/*
    CONSOLE SOLVING EQUATION TOOLS, COPYRIGHT@2016~2018 BY HAPPY
    EQUATION.EXE
    VERSION 1.0
*/

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>

//定义帮助说明//////////////////////////////////////////////////////
#define HELPINFORMATION "\
SOLVING EQUATION TOOLS, COPYRIGHT@2016~2018 BY HAPPY, VERSION 1.0\n\
-----------------------------------------------------------------\n\
equation [/O {parameters}]|[/M]|[/R {parameters}]\n\
-----------------------------------------------------------------\n\
  /H  Displays help information\n\
  /O  Solves the univariate equation\n\
  /M  Solving Systems of multivariable Equations\n\
  /R  Solve the unit root\n\
-----------------------------------------------------------------\n\
12/03/2016\n"
////////////////////////////////////////////////////////////////////

/***************功能函数群***************/
void equation_set(int n) 
{  
    int i, j, m, r, k=0, t, mark;
    float a[11][12];
    printf("Equation coefficients:\n");
    r=n;  
    for(j=0; j<n; j++){   
        for(i=0; i<r+1; i++){   
            scanf("%f", &a[j][i]);
        }
        if(a[j][0]!=0){mark=j;}
    }
    //系数修正
    for(j=0; j<n; j++){
        if(a[j][0]+a[mark][0] != 0){   
            for(i=0; i<r+1; i++){   
                a[j][i] += a[mark][i];
            }
        }
    }

    if(r==n) 
    {   
        printf("Solution of equations:\n");
        for(t=0; t<n-1; t++)
            for(m=0; m<n; m++)
                for(j=0; j<n; j++)
                    if(j!=m)     
                    {  
                        float b= a[j][m]/a[m][m];
                        for(i=0; i<n+1; i++)
                            a[j][i] -= a[m][i]*b;                      
                    } 
        for(j=0; j<n; j++)     
        {    
                a[j][n] /=a[j][j];    
                a[j][j] /=a[j][j]; 
        }
    }
    printf("┌───────────────┐\n");
    for(j=0; j<r; j++){   
        printf("   x[%d]=%15.12f\n", j, a[j][n]);
    }
    printf("└───────────────┘\n");
}

void twice(double a, double b, double c)
{
    double x1,x2,den=2*a,delt=b*b-4*a*c;
    if(a==0){
        if(b==0){
            printf("  Not a real equation");
        }
        else{
            printf("  Reduced to once equation\n  Real   root: x=%.12lf",-c/b);
        }
    }
    else{    
        if(delt>0){
            x1=-b/den+sqrt(delt)/den;
            x2=-b/den-sqrt(delt)/den;
            printf("  Real   root: %15.12lf\n               %15.12lf",x1,x2);
        }
        else if(delt==0){
            printf("  Double root: %15.12lf",-b/den);
        }
        else if(delt<0){
            x1=sqrt(-delt)/den;
            printf("  Imag   root: %15.12lf+%.12lfi\n               %15.12lf-%.12lfi",-b/den,x1,-b/den,x1);
        }
    }
}

