messyscript/mathCheat.py

#出现问题conda activate base

import sys

#等差乘等比——错位相减法
def cuoWeiXiangJian():
   from fractions import Fraction
   print("错位相减法求前n项和，若通项为a_n=(a*n+b)*q^(n+m)，请填写")
   a=Fraction(input("a="))
   b=Fraction(input("b="))
   q=Fraction(input("q="))
   m=int(input("m="))

   #将指数统一为n-1
   a=a*pow(q,(m+1))
   b=b*pow(q,(m+1))

   #计算A,B
   A=a/(q-1)
   B=(b-A)/(q-1)
   print("结果为S_n=(An+B)*q^n-B")
   print("A=",A, "B=",B)

#二项分布
def binomial():
    from fractions import Fraction
    from math import comb
    n=int(input("n="))
    p=Fraction(input("p="))
    print("EX=",n*p)
    print("DX=",n*p*(1-p))
    for i in range(n+1):
        print("P(X=",i,")=",comb(n,i)*pow(p,i)*pow(1-p,n-i))


#超几何分布
def hypergeometric():   
    from fractions import Fraction
    from math import comb
    N=int(input("总数N=")) #总数
    M=int(input("满足条件数M="))  #次品数
    n=int(input("抽取数n="))  #抽取数
    m=max(0,n-N+M)
    r=min(n,M)
    print("EX=",Fraction(n*M,N))
    print("DX=",Fraction(n*M*(N-M)*(N-n),N*N*(N-1)))
    for k in range(m,r+1):
        print("P(X=",k,")=",Fraction(comb(M,k)*comb(N-M,n-k),comb(N,n)))

#卡方计算
def k2():
    from fractions import Fraction
    print("请输入核心2✖️2单元的abcd")
    a=int(input("a="))
    b=int(input("b="))
    c=int(input("c="))
    d=int(input("d="))
    n=a+b+c+d
    K2=Fraction(n*((a*d-b*c)**2),(a+b)*(c+d)*(a+c)*(b+d))
    print("K^2=",K2)
    print("近似值为",float(K2))

#一元线性回归模型
def regression():
    from math import sqrt
    x = input("请输入x（用空格分割）：").split()
    x = list(map(float,x))
    y = input("请输入y（用空格分割）：").split()
    y = list(map(float,y))
    sx=0
    sy=0
    sx2=0
    sy2=0
    sxy=0
    if len(x)==len(y):
        n = len(x)
        for i in range(n):
            sx += x[i]
            sy += y[i]
            sx2 += x[i]**2
            sy2 += y[i]**2
            sxy += x[i]*y[i]
        xBar = sx/n
        yBar = sy/n
        sigmaX = sx2 - n*xBar*xBar
        sigmaY = sy2 - n*yBar*yBar
        sigmaXY = sxy - n*xBar*yBar
        r = sigmaXY/sqrt(sigmaX*sigmaY)
        b = sigmaXY/sigmaX
        a = yBar-b*xBar

        se2=0
        for i in range(n):
            se2 += (y[i]-b*x[i]-a)**2
        R2 = 1 - se2/sigmaY
        print("x_bar=",xBar)
        print("y_bar=",yBar)
        print("sigma (x-x)^2 =",sigmaX)
        print("sigma (y-y)^2 =",sigmaY)
        print("sigma (x-x)(y-y) =",sigmaXY)
        print("相关系数r=",r)
        print("b=",b)
        print("a=",a)
        print("残差平方和为",se2)
        print("决定系数R^2=",R2)

    else:
        print("x,y长度不一致")


#混合方差
def mixS2():
    from fractions import Fraction
    x = input("请输入各层样本量（用空格分割）：").split()
    x = list(map(Fraction,x))
    y = input("请输入各层对应的均值（用空格分割）：").split()
    y = list(map(Fraction,y))
    z = input("请输入各层对应的方差（用空格分割）：").split()
    z = list(map(Fraction,z))
    if ((len(x)==len(y))&(len(x)==len(z))):
        m = 0
        j = 0
        f = 0
        for i in range(len(x)):
            m += x[i]
            j += x[i]*y[i]
        j = j/m
        for i in range(len(x)):
            f += x[i]*(z[i]+(y[i]-j)**2)/m
        print("总均值为",j)
        print("总方差为",f)

    else:
        print("输入有误！")

