add an example to compute matrix ranks

this MR

• implements the Display trait for Matrix to allow to show it
• makes from_vec_vec and rank public
• add rank.rs

example

Note

• this has been run with Nushell
• a -1 is an impossible value and thus will generate a random element instead

cargo run --example rank -- ...[
    "1,0,-1"
    "0,0,-1"
    "0,1,-1"
    "0,0,-1"
    "0,0,-1"
]

will output

/1 0 314995448938783965509764369801440879676\
|0 0 236699644179594774251145667390896459418|
|0 1 187004145196223910655928022134499908037|
|0 0 273500202756822505549423242088598868403|
\0 0 286599222098418496365691949902317095505/

m: 5
n: 3
r: 5

examples/rank.rs

+use ark_bls12_381::Fr;
+use ark_ff::Field;
+use komodo::linalg::Matrix;
+use rand::{rngs::ThreadRng, Rng};
+
+fn rand<T: Field>(rng: &mut ThreadRng) -> T {
+    let element: u128 = rng.gen();
+    T::from(element)
+}
+
+fn main() {
+    let mut rng = rand::thread_rng();
+
+    let elements = std::env::args()
+        .skip(1)
+        .map(|r| {
+            r.clone()
+                .split(',')
+                .map(|x| {
+                    if x == "-1" {
+                        rand(&mut rng)
+                    } else {
+                        let y: u128 = x.parse().unwrap();
+                        Fr::from(y)
+                    }
+                })
+                .collect::<Vec<_>>()
+        })
+        .collect::<Vec<_>>();
+
+    let m = Matrix::from_vec_vec(elements).unwrap();
+
+    eprintln!("{}", m);
+    eprintln!("m: {}", m.height);
+    eprintln!("n: {}", m.width);
+    eprintln!("r: {}", m.rank());
+}