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,
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216] reduced the question of uniform finiteness in the quadratic case to proving finite cyclicity of 121 graphics. Today ca 85 of these have been successfully dealt with ,
, , vol.156
,
, , p.13
16 Let G and g be as in Assumption 9, vol.9 ,
,
Using Proposition 9.15, one needs to prove that G g r ?(L · f )dx and ?G L L (f, g r ?) · n dS are zero. The first one is trivial since L ? Ann(f ). For the second, L L (f, g r ?) involves derivatives ? ? x (g r ?) with |?| < r ,
and g ? |[x] vanishing over ?G, each operator g r i L i (with r i the order of L i ) annihilates f ? G as a distribution. Therefore, each operator R i := (g r i L i ) M gives a valid recurrence for the sequence of moments ,
, g r k L k } is holonomic. Similarly, we are not able to prove (or refute) that {R 1 , . . . , R k } is holonomic in general. Nevertheless, one can apply a Gröbner basis algorithm, which will possibly return a basis of a holonomic ideal. This heuristic is given in Algorithm RecurrencesMoments, However, from the fact that f is holonomic one can not directly guarantee that the ideal generated by {g r 1 L 1
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