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
def CallDiff(exp,var):
res=extract.argumentSeparator(exp)
res=differentiation(extract.convert_infix(res),var)
res= extract.post_infix(res)
return res