  Using the Oxford Short Wavelength Integral Field specTrograph (SWIFT), we
investigate radial variations of several initial mass function (IMF) dependent
absorption features in M31 and M32. We obtain high signal-to-noise spectra at
six pointings along the major axis of M31 out to ~ 700" (2.7 kpc) and a single
pointing of the central 10 pc for M32. In M31 the sodium NaI {\lambda}8190
index shows a flat equivalent width profile at ~ 0.4 {\AA} through the majority
of the bulge, with a strong gradient up to 0.8 {\AA} in the central 10" (38
pc); the Wing-Ford FeH {\lambda}9916 index is measured to be constant at 0.4
{\AA} for all radii; and calcium triplet CaT {\lambda}8498, 8542, 8662 shows a
gradual increase through the bulge towards the centre. M32 displays flat
profiles for all three indices, with FeH at ~ 0.5 {\AA}, very high CaT at ~ 0.8
{\AA} and low NaI at ~ 0.1 {\AA}. We analyse these data using stellar
population models. We find that M31 is well described on all scales by a
Chabrier IMF, with a gradient in sodium enhancement of [Na/Fe] ~ +0.3 dex in
the outer bulge, rising within the central 10" to perhaps [Na/Fe] ~ +1.0 dex in
the nuclear region. We find M32 is described by a Chabrier IMF and young
stellar age in line with other studies. Models show that CaT is much more
sensitive to metallicity and [{\alpha}/Fe] than to IMF. We note that the
centres of M31 and M32 have very high stellar densities and yet we measure
Chabrier IMFs in these regions.