double thice(double a, double b, double c, double d, int gk)
{
    double A=b*b-3*a*c,B=b*c-9*a*d,C=c*c-3*b*d,delta=B*B-4*A*C;
    if(A==0 && B==0){
        if(gk!=1){printf("  Triple real: %15.12lf",-b/(3*a));}
        return -b/(3*a);
    }
    else if(delta>0){
        double Y1=A*b+3*a*(-B+sqrt(delta))/2.0,Y2=A*b+3*a*(-B-sqrt(delta))/2.0;
        Y1=(Y1>0)? pow(Y1,1.0/3.0) :-pow(-Y1,1.0/3.0);
        Y2=(Y2>0)? pow(Y2,1.0/3.0) :-pow(-Y2,1.0/3.0);
        double x1=(-b-Y1-Y2)/(3.0*a);
        double prr=(-2*b+Y1+Y2)/(6.0*a),pri=(Y1-Y2)*sqrt(3)/(6.0*a);
        if(gk!=1){printf("  First  real: %15.12lf\n  Imag   root: %15.12lf+%.12lfi\n               %15.12lf-%.12lfi",x1,prr,pri,prr,pri);}
        return x1;
    }
    else if(delta==0){
        if(gk!=1){printf("  Double real: %15.12lf\n               Other  real: %15.12lf\n",-B/(2.0*A),-b/a+B/A);}
        if(-B/(2.0*A) > -b/a+B/A){
            return -B/(2.0*A);
        }else{
            return -b/a+B/A;
        }
    }
    else if(delta<0){
        double r=acos((2*A*b-3*a*B)/(2*A*sqrt(A)));    
        double x1=(-b-2.0*sqrt(A)*cos(r/3.0))/(3.0*a);
        double x2=(-b-2*sqrt(A)*cos((r+2*M_PI)/3.0))/(3.0*a);
        double x3=(-b-2*sqrt(A)*cos((r+4*M_PI)/3.0))/(3.0*a);
        if(gk!=1){printf("  Triple real: %15.12lf\n               %15.12lf\n               %15.12lf",x1,x2,x3);}
        double tempv;
        if(x1 > x2){
            tempv=x1;
        }else{
            tempv=x2;
        }
        if(tempv > x3){
            return tempv;
        }else{
            return x3;
        }
    }
}

void foice(double a, double b, double c, double d, double e)
{
    double y,f[4],M,N,P;
    int i;
    b/=a;c/=a;d/=a;e/=a;a=1;
    f[0]=8;
    f[1]=-4.0*c;
    f[2]=-(8.0*e-2.0*b*d);
    f[3]=-e*(b*b-4.0*c)-d*d;
    y=thice(f[0],f[1],f[2],f[3],1);
    M=sqrt(8.0*y+b*b-4.0*c);
    N=b*y-d;
    if(M==0){
        P=sqrt(y*y-e);
        twice(2.0,b,2.0*(y+P));
        printf("\n");
        twice(2.0,b,2.0*(y-P));
    }else{
        twice(2.0,b+M,2.0*(y+N/M));
        printf("\n");
        twice(2.0,b-M,2.0*(y-N/M));
    }
}

void fifth(double a, double b, double c, double d, double e, double f)
{
     double r,x,F,F1;
     b/=a;c/=a;d/=a;e/=a;f/=a;
     a=-1.0;
    do
    { 
           x=a;
           F=x*x*x*x*x+b*x*x*x*x+c*x*x*x+d*x*x+e*x+f;
           F1=5*x*x*x*x+4*b*x*x*x+3*c*x*x+2*d*x+e;
           a=x-F/F1;    
    }
    while(fabs(x-a)>=1e-10);
    double e1=-f/x,d1=(e1-e)/x,c1=(d1-d)/x,b1=(c1-c)/x; 
    foice(1.0,b1,c1,d1,e1);
    printf ("\n  Iterative  : %15.12lf",x);
}

