{* Code for the talk 10/6/15 *}
{* Madeline Brandt *}



{*badRes will compute a free resolution in the “naive” way—*}
{* it will repeatedly compute kernels *}

badRes = I -> (
f := gens I;
L:= {};
 while f != 0 do (L = append(L,f); f =gens ker gens image f);
append(L,f);
chainComplex(L)
)



{* How much worse is badRes than the way Macaulay2 computes free resolutions?*}
{* timeRes will take in an integer i output the free resolution and also the times for badRes and res, for the ideal I = (x_0..x_i)*}

timeRes = i -> (
R := QQ[x_0..x_i];
I := ideal(vars R);
time(badRes(I)),
time(res(I))
)





{* EXAMPLE 

R = QQ[x,y,z]
I = ideal(x^2,y^3,z^6)
rs = res I
rs.dd

clearAll
R = QQ[x_0 .. x_14]
load “badres.M2”
time badRes I
time res I
*}