Mathematics Function Examples

def round6(value)=round(value*10^6)/10^6;
def max(a,b){
  if(a>=b){
    return a;
  }
  else{
    return b;
  }
}
def min(a,b){
  if(a<=b){
    return a;
  }
  else{
    return b;
  }
}

def facorial(n)=n*factorial(n−1);
factorial(0)=1;


def fibonacci(n)=fibonacci(n−1)+fibonacci(n−2);
fibonacci(1)=1;
fibonacci(2)=1;

def isPrime(n){
  if(n<=1){
    return false;
  }
  var i=2;
  while(i*i<=n){
    if(n%i==0){
      return false;
    }
    i=i+1;
  }
  return true;
}

def nthPrime(n){
  var count=0;
  var num=2;
  while(count<n){
    if(isPrime(num)){
      count=count+1;
    }
    if(count==n){
      return num;
    }
    num=num+1;
  }
  return num−1;
}

def det2(a,b,c,d){
  return a*d−b*c;
}

def solveX2(a,b,c,d,m,n){
  var det=det2(a,b,c,d);
  if(det==0){
    return -515151;
  }
  var detX=det2(m,b,n,d);
  return detX/det;
}

def solveY2(a,b,c,d,m,n){
  var det=det2(a,b,c,d);
  if(det==0){
    return -515151;
  }
  var detY=det2(a,m,c,n);
  return detY/det;
}

def solve2(a,b,m,c,d,n,xy){
  if(xy==1){
    return solveX2(a,b,c,d,m,n);
  }
  else{
    return solveY2(a,b,c,d,m,n);
  }
}


def det3(a1,b1,c1,a2,b2,c2,a3,b3,c3)=a1*(b2*c3−c2*b3)−b1*(a2*c3−c2*a3)+c1*(a2*b3−b2*a3);

def solveX3(a1,b1,c1,d1,a2,b2,c2,d2,a3,b3,c3,d3){
  var det=det3(a1,b1,c1,a2,b2,c2,a3,b3,c3);
  if(det==0){
    return -515151;
  }
  var detX=det3(d1,b1,c1,d2,b2,c2,d3,b3,c3);
  return detX/det;
}

def solveY3(a1,b1,c1,d1,a2,b2,c2,d2,a3,b3,c3,d3){
  var det=det3(a1,b1,c1,a2,b2,c2,a3,b3,c3);
  if(det==0){
    return -515151;
  }
  var detY=det3(a1,d1,c1,a2,d2,c2,a3,d3,c3);
  return detY/det;
}

def solveZ3(a1,b1,c1,d1,a2,b2,c2,d2,a3,b3,c3,d3){
  var det=det3(a1,b1,c1,a2,b2,c2,a3,b3,c3);
  if(det==0){
    return -515151;
  }
  var detZ=det3(a1,b1,d1,a2,b2,d2,a3,b3,d3);
  return detZ/det;
}

def solveFor3(a1,b1,c1,d1,a2,b2,c2,d2,a3,b3,c3,d3,xyz){
  if(xyz==1){
    return solveX3(a1,b1,c1,d1,a2,b2,c2,d2,a3,b3,c3,d3);
  }
  if(xyz==2){
    return solveY3(a1,b1,c1,d1,a2,b2,c2,d2,a3,b3,c3,d3);
  }
  return solveZ3(a1,b1,c1,d1,a2,b2,c2,d2,a3,b3,c3,d3);
}

def RiemannSum(a,b,c,start,end,n){
  var Sn=0;
  var delta=(end−start)/n;
  var k=1;
  while(k<=n){
    var x=start+delta*(k−0.5);
    var h=a*x*x+b*x+c;
    var s=delta*abs(h);
    Sn=Sn+s;
    k=k+1;
  }
  return Sn;
}

def 이차방정식실근(a,b,c,선택,실허)=iSolveQuadraticAI(a,b,c,선택,실허);

def 이차방정식복소해(a,b,c,선택,실허)=iSolveQuadraticAI(a,b,c,선택,실허);

def 이원연립해(a,b,m,c,d,n,xy)=solve2(a,b,m,c,d,n,xy);


def 삼원연립해(a1,b1,c1,d1,a2,b2,c2,d2,a3,b3,c3,d3,xyz)=solveFor3(a1,b1,c1,d1,a2,b2,c2,d2,a3,b3,c3,d3,xyz);


def roundToPrecision(value){
  var epsilon=0.0000001;
  if(abs(value−round(value))<epsilon){
    return round(value);
  }
  return value;
}




def solveQuadratic(a,b,c,xy){
  var D=b*b−4*a*c;
  if(D<0){
    return -515151.515151;
  }
  var sqrtD=sqrt(D);
  if(xy==1){
    return (-b+sqrtD)/(2*a);
  }
  return (-b−sqrtD)/(2*a);
}

