Setting $0^0$ to 1

Questions
1

Can Mathematica or one of its sessions set 0^0 to 1? I wish to use the combinatoric 0^0==1 in Mathematica’s internal calculations instead of it generating an Indeterminate error. I do know that Limit[x^x, x -> 0] is 1.

2

You could unprotect Power and add the definition for 0^0 . The definition will only be in effect during the current Mathematica session.

Unprotect[Power];
Power[0, 0] = 1;

Test it:

In[3]:= 0^0
Out[3]= 1
3

Building on Hans’s idea, one can use WithCleanup to localized the redefinition of Power to a single execution:

runInCombinatorialMode // ClearAll;
runInCombinatorialMode // Attributes = {HoldAll};
runInCombinatorialMode[code_] := WithCleanup[
   Unprotect@Power;
   0^0 = 1;
   Protect@Power
   ,
   code,
   Unprotect@Power;
   0^0 =.;
   Protect@Power
   ];

runInCombinatorialMode[
 vec = Range[0, 4];
 Total[vec^vec]
 ]

(*  289  *)

0^0

Power::indet: Indeterminate expression 0^0 encountered.

(*  Indeterminate *)