# tangentSpace -- tangent space to a projective variety at a point

## Synopsis

• Usage:
tangentSpace(X,p)
tangentSpace(p,X)
• Inputs:
• p, , a point on $X$
• Outputs:
• , the embedded tangent space $T_p(X)$ to $X$ at the point $p$

## Description

 i1 : X = PP_(ZZ/333331)^(3,2); o1 : ProjectiveVariety, threefold in PP^9 i2 : p := point X o2 = point of coordinates [-63251, 140212, 25299, -105446, -91880, -117577, 129587, 38839, 41433, 1] o2 : ProjectiveVariety, a point in PP^9 i3 : tangentSpace(X,p) o3 = threefold in PP^9 cut out by 6 hypersurfaces of degree 1 o3 : ProjectiveVariety, threefold in PP^9