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.