree: impl Into<MultiDegree<N>>,
r: FpSlice,
s_degree: i32,
s_degree: impl Into<MultiDegree<N>>,
s_idx: usize,
) {
let p = self.prime();
let r_degree = r_degree.into();
let s_degree = s_degree.into();
for (i, v) in r.iter_nonzero() {
self.multiply_basis_elements(
result.copy(),
Expand All @@ -128,12 +141,14 @@ pub trait Algebra: std::fmt::Display + Send + Sync + 'static {
&self,
mut result: FpSliceMut,
coeff: u32,
r_degree: i32,
r_degree: impl Into<MultiDegree<N>>,
r: FpSlice,
s_degree: i32,
s_degree: impl Into<MultiDegree<N>>,
s: FpSlice,
) {
let p = self.prime();
let r_degree = r_degree.into();
let s_degree = s_degree.into();
for (i, v) in s.iter_nonzero() {
self.multiply_element_by_basis_element(
result.copy(),
Expand All @@ -158,7 +173,7 @@ pub trait Algebra: std::fmt::Display + Send + Sync + 'static {
}

/// Converts a basis element into a string for display.
fn basis_element_to_string(&self, degree: i32, idx: usize) -> String;
fn basis_element_to_string(&self, degree: impl Into<MultiDegree<N>>, idx: usize) -> String;

/// Non-panicking variant of [`Self::basis_element_to_string`]. Returns `None`
/// when `degree` is negative or `idx` is out of range for that degree, instead
Expand All @@ -167,8 +182,13 @@ pub trait Algebra: std::fmt::Display + Send + Sync + 'static {
/// These are the usual failure conditions. An implementation of
/// [`Self::basis_element_to_string`] that can fail for other reasons should override both
/// that method and this one, keeping them consistent.
fn try_basis_element_to_string(&self, degree: i32, idx: usize) -> Option<String> {
if degree < 0 {
fn try_basis_element_to_string(
&self,
degree: impl Into<MultiDegree<N>>,
idx: usize,
) -> Option<String> {
let degree = degree.into();
if degree.t() < 0 {
return None;
}
self.compute_basis(degree);
Expand All @@ -187,7 +207,8 @@ pub trait Algebra: std::fmt::Display + Send + Sync + 'static {
fn basis_element_from_string(&self, elt: &str) -> Option<(i32, usize)>;

/// Converts a general element into a string for display.
fn element_to_string(&self, degree: i32, element: FpSlice) -> String {
fn element_to_string(&self, degree: impl Into<MultiDegree<N>>, element: FpSlice) -> String {
let degree = degree.into();
let result = element
.iter_nonzero()
.map(|(idx, value)| {
Expand Down
19 changes: 10 additions & 9 deletions ext/crates/algebra/src/algebra/field.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -4,6 +4,7 @@ use fp::{
prime::ValidPrime,
vector::{FpSlice, FpSliceMut},
};
use sseq::coordinates::MultiDegree;

use crate::algebra::{Algebra, Bialgebra};

Expand Down Expand Up @@ -34,19 +35,19 @@ impl Algebra for Field {
self.prime
}

fn compute_basis(&self, _degree: i32) {}
fn compute_basis(&self, _degree: impl Into<MultiDegree<1>>) {}

fn dimension(&self, degree: i32) -> usize {
usize::from(degree == 0)
fn dimension(&self, degree: impl Into<MultiDegree<1>>) -> usize {
usize::from(i32::from(degree.into()) == 0)
}

fn multiply_basis_elements(
&self,
mut result: FpSliceMut,
coeff: u32,
_r_degree: i32,
_r_degree: impl Into<MultiDegree<1>>,
_r_idx: usize,
_s_degree: i32,
_s_degree: impl Into<MultiDegree<1>>,
_s_idx: usize,
) {
result.add_basis_element(0, coeff)
Expand All @@ -56,13 +57,13 @@ impl Algebra for Field {
vec![]
}

fn basis_element_to_string(&self, degree: i32, _idx: usize) -> String {
assert!(degree == 0);
fn basis_element_to_string(&self, degree: impl Into<MultiDegree<1>>, _idx: usize) -> String {
assert!(i32::from(degree.into()) == 0);
"1".to_string()
}

fn element_to_string(&self, degree: i32, element: FpSlice) -> String {
assert!(degree == 0);
fn element_to_string(&self, degree: impl Into<MultiDegree<1>>, element: FpSlice) -> String {
assert!(i32::from(degree.into()) == 0);
format!("{}", element.entry(0))
}

