projectiveVariety(List,Ring) -- product of projective spaces

• Function: projectiveVariety

• Usage:

  projectiveVariety(n,K)

  PP_K^n

• Inputs:
  • n, a list, a list of non-negative integers $n=\{n_1,n_2,\ldots,n_r\}$
  • K, a ring, a field
• Optional inputs:
  • MinimalGenerators => ..., default value true, whether to trim the ideal (intended for internal use only)
  • Saturate => ..., default value true, whether to compute the multi-saturation of the ideal (intended for internal use only)
• Outputs:
  • a multi-projective variety, the product of projective spaces $\mathbb{P}^{n_1}\times\mathbb{P}^{n_2}\times\cdots\times\mathbb{P}^{n_r}$ over $K$

i1 : projectiveVariety({2,1,3},ZZ/33331);

o1 : ProjectiveVariety, PP^2 x PP^1 x PP^3

i2 : PP_(ZZ/33331)^{2,1,3};

o2 : ProjectiveVariety, PP^2 x PP^1 x PP^3

i3 : PP_QQ^{1,1,1,1};

o3 : ProjectiveVariety, PP^1 x PP^1 x PP^1 x PP^1

i4 : PP_QQ^{};

o4 : ProjectiveVariety, empty scheme