Using BERNINA from within MAPLE

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 $D$ and $x$ 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 $D$ and $x$ symbols as parameters, you must provide a third symbol $u$, 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).