check reduced grobner basis

src/poly/tests.rs

@@ -1,5 +1,6 @@
 use super::buchberger::{groebner_basis, is_groebner_basis};
 use super::flat::{Mono, Poly, lex_cmp};
+use super::ideal::{Generators, GroebnerBasis, Ideal};
 use super::var::StaticVar;
 
 #[test]
@@ -377,3 +378,87 @@ fn test_is_groebner_basis() {
     let basis = groebner_basis(vec![f, g]);
     assert!(is_groebner_basis(&basis));
 }
+
+#[test]
+fn test_ideal() {
+    // Construction from Vec and iterator
+    let f: Poly<StaticVar> = [(1, [("x", 2)])].into();
+    let g: Poly<StaticVar> = [(1, [("y", 1)])].into();
+    let ideal = Ideal::new(vec![f.clone(), g.clone()]);
+    assert_eq!(ideal.generators().len(), 2);
+    let ideal: Ideal<StaticVar, Generators> = [f.clone(), g.clone()].into_iter().collect();
+    assert_eq!(ideal.generators().len(), 2);
+
+    // Construction via From / .into()
+    let ideal: Ideal<StaticVar, Generators> = vec![f.clone(), g.clone()].into();
+    assert_eq!(ideal.generators().len(), 2);
+
+    // Display: <x², y>
+    let ideal = Ideal::new(vec![f, g]);
+    assert_eq!(ideal.to_string(), "<x\u{00B2}, y>");
+
+    // groebner_basis transitions state and result satisfies the criterion
+    let f: Poly<StaticVar> = [
+        (1i32, Mono::from([("x", 2u32), ("y", 1u32)])),
+        (-1i32, Mono::from([("x", 1u32)])),
+    ]
+    .into_iter()
+    .collect();
+    let g: Poly<StaticVar> = [
+        (1i32, Mono::from([("x", 1u32), ("y", 2u32)])),
+        (-1i32, Mono::from([("y", 1u32)])),
+    ]
+    .into_iter()
+    .collect();
+    let ideal: Ideal<StaticVar, Generators> = [f, g].into_iter().collect();
+    let gb: Ideal<StaticVar, GroebnerBasis> = ideal.groebner_basis();
+    assert!(is_groebner_basis(gb.generators()));
+}
+
+#[test]
+fn test_groebner_sagemath() {
+    // I = (x³ - 2xy, x²y - 2y² + x) ⊆ k[x, y]
+    // grobner basis: {4y³, x - 2y²}
+
+    // f1 = x³ - 2xy
+    let f1: Poly<StaticVar> = [
+        (1i32, Mono::from([("x", 3u32)])),
+        (-2i32, Mono::from([("x", 1u32), ("y", 1u32)])),
+    ]
+    .into_iter()
+    .collect();
+
+    // f2 = x²y - 2y² + x
+    let f2: Poly<StaticVar> = [
+        (1i32, Mono::from([("x", 2u32), ("y", 1u32)])),
+        (-2i32, Mono::from([("y", 2u32)])),
+        (1i32, Mono::from([("x", 1u32)])),
+    ]
+    .into_iter()
+    .collect();
+
+    let gb = Ideal::new(vec![f1.clone(), f2.clone()]).groebner_basis();
+
+    assert!(is_groebner_basis(gb.generators()));
+    assert_eq!(gb.generators().len(), 2);
+
+    // -x + 2y²
+    let neg_x_plus_2y2: Poly<StaticVar> = [
+        (-1i32, Mono::from([("x", 1u32)])),
+        (2i32, Mono::from([("y", 2u32)])),
+    ]
+    .into_iter()
+    .collect();
+
+    // -4y³
+    let neg_4y3: Poly<StaticVar> = [(-4i32, Mono::from([("y", 3u32)]))].into_iter().collect();
+
+    let expected = [neg_x_plus_2y2, neg_4y3];
+    for e in &expected {
+        assert!(
+            gb.generators()
+                .iter()
+                .any(|a| *a == *e || *a == -1i32 * e.clone())
+        );
+    }
+}