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It is possible to use MAPLE as a front end
to BERNINA, provided that
the BERNINA executable is in your path and that the file `bernina.m`
is in the MAPLE library path (you can use the *libname* variable within
MAPLE to ensure the latter). After loading the MAPLE-BERNINA interface
via the `with(bernina)` command, the following functions are available:
`adjoint`, `apply`,
`decompose`, `dfactor`,
`Darboux`,
`eigenring`, `exponentialSolutions`, `exteriorPower`,
`leftGcd`, `leftLcm`, `Loewy`,
`makeIntegral`, `normalize`,
`polynomialKernel`,
`polynomialSolution`,

`radicalSolutions`,
`rationalKernel`, `rationalSolution`,
`rightGcd`, `rightLcm`, `rightQuotient`,
`symmetricKernel`
and `symmetricPower`. Except for the exception noted below, those functions take the
same arguments than their BERNINA analogues, *plus* the two symbols
and that you use for the derivation and independent variable
respectively. For example, where you would use
`-> L12 := symmetricPower(D^2 - x, 12)`

in BERNINA, use
`> L12 := symmetricPower(D^2 - x, 12, D, x)`

from within MAPLE.
See the sample MAPLE worksheet that is provided with BERNINA for
more details. Note that in order not to conflict with the
`factor` and `linalg[kernel]` functions in MAPLE,
the functions `factor` and `kernel`
of BERNINA are provided under MAPLE under the names
`dfactor`,
`polynomialKernel` and `rationalKernel`.
The
exception
to the parameter-passing rule
is
`Darboux`,
for which in addition to the and symbols as parameters,
you must provide a third symbol , to be used as dependent variable
for the bivariate polynomials produced.
Note also that the functions
`decompose`, `dfactor`,
`eigenring`, `exponentialSolutions`,
`polynomialSolution`,
`radicalSolutions` and `rationalSolution`
do some additional processing of the output of BERNINA
when called from within MAPLE (see the corresponding reference
pages for details).

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Manuel Bronstein
2002-09-04