mathtools/cmd/convergents.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"
)

func gaussianBrackets(x, xprev, a *big.Int) {
	tmp := new(big.Int)
	tmp.Mul(a, x)
	tmp.Add(tmp, xprev)
	xprev.Set(x)
	x.Set(tmp)
}

func convergents(cmd *cobra.Command, args []string) {
	hprev := big.NewInt(0)
	kprev := big.NewInt(1)

	h := big.NewInt(1)
	k := big.NewInt(0)

	a0, ok := new(big.Int).SetString(args[0], 10)
	if !ok {
		cobra.CheckErr("invalid input " + args[0])
	}

	denoms := make([]big.Int, len(args[1:]))
	for i, d := range args[1:] {
		_, ok = denoms[i].SetString(d, 10)
		if !ok {
			cobra.CheckErr("invalid input " + d)
		}
	}

	gaussianBrackets(h, hprev, a0)
	gaussianBrackets(k, kprev, a0)

	r := new(big.Rat).SetFrac(h, k)
	fmt.Println(r)

	for i := 0; true; i = (i + 1) % len(denoms) {
		a := &denoms[i]
		gaussianBrackets(h, hprev, a)
		gaussianBrackets(k, kprev, a)

		r.SetFrac(h, k)
		fmt.Println(r)
	}
}

// FIXME: should support an initial block of non-periodic denominators (will need flags)
// convergentsCmd represents the convergents command
var convergentsCmd = &cobra.Command{
	Use:   "convergents N N [N ...]",
	Short: "Compute convergents of a periodic continued fraction",
	Long:  `Compute convergents of a periodic continued fraction.`,
	Args:  cobra.MinimumNArgs(2),
	Run:   convergents,
}

func init() {
	rootCmd.AddCommand(convergentsCmd)

	// Here you will define your flags and configuration settings.

	// Cobra supports Persistent Flags which will work for this command
	// and all subcommands, e.g.:
	// convergentsCmd.PersistentFlags().String("foo", "", "A help for foo")

	// Cobra supports local flags which will only run when this command
	// is called directly, e.g.:
	// convergentsCmd.Flags().BoolP("toggle", "t", false, "Help message for toggle")
}