is an ideal, it is regarded as a module in the evident way.
i1 : R = ZZ/32003[a..d];
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i2 : I = monomialCurveIdeal(R,{1,3,4})
3 2 2 2 3 2
o2 = ideal (b*c - a*d, c - b*d , a*c - b d, b - a c)
o2 : Ideal of R
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i3 : M = R^1/I
o3 = cokernel | bc-ad c3-bd2 ac2-b2d b3-a2c |
1
o3 : R-module, quotient of R
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i4 : f = inducedMap(R^1,module I)
o4 = | bc-ad c3-bd2 ac2-b2d b3-a2c |
o4 : Matrix
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i5 : Ext^1(M,f)
o5 = 0
o5 : Matrix
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i6 : g = Ext^2(M,f)
o6 = 0
o6 : Matrix
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i7 : source g == Ext^2(M,source f)
o7 = true
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i8 : target g == Ext^2(M,target f)
o8 = true
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i9 : Ext^3(f,R)
o9 = 0
o9 : Matrix 0 <--- 0
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