This is OnlineLookup.info, produced by Macaulay2, version 1.25.05

OnlineLookup -- Look up mathematical information online
*******************************************************

Description
===========

The purpose of this package is to collect helper functions that allow to query
web sites for mathematical information and format it into Macaulay2 output. At
present, it contains two such functions, see oeis, and isc,
but more will be implemented in the future.

Author
======

  * Paul Zinn-Justin (see http://blogs.unimelb.edu.au/paul-zinn-justin/ )
    <pzinn@unimelb.edu.au>

Version
=======

This documentation describes version 0.7 of OnlineLookup.

Citation
========

If you have used this package in your research, please cite it as follows:

+-----------------------------------------------------------------------------+
|@misc{OnlineLookupSource,                                                    |
|  title = {{OnlineLookup: Look up mathematical information online. Version   |
|  author = {Paul Zinn-Justin},                                               |
|  howpublished = {A \emph{Macaulay2} package available at                    |
|    \url{https://github.com/Macaulay2/M2/tree/master/M2/Macaulay2/packages   |
|}                                                                            |
|-----------------------------------------------------------------------------|
|~0.7}},                                                                      |
|                                                                             |
|                                                                             |
|}}                                                                           |
+-----------------------------------------------------------------------------+

Exports
=======

  * Functions and commands
      * isc -- ISC lookup
      * oeis -- OEIS lookup
  * Methods
      * "isc(Constant)" -- see isc, -- ISC lookup
      * "isc(Number)" -- see isc, -- ISC lookup
      * "isc(RR)" -- see isc, -- ISC lookup
      * "isc(String)" -- see isc, -- ISC lookup
      * "oeis(String)" -- see oeis, -- OEIS lookup
      * "oeis(VisibleList)" -- see oeis, -- OEIS lookup

For the programmer
==================

The object OnlineLookup, is a package (Macaulay2Doc),
defined in OnlineLookup.m2, with auxiliary files in OnlineLookup/.

-------------------------------------------------------------------------------

The source of this document is in OnlineLookup.m2:159:0.

isc -- ISC lookup
*****************

Description
===========

This function looks up the argument (a real number or a string) in the Inverse
Symbolic Calculator. (http://wayback.cecm.sfu.ca/projects/ISC/).

+-------------------------------------------------------------------------+
|i1 : isc (sqrt 2*pi)                                                     |
|                                                                         |
|o1 = {Mixed constants with 5 operations                                 }|
|     {4442882938158366 = 2*Pi/sr(2)                                     }|
|     {Beta(a,b), a and b elements of F24: GAMMA function                }|
|     {4442882938158366 = Beta(1/4,3/4)                                  }|
|     {Mixed constants, 2 with elementary transforms.                    }|
|     {4442882938158366 = GAM(1/4)*GAM(3/4)                              }|
|     {Mixed constants with 5 operations                                 }|
|     {4442882938158366 = GAM(1/6)/sr(2)*GAM(5/6)                        }|
|     {Dirichlet constants, sums of Digamma function with rat. arguments.}|
|     {4442882938158366 = -Psi(1/4)-Psi(3/8)+Psi(5/8)+Psi(3/4)           }|
|     {                                                                  }|
|                                                                         |
|o1 : VerticalList                                                        |
+-------------------------------------------------------------------------+

Ways to use isc:
================

  * "isc(Constant)"
  * "isc(Number)"
  * "isc(RR)"
  * "isc(String)"

For the programmer
==================

The object isc, is a method function (Macaulay2Doc).

-------------------------------------------------------------------------------

The source of this document is in OnlineLookup.m2:159:0.

oeis -- OEIS lookup
*******************

Description
===========

This function looks up the argument (a list of integers or a string) in the
Online Encyclopedia of Integer Sequences (http://oeis.org/).

+-----------------------------------------------------------------------------+
|i1 : oeis {1,3,31,1145}                                                      |
|                                                                             |
|o1 = {0 => (A029729 (see https://oeis.org/A029729 ) Degree of the variety of |
|     {1 => (A094579 (see https://oeis.org/A094579 ) Duplicate of A029729.)   |
|                                                                             |
|o1 : NumberedVerticalList                                                    |
|-----------------------------------------------------------------------------|
|pairs of commuting n X n matrices.)}                                         |
|                                   }                                         |
+-----------------------------------------------------------------------------+

Optional arguments Limit and Position allow to control the maximum amount of
listed answers.

+-----------------------------------------------------------------------------+
|i2 : L = apply(5,n->n!);                                                     |
+-----------------------------------------------------------------------------+
|i3 : oeis (L,Limit=>5)                                                       |
|                                                                             |
|o3 = {0 => (A000142 (see https://oeis.org/A000142 )                          |
|     {1 => (A072856 (see https://oeis.org/A072856 )                          |
|     {2 => (A061602 (see https://oeis.org/A061602 )                          |
|     {3 => (A177523 (see https://oeis.org/A177523 )                          |
|     {4 => (A263777 (see https://oeis.org/A263777 )                          |
|                                                                             |
|o3 : NumberedVerticalList                                                    |
|-----------------------------------------------------------------------------|
|Factorial numbers: n! = 1*2*3*4*...*n (                                      |
|Number of permutations satisfying i-4<=                                      |
|Sum of factorials of the digits of n.)                                       |
|Number of permutations of 1..n avoiding                                      |
|Number of inversion sequences avoiding                                       |
|-----------------------------------------------------------------------------|
|order of symmetric group S_n, number of permutations of n letters).)}        |
|p(i)<=i+4, i=1..n (permutations of length n within distance 4).)    }        |
|                                                                    }        |
| adjacent step pattern up, up, up, up.)                             }        |
|pattern 201 (or 210).)                                              }        |
+-----------------------------------------------------------------------------+
|i4 : oeis (L,Limit=>1,Position=>2)                                           |
|                                                                             |
|o4 = {0 => (A061602 (see https://oeis.org/A061602 ) Sum of factorials of the |
|                                                                             |
|o4 : NumberedVerticalList                                                    |
|-----------------------------------------------------------------------------|
|digits of n.)}                                                               |
+-----------------------------------------------------------------------------+

Ways to use oeis:
=================

  * "oeis(String)"
  * "oeis(VisibleList)"

For the programmer
==================

The object oeis, is a method function with options (Macaulay2Doc).

-------------------------------------------------------------------------------

The source of this document is in OnlineLookup.m2:159:0.