A problem with symsum() and isAlways
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Yang Li
il 15 Set 2020
Commentato: Walter Roberson
il 16 Set 2020
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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Neeraj Kulkarni
il 16 Set 2020
Modificato: Neeraj Kulkarni
il 16 Set 2020
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 :
1 Commento
Walter Roberson
il 16 Set 2020
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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