degreeMap(MultirationalMap) -- degree of a multi-rational map

Synopsis

• Function: degreeMap

• Usage:

  degreeMap Phi

  degree Phi

• Inputs:
  • Phi, a multi-rational map
• Optional inputs:
  • BlowUpStrategy => ..., default value Eliminate,
  • MathMode => ..., default value false,
  • Verbose => ..., default value true,
• Outputs:
  • an integer, the degree of Phi. So this value is 1 if and only if the map is birational onto its image.

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 degree Phi
     -- used 2.29667 seconds

o3 = 1

See also

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