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Drestriction.exa.m2
restart needsPackage "Dmodules" ------------------------- EXAMPLES for Drestriction -------------------------------- -- Example 1: Restriction of a rational function W = QQ[y,t,Dy,Dt, WeylAlgebra => {y=>Dy, t=>Dt}] I = ideal(2*t*Dy+Dt, t*Dt+2*y*Dy+2) -- annihilator of 1/(t^2-y) Drestriction(0, I, {1,0}) -- restriction to y = 0 produces annihilator of 1/t^2 Drestriction(0, I, {0,1}) -- restriction to t = 0 produces annihilator of 1/y --Example 2: Derived restriction of a GKZ hypergeometric system I = gkz(matrix{{1,1,1},{0,1,3}}, {2,3}) W = ring I -- Restriction ideal DrestrictionIdeal(I, {1,0,0}) -- 0th derived restriction module Drestriction(0, I, {1,3,5}) -- restriction to origin Drestriction(0, I, {1,3,0}) -- restriction to {x_1 = x_2 = 0} Drestriction(0, I, {1,0,0}) -- restriction to {x_1 = 0} -- All derived restriction modules Drestriction(I, {1,3,5}) Drestriction(I, {1,3,0}) Drestriction(I, {1,0,0}) -- Explicit generating cycles of derived restriction modules DrestrictionClasses(I, {1,3,5}) DrestrictionClasses(I, {1,3,0}) DrestrictionClasses(I, {1,0,0}) -- Derived restriction complex DrestrictionComplex(I, {1,3,5}) DrestrictionComplex(I, {1,3,0}) DrestrictionComplex(I, {1,0,0}) -- Supplementary info DrestrictionAll(I, {1,3,5}) DrestrictionAll(I, {1,3,0}) DrestrictionAll(I, {1,0,0}) ------------------------- EXAMPLES for Dintegration -------------------------------- -- Example 1: Integration of a rational function W = QQ[y,t,Dy,Dt, WeylAlgebra => {y=>Dy, t=>Dt}] I = ideal(2*t*Dy+Dt, t*Dt+2*y*Dy+2) -- annihilator of 1/(t^2-y) Dintegration(0, I, {1,0}) -- Integrating out y Dintegration(0, I, {0,1}) -- Integrating out t --Example 2: Derived integration of a GKZ hypergeometric system I = gkz(matrix{{1,1,1},{0,1,3}}, {-3,-2}) W = ring I -- 0th derived integration module Dintegration(0, I, {1,3,5}) -- integration to origin Dintegration(0, I, {1,3,0}) -- integration to {x_1 = x_2 = 0} Dintegration(0, I, {1,0,0}) -- integration to {x_1 = 0} -- All derived integration modules Dintegration(I, {1,3,5}) Dintegration(I, {1,3,0}) Dintegration(I, {1,0,0}) -- Explicit generating cycles of derived integration modules DintegrationClasses(I, {1,3,5}) DintegrationClasses(I, {1,3,0}) DintegrationClasses(I, {1,0,0}) -- Derived integration complex DintegrationComplex(I, {1,3,5}) DintegrationComplex(I, {1,3,0}) DintegrationComplex(I, {1,0,0}) -- supplementary info DintegrationAll(I, {1,3,5}) DintegrationAll(I, {1,3,0}) DintegrationAll(I, {1,0,0})