The documentation for Macaulay 2 is available in several formats: text format while in Macaulay2, in info format, and the most important, html format.
The following functions for available for accessing the documentation.While in Macaulay 2, type help to get a summary of the most useful ways of obtaining help on a topic or function. TypeviewHelp to start the web browser (if necessary) and to point it at the page index.html in your .Macaulay2 directory. For help on a specific topic, e.g., the jacobian function, use viewHelp jacobian or viewHelp "jacobian" or if you want the documentation for jacobian of an Ideal, use viewHelp (jacobian,Ideal)
Using 'help' instead of 'viewHelp' results in the help text appearing in your Macaulay2 session.
i1 : help "jacobian"
o1 = jacobian -- the Jacobian matrix of partial derivatives
******************************************************
Description
===========
See also
========
* "diff" -- differentiate or take difference
* "contract" -- contract one matrix by another
Ways to use jacobian :
======================
* "jacobian(Ideal)" -- the Jacobian matrix of the generators of an
ideal
* jacobian(MonomialIdeal), see "jacobian(Ideal)" -- the Jacobian
matrix of the generators of an ideal
* "jacobian(Matrix)" -- the matrix of partial derivatives of
polynomials in a matrix
* "jacobian(Ring)" -- the Jacobian matrix of the polynomials defining
a quotient ring
o1 : DIV
|
A useful tip: in emacs, if you place your cursor on one of the lines which starts with a '*', and press return, then you will get help on that topic.
i2 : * "jacobian(Ideal)"
o2 = jacobian(Ideal) -- the Jacobian matrix of the generators of an ideal
********************************************************************
Synopsis
========
* Usage: jacobian I
* Function: "jacobian"
* Inputs:
* I, an ideal, in a polynomial ring
* Outputs:
* a matrix, the Jacobian matrix of partial derivatives of the
generators of I
Description
===========
This is identical to jacobian generators I. See "jacobian(Matrix)" for
more information.
+-----------------------------+
|R = QQ[x,y,z]; |
+-----------------------------+
|I = ideal(y^2-x*(x-1)*(x-13))|
+-----------------------------+
|jacobian I |
+-----------------------------+
If the ring of I is a polynomial ring over a polynomial ring, then
indeterminates in the coefficient ring are treated as constants.
+---------------------------------+
|R = ZZ[a,b,c][x,y,z] |
+---------------------------------+
|jacobian ideal(a*y*z+b*x*z+c*x*y)|
+---------------------------------+
o2 : DIV
|
The function apropos is useful to find functions and other defined symbols which match a search string. For example, to find all symbols in Macaulay2 which contain the string 'deal', use
i3 : apropos "deal"
o3 = {fittingIdeal, graphIdeal, Ideal, ideal, isIdeal, isMonomialIdeal,
------------------------------------------------------------------------
monomialCurveIdeal, MonomialIdeal, monomialIdeal, monomialSubideal}
o3 : List
|
The documentation for most functions comes with example code. You can obtain the text of this example code using examples.
i4 : examples "jacobian(Ideal)"
o4 = R = QQ[x,y,z];
I = ideal(y^2-x*(x-1)*(x-13))
jacobian I
R = ZZ[a,b,c][x,y,z]
jacobian ideal(a*y*z+b*x*z+c*x*y)
|
which returns it as a string. To place these on their own lines, print the string.
i5 : print examples "jacobian(Ideal)" R = QQ[x,y,z]; I = ideal(y^2-x*(x-1)*(x-13)) jacobian I R = ZZ[a,b,c][x,y,z] jacobian ideal(a*y*z+b*x*z+c*x*y) |