Read model .pkl and display

import sympy as sp
from multipie import MaterialModel
to_tuple = lambda x: tuple(map(to_tuple, x)) if isinstance(x, tuple) else x

mm = MaterialModel(verbose=True) # initialize material model.

model = "graphene" # model name.
mm.load(model) # load model pkl.
group = mm.group # alias for group object.

load binary from 'examples/graphene/graphene.pkl'.
"""
Model: graphene
* Group: D6h^1
* SAMB selection: {'X': ['Q', 'G'], 'l': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 'Gamma': ['A1g', 'A2g', 'B1g', 'B2g', 'E1g', 'E2g', 'A1u', 'A2u', 'B1u', 'B2u', 'E1u', 'E2u'], 's': [0, 1]}
* atomic selection: {'X': ['Q', 'G', 'M', 'T'], 'l': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 'Gamma': ['A1g', 'A2g', 'B1g', 'B2g', 'E1g', 'E2g', 'A1u', 'A2u', 'B1u', 'B2u', 'E1u', 'E2u'], 's': [0, 1]}
* site-cluster selection: {'l': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 'Gamma': ['A1g', 'A2g', 'B1g', 'B2g', 'E1g', 'E2g', 'A1u', 'A2u', 'B1u', 'B2u', 'E1u', 'E2u'], 'X': ['Q', 'G', 'M', 'T'], 's': [0, 1]}
* bond-cluster selection: {'X': ['Q', 'G', 'M', 'T'], 'l': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 'Gamma': ['A1g', 'A2g', 'B1g', 'B2g', 'E1g', 'E2g', 'A1u', 'A2u', 'B1u', 'B2u', 'E1u', 'E2u'], 's': [0, 1]}
  32 (all 32) basis set
"""

Site-cluster SAMB

cluster_samb = mm["cluster_samb"]
for wp, samb in cluster_samb.items():
    if "@" in wp:
        continue
    print(f"== {wp} ==")
    for idx, (mat, ex) in samb.items():
        tag = group.tag_multipole(idx,latex=True,superscript="s")
        for e, m in zip(tag,mat):
            d = sp.Eq(sp.Symbol(e),sp.Matrix(m).T, evaluate=False)
            display(d)

== 2c ==

\[\displaystyle \mathbb{Q}_{0}^{(s)}(A_{1g}) = \left[\begin{matrix}\frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2}\end{matrix}\right]\]

\[\displaystyle \mathbb{Q}_{3}^{(s)}(B_{1u}) = \left[\begin{matrix}\frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2}\end{matrix}\right]\]

Bond-cluster SAMB

for wp, samb in cluster_samb.items():
    if "@" not in wp:
        continue
    print(f"== {wp} ==")
    for idx, (mat, ex) in samb.items():
        tag = group.tag_multipole(idx,latex=True,superscript="b")
        for e, m in zip(tag,mat):
            d = sp.Eq(sp.Symbol(e),sp.Matrix(m).T, evaluate=False)
            display(d)

== 3a@3f ==

\[\displaystyle \mathbb{Q}_{0}^{(b)}(A_{1g}) = \left[\begin{matrix}\frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3}\end{matrix}\right]\]

\[\displaystyle \mathbb{T}_{3}^{(b)}(B_{1u}) = \left[\begin{matrix}\frac{\sqrt{3} i}{3} & \frac{\sqrt{3} i}{3} & \frac{\sqrt{3} i}{3}\end{matrix}\right]\]

\[\displaystyle \mathbb{T}_{1,1}^{(b)}(E_{1u}) = \left[\begin{matrix}0 & - \frac{\sqrt{2} i}{2} & \frac{\sqrt{2} i}{2}\end{matrix}\right]\]

\[\displaystyle \mathbb{T}_{1,2}^{(b)}(E_{1u}) = \left[\begin{matrix}\frac{\sqrt{6} i}{3} & - \frac{\sqrt{6} i}{6} & - \frac{\sqrt{6} i}{6}\end{matrix}\right]\]

\[\displaystyle \mathbb{Q}_{2,1}^{(b)}(E_{2g}) = \left[\begin{matrix}\frac{\sqrt{6}}{3} & - \frac{\sqrt{6}}{6} & - \frac{\sqrt{6}}{6}\end{matrix}\right]\]

\[\displaystyle \mathbb{Q}_{2,2}^{(b)}(E_{2g}) = \left[\begin{matrix}0 & \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2}\end{matrix}\right]\]

