For example, consider embedded deformations of the fat points in the plane defined by the square and cube of the homogeneous maximal ideal. The following lifts a first order NestedDeformation for this pair to higher order:
i1 : R=QQ[x,y];
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i2 : F0Y=basis(3,R);
1 4
o2 : Matrix R <-- R
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i3 : F0X=basis(2,R);
1 3
o3 : Matrix R <-- R
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i4 : T1Y=normalMatrix(F0Y);
4 12
o4 : Matrix R <-- R
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i5 : T1X=normalMatrix(F0X);
3 6
o5 : Matrix R <-- R
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i6 : T2X=CT^2(F0X);
2 1
o6 : Matrix R <-- R
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i7 : T2Y=CT^2(F0Y);
3 3
o7 : Matrix R <-- R
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i8 : T2XY=nestedObstruction(F0X,F0Y);
4 8
o8 : Matrix R <-- R
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i9 : D=setupNestedDeformation({F0X,T1X,T2X,F0Y,T1Y,T2Y,T2XY});
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i10 : E=versalDeformation(D,Verbose=>4);
Starting lifting
Order 2
Lifting family for X
Calculating tangent cone for obstructions
Calculating residual terms
Lifting Family
Calculating Obstruction Equations
Lifting Relations and Coefficients
Lifting family for Y
Calculating tangent cone for obstructions
Calculating residual terms
Lifting Family
Calculating Obstruction Equations
Lifting Relations and Coefficients
Calculating tangent cone for new obstructions
Calculating joint residual terms
Calculating Joint Obstruction Equations
Changing Families
Changing Relations
Lifting Submodule Relation
Correcting Coefficients
Doing Sanity Check
Checking polynomial lifting
Order 3
Lifting family for X
Calculating tangent cone for obstructions
Calculating residual terms
Lifting Family
Calculating Obstruction Equations
Lifting Relations and Coefficients
Lifting family for Y
Calculating tangent cone for obstructions
Calculating residual terms
Lifting Family
Calculating Obstruction Equations
Lifting Relations and Coefficients
Calculating tangent cone for new obstructions
Calculating joint residual terms
Calculating Joint Obstruction Equations
Changing Families
Changing Relations
Lifting Submodule Relation
Correcting Coefficients
Doing Sanity Check
Checking polynomial lifting
Solution is polynomial
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i11 : obstructions E
o11 = | 0
| 0
| 0
| 0
| s_1s_2+s_1s_3-s_5t_1-s_3t_2-s_1t_3+t_3t_4-t_4t_5-t_1t_6+t_2t_7-t_4t_7
| s_2^2-s_2s_3+s_3^2+2s_1s_4-s_1s_5-s_6t_1-s_4t_2-s_2t_3+t_3t_5-t_5^2-t
| s_3^2+s_1s_4-s_5t_4-s_3t_5-s_1t_6+t_4t_6+t_5t_7-t_7^2-t_4t_8-t_1t_9+t
| s_2s_4+s_1s_6-s_6t_4-s_4t_5-s_2t_6+t_5t_6-t_2t_9+t_4t_9-t_1t_12
| s_3s_5+s_1s_6-s_5t_7-s_3t_8+t_7t_8-s_1t_9+t_4t_9-t_4t_11-t_1t_12
| s_4^2+s_3s_6-t_6^2-s_6t_7-s_4t_8+t_6t_8-s_2t_9+t_3t_9-t_5t_9+t_7t_9-t
| s_4^2-s_4s_5+s_5^2-s_2s_6+2s_3s_6-t_6^2+t_6t_8-t_8^2+t_3t_9-2t_5t_9+t
| s_4s_6+s_5s_6-t_6t_9-t_8t_9-s_6t_10+t_9t_10-s_4t_11+t_6t_11-s_2t_12+t
-----------------------------------------------------------------------
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+t_1t_10 |
_2t_6+t_4t_6+t_5t_7-t_7^2+t_2t_8-2t_4t_8-t_1t_9+t_4t_10+t_1t_11 |
_4t_10 |
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_4t_12 |
_7t_9-s_5t_10+t_8t_10-s_3t_11+t_5t_11-t_7t_11-s_1t_12+t_2t_12-t_4t_12 |
_3t_12-t_7t_12 |
12 1
o11 : Matrix (R[s ..s , t ..t ]) <-- (R[s ..s , t ..t ])
1 6 1 12 1 6 1 12
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