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User:Charles R Greathouse IV/Standards

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These are my personal editorial standards for various types of sequences. If you are submitting one of these types of sequences, I recommend following these guidelines when possible.

Constants

In most cases, the primary sequence for a constant should be its decimal expansion. The remarks below apply to this case; other associated sequences (continued fraction representation, binary expansion, Engel expansion, etc.) should be mentioned in the crossreferences. Such constants should have the keyword cons and have terms exclusively from {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} (some, of course, will not use all of these). Further, such sequences should never have the keyword sign (see Keyword compatibility).

Rational

Give the number's numerator and denominator unless they are large (in which case one can typically give the number of digits in each). Give the period of the decimal expansion unless terminating.

If the number is an integer, instead say so (unless this fact is very much obvious from the definition) and give its length in decimal digits (approximately, if necessary).

Algebraic Irrational

Give the number's degree, its denominator, and its minimal polynomial if sufficiently small or otherwise compact. If the denominator is 1, instead write that it is an algebraic integer. If the minimal polynomial is too large, write its degree instead. For example:

A quartic number of denominator 2 and minimal polynomial 16x^4 - 20x^2 + 5.

or

A quadratic integer with minimal polynomial x^2 - 3x - 2.

or

An algebraic number of degree 24 and denominator 2.

Transcendental

It can be useful to note that a number is transcendental, either by a standard theorem (please give the theorem for future readers!) or by a reference/link. This is not necessary for very obvious transcendental numbers, e.g., rational multiples of Pi, but please link in all cases to the Index:

<a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

Unknown

If the status of the number has been explicitly mentioned as open/unknown or conjectured in a paper, please mention this in the sequence and cite the paper.