The directory PJ contains public domain Mathematica software written by
Pekka Janhunen
Finnish Meteorological Institute
Geophysics Dept.
email: pjanhune@finsun.csc.fi
Most of the files are also available at the Mathematica User Group
anonymous FTP server, 128.174.20.50, Symbolic/Mathematica/Packages/JANHUNEN.
Here is a list of the files and a brief description of each:
Mma program Test file etc.
----------- --------------
Declare.m DeclareDemo.m
DFormat.m --
DSubst.m --
NonlinearFit.m NLFitTest.m
FortranDef.m FortranDefDemo.m
DeltaTheta.m TotalTest.m Trig.m
EinsteinTensor.m EinsteinTensorDemo.m
Declare.m
---------
This package gives Mma more intelligence in handling mathematical relations
symbolically. It enables you to declare variables to be Even, Odd, Integer,
Positive, Negative, Real, etc. and uses that information cleverly. For example,
if you Declare[x,Real], then Sqrt[-x^2] will return I Abs[x] instead of
just I x as it normally would.
Testing: see TotalTest.m where this package is used together with other ones.
See also: DeclareDemo.m.
DFormat.m
---------
This small script alters the format in which Mma outputs symbolic partial deriva
tives.
The new notation contains the familiar partial derivative (the modified "d") sig
ns.
DSubst.m
--------
This package makes it possible to perform changes of variables and dependent
functions in (systems of) differential equations.
DeltaTheta.m
------------
This package defines the Dirac Delta and Heaviside Theta functions and assigns
full symbolic rules to them. For instance, after loading this package Mma
knows that Integrate[DiracDelta[x]f[x],{x,-Infinity,Infinity}] gives f[0].
Testing: see TotalTest.m.
NonlinearFit.m
--------------
This package enables one to do nonlinear fittings to numerical data (a generaliz
ation
of the standard function Fit[]). The data may be multidimensional. The program
uses the Levenberg-Marquardt iterative method.
Testing: see NLFitTest.m.
FortranDef.m
------------
Given a Mathematica expression, this package generates automatically a Fortran
program that computes the value(s) of this expression. There are many options
available. Testing: see FortranDefDemo.m.
Trig.m
------
This is a trivial modification of the standard package Trigonometry.m that
works better with Declare.m.
EinsteinTensor.m
----------------
This simple "package" computes the Einstein tensor in general relativity.
Sample usage: see EinsteinTensorDemo.m
EinsteinTensorDemo.m
--------------------
This script uses EinsteinTensor.m and computes symbolically the Einstein tensors
for various well-known spacetimes, for instance, for the Schwarzschild geometry
(a nonrotating, non-charged black hole).