From: nma@12000.org   
      
   On 7/4/2019 12:37 PM, clicliclic@freenet.de wrote:   
   >   
   > Hello,   
   >   
   > can this trivariate polynomial:   
   >   
   > 256*a^5*c^3 - a^4*(128*b^2*c^2 - 144*b*c - 512*c^4 + 27)   
   >   + a^3*(16*b^4*c - 4*b^3 - 512*b^2*c^3 + 208*b*c^2 + 4*c*(64*c^4 - 9))   
   >   + 2*a^2*(80*b^4*c^2 - 82*b^3*c + b^2*(15 - 64*c^4) - 104*b*c^3 - c^2)   
   >   - 4*a*(4*b^6*c - b^5 - 4*b^4*c^3 - 41*b^3*c^2 + 35*b^2*c   
   >         + 6*b*(6*c^4 - 1) + 9*c^3)   
   >   - 4*b^5*c + b^4 + 4*b^3*c^3 + 30*b^2*c^2 - 24*b*c - 27*c^4 + 4   
   >   
   > be factored over the algebraic extension combining 2^(1/4), 3^(1/8),   
   > and SQRT(SQRT(3) + 1)? In FriCAS one would enter:   
   >   
   > r2:=rootOf(r2^4-2)   
   > r3:=rootOf(r3^8-3)   
   > rs:=rootOf(rs^2-r3^4-1)   
   > factor(256*a^5*c^3 - a^4*(128*b^2*c^2 - 144*b*c - 512*c^4 + 27) +   
   > a^3*(16*b^4*c - 4*b^3 - 512*b^2*c^3 + 208*b*c^2 + 4*c*(64*c^4 - 9)) +   
   > 2*a^2*(80*b^4*c^2 - 82*b^3*c + b^2*(15 - 64*c^4) - 104*b*c^3 - c^2) -   
   > 4*a*(4*b^6*c - b^5 - 4*b^4*c^3 - 41*b^3*c^2 + 35*b^2*c + 6*b*(6*c^4 -   
   > 1) + 9*c^3) - 4*b^5*c + b^4 + 4*b^3*c^3 + 30*b^2*c^2 - 24*b*c -   
   > 27*c^4 + 4, [r2, r3, rs])   
   >   
   > but the web interface bumps into its 5min timeout.   
   >   
   > Martin :(.   
   >   
      
   on Liux it finished agfter about 8-10 minutes. But as metioned, it did   
   not factor to product of terms. Here is the result   
      
       (6)   
      "256::AlgebraicNumber()*primeFactor((1::AlgebraicNumber()*a^3   
   c^5+(((-1)/2)::   
      AlgebraicNumber()*a^2*b^2+((-9)/16)::AlgebraicNumber()*a*b+(2   
   :AlgebraicNumbe   
      r()*a^4+((-27)/256)::AlgebraicNumber()))*c^4+((1/16)::Algebra   
   cNumber()*a*b^4   
      +(1/64)::AlgebraicNumber()*b^3+(-2)::AlgebraicNumber()*a^3*b^   
   +((-13)/16)::Al   
      gebraicNumber()*a^2*b+(1::AlgebraicNumber()*a^5+((-9)/64)::Al   
   ebraicNumber()*   
      a))*c^3+((5/8)::AlgebraicNumber()*a^2*b^4+(41/64)::AlgebraicN   
   mber()*a*b^3+((   
      (-1)/2)::AlgebraicNumber()*a^4+(15/128)::AlgebraicNumber())*b   
   2+(13/16)::Alge   
      braicNumber()*a^3*b+((-1)/128)::AlgebraicNumber()*a^2)*c^2+((   
   -1)/16)::Algebr   
      aicNumber()*a*b^6+((-1)/64)::AlgebraicNumber()*b^5+(1/16)::Al   
   ebraicNumber()*   
      a^3*b^4+((-41)/64)::AlgebraicNumber()*a^2*b^3+((-35)/64)::Alg   
   braicNumber()*a   
      *b^2+((9/16)::AlgebraicNumber()*a^4+((-3)/32)::AlgebraicNumbe   
   ())*b+((-9)/64)   
      ::AlgebraicNumber()*a^3)*c+((1/64)::AlgebraicNumber()*a*b^5+(   
   /256)::Algebrai   
      cNumber()*b^4+((-1)/64)::AlgebraicNumber()*a^3*b^3+(15/128)::   
   lgebraicNumber(   
      )*a^2*b^2+(3/32)::AlgebraicNumber()*a*b+(((-27)/256)::Algebra   
   cNumber()*a^4+(   
      1/64)::AlgebraicNumber())))::Polynomial(AlgebraicNumber()),1)"   
      
   Which is hard to read, so the latex version is here   
      
   https://www.12000.org/tmp/070419/foo.pdf   
      
   --Nasser   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)