The Rif Package
The Rif package can be used for the simplification of overdetermined
ODE and PDE systems.
It is the successor of the Standard Form project, and has the following
A quick worksheet illustration of the package can be found
here and html versions of the help pages
can be found here.
- Computation with nonlinear systems.
- Advanced case splitting capablilities for discovery of particular
solution branches with desired properties.
- A visualization tool for examination of the binary tree that results from
- Algorithms for working with formal power series solutions of the system.
Information on how to use Maple library and help database files can be
This release (version 1.13 updated
December-24-2002) is a major upgrade of
release 1.10 previously available at this web site.
Release 1.13 is a bug-fix update of release 1.11 and 1.12.
Changes for 1.13 (all releases):
- Adjustment of initialdata and rtaylor (taylorseries) commands to now
properly use Maple's D notation.
- Adjust the use of initial data with rtaylor to allow specialized data,
and still produce a proper expansion.
- Addition of the 'point'=[x=1,...] option to rtaylor, to specify an
Changes for 1.12 (needed for R7 and earlier):
- Repair incorrect handling of inequations (i.e. U[x] <> 0)
when the inequation occurred as a factor in a nonlinear equation.
Changes for 1.11 (needed for R7 and earlier):
- The addition of a new command maxdimsystems, which provides
an efficient way to compute only the highest dimensional cases for
- The addition of new options to allow investigation of only the generic
cases of a problem (arbitrary), those with certain minimum
dimension in certain dependent variables (mindim), and greater
control over the computation path for the problem and the output
- Significant enhancements to the integrability computation code, providing
greater elimination of redundant conditions, resulting in faster computation.
- Significant enhancements to non-linear PDE handling, now using a
combination of decomposition techniques, and Groebner basis methods,
providing a speed up for computation with nonlinear ODE and PDE systems.
- Other miscellaneous code enhancements to provide faster results.
- Miscellaneous bug-fixes from prior version (including the version
released in Maple7).
The latest package in Maple library format (with a help database) is
available in zip format for Release 5:
for Maple 6.x :
and for Maple 7 and 8.x:
Sorry there is no version of Rif that will run under Release 4 or earlier.
Please note: There are a number of differences between how the
package can be used in the different releases of Maple. This is primarily
because the DEtools package references different subsets of the Rif
commands for different Maple versions. These are listed here:
- In this version of Maple, Rif is not part of the DEtools package,
so all Rif commands can be accessed after issuing the command
Some of the examples in the help pages require recent versions of
the ODEtools and PDEtools packages, which are available
- In this version of Maple, some of the Rif commands are part
of DEtools, so the downloaded library updates these commands, as
well as providing all commands for access using with(Rif).
In this case also, some of the examples in the help pages require a recent
version of the ODEtools and PDEtools packages, which are
- In these versions of Maple, all of the Rif commands are part
of DEtools, so the downloaded library updates these commands
only. All commands can be accessed using with(DEtools).
Note: when reading the on-line help pages, please substitute
with(DEtools) for any occurrences of with(Rif).
Note: the help database only contains updated help pages.
The Maple help pages for the Rif package have been converted to html
(using Maple's worksheet to html converter) and can be found below:
If there are any difficulties in using the package, or you suspect bugs,
please make sure they are not addressed in the list below, and send me a mail.
- maxdimsystems and rifsimp with the mindim option does
not always find the minimum dimension case for highly nonlinear systems.
This is true, and part of the design. Only the linear part of the system
is examined when computing the dimension.
- rifsimp seems to run forever.
Though it is true that the algorithm will terminate in theory, it is not
always possible to obtain a solution in finite time and memory due to
intermediate expression swell.
Last updated Dec-24-2002.