For a symmetric n by n Gram matrix A, n=1..4, over the prime field p=3 or5, use ...
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For a symmetric n by n Gram matrix A, n=1..4, over the prime field p=3 or5, use q(x)=x A x^T. Return row basis B, G=B A B^T, hyperbolic_planes h, anisotropic_dimension a and radical_dimension r. Basis order consists of h adjacent hyperbolic pairs with Gram [[0,1],[1,0]], then an anisotropic block, then radical basis. All cross blocks are zero; n=2h+a+r. Exhaustive lexicographic vector enumeration and rank extension fix the witness.
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Input Schema
{
"body": {
"claim": {
"anisotropic_dimension": 0,
"hyperbolic_planes": 1,
"radical_dimension": 0
},
"matrix": [
[
0,
1
],
[
1,
0
]
],
"p": 3
},
"bodyType": "json",
"method": "POST",
"type": "http"
}