diff --git a/cmd/convergents.go b/cmd/convergents.go
index 73ed939..e5b9bda 100644
--- a/cmd/convergents.go
+++ b/cmd/convergents.go
@@ -21,67 +21,9 @@ import (
 	"math/big"
 
 	"github.com/spf13/cobra"
+	"scm.dairydemon.net/filifa/mathtools/internal/lib"
 )
 
-func cycle(seq []*big.Int) <-chan *big.Int {
-	ch := make(chan *big.Int)
-	n := len(seq)
-	go func() {
-		for i := 0; true; i = (i + 1) % n {
-			ch <- seq[i]
-		}
-	}()
-
-	return ch
-}
-
-func gaussianBrackets(ch <-chan *big.Int) <-chan *big.Int {
-	out := make(chan *big.Int)
-
-	xprev := big.NewInt(0)
-	x := big.NewInt(1)
-
-	go func() {
-		tmp := new(big.Int)
-		for a := range ch {
-			out <- x
-
-			tmp.Mul(a, x)
-			tmp.Add(tmp, xprev)
-
-			xprev.Set(x)
-			x = new(big.Int).Set(tmp)
-		}
-	}()
-
-	return out
-}
-
-func cFracConvergents(a0 *big.Int, denoms []*big.Int) <-chan *big.Rat {
-	hc := cycle(denoms)
-	_ = <-hc
-	hch := gaussianBrackets(hc)
-
-	kc := cycle(denoms)
-	kch := gaussianBrackets(kc)
-	_ = <-kch
-
-	a := new(big.Rat).SetInt(a0)
-
-	out := make(chan *big.Rat)
-
-	go func() {
-		for {
-			h, k := <-hch, <-kch
-			r := new(big.Rat).SetFrac(h, k)
-			r.Add(r, a)
-			out <- r
-		}
-	}()
-
-	return out
-}
-
 func convergents(cmd *cobra.Command, args []string) {
 	a0, ok := new(big.Int).SetString(args[0], 10)
 	if !ok {
@@ -97,7 +39,7 @@ func convergents(cmd *cobra.Command, args []string) {
 		}
 	}
 
-	for r := range cFracConvergents(a0, denoms) {
+	for r := range lib.CFracConvergents(a0, denoms) {
 		fmt.Println(r)
 	}
 }
diff --git a/cmd/pell.go b/cmd/pell.go
index 6251da6..9124071 100644
--- a/cmd/pell.go
+++ b/cmd/pell.go
@@ -47,8 +47,9 @@ func pell(cmd *cobra.Command, args []string) {
 		period = 2 * r
 	}
 
-	ch := cFracConvergents(a0, repetend)
+	ch := lib.CFracConvergents(a0, repetend)
 
+	// TODO: consider breaking after finding the fundamental solution and using the recurrence relation to find the following solutions
 	for i := 1; true; i = (i + 1) % period {
 		r := <-ch
 		if i == period-1 {
diff --git a/internal/lib/continuedFrac.go b/internal/lib/continuedFrac.go
index 66d2eb6..1f96e8d 100644
--- a/internal/lib/continuedFrac.go
+++ b/internal/lib/continuedFrac.go
@@ -36,3 +36,62 @@ func SqrtRepetend(x *big.Int) ([]*big.Int, error) {
 
 	return repetend, nil
 }
+
+func cycle(seq []*big.Int) <-chan *big.Int {
+	ch := make(chan *big.Int)
+	n := len(seq)
+	go func() {
+		for i := 0; true; i = (i + 1) % n {
+			ch <- seq[i]
+		}
+	}()
+
+	return ch
+}
+
+func GaussianBrackets(ch <-chan *big.Int) <-chan *big.Int {
+	out := make(chan *big.Int)
+
+	xprev := big.NewInt(0)
+	x := big.NewInt(1)
+
+	go func() {
+		tmp := new(big.Int)
+		for a := range ch {
+			out <- x
+
+			tmp.Mul(a, x)
+			tmp.Add(tmp, xprev)
+
+			xprev.Set(x)
+			x = new(big.Int).Set(tmp)
+		}
+	}()
+
+	return out
+}
+
+func CFracConvergents(a0 *big.Int, denoms []*big.Int) <-chan *big.Rat {
+	hc := cycle(denoms)
+	_ = <-hc
+	hch := GaussianBrackets(hc)
+
+	kc := cycle(denoms)
+	kch := GaussianBrackets(kc)
+	_ = <-kch
+
+	a := new(big.Rat).SetInt(a0)
+
+	out := make(chan *big.Rat)
+
+	go func() {
+		for {
+			h, k := <-hch, <-kch
+			r := new(big.Rat).SetFrac(h, k)
+			r.Add(r, a)
+			out <- r
+		}
+	}()
+
+	return out
+}