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

Synopsis

• Function: degree

• Usage:

  degree Phi

• Inputs:
  • Phi, a multi-rational map
• 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 is just a shortcut for (last multidegree Phi)/(degree image Phi).

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 rationalMap {f,g};

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 0.367926s (cpu); 0.286869s (thread); 0s (gc)

o3 = 1

See also

• degree(MultirationalMap,Option) -- degree of a multi-rational map using a probabilistic approach
• degree(RationalMap) -- degree of a rational map
• multidegree(MultirationalMap) -- projective degrees of a multi-rational map
• degreeMap(RationalMap) -- degree of a rational map