A variety V (that is not necessarily a complete intersection) of codimension k is a component of a complete intersection of codimension k defined by k general linear combinations of any generating set of the defining ideal of V.
This function automates the above construction.
i1 : R = CC[x,y,z]; |
i2 : F = {x*y, x^2 - y, x*z};
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i3 : L = generalEquations(2,F)
2
o3 = {(.29398 + .632944*ii)x + (.892712 + .673395*ii)x*y + (.0258884 +
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2
.714827*ii)x*z + (- .29398 - .632944*ii)y, (.461944 + .775187*ii)x +
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(.89189 + .231053*ii)x*y + (.909047 + .314897*ii)x*z + (- .461944 -
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.775187*ii)y}
o3 : List
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The object generalEquations is a method function.