== 3b@1a ==

\[\displaystyle \mathbb{Q}_{0}^{(b)}(A_{1g}) = \left[\begin{matrix}\frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3}\end{matrix}\right]\]

\[\displaystyle \mathbb{T}_{3}^{(b)}(B_{1u}) = \left[\begin{matrix}\frac{\sqrt{3} i}{3} & \frac{\sqrt{3} i}{3} & \frac{\sqrt{3} i}{3}\end{matrix}\right]\]

\[\displaystyle \mathbb{T}_{1,1}^{(b)}(E_{1u}) = \left[\begin{matrix}0 & - \frac{\sqrt{2} i}{2} & \frac{\sqrt{2} i}{2}\end{matrix}\right]\]

\[\displaystyle \mathbb{T}_{1,2}^{(b)}(E_{1u}) = \left[\begin{matrix}\frac{\sqrt{6} i}{3} & - \frac{\sqrt{6} i}{6} & - \frac{\sqrt{6} i}{6}\end{matrix}\right]\]

\[\displaystyle \mathbb{Q}_{2,1}^{(b)}(E_{2g}) = \left[\begin{matrix}\frac{\sqrt{6}}{3} & - \frac{\sqrt{6}}{6} & - \frac{\sqrt{6}}{6}\end{matrix}\right]\]

\[\displaystyle \mathbb{Q}_{2,2}^{(b)}(E_{2g}) = \left[\begin{matrix}0 & \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2}\end{matrix}\right]\]

== 6b@6l ==

\[\displaystyle \mathbb{Q}_{0}^{(b)}(A_{1g}) = \left[\begin{matrix}\frac{\sqrt{6}}{6} & \frac{\sqrt{6}}{6} & \frac{\sqrt{6}}{6} & \frac{\sqrt{6}}{6} & \frac{\sqrt{6}}{6} & \frac{\sqrt{6}}{6}\end{matrix}\right]\]

\[\displaystyle \mathbb{M}_{1}^{(b)}(A_{2g}) = \left[\begin{matrix}\frac{\sqrt{6} i}{6} & \frac{\sqrt{6} i}{6} & \frac{\sqrt{6} i}{6} & \frac{\sqrt{6} i}{6} & \frac{\sqrt{6} i}{6} & \frac{\sqrt{6} i}{6}\end{matrix}\right]\]

\[\displaystyle \mathbb{Q}_{3}^{(b)}(B_{1u}) = \left[\begin{matrix}\frac{\sqrt{6}}{6} & \frac{\sqrt{6}}{6} & \frac{\sqrt{6}}{6} & - \frac{\sqrt{6}}{6} & - \frac{\sqrt{6}}{6} & - \frac{\sqrt{6}}{6}\end{matrix}\right]\]

\[\displaystyle \mathbb{T}_{3}^{(b)}(B_{2u}) = \left[\begin{matrix}\frac{\sqrt{6} i}{6} & \frac{\sqrt{6} i}{6} & \frac{\sqrt{6} i}{6} & - \frac{\sqrt{6} i}{6} & - \frac{\sqrt{6} i}{6} & - \frac{\sqrt{6} i}{6}\end{matrix}\right]\]

\[\displaystyle \mathbb{Q}_{1,1}^{(b)}(E_{1u}) = \left[\begin{matrix}0 & - \frac{1}{2} & \frac{1}{2} & 0 & \frac{1}{2} & - \frac{1}{2}\end{matrix}\right]\]

