A problem with symsum() and isAlways

I have defined fl=symsum(1/factorial(n),n,0,inf) and it turned out to be exp(1). But when I write "isAlways(fl==exp(1))" or "isAlways(fl==sym(exp(1))",the result is logical 0. It's cofusing.

fl=symsum(1/factorial(n),n,0,inf)
isAlways(fl==exp(1))
isAlways(fl==sym(exp(1)))

Answer 1

[Neeraj Kulkarni]

Hi Yang Li,

sym() is to be used on subexpressions instead of entire expression for better accuracy.

For example:

>> x = sym(exp(1))
  
x =
  
3060513257434037/1125899906842624
  
>> x = exp(sym(1))
  
x =
  
exp(1)

The second way of creating symbolic number will give logical 1 for your isAlways() evaluation.

Please refer the following document to create symbolic numbers :

sym()

[Walter Roberson]

Right. The code that looks at floating point numbers and tries to figure out which symbolic number they represent does not try to figure out if the inputs might happen to be exp() of an "interesting" number. Using exp(sym(1)) is the correct way to proceed here.

Remember that the == operation looks for exact comparisons, never just for "equal to within roundoff errors"