This computes the distraction of a torus fixed D-ideal [SST, Corollary 2.3.5]. This is necessary to compute indicial ideals [SST, Theorem 2.3.9, Corollary 2.3.5]; the roots of the indicial ideals are the exponents of the starting terms of canonical series solutions of regular holonomic D-ideals.
i1 : R1 = QQ[z] o1 = R1 o1 : PolynomialRing |
i2 : W1 = makeWA R1 o2 = W1 o2 : PolynomialRing, 1 differential variables |
i3 : a=1/2
1
o3 = -
2
o3 : QQ
|
i4 : b=3 o4 = 3 |
i5 : c=5/3
5
o5 = -
3
o5 : QQ
|
i6 : J = ideal(z*(1-z)*dz^2+(c-(a+b+1)*z)*dz-a*b) -- the Gauss hypergeometric equation, exponents 0, 1-c
2 2 2 9 5 3
o6 = ideal(- z dz + z*dz - -z*dz + -dz - -)
2 3 2
o6 : Ideal of W1
|
i7 : cssExpts(J,{1})
2
o7 = {{0}, {- -}}
3
o7 : List
|
i8 : K = inw(J,{-1,1})
2
o8 = ideal(6z*dz + 10dz)
o8 : Ideal of W1
|
i9 : distraction(K,QQ[s])
2
o9 = ideal(6s + 4s)
o9 : Ideal of QQ[s]
|
The object indicialIdeal is a method function.