Revert unnecessary comment modifications

matrix.go

@@ -163,7 +163,7 @@ func MatMul[E Element[E]](a, b Matrix[E]) (Matrix[E], error) {
 	return res, nil
 }
 
-// left Matrix multiplication, denote by m*V, where m is the matrix, and V is the vector.
+// left Matrix multiplication, denote by M*V, where M is the matrix, and V is the vector.
 func LeftMatMul[E Element[E]](m Matrix[E], v Vector[E]) (Vector[E], error) {
 	if !IsSquareMatrix(m) {
 		panic("matrix is not square!")
@@ -185,7 +185,7 @@ func LeftMatMul[E Element[E]](m Matrix[E], v Vector[E]) (Vector[E], error) {
 	return res, nil
 }
 
-// right Matrix multiplication, denote by V*m, where V is the vector, and m is the matrix.
+// right Matrix multiplication, denote by V*M, where V is the vector, and M is the matrix.
 func RightMatMul[E Element[E]](v Vector[E], m Matrix[E]) (Vector[E], error) {
 	if !IsSquareMatrix(m) {
 		return nil, errors.New("matrix is not square")

mds.go

@@ -22,18 +22,18 @@ type mdsMatrices[E Element[E]] struct {
 	mPrime Matrix[E]
 	// mDoublePrime is the matrix m'' in the paper, and it holds m = m'*m''.
 	// mDoublePrime consists of:
-	// m_00  |  V
+	// m_00  |  v
 	// w_hat |  I
 	// where M_00 is the first element of the mds matrix,
-	// w_hat and V are t-1 length vectors,
+	// w_hat and v are t-1 length vectors,
 	// I is the (t-1)*(t-1) identity matrix.
 	mDoublePrime Matrix[E]
 }
 
-// SparseMatrix is specifically one of the form of m”.
+// SparseMatrix is specifically one of the form of m''.
 // This means its first row and column are each dense, and the interior matrix
 // (minor to the element in both the row and column) is the identity.
-// For simplicity, we omit the identity matrix in m”.
+// For simplicity, we omit the identity matrix in m''.
 type SparseMatrix[E Element[E]] struct {
 	// WHat is the first column of the m'' matrix, this is a little different with the WHat in the paper because
 	// we add M_00 to the beginning of the WHat.
@@ -108,7 +108,7 @@ func deriveMatrices[E Element[E]](m Matrix[E]) (*mdsMatrices[E], error) {
 	return &mdsMatrices[E]{m, mInv, mHat, mHatInv, mPrime, mDoublePrime}, nil
 }
 
-// generate the matrix m', where m = m'*m”.
+// generate the matrix m', where m = m'*m''.
 func genPrime[E Element[E]](m Matrix[E]) Matrix[E] {
 	prime := make([][]E, row(m))
 	prime[0] = append(prime[0], one[E]())
@@ -126,7 +126,7 @@ func genPrime[E Element[E]](m Matrix[E]) Matrix[E] {
 	return prime
 }
 
-// generate the matrix m”, where m = m'*m”.
+// generate the matrix m'', where m = m'*m''.
 func genDoublePrime[E Element[E]](m, mHatInv Matrix[E]) (Matrix[E], error) {
 	w, v := genPreVectors(m)
 
@@ -195,8 +195,8 @@ func parseSparseMatrix[E Element[E]](m Matrix[E]) (*SparseMatrix[E], error) {
 // we refer to the paper https://eprint.iacr.org/2019/458.pdf page 20 and
 // the implementation in https://github.com/filecoin-project/neptune.
 // at each partial round, use a sparse matrix instead of a dense matrix.
-// to do this, we have to factored into two components, such that m' x m” = m,
-// use the sparse matrix m” as the mds matrix,
+// to do this, we have to factored into two components, such that m' x m'' = m,
+// use the sparse matrix m'' as the mds matrix,
 // then the previous layer's m is replaced by m x m' = m*.
 // from the last partial round, do the same work to the first partial round.
 func genSparseMatrix[E Element[E]](m Matrix[E], rp int) ([]*SparseMatrix[E], Matrix[E], error) {

poseidon.go

@@ -218,7 +218,7 @@ func sbox[E Element[E]](e E, pre, post *E) {
 	}
 }
 
-// staticPartialRounds computes arc->sbox->m, which has partial sbox layers,
+// staticPartialRounds computes arc->sbox->M, which has partial sbox layers,
 // see https://eprint.iacr.org/2019/458.pdf page 6.
 // The partial round is the same as the full round, with the difference
 // that we apply the S-Box only to the first element.
@@ -231,7 +231,7 @@ func staticPartialRounds[E Element[E]](state []E, offset int, pdsConsts *Poseido
 	return state
 }
 
-// staticFullRounds computes arc->sbox->m, which has full sbox layers,
+// staticFullRounds computes arc->sbox->M, which has full sbox layers,
 // see https://eprint.iacr.org/2019/458.pdf page 6.
 func staticFullRounds[E Element[E]](state []E, lastRound bool, offset int, pdsConsts *PoseidonConst[E]) []E {
 	// in the last round, there is no need to add round constants because
@@ -249,7 +249,7 @@ func staticFullRounds[E Element[E]](state []E, lastRound bool, offset int, pdsCo
 	}
 
 	// in the fourth full round, we should compute the product between the elements
-	// and the pre-sparse matrix (m*m'), see https://eprint.iacr.org/2019/458.pdf page 20.
+	// and the pre-sparse matrix (M*M'), see https://eprint.iacr.org/2019/458.pdf page 20.
 	if offset == 4*len(state) {
 		state = productPreSparseMatrix(state, pdsConsts.PreSparse)
 	} else {
@@ -289,7 +289,7 @@ func dynamicFullRounds[E Element[E]](state []E, current, next bool, offset int,
 			copy(postVec, pdsContants.RoundConsts[offset:offset+t])
 		}
 
-		// m^-1(s)
+		// M^-1(s)
 		inv, err := RightMatMul(postVec, pdsContants.Mds.mInv)
 		if err != nil {
 			panic(err)
@@ -386,18 +386,18 @@ func productPreSparseMatrix[E Element[E]](state []E, preSparseMatrix Matrix[E])
 // productSparseMatrix computes the product between the elements and the sparse matrix.
 func productSparseMatrix[E Element[E]](state []E, offset int, sparse []*SparseMatrix[E]) []E {
 	// this part is described in https://eprint.iacr.org/2019/458.pdf page 20.
-	// the sparse matrix m'' consists of:
+	// the sparse matrix M'' consists of:
 	//
-	// M_00  |  V
+	// M_00  |  v
 	// w_hat |  I
 	//
 	// where M_00 is the first element of the mds matrix,
-	// w_hat and V are t-1 length vectors,
+	// w_hat and v are t-1 length vectors,
 	// I is the (t-1)*(t-1) identity matrix.
-	// to compute ret = state * m'',
+	// to compute ret = state * M'',
 	// we can first compute ret[0] = state * [M_00, w_hat],
 	// then for 1 <= i < t,
-	// compute ret[i] = state[0] * V[i-1] + state[i].
+	// compute ret[i] = state[0] * v[i-1] + state[i].
 	res := make([]E, len(state))
 	res[0] = NewElement[E]()
 	for i := 0; i < len(state); i++ {