Add secondary_basis example

ext/examples/secondary_basis.rs

@@ -0,0 +1,43 @@
+use std::sync::Arc;
+
+use ext::{chain_complex::FreeChainComplex, secondary::*, utils::query_module};
+use sseq::coordinates::{Bidegree, BidegreeElement, BidegreeGenerator};
+
+fn main() -> anyhow::Result<()> {
+    ext::utils::init_logging();
+
+    let resolution = Arc::new(query_module(Some(algebra::AlgebraType::Milnor), true)?);
+    let p = resolution.prime();
+
+    let lift = SecondaryResolution::new(Arc::clone(&resolution));
+    lift.extend_all();
+
+    let sseq = lift.e3_page();
+    let get_page_data = |b: Bidegree| {
+        let d = sseq.page_data(b.n(), b.s() as i32);
+        &d[std::cmp::min(3, d.len() - 1)]
+    };
+
+    for b in resolution.iter_nonzero_stem() {
+        let subquotient = get_page_data(b);
+
+        let ambient = subquotient.ambient_dimension();
+
+        let boundary = subquotient
+            .zeros()
+            .iter()
+            .map(|v| ("B", BidegreeElement::new(b, v.to_owned())));
+        let cycle = subquotient
+            .gens()
+            .map(|v| ("Z", BidegreeElement::new(b, v.to_owned())));
+        let rest = subquotient
+            .complement_pivots()
+            .map(|i| ("E", BidegreeGenerator::new(b, i).into_element(p, ambient)));
+
+        for (prefix, v) in boundary.chain(cycle).chain(rest) {
+            println!("{} {:#}", prefix, v);
+        }
+    }
+
+    Ok(())
+}