Instructions for using the Lookups

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  1. All numbers should be in BASE 10 and in ABSOLUTE VALUE.
  2. 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.
    [Note: Pi=3.141592653589793238462643383279...]
  3. 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...
  4. 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.
  5. 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).
  6. In the input, only strings of digits (0 to 9) and a decimal is accepted, all other characters are IGNORED.
  7. 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.