I have an expression where the variables are algebraic integers: $p4 = \frac{p12 - p41 \cdot p21}{p22}$ p12 is degree 48 and p22 is most likely degree 48 too. p41 is degree 32 and p21 is degree 24. I am trying to avoid a geometric increase in degrees, p41*p21 is 32*24 = 768 and p12 - p41*p21 would be 48*768 = 36864 and then dividing this by p22 would give 48*36864 = degree 1769472 would is well beyond the capability of my computer (using GP-Pari)

How can this be simpified? I strongly suspect that p42 is degree 192, but have no way to determine this unless I grind it out using the algdep command of GP-Pari which depends upon the accuracy of the digits (which will have to be around 20K) This would take several days to run.

Thanks for your suggestions.

- Randall