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8.9.32 bfunction, bfct, generic_bfct, ann, ann0

bfunction(f)
bfct(f)
generic_bfct(plist,vlist,dvlist,weight)
:: Computes the global b function of a polynomial or an ideal
ann(f)
ann0(f)
:: Computes the annihilator of a power of polynomial

return
polynomial or list
f
polynomial
plist
list of polynomials
vlist dvlist
list of variables

 
[0] load("bfct")$
[216] bfunction(x^3+y^3+z^3+x^2*y^2*z^2+x*y*z);
-9*s^5-63*s^4-173*s^3-233*s^2-154*s-40
[217] fctr(@);
[[-1,1],[s+2,1],[3*s+4,1],[3*s+5,1],[s+1,2]]
[218] F = [4*x^3*dt+y*z*dt+dx,x*z*dt+4*y^3*dt+dy,
x*y*dt+5*z^4*dt+dz,-x^4-z*y*x-y^4-z^5+t]$
[219] generic_bfct(F,[t,z,y,x],[dt,dz,dy,dx],[1,0,0,0]);
20000*s^10-70000*s^9+101750*s^8-79375*s^7+35768*s^6-9277*s^5
+1278*s^4-72*s^3
[220] P=x^3-y^2$
[221] ann(P);
[2*dy*x+3*dx*y^2,-3*dx*x-2*dy*y+6*s]
[222] ann0(P);
[-1,[2*dy*x+3*dx*y^2,-3*dx*x-2*dy*y-6]]

References
8.8 Weyl algebra.



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