高斯消元法求解线性方程组（分数精确表示）

最新推荐文章于 2024-06-15 12:58:49 发布

一碗风

最新推荐文章于 2024-06-15 12:58:49 发布

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分类专栏： math Algorithm

本文链接：https://blog.youkuaiyun.com/hffhjh111/article/details/80650750

原理可以参考

https://zh.wikipedia.org/wiki/%E9%AB%98%E6%96%AF%E6%B6%88%E5%8E%BB%E6%B3%95

这里给出使用分数表示计算过程的高斯消元法写法

github地址：https://github.com/YIWANFENG/Algorithm-github

#!/usr/bin/env python3.5
# -*-coding: utf-8 -*-
"""
Created on 2018-6-9
@author: YWF

高斯消元法求解线性方程，
数字采用分数精确表示，无近似

"""
import numpy as np

def gcd(a,b):
    if a < b:
        c = a
        a = b
        b = c
    while a % b != 0:
        c = a % b
        a = b
        b = c
    return b

def lcm(a,b):
    return a * b / gcd(a,b)


class Fractional:

    def __init__(self,num,den):
        self.numerator = num
        if(den == 0):
            print("Error den")
        self.denominator = den
        pass
    def Simplify(self):
        if self.numerator == 0:
            return Fractional(0,1)
        gcd_ = gcd(self.denominator,self.numerator)
        if gcd_ != 1:
            self.denominator /= gcd_
            self.numerator /= gcd_
        return self
    def __sub__(self, other):
        lcm_ = lcm(self.denominator,other.denominator)
        self.numerator *= lcm_ / self.denominator
        num = self.numerator - other.numerator * lcm_ / other.denominator
        return Fractional(num,lcm_).Simplify()
    def __add__(self, other):
        lcm_ =