Subject: Is Dr. Math wrong? (Re: [Maxima] 0^0 question)
From: Barton Willis
Date: Fri, 25 Apr 2003 14:25:24 -0500
To experiment with 0^0 => 1 in Maxima, use
(C1) simp : false;
(D1) FALSE
(C2) tellsimp(0^0,1);
(D2) [^RULE1, SIMPEXPT]
(C3) simp : true;
(D3) TRUE
(C4) display2d : false;
(D4) FALSE
(C5) s : sum(x^k,k,0,inf);
(D5) 'SUM(x^k,k,0,INF)
The 0^0 problem isn't fixed because Maxima never doesn't "see" 0^0 in the
sum, rather it sees 0^k that evaluates to 0.
(C6) subst(0,x,s);
(D6) 0
(C7)
To fix this, try something like
(C1) simp : false;
(D1) FALSE
(C2) matchdeclare(x,true);
(D2) DONE
(C3) tellsimp(0^x,kron_delta(x,0));
(D3) [^RULE1, SIMPEXPT]
(C4) simp : true;
(D4) TRUE
(C5) display2d : false;
(D5) FALSE
(C6) s : sum(x^k,k,0,inf);
(D6) 'SUM(x^k,k,0,INF)
(C7) ev(s,x=0);
(D7) 'SUM(kron_delta(k,0),k,0,INF)
(C8)
But we'd have to figure out how to make a kron_delta collapse the
summation
Additionally, I don't think Maxima defines kron_delta.
No, I don't think Dr. Math is wrong. All arguments that say that 0^0
must be <stuff> because limit <stuff> = <stuff> are specious. If you
have ever claimed that
exp(x) = sum(x^k / k!,k,0,inf)
for all complex x, you'd better be in the 0^0 = 1 camp.
Barton