bfunction
, bfct
, generic_bfct
, ann
, ann0
bfunction(f)
and bfct(f)
compute the global b-function b(s)
of
a polynomial f.
b(s)
is a polynomial of the minimal degree
such that there exists P(x,s)
in D[s], which is a polynomial
ring over Weyl algebra D
, and P(x,s)f^(s+1)=b(s)f^s
holds.
generic_bfct(f,vlist,dvlist,weight)
computes the global b-function of a left ideal I
in D
generated by plist, with respect to weight.
vlist is the list of x
-variables,
vlist is the list of corresponding D
-variables.
bfunction(f)
and bfct(f)
implement
different algorithms and the efficiency depends on inputs.
ann(f)
returns the generator set of the annihilator
ideal of f^s
.
ann(f)
returns a list [a,list]
,
where a is the minimal integral root of the global b-function
of f, and list is a list of polynomials obtained by
substituting s
in ann(f)
with a.
[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]]
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