check reduced grobner basis

src/poly/buchberger.rs

@@ -24,6 +24,30 @@ pub fn groebner_basis<V: Var>(generators: Vec<Poly<V>>) -> Vec<Poly<V>> {
         i += 1;
     }
 
+    // Minimize: remove any g whose LM is divisible by LM(h) for some other h.
+    let mut i = 0;
+    while i < g.len() {
+        let lm_i = g[i].leading_term_lex().unwrap().0.clone();
+        let redundant =
+            (0..g.len()).any(|j| j != i && lm_i.contains(&g[j].leading_term_lex().unwrap().0));
+        if redundant {
+            g.remove(i);
+        } else {
+            i += 1;
+        }
+    }
+
+    // Interreduce: replace each generator with its normal form modulo the others.
+    for i in 0..g.len() {
+        let others: Vec<Poly<V>> = g
+            .iter()
+            .enumerate()
+            .filter(|(j, _)| *j != i)
+            .map(|(_, p)| p.clone())
+            .collect();
+        g[i] = reduce(&g[i], &others);
+    }
+
     g
 }
 
@@ -47,7 +71,7 @@ pub fn is_groebner_basis<V: Var>(basis: &[Poly<V>]) -> bool {
 /// by the leading monomial of any element in `basis`.
 ///
 /// Uses the pseudo-division remainder and repeats until stable.
-fn reduce<V: Var>(f: &Poly<V>, basis: &[Poly<V>]) -> Poly<V> {
+pub(crate) fn reduce<V: Var>(f: &Poly<V>, basis: &[Poly<V>]) -> Poly<V> {
     let mut p = f.clone();
 
     'outer: loop {