DegreeCapSB $\rightarrow aNumber1$ and DegreeSumCapSB $\rightarrow aNumber2$

Beginners should skip this part of Appendix 22 and rely on the $NCProcess$ defaults. The reducing algorithms $SmallBasis$ and $SmallBasisByCategory$ call $NCMakeGB$ (§12.3). These calls to $NCMakeGB$ can be very time consuming and so it can be beneficial to direct $NCMakeGB$. The $NCProcess$ options $DegreeCapSB$ and $DegreeSumCapSB$ are used when $NCProcess$ calls $SmallBasis$ or $SmallBasisByCategory$. Thus DegreeCaps are valuable in limiting the time they consume. In particular,

NCProcess[polys, iters, "filename", DegreeCapSB -> j1,
                          DegreeSumCapSB -> j2, OtherOptions]

produces the call

NCMakeGB[polys, iters, DegreeCap -> j1, DegreeSumCap -> j2, OtherOptions]

inside $SmallBasis$ or $SmallBasisByCategory$ (§ More appears on this in the long document describing the commands $SmallBasis$ and $SmallBasisByCategory$.

The defaults at the moment inside of $NCProcess$ are

$$DegreeCapSB \rightarrow -1$$

$$DegreeSumCapSB \rightarrow -1$$