decompose(MultiprojectiveVariety) -- irreducible components of a variety

Synopsis

• Function: decompose

• Usage:

  decompose X

• Inputs:
  • X, a multi-projective variety
• Outputs:
  • a list, the list of multi-projective varieties defined by the minimal associated primes of the ideal of X

Description

This calculation is performed using the function decompose(Ideal).

i1 : C = PP_(ZZ/100003)^(1,4);

o1 : ProjectiveVariety, curve in PP^4

i2 : L = linearSpan sum{point C,point C}, L' = linearSpan sum{point C,point ambient C};

i3 : X = ⋃ {C,L,L'};

o3 : ProjectiveVariety, curve in PP^4

i4 : D = decompose X

o4 = {curve in PP^4 cut out by 3 hypersurfaces of degree 1, curve in PP^4 cut
     ------------------------------------------------------------------------
     out by 3 hypersurfaces of degree 1, curve in PP^4 cut out by 6
     ------------------------------------------------------------------------
     hypersurfaces of degree 2}

o4 : List

i5 : assert(X == ⋃ D)

See also

• support(MultiprojectiveVariety) -- support of a multi-projective variety
• topComponents(MultiprojectiveVariety) -- union of the top dimensional components of a multi-projective variety
• decompose(Ideal)