#531 Combining Taylor series of different orders

[Stavros Macrakis]

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