tangentSpacePoint -- compute the complete intersection of quadrics in the tangent space at a given point

Synopsis

Usage:

(Z,phi) = tangentSpacePoint(point1,J,relPfaf)
Inputs:
- point1, an ideal, defining a point in the complete intersection of the four quadrics Q
- J, an ideal,
- relPfaf, a matrix, a row matrix containing the four quadratic (Pfaffian) relations
Outputs:
- Z, an ideal, in the tangent space of Q at the given point
- phi, a ring map, from the coordinate ring of the P^11 to the coordinate ring of the tangent space

Description

The tangent space of the complete intersection $Q$ at a point $p$ is a linear space isomorphic to a $\mathbb{P}^k$. We compute the projection of the complete intersection $Q$ into this space and the polynomial map on coordinate rings corresponding to this projection. If a second ideal $J$ is given, we compute the intersection of $Q$ with the corresponding variety in $T_p(Q)$.

Ways to use `tangentSpacePoint` :

"tangentSpacePoint(Ideal,Ideal,Matrix)"
"tangentSpacePoint(Ideal,Matrix)"

For the programmer

The object tangentSpacePoint is a method function.

tangentSpacePoint -- compute the complete intersection of quadrics in the tangent space at a given point

Synopsis

Description

Ways to use tangentSpacePoint :

For the programmer

Ways to use `tangentSpacePoint` :