Combining Taylor series of different orders

Imported from SourceForge on 2024-07-07 06:24:16 Created by macrakis on 2004-03-04 19:06:19 Original: https://sourceforge.net/p/maxima/bugs/531

taylor(exp(x),x,0,2) - taylor(exp(x),x,0,0) => x + x^2/2 + ...

This is wrong. The result should be 0+... (order 0).

taylor(exp(x),x,0,2) - taylor(exp(x),x,0,1) => 0 + ...

taylor(exp(x),x,0,2) * taylor(exp(x),x,0,5) => 1 + 2*x + 2*x^2 + ...

This time, the printed results are correct: the expansion is only as good as the longest of the component expansions.

But taylorinfo of the result is [[x,0,2]], that is, taylor thinks that it is 0 + 0*x + 0*x^2 + ...

taylor(taylor(exp(x),x,0,2),x,0,5) => 1 + x + x^2/2 + ...

This is correct, and the taylorinfo is correctly [[x,0,2]], but shouldn't it give a warning?

taylor(x^2,x,0,1)/x politely gives a warning ("0+... assumed to be zero in Taylor"), but the result has taylorinfo [[x,0,2]]. Shouldn't it have taylorinfo [[x,0,1]]?

-s

rtoy / maxima

Combining Taylor series of different orders #2915