Macaulay2 » Documentation
Packages » MultiprojectiveVarieties :: multidegree(MultirationalMap)
next | previous | forward | backward | up | index | toc

# multidegree(MultirationalMap) -- projective degrees of a multi-rational map

- Function: multidegree
- Usage:
    `multidegree Phi`
- Inputs:
  - Phi, a multi-rational map
- Outputs:
  - a list, the list of projective degrees of Phi

## Description

This calculates the multidegree of the graph and converts it to the list of projective degrees.

    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 multidegree Phi
     -- used 0.435996s (cpu); 0.350715s (thread); 0s (gc)

    o3 = {66, 46, 31, 20}

    o3 : List

    i4 : (degree source Phi,degree image Phi)

    o4 = (66, 20)

    o4 : Sequence

## References

ArXiv preprint: Computations with rational maps between multi-projective varieties.

## See also

- multidegree(ZZ,MultirationalMap) -- i-th projective degree of a multi-rational map using a probabilistic approach
- multidegree(RationalMap) -- projective degrees of a rational map
- degree(MultirationalMap) -- degree of a multi-rational map
- projectiveDegrees(RationalMap) -- projective degrees of a rational map

## Ways to use this method:

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

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/MultiprojectiveVarieties.m2:3220:0.