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Usage

Parameter Type Description
L A differential operator
m A positive integer

Returns

Returns a matrix

such that the radical solutions of L are described by

where and the are arbitrary constants. If a second argument is present, then only the solutions such that are returned.

Remarks

radicalSolutions returns only the solutions that are radical over , i.e. the solutions such that for some integer . It does not return any eventual solution that is radical over but not over .

Example

We compute the radical solutions of

 (7)

as follows:
1 --> L := 16*D^2 + 3/x^2;
3 --> tex(r);


This means that the radical solutions of (7) form a two-dimensional vector space over the constants generated by and .

Usage within MAPLE

• When using radicalSolutions from inside MAPLE, the result returned from BERNINA is transformed into actual radicals, so the above example in MAPLE would be:
> L := 16*D^2 + 3/x^2;