\[\displaystyle \mathbb{Q}_{1,2}^{(b)}(E_{1u}) = \left[\begin{matrix}\frac{\sqrt{3}}{3} & - \frac{\sqrt{3}}{6} & - \frac{\sqrt{3}}{6} & - \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{6} & \frac{\sqrt{3}}{6}\end{matrix}\right]\]

\[\displaystyle \mathbb{T}_{1,1}^{(b)}(E_{1u}) = \left[\begin{matrix}\frac{\sqrt{3} i}{3} & - \frac{\sqrt{3} i}{6} & - \frac{\sqrt{3} i}{6} & - \frac{\sqrt{3} i}{3} & \frac{\sqrt{3} i}{6} & \frac{\sqrt{3} i}{6}\end{matrix}\right]\]

\[\displaystyle \mathbb{T}_{1,2}^{(b)}(E_{1u}) = \left[\begin{matrix}0 & \frac{i}{2} & - \frac{i}{2} & 0 & - \frac{i}{2} & \frac{i}{2}\end{matrix}\right]\]

\[\displaystyle \mathbb{Q}_{2,1}^{(b)}(E_{2g}) = \left[\begin{matrix}\frac{\sqrt{3}}{3} & - \frac{\sqrt{3}}{6} & - \frac{\sqrt{3}}{6} & \frac{\sqrt{3}}{3} & - \frac{\sqrt{3}}{6} & - \frac{\sqrt{3}}{6}\end{matrix}\right]\]

\[\displaystyle \mathbb{Q}_{2,2}^{(b)}(E_{2g}) = \left[\begin{matrix}0 & \frac{1}{2} & - \frac{1}{2} & 0 & \frac{1}{2} & - \frac{1}{2}\end{matrix}\right]\]

\[\displaystyle \mathbb{T}_{2,1}^{(b)}(E_{2g}) = \left[\begin{matrix}0 & \frac{i}{2} & - \frac{i}{2} & 0 & \frac{i}{2} & - \frac{i}{2}\end{matrix}\right]\]

\[\displaystyle \mathbb{T}_{2,2}^{(b)}(E_{2g}) = \left[\begin{matrix}- \frac{\sqrt{3} i}{3} & \frac{\sqrt{3} i}{6} & \frac{\sqrt{3} i}{6} & - \frac{\sqrt{3} i}{3} & \frac{\sqrt{3} i}{6} & \frac{\sqrt{3} i}{6}\end{matrix}\right]\]

== 6c@2c ==

\[\displaystyle \mathbb{Q}_{0}^{(b)}(A_{1g}) = \left[\begin{matrix}\frac{\sqrt{6}}{6} & \frac{\sqrt{6}}{6} & \frac{\sqrt{6}}{6} & \frac{\sqrt{6}}{6} & \frac{\sqrt{6}}{6} & \frac{\sqrt{6}}{6}\end{matrix}\right]\]

\[\displaystyle \mathbb{M}_{1}^{(b)}(A_{2g}) = \left[\begin{matrix}\frac{\sqrt{6} i}{6} & \frac{\sqrt{6} i}{6} & \frac{\sqrt{6} i}{6} & \frac{\sqrt{6} i}{6} & \frac{\sqrt{6} i}{6} & \frac{\sqrt{6} i}{6}\end{matrix}\right]\]

\[\displaystyle \mathbb{Q}_{3}^{(b)}(B_{1u}) = \left[\begin{matrix}\frac{\sqrt{6}}{6} & \frac{\sqrt{6}}{6} & \frac{\sqrt{6}}{6} & - \frac{\sqrt{6}}{6} & - \frac{\sqrt{6}}{6} & - \frac{\sqrt{6}}{6}\end{matrix}\right]\]

\[\displaystyle \mathbb{T}_{3}^{(b)}(B_{2u}) = \left[\begin{matrix}\frac{\sqrt{6} i}{6} & \frac{\sqrt{6} i}{6} & \frac{\sqrt{6} i}{6} & - \frac{\sqrt{6} i}{6} & - \frac{\sqrt{6} i}{6} & - \frac{\sqrt{6} i}{6}\end{matrix}\right]\]