def GCD(a,b){
  if(b==0){
    return a;
  }
  return GCD(b,a%b);
}

def LCM(a,b){
  if(a==0||b==0){
    return 0;
  }
  return (a*b)/GCD(a,b);
}


def solveAxPlusBEqualsC(a,b,c)=(c−b)/a;


def solveABequalsCD(a,b,c,d){
  var nom=d−b;
  var denom=(a−b);
  return nom/denom;
}


def iSolveQuadraticAI(a,b,c,x12,real){
  if(a==0){
    return -515151;
  }
  var D=b*b−4*a*c;
  var sqrtD=sqrt(abs(D));
  var realPart=-b/(2*a);
  var imaginaryPart=sqrtD/(2*a);
  if(D<0){
    if(real==1){
      return realPart;
    }
    if(x12==1){
      return imaginaryPart;
    }
    return -imaginaryPart;
  }
  if(real!=1){
    return 0;
  }
  if(x12==1){
    return realPart+sqrtD/(2*a);
  }
  return realPart−sqrtD/(2*a);
}

def cubeEqNew(a,b,c,d,x123){
  var A=b/a;
  var B=c/a;
  var C=d/a;
  var Q=(A^2−3*B)/9;
  var R=(2*A^3−9*A*B+27*C)/54;
  var M=R^2−Q^3;
  if(M<0){
    var angle=R/sqrt(Q^3);
    var theta=acos(angle);
    var x1=-(2*sqrt(Q)*cos(theta/3))−A/3;
    var x2=-(2*sqrt(Q)*cos((theta+2*pi)/3))−A/3;
    var x3=-(2*sqrt(Q)*cos((theta−2*pi)/3))−A/3;
    if(x123==1){
      return round6(x1);
    }
    elseif(x123==2){
      return round6(x2);
    }
    return round6(x3);
  }
  elseif(M>0){
    var sign=R/abs(R);
    var inner=abs(R)+sqrt(M);
    var S=-sign*cbrt(inner);
    var T=Q/S;
    var x1=S+T−A/3;
    var bb=A+x1;
    var cc=-C/x1;
    var D=bb^2−4*cc;
    var x2=-515151.515151;
    var x3=-515151.515151;
    if(D>=0){
      if(x123==1){
        return round6(x1);
      }
      elseif(x123==2){
        return round6((-bb+sqrt(D))/2);
      }
      return round6((-bb−sqrt(D))/2);
    }
    return round6(x1);
  }
  else{
    return -515151.515151;
  }
}

def atan2(y,x){
  if(x>0){
    return atan(y/x);
  }
  elseif(x<0&&y>=0){
    return atan(y/x)+pi;
  }
  elseif(x<0&&y<0){
    return atan(y/x)−pi;
  }
  elseif(x==0&&y>0){
    return pi/2;
  }
  elseif(x==0&&y<0){
    return -pi/2;
  }
  else{
    return -515151.515151;
  }
}

def complexAngleInDegrees(real,imag){
  var angleInRadians=atan2(imag,real);
  if(angleInRadians==-515151.515151){
    return -515151.515151;
  }
  var angleInDegrees=toDegrees(angleInRadians);
  return angleInDegrees;
}


def fibIter(n){
  if(n<=2){
    return 1;
  }
  var r;
  var t;
  var a=1;
  var b=1;
  var i=3;
  while(i<=n){
    r=a+b;
    t=a;
    a=r;
    b=t;
    i=i+1;
  }
  return r;
}

def K(num,n)=num*K(num,n−1)+1;
K(num,0)=1;


def sumOfPowersOf8(n)=8^n+sumOfPowersOf8(n−1);
sumOfPowersOf8(0)=1;


def sumOfPowersOfbase(base,n)=base^n+sumOfPowersOfbase(base,n−1);
sumOfPowersOfbase(밑수,0)=1;

def calculateSlope(x1,y1,x2,y2,x3,y3,x4,y4,x5,y5){
  var n=5;
  var sumX=x1+x2+x3+x4+x5;
  var sumY=y1+y2+y3+y4+y5;
  var sumXY=(x1*y1)+(x2*y2)+(x3*y3)+(x4*y4)+(x5*y5);
  var sumX2=(x1*x1)+(x2*x2)+(x3*x3)+(x4*x4)+(x5*x5);
  var denominator=(n*sumX2)−(sumX*sumX);
  var slope;
  if(denominator==0){
    return 0;
  }
  slope=((n*sumXY)−(sumX*sumY))/denominator;
  return slope;
}