Expand Down
40 changes: 26 additions & 14 deletions ext/crates/algebra/src/algebra/milnor_algebra.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -8,6 +8,7 @@ use itertools::Itertools;
use once::OnceVec;
use rustc_hash::FxHashMap as HashMap;
use serde::{Deserialize, Serialize};
use sseq::coordinates::MultiDegree;

use crate::algebra::{Algebra, Bialgebra, GeneratedAlgebra, UnstableAlgebra, combinatorics};

Expand Down Expand Up @@ -416,7 +417,8 @@ impl Algebra for MilnorAlgebra {
.collect()
}

fn compute_basis(&self, max_degree: i32) {
fn compute_basis(&self, max_degree: impl Into<MultiDegree<1>>) {
let max_degree = i32::from(max_degree.into());
self.compute_ppart(max_degree);

if self.generic() {
Expand Down Expand Up @@ -470,7 +472,8 @@ impl Algebra for MilnorAlgebra {
}
}

fn dimension(&self, degree: i32) -> usize {
fn dimension(&self, degree: impl Into<MultiDegree<1>>) -> usize {
let degree = i32::from(degree.into());
if degree < 0 {
return 0;
}
Expand All @@ -482,16 +485,16 @@ impl Algebra for MilnorAlgebra {
&self,
result: FpSliceMut,
coef: u32,
r_degree: i32,
r_degree: impl Into<MultiDegree<1>>,
r_idx: usize,
s_degree: i32,
s_degree: impl Into<MultiDegree<1>>,
s_idx: usize,
) {
self.multiply(
result,
coef,
self.basis_element_from_index(r_degree, r_idx),
self.basis_element_from_index(s_degree, s_idx),
self.basis_element_from_index(i32::from(r_degree.into()), r_idx),
self.basis_element_from_index(i32::from(s_degree.into()), s_idx),
);
}

Expand All @@ -500,11 +503,13 @@ impl Algebra for MilnorAlgebra {
&self,
mut result: FpSliceMut,
coef: u32,
r_degree: i32,
r_degree: impl Into<MultiDegree<1>>,
r_idx: usize,
s_degree: i32,
s_degree: impl Into<MultiDegree<1>>,
s_idx: usize,
) {
let r_degree = i32::from(r_degree.into());
let s_degree = i32::from(s_degree.into());
result.add(
self.multiplication_table[r_degree as usize][s_degree as usize][r_idx][s_idx]
.as_slice(),
Expand All @@ -516,12 +521,14 @@ impl Algebra for MilnorAlgebra {
&self,
mut result: FpSliceMut,
coeff: u32,
r_degree: i32,
r_degree: impl Into<MultiDegree<1>>,
r_idx: usize,
s_degree: i32,
s_degree: impl Into<MultiDegree<1>>,
s: FpSlice,
) {
let p = self.prime();
let r_degree = i32::from(r_degree.into());
let s_degree = i32::from(s_degree.into());
let r = self.basis_element_from_index(r_degree, r_idx);
PPartAllocation::with_local(|mut allocation| {
for (i, v) in s.iter_nonzero() {
Expand All @@ -542,11 +549,13 @@ impl Algebra for MilnorAlgebra {
&self,
mut res: FpSliceMut,
coef: u32,
r_deg: i32,
r_deg: impl Into<MultiDegree<1>>,
r: FpSlice,
s_deg: i32,
s_deg: impl Into<MultiDegree<1>>,
s: FpSlice,
) {
let r_deg = i32::from(r_deg.into());
let s_deg = i32::from(s_deg.into());
PPartAllocation::with_local(|mut allocation| {
for (i, c) in r.iter_nonzero() {
allocation = self.multiply_basis_by_element_with_allocation(
Expand All @@ -562,8 +571,11 @@ impl Algebra for MilnorAlgebra {
})
}

fn basis_element_to_string(&self, degree: i32, idx: usize) -> String {
format!("{}", self.basis_element_from_index(degree, idx))
fn basis_element_to_string(&self, degree: impl Into<MultiDegree<1>>, idx: usize) -> String {
format!(
"{}",
self.basis_element_from_index(i32::from(degree.into()), idx)
)
}

fn basis_element_from_string(&self, elt: &str) -> Option<(i32, usize)> {
Expand Down
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