add pell subcommand

cmd/pell.go

@@ -0,0 +1,93 @@
+/*
+Copyright © 2025 filifa
+
+This program is free software: you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation, either version 3 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License
+along with this program. If not, see <http://www.gnu.org/licenses/>.
+*/
+package cmd
+
+import (
+	"fmt"
+	"math/big"
+
+	"github.com/spf13/cobra"
+	"scm.dairydemon.net/filifa/mathtools/internal/lib"
+)
+
+var pellCoeff string
+
+func pell(cmd *cobra.Command, args []string) {
+	d, ok := new(big.Int).SetString(pellCoeff, 10)
+	if !ok {
+		cobra.CheckErr("invalid input " + args[0])
+	}
+
+	a0 := new(big.Int).Sqrt(d)
+
+	repetend, err := lib.SqrtRepetend(d)
+	if err != nil {
+		cobra.CheckErr(pellCoeff + " is a perfect square")
+	}
+
+	hprev := big.NewInt(0)
+	kprev := big.NewInt(1)
+
+	h := big.NewInt(1)
+	k := big.NewInt(0)
+
+	seq(h, hprev, a0)
+	seq(k, kprev, a0)
+
+	for i := 0; true; i = (i + 1) % len(repetend) {
+		foo := new(big.Int).Exp(k, big.NewInt(2), nil)
+		foo.Mul(d, foo)
+
+		bar := new(big.Int).Exp(h, big.NewInt(2), nil)
+		bar.Sub(bar, foo)
+
+		if bar.Cmp(big.NewInt(1)) == 0 {
+			fmt.Println(h, k)
+		}
+
+		a := repetend[i]
+		seq(h, hprev, a)
+		seq(k, kprev, a)
+	}
+}
+
+// pellCmd represents the pell command
+var pellCmd = &cobra.Command{
+	Use:   "pell",
+	Short: "Find solutions to a Pell equation",
+	Long:  `Find solutions to a Pell equation.`,
+	Run:   pell,
+}
+
+func init() {
+	rootCmd.AddCommand(pellCmd)
+
+	// Here you will define your flags and configuration settings.
+
+	// Cobra supports Persistent Flags which will work for this command
+	// and all subcommands, e.g.:
+	// pellCmd.PersistentFlags().String("foo", "", "A help for foo")
+
+	// Cobra supports local flags which will only run when this command
+	// is called directly, e.g.:
+	// pellCmd.Flags().BoolP("toggle", "t", false, "Help message for toggle")
+
+	pellCmd.Flags().StringVarP(&pellCoeff, "coefficient", "d", "", "coefficient")
+	pellCmd.MarkFlagRequired("coefficient")
+
+	// TODO: add support for generalized Pell equations
+}