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### Propagation of uncertainty

Is there any simple method in sage to do a calculation with uncertainties? Something like this: $10\pm2 * 3\pm1 = 30\pm18$. Or with a more sophisticated formula: $30\pm11.67\quad(10 \times 3 \times \sqrt{(2/10)^2 + (1/3)^2} = 11.67)$. Both ways are taken from here, but the second way is also described on wikipedia.

To do such calculations I have already seen a method using RIF's like the following:

R=RIF(8,12)*RIF(2,4)
R.str(error_digits=2); R.lower(); R.upper(); R.center()


Which outputs:

32.?16
16.0000000000000
48.0000000000000
32.0000000000000


But with as one can see the center result is $32$ ($\frac{16+48}{2}$) instead of $30$ ($10*3$). Also I think it is a bit complex, because one has to calculate the upper an lower limits before, instead of a simple thing like:

uncertain(10,2)


(And as last point, I think result with the question mark is not very nice)

PS: If one of my calculations is fundamentally wrong please let me know, because I am new to error calculations.

Is there any simple method in sage to do a calculation with uncertainties? Something like this: $10\pm2$(10\pm2) * 3\pm1 (3\pm1) = 30\pm18$. (30\pm18)$. Or with a more sophisticated formula: $30\pm11.67\quad(10$(30\pm11.67)$because of$(10 \times 3 \times \sqrt{(2/10)^2 + (1/3)^2} = 11.67)$. Both ways are taken from here, but the second way is also described on wikipedia. To do such calculations I have already seen a method using RIF's like the following: R=RIF(8,12)*RIF(2,4) R.str(error_digits=2); R.lower(); R.upper(); R.center()  Which outputs: 32.?16 16.0000000000000 48.0000000000000 32.0000000000000  But with as one can see the center result is$32$($\frac{16+48}{2}$) instead of$30$($10*3$). Also I think it is a bit complex, because one has to calculate the upper an lower limits before, instead of a simple thing like: uncertain(10,2)  (And as last point, I think result with the question mark is not very nice) PS: If one of my calculations is fundamentally wrong please let me know, because I am new to error calculations. ### Propagation of uncertainty Is there any simple method in sage to do a calculation with uncertainties? Something like this:$(10\pm2) * (3\pm1) = (30\pm18)$. Or with a more sophisticated "sophisticated" formula:$(30\pm11.67)$because of$(10 \times 3 \times \sqrt{(2/10)^2 + (1/3)^2} = 11.67)$. Both ways are taken from here, but the second way is also described on wikipedia. To do such calculations I have already seen a method using RIF's like the following: R=RIF(8,12)*RIF(2,4) R.str(error_digits=2); R.lower(); R.upper(); R.center()  Which outputs: 32.?16 16.0000000000000 48.0000000000000 32.0000000000000  But with as one can see the center result is$32$($\frac{16+48}{2}$) instead of$30$($10*3\$). Also I think it is a bit complex, because one has to calculate the upper an lower limits before, instead of a simple thing like:

uncertain(10,2)


(And as last point, I think result with the question mark is not very nice)

PS:

If one of my calculations is fundamentally wrong please let me know, because I am new to error calculations.