projectiveDegrees(MultirationalMap) -- projective degrees of a multi-rational map

Synopsis

• Function: projectiveDegrees

• Usage:

  projectiveDegrees Phi

  multidegree Phi

• Inputs:
  • Phi, a multi-rational map
• Optional inputs:
  • BlowUpStrategy => ..., default value Eliminate,
  • MathMode => ..., default value false,
  • NumDegrees => ..., default value infinity,
  • Verbose => ..., default value true,
• Outputs:
  • a list, the list of projective degrees of Phi

Description

This computation is performed by converting the multi-rational map to a standard rational map (using segre) and then applying the corresponding method for rational maps.

i1 : ZZ/300007[x_0..x_3], f = rationalMap {x_2^2-x_1*x_3, x_1*x_2-x_0*x_3, x_1^2-x_0*x_2}, g = rationalMap {x_1^2-x_0*x_2, x_0*x_3, x_1*x_3, x_2*x_3, x_3^2};

i2 : Phi = last graph multirationalMap {f,g}

o2 = Phi

o2 : MultirationalMap (rational map from threefold in PP^3 x PP^2 x PP^4 to PP^2 x PP^4)

i3 : time projectiveDegrees Phi
     -- used 5.09782 seconds

o3 = {66, 46, 31, 20}

o3 : List

i4 : (degree source Phi,degree image Phi)

o4 = (66, 20)

o4 : Sequence

See also

• projectiveDegrees(RationalMap) -- projective degrees of a rational map
• multidegree(RationalMap) -- projective degrees of a rational map
• degree(MultirationalMap) -- degree of a multi-rational map