|  |  7.5.5.0. fourier Procedure from librarydmodapp.lib(see  dmodapp_lib).
 
Example: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.
 
 See also:
 inverseFourier.|  | LIB "dmodapp.lib";
ring r = 0,(x,y,Dx,Dy),dp;
def D2 = Weyl();
setring D2;
ideal I = x*Dx+2*y*Dy+2, x^2*Dx+y*Dx+2*x;
intvec v = 2;
fourier(I,v);
==> _[1]=x*Dx-2*y*Dy
==> _[2]=x^2*Dx-Dx*Dy+2*x
fourier(I);
==> _[1]=-x*Dx-2*y*Dy-1
==> _[2]=x*Dx^2-x*Dy
 | 
 
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