#294 taylor problems with 2^x at infinity

[Stavros Macrakis]

taylor(2^x+3^x,x,inf,2)
=> Break: two equal vars generated
(a debug break)

Normal users should never see debug breaks....

Similarly for tlimit(2^x+3^x,x,inf).

More surprisingly, you also get a debug break for:

taylor(2^x/3^x,x,inf,2)*2
=> Break: bad singular datum

Note that here, unlike the previous case, there is
absolutely no mathematical subtlety.

There are also cases that give incorrect answers, not
errors:

taylor(2^x,x,inf,10)*2 => 2 + ... NO!

taylor(2^x,x,inf,2)*2^x => 1/%e^(-log(2)*x) NO!

Maxima 5.9.0 GCL 2.5.0 mingw32 Windows 2000 Athlon

[Stavros Macrakis]

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Similar problems turn up for log(x),x=0:

tl: taylor(log(x),x,0,3) => log(x)+... OK
2*tl == tl+1 => 2+... NO!
tl^2 => 1+... NO!
tl*log(x) => log(x)+... NO!
tl - log(x) => -log(x)+1+... NO!

[Stavros Macrakis]

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Another example:

expr: taylor(x^x,x,0,2)

expr-1 => x+x^2/2+... (NO!)
ratdisrep(expr)-1 ... OK