Use R ::= Q[x,y,z];
I := Ideal(x^5,y^3,z^2);
Ideal(0) : (I);
Ideal(0)
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$hom.Hom(R^1/Module(I), R^1); -- from Hom package
Module([0])
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Ext(0, R/I, R^1); --- all those things should be isomorphic
Module([0])
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Ext(0..4, R/I, R/Ideal(0)); -- another way to define the ring R as a quotient
Ext^0 = Module([0])
Ext^1 = Module([0])
Ext^2 = Module([0])
Ext^3 = R^1/Module([x^5], [-y^3], [z^2])
Ext^4 = Module([0])
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N := Module([x^2,y],[x+z,0]);
Ext(0..4,R/I,R^2/N);
Ext^0 = Module([0])
Ext^1 = Module([0])
Ext^2 = R^8/Module([0, 0, 0, -1, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0], [1, x - z, 0, 0, 0, 0, 0, 0], [0, 0, y, x - z, 1, 0, 0, 0], [0, 0, y, x - z, 0, 0, 0, 0], [0, x^3, 0, 0, 0, x + z, 0, 0], [y^2, 0, -z^2, 0, 0, 0, 0, 0], [0, x^4 - x^3z, 0, 0, 0, -z^2, -1, 0], [-y^3z, x^2y^3 - xy^3z + y^3z^2, 0, -x^4 + x^3z - x^2z^2, 0, y^3, 0, 0], [0, x^4 - x^3z, 0, 0, 0, -z^2, 0, 0], [0, 0, 0, 0, 0, 0, 0, -1], [-y^2z^3, -x^4y^2 + x^3y^2z, x^5 + z^5, 0, 0, y^2z^2, 0, 0])
Ext^3 = R^2/Module([x^5, 0], [0, x^5], [-y^3, 0], [0, -y^3], [z^2, 0], [0, z^2], [x^2, y], [x + z, 0])
Ext^4 = Module([0])
-------------------------------
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