115 lines
2.6 KiB
Go
115 lines
2.6 KiB
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"
|
||
|
|
"log"
|
||
|
|
"math/big"
|
||
|
|
|
||
|
|
"github.com/spf13/cobra"
|
||
|
|
)
|
||
|
|
|
||
|
|
var remainders []string
|
||
|
|
var moduli []string
|
||
|
|
|
||
|
|
func solveTwo(a1, n1, a2, n2 *big.Int) (*big.Int, *big.Int) {
|
||
|
|
m1 := new(big.Int)
|
||
|
|
m2 := new(big.Int)
|
||
|
|
tmp := new(big.Int)
|
||
|
|
tmp.GCD(m1, m2, n1, n2)
|
||
|
|
|
||
|
|
x := new(big.Int).Set(a1)
|
||
|
|
x.Mul(x, m2)
|
||
|
|
x.Mul(x, n2)
|
||
|
|
|
||
|
|
tmp.Set(a2)
|
||
|
|
tmp.Mul(tmp, m1)
|
||
|
|
tmp.Mul(tmp, n1)
|
||
|
|
|
||
|
|
x.Add(x, tmp)
|
||
|
|
|
||
|
|
N := new(big.Int).Set(n1)
|
||
|
|
N.Mul(N, n2)
|
||
|
|
|
||
|
|
x.Mod(x, N)
|
||
|
|
|
||
|
|
return x, N
|
||
|
|
}
|
||
|
|
|
||
|
|
func crt(cmd *cobra.Command, args []string) {
|
||
|
|
if len(remainders) != len(moduli) {
|
||
|
|
log.Fatal("number of remainders and moduli do not match")
|
||
|
|
}
|
||
|
|
|
||
|
|
// TODO: check for pairwise comprime
|
||
|
|
|
||
|
|
n1 := new(big.Int)
|
||
|
|
a1 := new(big.Int)
|
||
|
|
for i := range remainders {
|
||
|
|
n2, ok := new(big.Int).SetString(moduli[i], 10)
|
||
|
|
if !ok {
|
||
|
|
log.Fatal("invalid input " + moduli[i])
|
||
|
|
}
|
||
|
|
|
||
|
|
a2, ok := new(big.Int).SetString(remainders[i], 10)
|
||
|
|
if !ok {
|
||
|
|
log.Fatal("invalid input " + remainders[i])
|
||
|
|
}
|
||
|
|
|
||
|
|
if i != 0 {
|
||
|
|
x, N := solveTwo(a1, n1, a2, n2)
|
||
|
|
n1.Set(N)
|
||
|
|
a1.Set(x)
|
||
|
|
} else {
|
||
|
|
a1.Set(a2)
|
||
|
|
n1.Set(n2)
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
fmt.Println(a1)
|
||
|
|
fmt.Println(n1)
|
||
|
|
}
|
||
|
|
|
||
|
|
// 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",
|
||
|
|
Long: `Solve a system of linear congruences.`,
|
||
|
|
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")
|
||
|
|
}
|