\[\displaystyle \mathbb{Q}_{1,1}^{(b)}(E_{1u}) = \left[\begin{matrix}0 & - \frac{1}{2} & \frac{1}{2} & 0 & \frac{1}{2} & - \frac{1}{2}\end{matrix}\right]\]

\[\displaystyle \mathbb{Q}_{1,2}^{(b)}(E_{1u}) = \left[\begin{matrix}\frac{\sqrt{3}}{3} & - \frac{\sqrt{3}}{6} & - \frac{\sqrt{3}}{6} & - \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{6} & \frac{\sqrt{3}}{6}\end{matrix}\right]\]

\[\displaystyle \mathbb{T}_{1,1}^{(b)}(E_{1u}) = \left[\begin{matrix}\frac{\sqrt{3} i}{3} & - \frac{\sqrt{3} i}{6} & - \frac{\sqrt{3} i}{6} & - \frac{\sqrt{3} i}{3} & \frac{\sqrt{3} i}{6} & \frac{\sqrt{3} i}{6}\end{matrix}\right]\]

\[\displaystyle \mathbb{T}_{1,2}^{(b)}(E_{1u}) = \left[\begin{matrix}0 & \frac{i}{2} & - \frac{i}{2} & 0 & - \frac{i}{2} & \frac{i}{2}\end{matrix}\right]\]

\[\displaystyle \mathbb{Q}_{2,1}^{(b)}(E_{2g}) = \left[\begin{matrix}\frac{\sqrt{3}}{3} & - \frac{\sqrt{3}}{6} & - \frac{\sqrt{3}}{6} & \frac{\sqrt{3}}{3} & - \frac{\sqrt{3}}{6} & - \frac{\sqrt{3}}{6}\end{matrix}\right]\]

\[\displaystyle \mathbb{Q}_{2,2}^{(b)}(E_{2g}) = \left[\begin{matrix}0 & \frac{1}{2} & - \frac{1}{2} & 0 & \frac{1}{2} & - \frac{1}{2}\end{matrix}\right]\]

\[\displaystyle \mathbb{T}_{2,1}^{(b)}(E_{2g}) = \left[\begin{matrix}0 & \frac{i}{2} & - \frac{i}{2} & 0 & \frac{i}{2} & - \frac{i}{2}\end{matrix}\right]\]

\[\displaystyle \mathbb{T}_{2,2}^{(b)}(E_{2g}) = \left[\begin{matrix}- \frac{\sqrt{3} i}{3} & \frac{\sqrt{3} i}{6} & \frac{\sqrt{3} i}{6} & - \frac{\sqrt{3} i}{3} & \frac{\sqrt{3} i}{6} & \frac{\sqrt{3} i}{6}\end{matrix}\right]\]

== 6a@6l ==

\[\displaystyle \mathbb{Q}_{0}^{(b)}(A_{1g}) = \left[\begin{matrix}\frac{\sqrt{6}}{6} & \frac{\sqrt{6}}{6} & \frac{\sqrt{6}}{6} & \frac{\sqrt{6}}{6} & \frac{\sqrt{6}}{6} & \frac{\sqrt{6}}{6}\end{matrix}\right]\]

\[\displaystyle \mathbb{T}_{0}^{(b)}(A_{1g}) = \left[\begin{matrix}\frac{\sqrt{6} i}{6} & \frac{\sqrt{6} i}{6} & \frac{\sqrt{6} i}{6} & \frac{\sqrt{6} i}{6} & \frac{\sqrt{6} i}{6} & \frac{\sqrt{6} i}{6}\end{matrix}\right]\]

\[\displaystyle \mathbb{Q}_{3}^{(b)}(B_{1u}) = \left[\begin{matrix}\frac{\sqrt{6}}{6} & \frac{\sqrt{6}}{6} & \frac{\sqrt{6}}{6} & - \frac{\sqrt{6}}{6} & - \frac{\sqrt{6}}{6} & - \frac{\sqrt{6}}{6}\end{matrix}\right]\]

