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 = {(.20746 + .34883*ii)x + (.486298 + .360247*ii)x*y + (.023807 +
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2
.13525*ii)x*z + (- .20746 - .34883*ii)y, (.823972 + .613244*ii)x +
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(.465658 + .832008*ii)x*y + (.745831 + .445707*ii)x*z + (- .823972 -
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.613244*ii)y}
o3 : List
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