Instructions for using the Lookups
- All numbers should be in BASE 10 and in ABSOLUTE VALUE.
- All numbers are always TRUNCATED, not
ROUNDED. It is very important that the number you input is
truncated to the last valid digit you know. Approximations won't
produce any results. For example, inputting 3.1416 for Pi, using only 3
valid decimal digits (141), won't give Pi as a result.
- All numbers are NORMALIZED. They appear as
strings of digits. This choice was made in order to be consistent with
all the tables. It means that a number like exp(Pi) = 23.140... appears
as 23140... with NO EXPONENT. Since our programs can detect
a simple rational times any real number, it is not necessary to 'know'
that exp(Pi) is 23.140 instead of 23140...
- All results are usually filtered against small tables of
rationals. This is necessary to avoid an overload of the output. You
wouldn't want an output of 10 pages or more. It means that if your input
is a simple rational the program will detect that and will propose a
set of rationals. If the result of the search is a huge number of
rationals then it is filtered so that the answer is not overly large.
Don't worry, no precious information is lost this way.
- The dumb lookup requires AT LEAST 4 DIGITS, and the smart lookup
requires AT LEAST 9 DIGITS. There are millions of constants in
the database and it detects rationals. This means that we can match
ANY real number of 5 digits or more. For example, you may try your
birthday. It will usually find an expression for it (it worked with
mine). With inputs of 4 digits and less, it just produces too many
candidates (hundreds of them).
- In the input, only strings of digits (0 to 9) and a
decimal is accepted, all other characters are IGNORED.
- AT LEAST 15 DIGITS are required for the Generalized
Expansions and Integer Relation algorithms to perform the
calculations. It just won't work with less.