rwg>For etas, you want to avoid nonconstant coefficients in
the reduction process, and all you really need is the ECHELON function. And more than an I286 worth of VM. So for 17, moved to MMa. Which has no Echelon function! So, just use RowReduce. What can it cost? A factor of two? Try a few thousand! With RowReduce, it couldn't even do the 13 case! So I had to bleeping write my own Echelon:
4294967296*h17^2*h2^96-1648529244160*h1^12*h17^6*h2^80+67108864*h1^24*h17^2*h2^72-7771775074107392*h1^18*h17^16*h2^64+137158277070848*h1^24*h17^10*h2^64-9110093824*h1^30*h17^4*h2^64-19318702080*h1^36*h17^6*h2^56-5071143952847839744*h1^24*h17^26*h2^48-94961376686749696*h1^30*h17^20*h2^48-922310028528640*h1^36*h17^14*h2^48-2119493040128*h1^42*h17^8*h2^48+138752*h1^48*h17^2*h2^48-60716992766464*h1^42*h17^16*h2^40+1071549039616*h1^48*h17^10*h2^40-71172608*h1^54*h17^4*h2^40-827240261886336764177*h1^30*h17^36*h2^32-28624230515098157930*h1^36*h17^30*h2^32-437549300159550511*h1^42*h17^24*h2^32-3052451941032780*h1^48*h17^18*h2^32-7818231011807*h1^54*h17^12*h2^32+2834555350*h1^60*h17^6*h2^32-h1^66*h2^32-19809156065811874*h1^48*h17^26*h2^24-370942877682616*h1^54*h17^20*h2^24-3602773548940*h1^60*h17^14*h2^24-8279269688*h1^66*h17^8*h2^24+30*h1^72*h17^2*h2^24-118587876497*h1^66*h17^16*h2^16+2092869218*h1^72*h17^10*h2^16-139009*h1^78*h17^4*h2^16-98260*h1^84*h17^6*h2^8+h1^96*h17^2 2 96 12 6 80 4294967296 h17 h2 - 1648529244160 h1 h17 h2 24 2 72 18 16 64 + 67108864 h1 h17 h2 - 7771775074107392 h1 h17 h2 24 10 64 30 4 64 + 137158277070848 h1 h17 h2 - 9110093824 h1 h17 h2 36 6 56 24 26 48 - 19318702080 h1 h17 h2 - 5071143952847839744 h1 h17 h2 30 20 48 36 14 48 - 94961376686749696 h1 h17 h2 - 922310028528640 h1 h17 h2 42 8 48 48 2 48 - 2119493040128 h1 h17 h2 + 138752 h1 h17 h2 42 16 40 48 10 40 - 60716992766464 h1 h17 h2 + 1071549039616 h1 h17 h2 54 4 40 30 36 32 - 71172608 h1 h17 h2 - 827240261886336764177 h1 h17 h2 36 30 32 - 28624230515098157930 h1 h17 h2 42 24 32 - 437549300159550511 h1 h17 h2 48 18 32 54 12 32 - 3052451941032780 h1 h17 h2 - 7818231011807 h1 h17 h2 60 6 32 66 32 + 2834555350 h1 h17 h2 - h1 h2 48 26 24 54 20 24 - 19809156065811874 h1 h17 h2 - 370942877682616 h1 h17 h2 60 14 24 66 8 24 - 3602773548940 h1 h17 h2 - 8279269688 h1 h17 h2 72 2 24 66 16 16 + 30 h1 h17 h2 - 118587876497 h1 h17 h2 72 10 16 78 4 16 + 2092869218 h1 h17 h2 - 139009 h1 h17 h2 84 6 8 96 2 - 98260 h1 h17 h2 + h1 h17 There is very probably a simpler p{a,b,17}, but the Resultants are so enormous that it is probably easier to Echelon for it de novo. --rwg PS, there's probably nothing wrong with RowReduce--it's just the wrong tool for this job.