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7.7.4.0. fourier
Procedure from library dmodapp.lib (see dmodapp_lib).
- Usage:
- fourier(I[,v]); I an ideal, v an optional intvec
- Return:
- ideal
- Purpose:
- computes the Fourier transform of an ideal in a Weyl algebra
- Assume:
- The basering is the n-th Weyl algebra over a field of characteristic 0
and for all 1<=i<=n the identity var(i+n)*var(i)=var(i)*var(i+1)+1
holds, i.e. the sequence of variables is given by
x(1),...,x(n),D(1),...,D(n), where D(i) is the differential operator
belonging to x(i).
- Note:
- The Fourier automorphism is defined by mapping x(i) to -D(i) and
D(i) to x(i).
If v is an intvec with entries ranging from 1 to n, the Fourier
transform of I restricted to the variables given by v is computed.
Example:
See also:
inverseFourier.
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