A problem with symsum() and isAlways

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Yang Li 2020-9-15

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评论： Walter Roberson 2020-9-16

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)))

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Answer 1

Neeraj Kulkarni 2020-9-16

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https://ww2.mathworks.cn/matlabcentral/answers/593962-a-problem-with-symsum-and-isalways#answer_495202

编辑：Neeraj Kulkarni 2020-9-16

在 MATLAB Online 中打开

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()

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Walter Roberson 2020-9-16

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"

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