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-- Frank Schreyer
artinianGorensteinRing = (p,n,d,s) -> (
-- p = characteristic
-- n+1 = number of variables
-- d = degree of the socle
-- s = number of powers presenting the dual socle
R := ZZ/p[vars(0 .. n)];
if s <= n then error "expected s to be more than the number of variables";
D := sum(n+1,i->R_i^d) + (
if s > n+1
then (sum(n+1,i->R_i))^d + sum(s-n-2,i->(random(1,R))^d)
else 0
); -- a diff'l operator
-- switch point of view and find which polynomials of each degree e,
-- when regarded as diff'l operators, annihilate D
e := 2;
I := map(R^1,R^0,0);
v := symmetricPower(d,vars R);
while (
c := codim cokernel I;
c < n+1
-- or c === n+1 and numgens source mingens image (v % I) > 1
) do (
w := symmetricPower(e,vars R);
I = mingens image (I | w * (syz(diff(w,matrix {{D}})
-- ,{d-e} -- ??
)));
e = e+1;
);
I)
p = 101
-- put an hour time limit later on each one
--scan(3 .. 20, n ->
-- scan(2 .. 10, d ->
-- try scan(n+1 .. n + (binomial(n+d,n)) // n,
-- s -> (
-- << "n = " << n << " d = " << d << " s = " << s << "\n";
-- I := artinianGorensteinRing(p,n,d,s);
-- gbTrace = 2;
-- time C := resolution I;
-- gbTrace = 0;
-- betti C;
-- )
-- )
-- else << "terminating inner loop\n"
-- )
-- )
--
-- Frank is interested in the set of (d,n) such that computations of resolution I,
-- for the last s, can be done in less than time T, for various T, 1min, 1hr, 1day.
end
-- Local Variables:
-- compile-command: "make -C $M2BUILDDIR/Macaulay2/packages/Macaulay2Doc/test schreyer.out"
-- End:
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