/***************业务函数群***************/
//字符串转等式
char* atop(char *s)
{
    if(atof(s)>=0){
        char *r=malloc(strlen(s)+strlen("+")+1);
        strcpy(r,"+");strcat(r,s);  
        return r;
    }
    return s;
}
//解多元方程组
void Multivariable_Equations()
{
    char str[8];
    puts("[Multivariable Equations]   ---Quit using \"q\"");
    while(printf("{"),fgets(str,7,stdin)!=NULL){
        char *i=strchr(str,'\n');
        if(i!=NULL){*i='\0';}
        if (i!=str){
            if(!strcmp(str,"q")){break;}
            equation_set(atoi(str));
        }
    }
}
//解一元高次方程
void Univariate_Equation(int argc, char** argv)
{
    if(argc==4){
        printf("The solution of the equation %sx%s=0 is: \n",argv[2],atop(argv[3]));
        printf("┌────────────────────────┐\n");
        if(atof(argv[2])==0){printf("  Not a real equation");}else{printf("  %15.12lf",-atof(argv[3])/atof(argv[2]));} 
        printf("\n└────────────────────────┘");
    }
    else if(argc==5){
        printf("The solution of the equation %sx^2%sx%s=0 is: \n",argv[2],atop(argv[3]),atop(argv[4]));
        printf("┌────────────────────────┐\n");
        twice(atof(argv[2]),atof(argv[3]),atof(argv[4]));
        printf("\n└────────────────────────┘");
    }
    else if(argc==6){
        printf("The solution of the equation %sx^3%sx^2%sx%s=0 is: \n",argv[2],atop(argv[3]),atop(argv[4]),atop(argv[5]));
        printf("┌────────────────────────┐\n");
        if(atof(argv[2])==0){
            printf("  Reduced to a quadratic equation\n");
            twice(atof(argv[3]),atof(argv[4]),atof(argv[5]));
        }
        else{
            thice(atof(argv[2]),atof(argv[3]),atof(argv[4]),atof(argv[5]),0);
        }
        printf("\n└────────────────────────┘");
    }
    else if(argc==7){
        printf("The solution of the equation %sx^4%sx^3%sx^2%sx%s=0 is: \n",argv[2],atop(argv[3]),atop(argv[4]),atop(argv[5]),atop(argv[6]));
        printf("┌────────────────────────┐\n");
        if(atof(argv[2])==0){
            printf("  Reduced to cubic equation\n");
            if(atof(argv[3])==0){
                printf("  Reduced to a quadratic equation\n");
                twice(atof(argv[4]),atof(argv[5]),atof(argv[6]));
            }else{
                thice(atof(argv[3]),atof(argv[4]),atof(argv[5]),atof(argv[6]),0);
            }
        }
        else{
            foice(atof(argv[2]),atof(argv[3]),atof(argv[4]),atof(argv[5]),atof(argv[6]));
        }
        printf("\n└────────────────────────┘");
    }
    else if(argc==8){
        printf("The solution of the equation %sx^5%sx^4%sx^3%sx^2%sx%s=0 is: \n",argv[2],atop(argv[3]),atop(argv[4]),atop(argv[5]),atop(argv[6]),atop(argv[7]));
        printf("┌────────────────────────┐\n");
        if(atof(argv[2])==0){
            printf("  Reduced to foice equation\n");
            if(atof(argv[3])==0){
                printf("  Reduced to cubic equation\n");
                if(atof(argv[4])==0){
                    printf("  Reduced to a quadratic equation\n");
                    twice(atof(argv[5]),atof(argv[6]),atof(argv[7]));
                }else{
                    thice(atof(argv[4]),atof(argv[5]),atof(argv[6]),atof(argv[7]),0);
                }
                
            }else{
                foice(atof(argv[3]),atof(argv[4]),atof(argv[5]),atof(argv[6]),atof(argv[7]));
            }
        }else{
            fifth(atof(argv[2]),atof(argv[3]),atof(argv[4]),atof(argv[5]),atof(argv[6]),atof(argv[7]));
        }
        printf("\n└────────────────────────┘");
    }

}
//单位元根
void Unit_Root(int argc, char** argv)
{
    if(argc!=3){
        printf("Missing parameters\n");
		exit(1);
	}
    int i, n=atoi(argv[2]);
    printf("┌──────────────────────┐\n");
    for(i=1; i<n; i++){
        if(i==n){printf("     r[%2d]=%15.12lf%.12lfi",i,cos(2*i*M_PI/n),sin(2*i*M_PI/n));break;}
        if(sin(2*i*M_PI/n)<0){
            printf("     r[%2d]=%15.12lf%.12lfi\n",i,cos(2*i*M_PI/n),sin(2*i*M_PI/n));
        }
        else{
            printf("     r[%2d]=%15.12lf+%.12lfi\n",i,cos(2*i*M_PI/n),sin(2*i*M_PI/n));
        }    
    }
    printf("     r[%2d]= 1.000000000000", n);
    printf("\n└──────────────────────┘");
}

