The subroutines described earlier in this book for converting between the various coordinate systems are quite satisfactory for normal use where you have a requirement for one particular conversion. However, it is sometimes convenient to have a more general routine to hand which can be used to convert from one system to any other system, at the flick of a (software) switch. We can use matrices for this purpose, ordered sets of numbers set out in rows and columns. The manipulation of the matrices is always the same; to change from one system to another you merely have to change the numbers in the matrices.

Subroutine GENCON is able to produce and manipulate just four different matrices, appropriate for conversions between azimuth/altitude and hour angle/declination, hour angle/declination and right ascension/declination, right ascension/declination and ecliptic longitude/latitude, and right ascension/ declination and galactic longitude/latitude. However, you can use it to convert coordinates from any of the systems to any other system by serial conversion. For example, suppose that you wish to know the azimuth and altitude of a pulsar whose galactic coordinates you have to hand. You would first convert to right ascension/declination, then to hour angle/declination, and finally to azimuth/altitude. GENCON will do this triple conversion automatically.