The function prem  returns the pseudo-remainder r such that

where  and m (the multiplier) is:

If the fourth argument is present it is assigned the value of the multiplier m defined above.  If the fifth argument is present, it is assigned the pseudo-quotient q defined above.

The function sprem has the same functionality as prem except that the multipler m will be  to the power of the number of division steps performed rather than the degree difference. When sprem can be used it is preferred because it is more efficient.