\[\displaystyle \mathbb{T}_{3}^{(b)}(B_{1u}) = \left[\begin{matrix}\frac{\sqrt{6} i}{6} & \frac{\sqrt{6} i}{6} & \frac{\sqrt{6} i}{6} & - \frac{\sqrt{6} i}{6} & - \frac{\sqrt{6} i}{6} & - \frac{\sqrt{6} i}{6}\end{matrix}\right]\]

\[\displaystyle \mathbb{Q}_{1,1}^{(b)}(E_{1u}) = \left[\begin{matrix}0 & - \frac{1}{2} & \frac{1}{2} & 0 & \frac{1}{2} & - \frac{1}{2}\end{matrix}\right]\]

\[\displaystyle \mathbb{Q}_{1,2}^{(b)}(E_{1u}) = \left[\begin{matrix}\frac{\sqrt{3}}{3} & - \frac{\sqrt{3}}{6} & - \frac{\sqrt{3}}{6} & - \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{6} & \frac{\sqrt{3}}{6}\end{matrix}\right]\]

\[\displaystyle \mathbb{T}_{1,1}^{(b)}(E_{1u}) = \left[\begin{matrix}0 & - \frac{i}{2} & \frac{i}{2} & 0 & \frac{i}{2} & - \frac{i}{2}\end{matrix}\right]\]

\[\displaystyle \mathbb{T}_{1,2}^{(b)}(E_{1u}) = \left[\begin{matrix}\frac{\sqrt{3} i}{3} & - \frac{\sqrt{3} i}{6} & - \frac{\sqrt{3} i}{6} & - \frac{\sqrt{3} i}{3} & \frac{\sqrt{3} i}{6} & \frac{\sqrt{3} i}{6}\end{matrix}\right]\]

\[\displaystyle \mathbb{Q}_{2,1}^{(b)}(E_{2g}) = \left[\begin{matrix}\frac{\sqrt{3}}{3} & - \frac{\sqrt{3}}{6} & - \frac{\sqrt{3}}{6} & \frac{\sqrt{3}}{3} & - \frac{\sqrt{3}}{6} & - \frac{\sqrt{3}}{6}\end{matrix}\right]\]

\[\displaystyle \mathbb{Q}_{2,2}^{(b)}(E_{2g}) = \left[\begin{matrix}0 & \frac{1}{2} & - \frac{1}{2} & 0 & \frac{1}{2} & - \frac{1}{2}\end{matrix}\right]\]

\[\displaystyle \mathbb{T}_{2,1}^{(b)}(E_{2g}) = \left[\begin{matrix}\frac{\sqrt{3} i}{3} & - \frac{\sqrt{3} i}{6} & - \frac{\sqrt{3} i}{6} & \frac{\sqrt{3} i}{3} & - \frac{\sqrt{3} i}{6} & - \frac{\sqrt{3} i}{6}\end{matrix}\right]\]

\[\displaystyle \mathbb{T}_{2,2}^{(b)}(E_{2g}) = \left[\begin{matrix}0 & \frac{i}{2} & - \frac{i}{2} & 0 & \frac{i}{2} & - \frac{i}{2}\end{matrix}\right]\]

== 6d@3f ==

\[\displaystyle \mathbb{Q}_{0}^{(b)}(A_{1g}) = \left[\begin{matrix}\frac{\sqrt{6}}{6} & \frac{\sqrt{6}}{6} & \frac{\sqrt{6}}{6} & \frac{\sqrt{6}}{6} & \frac{\sqrt{6}}{6} & \frac{\sqrt{6}}{6}\end{matrix}\right]\]

