4 ms·
Interesting with a side note about toying with Excel. When I plug in: 1/(3 sqrt(7)-8) and -3 sqrt(7)-8 ...into Excel, there must be a rounding
by Avitas 13y ago
Interesting with a side note about toying with Excel.
When I plug in:
1/(3 sqrt(7)-8)
and
-3 sqrt(7)-8
...into Excel, there must be a rounding error. They resolve to:
-15.9372539331939000
and
-15.9372539331938000
...respectively.
Time to plug these into Wolfram. I get:
-15.93725393319377177150484726091778127713077754924735054110500337760320646969085088328117865942363083184519373501549238...
and
-15.93725393319377177150484726091778127713077754924735054110500337760320646969085088328117865942363083184519373501549238...
...respectively.
- pygy_ 13y agoYour large numbers are breaking the page layout. It would be nice if you could prepend them with four spaces, to place them in code blocks (they have overflow:scroll), or break them into multiple lines (or both).
- hdevalence 13y agoIf you want to do exact computations, SAGE is handy, Free, and built on Python: sage: k.<a> = QuadraticField(7); k Number Field in a with defining polynomial x^2 - 7 sage: x = 3*a - 8 sage: x.is_integral() True sage: 1/x -3*a - 8 sage: x * (1/x) 1 sage: (1/x).is_integral() True (Note: the is_integral() is because we define k to be QQ(sqrt(7)), not ZZ(sqrt(7)), so we want to check that our elements are really integers, i.e., lie in ZZ(sqrt(7))).
- Someone 13y agoYou don't want to do this kind of stuff in Excel. See http://www.cs.berkeley.edu/~wkahan/Mind1ess.pdf http://www.cs.berkeley.edu/~wkahan/Mind1ess.pdf. It shows (a.o.) that adding parentheses around an expression can change its value.