#直方图
def histogram():
    from fractions import Fraction
    from math import floor
    a = Fraction(input("请输入直方图左端点："))
    d = Fraction(input("请输入直方图组距："))
    f = input("请输入各组频率（用空格分割）：").split()
    f = list(map(Fraction,f))
    p = input("请输入需求解的百分位数，无需求解请留空：")
    x = d/2
    s = 0
    n = len(f)
    sump = 0
    for pi in f:
        sump += pi
    if sump == 1:
        for i in range(n):
            x += (a+i*d)*f[i]
        for i in range(n):
            s += (a+i*d+d/2-x)**2*f[i]
        print("均值：",Fraction(x),"，近似值：",float(x))
        print("方差：",Fraction(s),"，近似值：",float(s))
        m = 0
        if p!="":
            p = Fraction(p)
            for i in range(n):
                if m >= p:
                    q = Fraction(a+i*d-(m-p)/f[i-1]*d)
                    print(p,"百分位数为",floor(q),"+",q-floor(q))
                    break
                else:
                    m += f[i]
        m = 0
        for i in range(n):
            if m >= 0.5:
                q = Fraction(a+i*d-(m-0.5)/f[i-1]*d)
                print("中位数为",floor(q),"+",q-floor(q))
                break
            else:
                m += f[i]
    else:
        print("频率之和不为1")

#二阶行列式
def det2(a,b,c,d):
    return a*d-b*c

#二元一次方程组
def tle(a1,b1,c1,a2,b2,c2):
    return((det2(c1,b1,c2,b2)/det2(a1,b1,a2,b2),det2(a1,c1,a2,c2)/det2(a1,b1,a2,b2)))

#点关于直线对称
def dot_line():
    from fractions import Fraction
    a=Fraction(input("请输入点的横坐标："))
    b=Fraction(input("请输入点的纵坐标："))
    A=Fraction(input("请输入直线一般方程x的系数："))
    B=Fraction(input("请输入直线一般方程y的系数："))
    C=Fraction(input("请输入直线一般方程的常数项："))
    m,n = tle(A,B,(-1)*(A*a+B*b+2*C),B,-A,a*B-A*b)
    print("对称点为:(",m,",",n,")")

#直线关于点对称
def line_dot():
    from fractions import Fraction 
    A=Fraction(input("请输入直线一般方程x的系数："))
    B=Fraction(input("请输入直线一般方程y的系数："))
    C=Fraction(input("请输入直线一般方程的常数项："))
    a=Fraction(input("请输入点的横坐标："))
    b=Fraction(input("请输入点的纵坐标："))
    m=-2*A*a-2*B*b-C
    print("对称直线三个系数分别为：",A,B,m)

#直线关于直线对称
def line_line():
    from fractions import Fraction 
    P=Fraction(input("请输入直线一般方程x的系数："))
    Q=Fraction(input("请输入直线一般方程y的系数："))
    R=Fraction(input("请输入直线一般方程的常数项："))
    A=Fraction(input("请输入对称轴一般方程x的系数："))
    B=Fraction(input("请输入对称轴一般方程y的系数："))
    C=Fraction(input("请输入对称轴一般方程的常数项："))
    k=2*(P*A+Q*B)/(A*A+B*B)
    print("对称直线三个系数分别为：",P-A*k,Q-B*k,R-C*k)

#三个点求圆的方程
def circle():
    from fractions import Fraction
    x1=Fraction(input("请输入第一个点的横坐标："))
    y1=Fraction(input("请输入第一个点的纵坐标："))
    x2=Fraction(input("请输入第二个点的横坐标："))
    y2=Fraction(input("请输入第二个点的纵坐标："))
    x3=Fraction(input("请输入第三个点的横坐标："))
    y3=Fraction(input("请输入第三个点的纵坐标："))
    z1=x1*x1+y1*y1
    z2=x2*x2+y2*y2
    z3=x3*x3+y3*y3
    D,E = tle(x1-x2,y1-y2,z2-z1,x1-x3,y1-y3,z3-z1)
    F = -z1-D*x1-E*y1
    r2 = D*D+E*E-4*F
    print("D=",D,"E=",E,"F=",F)
    print("圆心：（",-D/2,",",-E/2,")"," 半径的平方：",r2)

def main():
    if len(sys.argv) < 2:
        print("Usage: python mathCheat.py <tool_name>")
        sys.exit(1)

    tool_name = sys.argv[1]

    if tool_name in toolbox:
      try:
         toolbox[tool_name]()
      except:
         print("某些地方出错了！")
    else:
        print("工具名无效！")
        sys.exit(1)

if __name__ == "__main__":
    toolbox = {"错位相减":cuoWeiXiangJian,"错位相减法":cuoWeiXiangJian, "等差乘等比":cuoWeiXiangJian,
"二项分布":binomial,"超几何分布":hypergeometric,"K2":k2,"卡方":k2,"独立性检验":k2,
"回归分析":regression,"相关系数":regression,"最小二乘法":regression,"决定系数":regression,"残差平方和":regression,"线性回归":regression,
"混合方差":mixS2,"混合均值":mixS2,"直方图":histogram,
"点关于线对称":dot_line, "点关于直线对称":dot_line,  "直线关于点对称":line_dot, "线关于点对称":line_dot,  "直线关于直线对称":line_line, "线关于线对称":line_line,
"三个点求圆的方程":circle,"已知三点求圆的方程":circle,"求圆的方程":circle,           
               }
    main()