Waldek Hebisch schrieb:   
   >   
   > Using lexicographic order seem to take a lot of time and   
   > memory.  Using elimination order (homogeneous in blocks) in   
   > FriCAS I get only one polynomial in elimination ideal:   
   >   
   > (x4^6+(25/16)*x4^4+(625/768)*x4^2+(15625/110592))*x3^9+(-4*x4^7+(-245/48)*x4   
   > ^5+(-2375/1152)*x4^3+(-3125/12288)*x4)*x3^8+((85/12)*x4^8+(527/72)*x4^6+(2309   
   > 5/9216)*x4^4+(31625/73728)*x4^2+(3125/55296))*x3^7+((-787/108)*x4^9+(-439/72)   
   > *x4^7+(-19543/9216)*x4^5+(-63125/110592)*x4^3+(-625/8192)*x4)*x3^6+((691/144)   
   > *x4^10+(119/36)*x4^8+(77375/55296)*x4^6+(28571/65536)*x4^4+(4075/73728)*x4^2+   
   > (625/110592))*x3^5+((-151/72)*x4^11+(-179/144)*x4^9+(-6241/9216)*x4^7+(-11683   
   > 3/589824)*x4^5+(-32335/884736)*x4^3+(-125/24576)*x4)*x3^4+((1051/1728)*x4^12+   
   > (773/2304)*x4^10+(15941/73728)*x4^8+(3059/49152)*x4^6+(5011/294912)*x4^4+(235   
   > /147456)*x4^2+(125/884736))*x3^3+((-65/576)*x4^13+(-37/576)*x4^11+(-9085/2211   
   > 84)*x4^9+(-2309/147456)*x4^7+(-123/32768)*x4^5+(-187/442368)*x4^3+(-25/294912   
   > )*x4)*x3^2+((7/576)*x4^14+(97/12288)*x4^12+(49/12288)*x4^10+(139/49152)*x4^8+   
   > (91/442368)*x4^6+(79/589824)*x4^4+(1/98304)*x4^2)*x3+((-1/1728)*x4^15+(-17/36   
   > 864)*x4^13+(-5/36864)*x4^11+(-35/147456)*x4^9+(1/49152)*x4^7+(-1/65536)*x4^5)   
   >   
      
   Thanks for the private message. Meanwhile I have sped matters up by   
   teaching Derive how to do resultants:   
      
   resultant(f, g, x, n, m, a, h) := PROG(   
     n := POLY_DEGREE(f, x),   
     m := POLY_DEGREE(g, x),   
     IF(n > m,   
       RETURN (-1)^(n*m)*resultant(g, f, x),   
       PROG(   
         a := POLY_COEFF(f, x, n),   
         IF(n = 0,   
           RETURN a^m,   
           PROG(   
             h := REMAINDER(g, f, x),   
             IF(IDENTICAL?(h, 0),   
               RETURN 0,   
               RETURN a^(m - POLY_DEGREE(h, x))*resultant(f, h, x)))))))   
      
   Running resultant(resultant(lhs1, lhs2, x1), lhs3, x2) gives a result   
   quite similar to yours, albeit squared:   
      
   4194304*(16*x3^9*(110592*x4^6 + 172800*x4^4 + 90000*x4^2 + 15625)   
   - 48*x3^8*x4*(147456*x4^6 + 188160*x4^4 + 76000*x4^2 + 9375)   
   + 8*x3^7*(1566720*x4^8 + 1618944*x4^6 + 554280*x4^4 + 94875*x4^2   
   + 12500) - 8*x3^6*x4*(1611776*x4^8 + 1348608*x4^6 + 469032*x4^4   
   + 126250*x4^2 + 16875) + x3^5*(8491008*x4^10 + 5849088*x4^8   
   + 2476000*x4^6 + 771417*x4^4 + 97800*x4^2 + 10000)   
   - x3^4*x4*(3710976*x4^10 + 2199552*x4^8 + 1198272*x4^6 + 350499*x4^4   
   + 64670*x4^2 + 9000) + 2*x3^3*(538112*x4^12 + 296832*x4^10   
   + 191292*x4^8 + 55062*x4^6 + 15033*x4^4 + 1410*x4^2 + 125)   
   - 2*x3^2*x4*(99840*x4^12 + 56832*x4^10 + 36340*x4^8 + 13854*x4^6   
   + 3321*x4^4 + 374*x4^2 + 75) + x3*x4^2*(21504*x4^12 + 13968*x4^10   
   + 7056*x4^8 + 5004*x4^6 + 364*x4^4 + 237*x4^2 + 18)   
   - x4^5*(1024*x4^10 + 816*x4^8 + 240*x4^6 + 420*x4^4 - 36*x4^2   
   + 27))^2   
      
   The squaring doesn't worry me, but that the factors are not fully   
   proportional does very much. Could there be a bug somewhere?   
      
   Martin.   
      
   PS: Alas, my bivariate polynomial doesn't factor, nor does the next   
   higher one. The polynomials do possess an expected property, though -   
   they have no solutions for x3 >= 0, x4 <= 0 except [0,0] - but without   
   some simple common structure, this property seems hopeless to establish   
   for all orders.   
      
   --- SoupGate-Win32 v1.05   
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