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-- Copyright 1996 by Michael E. Stillman, David Eisenbud
-- based on David Eisenbud's
-- subring and push_forward1 scripts for Macaulay
-- Tests of the subring and pushForward code
-- pushForward1 has been removed, but we can simulate it:
pushforward1 = method(Options => options pushForward)
pushforward1(RingMap, Module) := opts -> (f,M) -> (
S := source f;
g := gens M;
N := source g;
assert( isFreeModule N );
N':= S^(- degrees N);
gens kernel map(M,N',f,id_N))
test1 = () -> (
-- One of the simplest: the rational quartic curve
R = ZZ/101[s,t];
S = ZZ/101[a..d];
f = map(R,S,matrix{{s^4,s^3*t,s*t^3,t^4}});
time J0 = generators kernel f;
time J2 = pushforward1(f,R^1);
assert(image J0 == image J2);
)
test1a = () -> (
R = ZZ/101[s,t];
S = ZZ/101[a..d];
f = map(R,S,matrix{{s^4,s^3*t,s*t^3,t^4}});
J0 = pushforward1(f,R^1,DegreeLimit=>5);
)
test2 = () -> (
-- image of an elliptic curve on the Veronese
-- tests the quotient ring case
R = ZZ/101[symbol x, symbol y, symbol z]/(y^2*z - x*(x+z)*(x-z));
S = ZZ/101[symbol a..symbol f];
F = map(R,S,symmetricPower(2,vars R));
time J0 = generators kernel F;
time J2 = pushforward1(F,R^1);
assert(image J0 == image J2);
)
test3 = () -> (
-- The middle monomial ribbon of genus 5
R = ZZ/101[symbol s, symbol t, symbol y]/(y^2);
S = ZZ/101[vars(0..4)];
f = map(R,S,matrix{{t^4, t^3*s, t^2*s^2, t*s^3-t^3*y, s^4-2*s*t^2*y}});
time J0 = generators kernel f;
time J2 = pushforward1(f,R^1);
assert(image J0 == image J2);
)
test4 = () -> (
-- a simple example where one of the image values is 0
R = ZZ/101[symbol a, symbol b];
f = map(R,R,map(R^1, R^{-1,-1}, {{a,0}}));
time J0 = generators kernel f;
time J2 = pushforward1(f,R^1);
assert(image J0 == image J2);
-- assert(image J1 == image J2);
)
test5 = () -> (
-- a simple example where the entries are not linear independent
R = ZZ/101[symbol a, symbol b, symbol c];
f = map(R,R,matrix{{a,b,a-b}});
time J0 = generators kernel f;
time J2 = pushforward1(f,R^1);
assert(image J0 == image J2);
)
test6 = () -> (
-- a simple example which caused a bug in Macaulay classic
R = ZZ/101[symbol a]/(a^4);
S = ZZ/101[symbol a];
use R;
f = map(R,S,matrix{{a}});
time J0 = generators kernel f;
time J2 = pushforward1(f,R^1);
assert(image J0 == image J2);
)
test7 = () -> (
-- sheaves on P1 x P1
x = symbol x;
y = symbol y;
z = symbol z;
R = ZZ/32003[x_0, x_1, y_0, y_1];
S = ZZ/32003[z_0 .. z_3];
f = map(R,S,matrix{{x_0,x_1}} ** matrix{{y_0,y_1}});
I = matrix{{x_0,y_0}}; -- a point
J = matrix{{x_0,x_1}}; -- the empty set
K = matrix{{x_0*y_0^2 + x_1*y_1^2}}; -- a twisted cubic (i.e. of type (1,2))
time J0 = pushforward1(f,cokernel I);
time J1 = pushforward1(f,cokernel J);
time J2 = pushforward1(f,cokernel K);
assert(image J0 == image matrix{{z_0,z_1,z_2}});
assert(image J1 == image matrix{{z_0,z_1,z_2,z_3}});
assert(image J2 == image matrix{{z_1*z_2-z_0*z_3, z_0*z_2+z_3^2, z_0^2+z_1*z_3}});
)
test8 = () -> (
-- A hard example
S = ZZ/32003[vars(0..3)];
R = ZZ/32003[vars(0..4)];
I = matrix{{a^5 + b^5 + c^5 + d^5 + e^5 - 5*a*b*c*d*e,
e*a^3*b + a*b^3*c + b*c^3*d + c*d^3*e + d*e^3*a,
e^2*a*b^2 + a^2*b*c^2 + b^2*c*d^2 + c^2*d*e^2 + d^2*e*a^2}};
f = map(R,S,matrix{{a+b,2*a+c,3*a+d,4*a+e}});
-- gbTrace = 3;
time J2 = pushforward1(f, cokernel I,MonomialOrder=>ProductOrder);
)
testx = () -> (
-- test the newCoordinateSystem routine, and give an example as to how it gets used
R = ZZ/101[vars(0..7)];
y = matrix{{a+b+c}};
J = matrix{{a-c+d, b-e}};
fg1 = newCoordinateSystem(R, y);
f1 = fg1#0;
g1 = fg1#1;
J1 = f1 J;
J2 = g1 J1;
assert(J == J2);
fg2 = newCoordinateSystem(R, J);
f2 = fg2#0;
g2 = fg2#1;
J3 = f2 y;
J4 = g2 J3;
assert(J4 == y);
)
testx1 = () -> (
-- test the newCoordinateSystem routine, and give an example as to how it gets used
-- Start with a non-saturated ideal, in a ring using an order other than
-- reverse lex.
-- see also 'sat1'.
S = ZZ/101[vars(0..3)];
R = ZZ/101[vars(0..3),MonomialOrder=>Eliminate 2];
I = intersect(
image matrix{{a+b, c^3, a*b^2}},
image matrix{{b^2 - c^2, c^3 - d^3}});
fg = newCoordinateSystem(S, matrix{{a+b}});
Fto = fg#0;
Fback = fg#1;
J1 = mingens image Fback (divideByVariable(generators gb Fto generators I,S_3))#0;
assert(image J1 == image matrix{{b^2 - c^2, c^3 - d^3}});
)
test1()
test2()
test3()
--test4()
test5()
test6()
test7()
test8()
testx()
testx1()
-- Local Variables:
-- compile-command: "make -C $M2BUILDDIR/Macaulay2/packages/Macaulay2Doc/test testsubring.out"
-- End:
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