In most places, 'dimension' is treated as projective dimension, but cylinderize takes it to be affine dimension (i.e., the "constant" term is taken to contribute a dimension).
In general, we're somewhat inconsistent about whether the column of constants qualifies as a dimension or not, whether it needs to be specified as part of the cylinderization coordinate map, ... . We should pick a sane convention and stick to it.
In most places, 'dimension' is treated as projective dimension, but
cylinderizetakes it to be affine dimension (i.e., the "constant" term is taken to contribute a dimension).In general, we're somewhat inconsistent about whether the column of constants qualifies as a dimension or not, whether it needs to be specified as part of the cylinderization coordinate map, ... . We should pick a sane convention and stick to it.