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 = {(.295188 + .186346*ii)x + (.159334 + .643289*ii)x*y + (.165003 +
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2
.18586*ii)x*z + (- .295188 - .186346*ii)y, (.875833 + .125011*ii)x +
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(.144017 + .172287*ii)x*y + (.904457 + .938437*ii)x*z + (- .875833 -
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.125011*ii)y}
o3 : List
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