implicitEq -- computes the gcd of the right-most map of the Z-complex in degree nu)

Synopsis

• Usage:

  iEq = implicitEq(polynomialList, nu)

• Inputs:

  • polynomialList, a list, polynomialList 'f={f0,...,fn}' defining the rational map
  • nu, a list, the multidegree where ti take the homogeneous strand of the map f (i.e.: R_d)
• Optional inputs:

  • Strategy => ..., -- computes the gcd of the right-most map of the Z-complex in degree nu)
• Outputs:

  • iEq, a matrix, An homogeneous polynomial in QQ[X_0,...,X_n] defining the implicit equation of f

Description

i1 : A=QQ[s,u,t,v,Degrees=>{{1,1,0},{1,1,0},{1,0,1},{1,0,1}}];

i2 : f0=s*t*u*v+t*u^2*v; f1=s*u*v^2; f2=u*t^2*s+u^2*t^2; f3=s^2*t*v+s*t*u*v;

i6 : implicitEq({f0,f1,f2,f3},{2,1,1})

o6 = | X_0  0    X_0  0    X_1  |
     | -X_2 0    0    X_0  0    |
     | 0    X_0  -X_3 0    X_1  |
     | 0    -X_2 0    -X_3 -X_3 |

                                4                          5
o6 : Matrix (QQ[X , X , X , X ])  <--- (QQ[X , X , X , X ])
                 0   1   2   3              0   1   2   3

See also

• representationMatrix -- computes the right-most map of the Z-complex in degree nu)
• degreeImplicitEq -- computes the degree of det((Z)_nu)
• Exact -- Strategy for functions that uses rank computation.
• Numeric -- Strategy for functions that uses rank computation.