### ** MULTIPLICITY**

Matlab software for computing **multiplicity structure of nonlinear systems**

### Key points:

**Purpose:** Multiplicity structure of nonlinear systems**Approach:** Closedness subspace method.**Author:** Wenrui Hao, Andrew Sommese, Zhonggang Zeng**Introduction:** ** MULTIPLICITY** uses closedness subspace method to calculate the multiplicity structure of nonlinear systems. The package implements algorithms based on equation-by-equation to compute the closedness subspace. Examples are presented in An algorithm and
software for computing multiplicity structures at zeros of nonlinear
systems.
**Cost:** ** MULTIPLICITY** is distributed free of charge on an ``as is'' basis. Its intended usage is educational, so that the user may gain a greater understanding of multiplicity structure of nonlinear systems. Any other use is strictly the user's responsibility.
**Citation and Attribution:**
In publications based on results obtained using ** MULTIPLICITY** or its successors, the use of ** MULTIPLICITY** should be acknowledged and the paper by (see above) should be cited. Any distribution of derived codes that extend or modify ** MULTIPLICITY** should acknowledge the original source and authorship.
**Feedback:**If you publish a result using ** MULTIPLICITY**, we would like to hear about it. You may write to one of us.

### Installation:

As a suite of m-files, ** MULTIPLICITY** becomes functional by simply adding
the folder containing the routines to Matlab's search path.

Let's say
that you have copied ** MULTIPLICITY** onto your machine with the full
path name of `c:\mypath\Multiplicity`, where "mypath" could
be any path in the file structure of your machine. There are three
basic options for adding ** MULTIPLICITY** to the Matlab path:

- In Matlab (v.6.5 and above), use "File -> Set Path" on
the Matlab menu bar to launch a dialog box
for setting the path and use it to add "
`c:\mypath\Multiplicity`"
to the top of the search path. The change becomes
effective immediately in the current session,
while the "Save" button in the dialog box records it for future
sessions.
OR
- At the Matlab prompt ("
`>>`"), use the command
"`>> addpath c:\mypath\Multiplicity`".
** MULTIPLICITY** will then be available for the current session only.

Any one of these options is sufficient. See the Matlab help
facility to obtain more detailed instructions on modifying the
search path.

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