mathtools/cmd/crt.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 remainders []string
var moduli []string

func crt(cmd *cobra.Command, args []string) {
	if len(remainders) != len(moduli) {
		cobra.CheckErr("number of remainders and moduli do not match")
	}

	ns := make([]*big.Int, len(moduli))
	rs := make([]*big.Int, len(remainders))
	for i := range moduli {
		var ok bool
		ns[i], ok = new(big.Int).SetString(moduli[i], 10)
		if !ok {
			cobra.CheckErr("invalid input " + moduli[i])
		}

		rs[i], ok = new(big.Int).SetString(remainders[i], 10)
		if !ok {
			cobra.CheckErr("invalid input " + remainders[i])
		}
	}

	// TODO: support non-pairwise coprime moduli
	if !lib.ArePairwiseCoprime(ns) {
		err := fmt.Errorf("moduli %v are not pairwise coprime", moduli)
		cobra.CheckErr(err)
	}

	x, N := lib.CRTSolution(rs, ns)

	fmt.Println(x)
	fmt.Println(N)
}

// crtCmd represents the crt command
var crtCmd = &cobra.Command{
	Use:   "crt -r R R [R ...] -m M M [M ...]",
	Short: "Solve a system of linear congruences with the Chinese remainder theorem",
	Long: `Solve a system of linear congruences by applying the Chinese remainder theorem.

To use, provide the remainder R of each congruence, along with the corresponding modulus M for each congruence. For instance,

mathtools crt -r 2 3 2 -m 3 5 7

will solve the system of congruences
x = 2 (mod 3)
x = 3 (mod 5)
x = 2 (mod 7)
`,
	Run: crt,
}

func init() {
	rootCmd.AddCommand(crtCmd)

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

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

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

	crtCmd.Flags().StringSliceVarP(&remainders, "remainders", "r", make([]string, 0), "remainders of congruences")
	crtCmd.MarkFlagRequired("remainders")

	crtCmd.Flags().StringSliceVarP(&moduli, "moduli", "m", make([]string, 0), "moduli of congruences")
	crtCmd.MarkFlagRequired("moduli")
}