coxMatrices -- compute the Cox matrices

Usage:

(A,B,A1,B1) = coxMatrices(a,b,k)
Inputs:
- a, an integer,
- b, an integer,
- k, an integer,
Outputs:
- A, a matrix,
- B, a matrix,
- A1, a matrix,
- B1, a matrix, over the Cox ring

Description

We compute the Hankel matrices over the Cox ring, which give rize to the relative quadrics of a degenerate K3 X_e(a,b) in case of k resonance within the resonance scroll, see ES2018

i1 : (A,B,A1,B1)=coxMatrices(6,5,4);

i2 : A,A1

o2 = (| u_0 u_1 su_2 u_3  |, | u_0 su_1 su_2 |)
      | u_1 u_2 u_3  tu_0 |  | u_1 su_2 u_3  |
                             | u_2 u_3  tu_0 |

o2 : Sequence

i3 : B,B1

o3 = (| v_0 sv_1 v_2 v_3  |, | sv_0 sv_1 v_2  |)
      | v_1 v_2  v_3 tv_0 |  | sv_1 v_2  v_3  |
                             | v_2  v_3  tv_0 |

o3 : Sequence

i4 : (A,B,A1,B1)=coxMatrices(7,4,4);

i5 : A,A1

o5 = (| u_0 u_1 u_2 su_3 |, | u_0 u_1 su_2 |)
      | u_1 u_2 u_3 tu_0 |  | u_1 u_2 su_3 |
                            | u_2 u_3 tu_0 |

o5 : Sequence

i6 : B,B1

o6 = (| sv_0 v_1 v_2 v_3  |, | sv_0 v_1 v_2  |)
      | v_1  v_2 v_3 tv_0 |  | v_1  v_2 v_3  |
                             | v_2  v_3 tv_0 |

o6 : Sequence

Ways to use coxMatrices:

coxMatrices(ZZ,ZZ,ZZ)

For the programmer

The object coxMatrices is a method function.

The source of this document is in K3Carpets.m2:2054:0.

coxMatrices -- compute the Cox matrices

Description

See also

Ways to use coxMatrices:

For the programmer