find-local-minmaxinfpts.sagews

load("http://omega.albany.edu:8008/Sim.py")

#----------------------

# define the funtion which finds its max/min and critical points and inflections.

def find0(a,b,f,ep=1e-1,split=1e-2):
    
    crit = []
    inflecpt = []
    n=0
    x=a
    while abs(b-a)>= n:
        instcrit = []
        df2val = df2(x)
        dfval = df(x)

        while (sign(df2val)==sign(df2(x))) and abs(b-a)>n:

            # where df(x) approximately equals to zero it means whether max or mean
            if abs(df2(x))<ep:
                instcrit.append(x)
                n = n+split
                x = x+split

            # where df(x) approximately does not equals to zero
            else:
                n = n+split
                x = x+split

        if instcrit!= [] :
            crit.append(max(instcrit))
            inflecpt.append("Inflection Point")
    if len(crit)>1:
        del crit[-1]
    html.table([(round(crit[x], ndigits=5),inflecpt[x]) for x in [0..len(crit)-1]])
    minmax(a,b,f,crit)


def minmax(a,b,f,infcrit,ep=1e-1,split=1e-2):

    crit = []
    MmI = []
    n=0
    x=a
    count =0

    while abs(b-a) >= n:
        instcrit = []
        df2val = df2(x)
        dfval = df(x)

        while (sign(dfval)==sign(df(x))) and abs(b-a)>=n:

            # where df(x) approximately equals to zero it means whether max or mean
            if abs(df(x))<ep:
                instcrit.append(x)
                n = n+split
                x = x+split

            # where df(x) approximately does not equals to zero
            else:
                n = n+split
                x = x+split

        if instcrit!= [] :

            crit.append(max(instcrit))
    if len(crit)>1:
        del crit[-1]

    while count<=len(infcrit) and len(crit)!=0:

        if count==0:

            if df(crit[count])<0:

                MmI.append("Local Min point")
                count = count+1
                sn=0

            else:
                MmI.append("Local Max point")
                count = count+1
                sn=1
        else:
            if sn==0:
                MmI.append("Local Max point")
                count = count+1
                sn=1
            else:
                MmI.append("Local Min point")
                count = count+1
                sn=0
    html.table([(round(crit[x], ndigits=5),MmI[x]) for x in [0..len(crit)-1]])


#Start
# define a function
f(x) = cos(x)
df(x) = diff(f,x)
df2(x) = diff(df,x)

# find0(range,range,function)
find0(-10,10,f)
print("END")

Using _k = _k_default = 5, TL = TL_all[0:-1] = ['_rr', '_dc', '_ps', '_el', '_sl', '_fs', '_Snj', '_Sdj', '_cb', '_xp', '_sr', '_er', '_es', '_fa', '_pf', '_mrs', '_pmrs']

-7.86	Inflection Point
-4.72	Inflection Point
-1.58	Inflection Point
1.57	Inflection Point
4.71	Inflection Point
7.85	Inflection Point

-9.43	Local Min point
-6.29	Local Max point
-3.15	Local Min point
-0.0	Local Max point
3.14	Local Min point
6.28	Local Max point
9.42	Local Min point

END