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 = {(.790217 + .937972*ii)x + (.577401 + .32535*ii)x*y + (.420206 +
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2
.385624*ii)x*z + (- .790217 - .937972*ii)y, (.170527 + .587609*ii)x +
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(.856732 + .541504*ii)x*y + (.897345 + .666045*ii)x*z + (- .170527 -
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.587609*ii)y}
o3 : List
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