Quiet@Remove["Global`*"];
$HistoryLength=2;
SetDirectory[NotebookDirectory[]];

?=

vyraz=x+y+Sin[(x^2)+2*y*x+3];
TreeForm[vyraz]

vyraz=x+y+Sin[(x^2)+2*y*x+3];
FullForm[vyraz]

Head[vyraz]

TreeForm[x*y]

x*y=5

x+y=5

Attributes[Plus]

(*o listech*)
listik={1,{2,3},{0,{alfa,romeo}}};
TreeForm[listik];

listik[[0]]

listik[[-1,2,-1]]

listik[[-1,2,-1]]=diCaprio

listik

Part[listik,-1]

(*volani funkci*)
{Sin[x],Sin@x,x//Sin}

listik={1,{2,3},{0,{alfa,romeo}}};
Length[listik];
Last[listik]
First[listik]

TreeForm[listik];

vyraz=x+y+Sin[(x^2)+2*y*x+3];
TreeForm[vyraz]

vyraz[[3,1,2,2]]

(*pravidla*)
(x^2)/.x->2

Rule[x,2]

ReplaceAll[(x^2),x->2]

ReplaceAll[Power[x,2],Rule[x,2]]

(x^2)+y/.{x->E+y,y->Pi+x,x->(Sqrt[2])}

(1/(I*ω*c))/.{c->10nF,nF->(10^(-9))}

?//.

(1/(I*ω*c))//.{c->10nF,nF->(10^(-9))}(*rekurze*)

(*x//.{x->y+x,y->x}*)

(x^2)/.{{x->2},{x->3},{x->4}}

x/.{{x->2},{x->3},{x->4}}

(*Equal, rovnice*)
Equal[lhs,rhs]
{1==1,1==2,Equal[1,1],Equal[1,2]}

(*pouziti pro praci s koreny rovnic*)
Quiet@Remove["Global`*"];
rce=(x^3)+(2+I)*(x^2)+2I*x+14.==0;
lhs=rce[[1]];
dosadZaIkska=Solve[rce]
x1=x/.dosadZaIkska[[1]];
x2=x/.dosadZaIkska[[2]];
vysledek=x1+2*x2;
Print["x1+2*x2= ",vysledek]

x/.{{x->2},{x->3},{x->4}}

(x/.dosadZaIkska).{1,2,0}
Dot[(x/.dosadZaIkska),{1,2,0}]

Range[100]/.List->Plus

N[Range[100]/.List->Times]

expr=y-x/.{{x->2},{x->3},{x->4}};
rce=Expand[(0==expr/.List->Times)/.y->x];
reseni=Solve[rce]

reseni[[1]]

x1=reseni[[1,1,2]]
TreeForm[x1];

x1=x/.reseni[[1]]

(*patterny*)
?_

?__

?___

vyraz=Sin[(x^2)+3]+(x^y)+(E^Pi)

vyraz/.((a_)^(b_)):>(b^a)

vyraz/.(x^(b_)):>(b^x)