linearSpan -- the linear span of an embedded projective variety

i1 : P = PP_(ZZ/333331)^7;

o1 : ProjectiveVariety, PP^7

i2 : S = apply(3,i -> point P)

o2 = {point of coordinates [8820, -164513, 57316, -59809, -48193, -56352,
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     -4010, 1], point of coordinates [52657, 80278, 91192, -134371, 89048,
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     94196, 149823, 1], point of coordinates [57356, -101469, 57168, 19678,
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     -41460, -89441, 75395, 1]}

o2 : List

i3 : L = linearSpan ⋃ S;

o3 : ProjectiveVariety, surface in PP^7

i4 : assert(L == linearSpan S)

i5 : assert(dim L == 2 and degree L == 1)