Trying to find an easy way to calculate the tangent space ("Cremona", "MultiprojectiveVarieties")

[Xiangru Zeng]

What I need to do is to calculate (the dimension of) the tangent space of a multiprojective variety at a point.

The first problem I came up with was to define a point using its coordinates, and what I ended up with was to define it as the image of a multiprojective map.

The second problem is that the function "tangentSpace" only works for objects of the class "EmbeddedProjectiveVariety", so I had to convert my point and my variety using the Segre embedding.

The third problem is about the method "segreEmbedding". If X is embedded into a multiprojective variety P, the image of "segreEmbedding X" is taken to be the linear span of the image of X under the Segre embedding of P, which leads to consistency problems.

I guess these packages recommend people code with maps instead of varieties. Any suggestions would be appreciated.