Grobner bases

 

In Reduce

For comparison with other CAS choose from: Axiom Derive Macsyma Maple Mathematica

inputs outputs

• load the module groebner for dealing with Grobner bases

      load_package groebner;
  
      polys := 45*p + 35*s - 165*b - 36,
                35*p + 40*z + 25*t - 27*s,
                15*w + 25*p*s + 30*z - 18*t - 165*b**2,
                - 9*w + 15*p*t + 20*z*s,
                w*p + 2*z*t - 11*b**3,
                99*w - 11*s*b + 3*b**2,
                b**2 + 33/50*b + 2673/10000$
  
      vars :=  w,p,z,t,s,b$
  
      groebner(polys,vars);
  

      {60000*w + 9500*b + 3969,
  
       1800*p - 3100*b - 1377,
  
       18000*z + 24500*b + 10287,
  
       750*t - 1850*b + 81,
  
       200*s - 500*b - 9,
  
              2
       10000*b  + 6600*b + 2673}

• solving a system of polynomial equations by Grobner bases

      groesolve(polys,vars);
  

            - 148*sqrt(11)*i - 461
      {{t=-------------------------,
                     500
  
           190*sqrt(11)*i - 139
        w=----------------------,
                  10000
  
           490*sqrt(11)*i - 367
        z=----------------------,
                   3000
  
            - 62*sqrt(11)*i + 59
        p=-----------------------,
                    300
  
           3*( - 5*sqrt(11)*i - 13)
        s=--------------------------,
                      50
  
           3*( - 4*sqrt(11)*i - 11)
        b=--------------------------},
                     100
  
           148*sqrt(11)*i - 461
       {t=----------------------,
                   500
  
            - 190*sqrt(11)*i - 139
        w=-------------------------,
                    10000
  
            - 490*sqrt(11)*i - 367
        z=-------------------------,
                    3000
  
           62*sqrt(11)*i + 59
        p=--------------------,
                  300
  
           3*(5*sqrt(11)*i - 13)
        s=-----------------------,
                    50
  
           3*(4*sqrt(11)*i - 11)
        b=-----------------------}}
                    100

• other examples