clicliclic@freenet.de schrieb:   
   >   
   > 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*x   
   ^7+(-245/48)*x4   
   > > ^5+(-2375/1152)*x4^3+(-3125/12288)*x4)*x3^8+((85/12)*x4^8+(5   
   7/72)*x4^6+(2309   
   > > 5/9216)*x4^4+(31625/73728)*x4^2+(3125/55296))*x3^7+((-787/10   
   )*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+(   
   075/73728)*x4^2+   
   > > (625/110592))*x3^5+((-151/72)*x4^11+(-179/144)*x4^9+(-6241/9   
   16)*x4^7+(-11683   
   > > 3/589824)*x4^5+(-32335/884736)*x4^3+(-125/24576)*x4)*x3^4+((   
   051/1728)*x4^12+   
   > > (773/2304)*x4^10+(15941/73728)*x4^8+(3059/49152)*x4^6+(5011/   
   94912)*x4^4+(235   
   > > /147456)*x4^2+(125/884736))*x3^3+((-65/576)*x4^13+(-37/576)*   
   4^11+(-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+((-1/17   
   8)*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?   
   >   
      
   Actually, when I copied the Groebner-basis result into Derive, some of   
   the coefficients were modified because spaces in numbers are interpreted   
   as products by Derive. In fact, the results do agree, normalization   
   apart! Good for Derive and for FriCAS.   
      
   Martin.   
      
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