Example #1
0
def differentiation(exp,var):
    if(not(var in exp)):
        return ["0"]
    diff=[]
    if(extract.isOperand(exp[len(exp)-1])==1):
        if(exp[len(exp)-1]==var):
            diff.append("1")
            return diff
        else:
            diff.append("0")
            return diff
    if(extract.isTrncdDef(exp[len(exp)-1])):
        op=exp[len(exp)-1]
        u=exp[0:len(exp)-1]
        du=differentiation(u,var)
        if(op=='sin'):
            diff=u+['cos']+du+['*']
            return diff
        if(op=='cos'):
            diff=['0']+u+['sin']+du+['*']+['-']
            return diff
        if(op=='exp'):
            diff=u+['exp']+du+['*']
            return diff
        if(op=='log'):
            diff=['1']+u+['/']+du+["*"]
            return diff
        if(op=='tan'):
            diff=u+['sec','2','^']+du+['*']
            return diff
        if(op=='cot'):
            diff=['0']+u+['cosec','2','^']+du+['*','-']
            return diff
        if(op=='sec'):
            diff=u+['sec']+u+['tan','*']+du+['*']
            return diff
        if(op=='cosec'):
            diff=['0']+u+['cosec']+u+['cot','*']+du+['*','-']
            return diff
        if(op=='sinh'):
            diff=u+['cosh']+du+['*']
            return diff
        if(op=='cosh'):
            diff=u+['sinh']+du+['*']
            return diff
        if(op=='tanh'):
            diff=['1']+u+['tan','2','^','-']+du+['*']
            return diff
        if(op=='asin'):
            diff=['1','1']+u+['2','^','-','0.5','^','/']+du+['*']
            return diff
        if(op=='acos'):
            diff=['0','1','1']+u+['2','^','-','0.5','^','/']+du+['*','-']
            return diff
        if(op=='atan'):
            diff=['1','1']+u+['2','^','+','/']+du+['*']
            return diff
        if(op=='mod'):
            diff=u+u+['mod','/']+du+['*']
            return diff
        
    k=0
    i=len(exp)-2
    while(k>=0):
        if(extract.isOperand(exp[i])==1):
           k=k-1
        elif(extract.isOperator(exp[i])==1):
           k=k+1
        i=i-1
    op=exp[len(exp)-1]
    u=exp[0:i+1]
    v=exp[i+1:len(exp)-1]
    du=differentiation(u,var)
    dv=differentiation(v,var)
    if(op=='+'):
        if(du==['0']):
            diff=(dv)
        elif(dv==["0"]):
            diff=(du)
        else:
            diff=(du+dv+['+'])
        return diff
    elif(op=='-'):
        if(du==["0"]):
            diff=(['0']+dv+["-"])
        elif(dv==["0"]):
            diff=(du)
        else:
            diff=(du+dv+["-"])
        return diff
    elif(op=='*'):
        if(du==["0"]):
            diff=(u+dv+["*"])
        elif(dv==["0"]):
            diff=(v+du+["*"])
        else:
            diff=u+dv+["*"]+v+du+["*"]+["+"]
        return diff
    elif(op=='/'):
        if(dv==["0"]):
            diff=(du+v+["/"])
        elif(du=="0"):
            diff=(["0"]+u+["-"]+dv+["*"]+v+["2","^","/"])
        else:
            diff=(v+du+["*"]+u+dv+["*","-"]+v+["2","^","/"])
        return diff
    else:
        if(not(var in v)):
            vs=[]
            for i in v:
                vs.append(i)
            try:
                vs=eval(extract.post_infix(vs))
                if(vs>0):
                    diff=[str(vs)]+u+[str(vs-1)]+['^']+['*']+du+['*']
                else:
                    diff=['0']+[str(vs*(-1))]+['-']+u+['0']+[str((vs-1)*-1)]+['-']+['^']+['*']+du+['*']
                return diff
            except:
                diff=v+u+v+['1']+['-']+['^']+['*']
                return diff
        elif(not(var in u)):
            diff=u+v+['^']+u+['log']+dv+['*','*']
            return diff
        else:
            diff=u+v+['^']+v+u+['/']+du+['*']+dv+u+['log','*','+','/']
            return diff
Example #2
0
def CallDiff(exp,var):
    res=extract.argumentSeparator(exp)
    res=differentiation(extract.convert_infix(res),var)
    res= extract.post_infix(res)
    return res