def Newton(f,p,pow=1,max=10):
    f1=diff(f(x),x)
    n=0
    error1=abs(f(p))
    while(n<max):
        p2=p-(f(p)/f1(p))
        error2=abs(p-p2)
        p=p2
        n=n+1
        print "%d steps error:%.15f ratio:%.15f"%(n,error2,error2/error1^pow)
        error1=error2
        if error2>10^3 or abs(p2)>10^3 or n>10^3:
            print "DIVERGE: root not found"
            return
    print "after %d steps" %n
    print "Root: %.15f"%p
    print "f(x): %.15f"%f(p)

def Secant(f,p1,p2,max=10,pow=1):
    n=0
    error1=abs(p1-p2)
    f1=f(p1)
    f2=f(p2)
    while(n<max):
        if f2==f1:
            print "DIVERGE: root not found"
            print p1
            print p2
            print n
            return
        p3=(p1*f2-p2*f1)/(f2-f1)
        p1=p2
        p2=p3
        f1=f2
        f2=f(p2)
        error2=abs(p1-p2)
        n=n+1
        print "%d steps error:%.15f ratio:%.15f"%(n,error2,error2/error1^pow)
        error1=error2
        #print p3
        if error2>10^3 or abs(f2)>10^3 or n>10^3:
            print "DIVERGE: root not found"
            return
    print "after %d steps" %n
    print "Root: %.15f"%p2
    print "f(x): %.15f"%f2
def FalsePos(f,p1,p2,pow=1,max=10):
    n=0
    error1=abs(p1-p2)
    f1=f(p1)
    f2=f(p2)
    #for better flase pos "Illonios algorithm" uncomment the commented lines below
    #flag=True
    while(n<max):
        if(f1*f2>=0):
            print "Unbracketed root!"
            return
        p3=(p1*f2-p2*f1)/(f2-f1)
        f3=f(p3)
        if(f1*f3>0):
     #       if flag==True:
      #          f2=f2/2
       #     flag=True
            error2=abs(p3-p1)
            p1=p3
            f1=f3
        else:
        #    if flag==False:
         #       f1=f1/2
          #  flag=False
            error2=abs(p3-p2)
            p2=p3
            f2=f3
        n=n+1
        print "%d steps error:%.15f ratio:%.15f"%(n,error2,error2/error1^pow)
        error1=error2
        #print p3
        if error2>10^3 or abs(f3)>10^3 or n>10^3:
            print "DIVERGE: root not found"
            print error1
            print n
            print p3
            return
    print "after %d steps" %n
    print "Root: %.15f"%p3
    print "f(x): %.15f"%f3

Newton(x^2-2,1)

Newton(x^2-2,1,pow=2) #quadratic convergence

Secant(x^2-2,0,2)

Secant(x^2-2,0,2,pow=2)

Secant(x^2-2,0,2,pow=(1+5^(.5))/2)#superlinear but subquadratic convergence

FalsePos(x^2-2,0,2) #linear convergenge

def fixedpoint(f,p,max=10,n=1):
    new=f(p)
    if abs(new)>10^3:
        print "DIVERGENCE!! (probably)"
        return
    diff=abs(new-p)
    print "after ",str(n),"iterations the guess %.9f changed by %.9f"%(new,diff)
    if n<max:
        fixedpoint(f,new,max,n+1)
fixedpoint((x+2)/(x+1),1)

Newton(tan(3.14159265359*x)-6,0.0)
Secant(tan(3.14159265359*x)-6,0.0,.48)
FalsePos(tan(3.14159265359*x)-6,0.0,.48)