I have a system of equations which are clearly linear with respect to some of the variables (in my problem these are b_0_8 and b_0_9). So technically one should be able to get the solution using only linsolve for solving only these variables. In giac I am able to arrive to the solution using Groebner basis ellimination, but I think this is too expensive for this system of equations (I don't know whats behind gbasis of giac, but is it correct to assume that it's more expensive to use gbasis than linsolve if both can arrive to the system of solutions?). I tried this both in giacpy and XCas yielding empty solutions with linsolve. In any case, I illustrate the problem here (in giacpy code):
Code : Tout sélectionner
from giacpy import giac, gbasis
vars = giac("[b_0_8,b_0_9,s,t]")
ideal = giac("[64*b_0_8*t^2-32*b_0_8+64*b_0_9*t-64*b_0_9+1280, 12*b_0_8*s^3*t-16*b_0_8*s*t^2+24*b_0_8*s*t-12*b_0_9*s^3*t^2-8*b_0_9*s*t^2+32*b_0_9*s+192*s^3*t^2-96*s^3*t+256*s*t^2-192*s*t, -16*b_0_8*s+12*b_0_9*s^3*t-16*b_0_9*s*t^2+24*b_0_9*s*t+192*s^3*t^2-192*s^3*t+384*s*t^2-384*s*t-384*s, -12*b_0_8*s^3*t^2-8*b_0_8*s*t^2+32*b_0_8*s-32*b_0_9*s+96*s^3*t^2-384*s^3*t+576*s*t^2-768*s*t+256*s, 8*b_0_8+128*t^2-64, 16*b_0_9+256*t-256, 16*b_0_8+256*t^2-128, 16*b_0_9+256*t-256,-4+3*s^4+(-4*t+4)*s^2,t^3-2]")
gb = gbasis(ideal,vars,"plex") #returns the correct solution, [b_0_8+16*t^2-8,b_0_9+16*t-16,3*s^4-4*s^2*t+4*s^2-4,t^3-2]
# print linsolve(ideal, giac("[b_0_8,b_0_9]") # does not return a solution, even if I remove the last two equations in ideal, why? this is linear wrt the given variables)