Wrong root of sinc expression

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Question:Wrong root of sinc expression

Posted: C_R 3747 Product: Maple

2 hours ago

Here is another case where an incorrect solution of a non-algebraic expression is returned.

How to make Maple exclude solutions obtained with allsolutions where the expression is not defined?

IMO, allsolutions facilities of Maple should do this automatically. Anything from a mathematical point of view that speaks against an automatic exclusion?

(Are there other commands that provide a correct solution?)

By the way:

solve(sin(x)/x)

does not return a single solution as stated on the solve help page ("In general for transcendental equations, the solve command returns only one solution,...") because solve correctly discards x=0 but does not consider returning x=pi.

(1)

The above expression is not defined at

Eval(sin(x)/x, x = 0)

(2)

Error, (in value/Eval) numeric exception: division by zero

Roots of the expression with RootOf

(3)

${_Z1}$

(4)

>	$about({_Z1}[])$

Originally _Z1, renamed _Z1~:
is assumed to be: integer

>	$getassumptions({_Z1})$

${_Z1::integer}$

(5)

(6)

(7)

(8)

The above should be false because is not defined for However, this is what automatic simplifcation does behind the scenes with the output (7)

(9)

For this particular case Maple should have returned a special name expressing nonzero integers, like .
or or are common symbols for that
So is incorrect in the solution and automatic simplification does something wrong.
Only substituing everything at once leads to a correct response: