Using the coefficients for the SIP-deprojection

It looks to me that astropy.wcs.WCS.all_world2pix() never uses the coefficients for de-projection (AP/BP_ORDER and AP/BP_i_j). Even if these coefficients do exist, such as for Spitzer images, the code always does an iterative solution.

While this may lead to a mathematical more accurate solutions, the de-projections from the coefficients might tell you something about the accuracy of the calibration in total.

So, is there a possibility to get the world2pix conversion on the basis of those coefficients, and if not, wouldn't it be good to have that?

Start with astropy.wcs.WCS.all_world2pix() and trace how its current iterative solution handles SIP deprojection. Investigate how AP/BP_ORDER and AP/BP_i_j coefficients are represented and whether a coefficient-based conversion can be exposed without changing existing behavior. Done means the supported behavior is defined and validated for images that provide these coefficients.

Written by the indexing model from the issue text.