mathtools/cmd/pell.go

/*
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")
	}

	r := len(repetend)
	var period int
	if r%2 == 0 {
		period = r
	} else {
		period = 2 * r
	}

	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 {
			fmt.Println(r.Num(), r.Denom())
		}
	}
}

// pellCmd represents the pell command
var pellCmd = &cobra.Command{
	Use:   "pell -d N",
	Short: "Find solutions to a Pell equation",
	Long: `Find integer solutions to a Pell equation x^2 - dy^2 = 1.

This will output solutions infinitely. Try piping to head to only output a certain number of solutions, like this:
mathtools pell -d 12 | head -n 5`,
	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
}