Singular

load("schubert.lib");
variety X;
X.dimension = 2;
ring r1 = 0,(x1,x2,x3,x4,u1,u2,u3),dp;
ideal m1 = x1-(u1+u2),x2-u3,x3-((1/2)*u1+(1/2)*u2),x4-(1/2)*u3;
X.baseRing = r1;
X.relations = m1;
;
variety Y;
Y.dimension = 2;
ring r2 = 0,x4,dp;
ideal m2 = x4;
Y.baseRing = r2;
Y.relations = m2;
;
variety M = productVariety(X,Y);
> variety M = productVariety(X,Y);
? `int` expected while building `productVariety(`
? error occurred in or before STDIN line 16: `variety M = productVariety(X,Y);`

Thre are 2 mistakes from your side:

- load is (usually) the wrong way to load a library as it does not publish
the procedure it, use LIB
(see https://www.singular.uni-kl.de/Manual/l ... ng_381.htm,
https://www.singular.uni-kl.de/Manual/l ... ng_276.htm)

- X and Y must not use the same names (x4) for their variables.