Returns generators for the intersection of the submodule I' = Hom(R/image f, E) and the submodule of E generated by y1^d ... yn^d. For this notation, and more details and examples, see
inverse systems.
If I = ideal f contains the powers x1^(d+1), ..., xn^(d+1), then toDual(d,f) is a matrix whose entries correspond to the generators of Hom_R(R/image f, E).
i1 : R = ZZ/32003[a..e];
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i2 : f = matrix{{a^2, b^2, c^2, d^2, e^3, a*d-e^2}}
o2 = | a2 b2 c2 d2 e3 ad-e2 |
1 6
o2 : Matrix R <--- R
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i3 : g = toDual(1,f)
o3 = {1} | abce |
{1} | bcde |
2 1
o3 : Matrix R <--- R
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i4 : ideal fromDual g == ideal f
o4 = false
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i5 : g = toDual(2,f)
o5 = {6} | abce |
{6} | bcde |
{6} | abcd+bce2 |
3 1
o5 : Matrix R <--- R
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i6 : ideal fromDual g == ideal f
o6 = true
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i7 : g = toDual(3,f)
o7 = {11} | abce |
{11} | bcde |
{11} | abcd+bce2 |
3 1
o7 : Matrix R <--- R
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i8 : ideal fromDual g == ideal f
o8 = true
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