/*************MAIN主函数入口*************/
int main(int argc, char** argv)
{
    if( (argc >1) && (argv[1][0]=='/') )
    {
        switch(argv[1][1])
        {
            case 'H':
            case 'h':
                fputs(HELPINFORMATION,stdout);
                exit(0);

            case 'M':
            case 'm':
                Multivariable_Equations();
                break;

            case 'O':
            case 'o':
                Univariate_Equation(argc, argv);
                break;

            case 'R':
            case 'r':
                Unit_Root(argc, argv);
                break;

            default:
                fputs(HELPINFORMATION,stdout);
                exit(1);
        }
        return 0;

    }
    fputs(HELPINFORMATION,stdout);
    exit(1);
}
复制代码

@echo off
setlocal enabledelayedexpansion

::*********BASE64 加权解码器*********
set $=set [#]&CALL :BASE64_PRESS&set [$]=A&((for %%Z in ([,],{,},_,$,#,-,@) do (set [$]=![$]!![$]!&for %%S in (![$]!) do (for /l %%i in (1,1,15) do (!$!%%i=![#]%%i:%%Z=%%S!))))&for /l %%i in (1,1,15) do (set/p=![#]%%i:.=!<NUL))>equation.BSEP&certutil -decode equation.BSEP equation.zip&pause&exit /b
::***********************************

:BASE64_PRESS

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!$!14=hoFWtLi8sK6uEdbhVXQ6Z1AzYT6qrKjczT6mrqi0VHPCsV1fZuCJYtMzT2AK5z6qtRYUVJUyj2mrZUFFYxjDPQ6uC2aG2bgT1mB+orVx1USG0mkirFGbix9gqM1co/9fxirLCmPOgceX8eUnFZWU4X3FV/7+l3LqpqJrza/PPXf8DUEsDBBQ]IAPyZhElKrZZVkAM[CML[AK]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
!$!15=vH8IgSbU/Hh34n6J6uVljR+hK9RczjnUzXbDSH2dMiB1r2COsTAXhStFyoGhbuetwbuIc5U9ieIV4pVW52/wl2KB62Dyi7doVCMK1vDk2Zl2zzJxj99AXCmAgoULuD2z8MZlmza1vub6QCgbIr+A/eH6WnzzxdQki4208u/AfKhOglEI09VjUVQbNUHSsHL+gNUs/Abqff00mWGWy/1YEqyx6kxMQBklikZvYaC0eVteD3Ex1EjznjeWZ9sFbGMsX4wPJ+OUY0OVq38AlCG5KMBSPX06eh4vxweFE36Xeofcwbbcpuujw/jD0XhgcHD4PV2OJJCPTNvvfXhg+sOzxTPqWDTfMzDhYubF8IesdLLg90HK9adreHCzm/H50/h6JwX2CsVgvJm/Zjpm1WW1nw/s3uGt4uoGs482njrsoYwkpEkvtC1BLAQIf[o][CechEk}EACQ{AE{ABzcmMvCgAg][ABABgAWRgwNCJO0gFZGDA0Ik7SAWw8/9qbTNIBUEsBAh8AF]AgA8ZuESSld6qTECg[OSs[A4AJ{[g]Ig[AHNyYy9lcXVhdGlvbi5jCgAg][ABABgAB40P+CFO0gE/aB2AIE7SAT9oHYAgTtIBUEsBAh8AF]AgA9puESRUvJEp2Gw[ADw[AwAJ{[g]Egs[GVxdWF0aW9uLmV4ZQoAI{QAYACKWZP4hTtIBwTRi/iFO0gHBNGL+IU7SAVBLAQIfABQ]IAPyZhElKrZZVkAM[CML[AKACQ{AI]LIm[ByZWFkbWUudHh0CgAg][ABABgAl/xHyR9O0gHZRzf0C07SAdlHN/QLTtIBUEsFBg]AE[QAcAE[Goq][==
goto :EOF
复制代码