def calculateIntercept(x1,y1,x2,y2,x3,y3,x4,y4,x5,y5){
  var n=5;
  var sumX=x1+x2+x3+x4+x5;
  var sumY=y1+y2+y3+y4+y5;
  var slope=calculateSlope(x1,y1,x2,y2,x3,y3,x4,y4,x5,y5);
  var intercept=(sumY−(slope*sumX))/n;
  return intercept;
}

def 리만합(a,b,c,시작,끝,등분)=RiemannSum(a,b,c,시작,끝,등분);

def 복소좌표각(실수부분,허수부분)=complexAngleInDegrees(실수부분,허수부분);


def 삼차방정식근(a,b,c,d,x123)=cubeEqNew(a,b,c,d,x123);


def sumKK(n){
  var result=0;
  var k=1;
  while(k<=n){
    result=result+1/k^k;
    k=k+1;
  }
  return result;
}

def RiemannSumForXX(start,end,n){
  var Sn=0;
  var delta=(end−start)/n;
  var k=1;
  while(k<=n){
    var x=start+delta*(k−0.5);
    var h=1/x^x;
    var s=delta*h;
    Sn=Sn+s;
    k=k+1;
  }
  return Sn;
}


def roundNearInteger(x){
  if(abs(x−round(x))<=0.0000000001){
    return round(x);
  }
  return x;
}

def iSolveCubicAI(a1,b1,c1,d1,x123,real1,x0){
  if(a1==0){
    return -515151;
  }
  var x1=x0;
  var tol1=0.000001;
  var maxIter1=100;
  var iter1=0;
  while(iter1<maxIter1){
    var f1=a1*x1*x1*x1+b1*x1*x1+c1*x1+d1;
    var fPrime1=3*a1*x1*x1+2*b1*x1+c1;
    if(abs(fPrime1)<tol1){
      return -515151;
    }
    var xNew1=x1−f1/fPrime1;
    if(abs(xNew1−x1)<tol1){
      x1=xNew1;
      break;
    }
    x1=xNew1;
    iter1=iter1+1;
  }
  if(iter1==maxIter1){
    return -515151;
  }
  var a2=a1;
  var b2=b1+a1*x1;
  var c2=c1+b1*x1+a1*x1*x1;
  var D1=b2*b2−4*a2*c2;
  var sqrtD1=sqrt(abs(D1));
  var realPart1=-b2/(2*a2);
  var imagPart1=sqrtD1/(2*a2);
  var x2=0;
  var x3=0;
  var xReal2=0;
  var xImag2=0;
  var xReal3=0;
  var xImag3=0;
  if(D1>0){
    x2=realPart1+imagPart1;
    x3=realPart1−imagPart1;
  }
  elseif(D1==0){
    x2=realPart1;
    x3=realPart1;
  }
  else{
    xReal2=realPart1;
    xImag2=imagPart1;
    xReal3=realPart1;
    xImag3=-imagPart1;
  }
  if(x123==1){
    if(real1==1){
      return x1;
    }
    return 0;
  }
  if(D1>=0){
    if(x123==2){
      if(real1==1){
        return x2;
      }
      return 0;
    }
    if(x123==3){
      if(real1==1){
        return x3;
      }
      return 0;
    }
  }
  else{
    if(x123==2){
      if(real1==1){
        return xReal2;
      }
      return xImag2;
    }
    if(x123==3){
      if(real1==1){
        return xReal3;
      }
      return xImag3;
    }
  }
  return -515151;
}

def iSolveQuadratic(a,b,c,x12,real){
  if(a==0){
    return -515151;
  }
  var D=b*b−4*a*c;
  var sqrtD=sqrt(abs(D));
  if(D<0){
    if(x12==1){
      if(real==1){
        return -b/(2*a);
      }
      else{
        return sqrtD/(2*a);
      }
    }
    else{
      if(real==1){
        return -b/(2*a);
      }
      else{
        return -sqrtD/(2*a);
      }
    }
  }
  if(real!=1){
    return 0;
  }
  if(x12==1){
    return (-b+sqrtD)/(2*a);
  }
  return (-b−sqrtD)/(2*a);
}

def solveAxPlusBEqualsC(a,b,c)=(c−b)/a;

def solveABequalsCD(a,b,c,d){
  var nom=d−b;
  var denom=(a−b);
  return nom/denom;
}

def LCM(a,b){
  if(a==0||b==0){
    return 0;
  }
  return (a*b)/GCD(a,b);
}

def GCD(a,b){
  if(b==0){
    return a;
  }
  return GCD(b,a%b);
}

def solveQuadratic(a,b,c,xy){
  var D=b*b−4*a*c;
  if(D<0){
    return -515151.515151;
  }
  var sqrtD=sqrt(D);
  if(xy==1){
    return (-b+sqrtD)/(2*a);
  }
  return (-b−sqrtD)/(2*a);
}

def 이차방정식(a,b,c,선택)=solveQuadratic(a,b,c,선택);



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