\[\displaystyle \mathbb{Q}_{6}^{(b)}(A_{2g}) = \left[\begin{matrix}\frac{\sqrt{6}}{6} & \frac{\sqrt{6}}{6} & \frac{\sqrt{6}}{6} & - \frac{\sqrt{6}}{6} & - \frac{\sqrt{6}}{6} & - \frac{\sqrt{6}}{6}\end{matrix}\right]\]

\[\displaystyle \mathbb{T}_{3}^{(b)}(B_{1u}) = \left[\begin{matrix}\frac{\sqrt{6} i}{6} & \frac{\sqrt{6} i}{6} & \frac{\sqrt{6} i}{6} & - \frac{\sqrt{6} i}{6} & - \frac{\sqrt{6} i}{6} & - \frac{\sqrt{6} i}{6}\end{matrix}\right]\]

\[\displaystyle \mathbb{T}_{3}^{(b)}(B_{2u}) = \left[\begin{matrix}\frac{\sqrt{6} i}{6} & \frac{\sqrt{6} i}{6} & \frac{\sqrt{6} i}{6} & \frac{\sqrt{6} i}{6} & \frac{\sqrt{6} i}{6} & \frac{\sqrt{6} i}{6}\end{matrix}\right]\]

\[\displaystyle \mathbb{T}_{1,1}^{(b)}(E_{1u},a) = \left[\begin{matrix}\frac{5 \sqrt{21} i}{42} & - \frac{2 \sqrt{21} i}{21} & - \frac{\sqrt{21} i}{42} & - \frac{\sqrt{21} i}{42} & \frac{5 \sqrt{21} i}{42} & - \frac{2 \sqrt{21} i}{21}\end{matrix}\right]\]

\[\displaystyle \mathbb{T}_{1,2}^{(b)}(E_{1u},a) = \left[\begin{matrix}\frac{\sqrt{7} i}{14} & \frac{\sqrt{7} i}{7} & - \frac{3 \sqrt{7} i}{14} & \frac{3 \sqrt{7} i}{14} & - \frac{\sqrt{7} i}{14} & - \frac{\sqrt{7} i}{7}\end{matrix}\right]\]

\[\displaystyle \mathbb{T}_{1,1}^{(b)}(E_{1u},b) = \left[\begin{matrix}\frac{\sqrt{7} i}{14} & \frac{\sqrt{7} i}{7} & - \frac{3 \sqrt{7} i}{14} & - \frac{3 \sqrt{7} i}{14} & \frac{\sqrt{7} i}{14} & \frac{\sqrt{7} i}{7}\end{matrix}\right]\]

\[\displaystyle \mathbb{T}_{1,2}^{(b)}(E_{1u},b) = \left[\begin{matrix}- \frac{5 \sqrt{21} i}{42} & \frac{2 \sqrt{21} i}{21} & \frac{\sqrt{21} i}{42} & - \frac{\sqrt{21} i}{42} & \frac{5 \sqrt{21} i}{42} & - \frac{2 \sqrt{21} i}{21}\end{matrix}\right]\]

\[\displaystyle \mathbb{Q}_{2,1}^{(b)}(E_{2g}) = \left[\begin{matrix}\frac{11 \sqrt{3}}{42} & \frac{\sqrt{3}}{21} & - \frac{13 \sqrt{3}}{42} & - \frac{13 \sqrt{3}}{42} & \frac{11 \sqrt{3}}{42} & \frac{\sqrt{3}}{21}\end{matrix}\right]\]

\[\displaystyle \mathbb{Q}_{2,2}^{(b)}(E_{2g}) = \left[\begin{matrix}- \frac{5}{14} & \frac{4}{7} & - \frac{3}{14} & \frac{3}{14} & \frac{5}{14} & - \frac{4}{7}\end{matrix}\right]\]

\[\displaystyle \mathbb{Q}_{4,1}^{(b)}(E_{2g},1) = \left[\begin{matrix}\frac{5}{14} & - \frac{4}{7} & \frac{3}{14} & \frac{3}{14} & \frac{5}{14} & - \frac{4}{7}\end{matrix}\right]\]

\[\displaystyle \mathbb{Q}_{4,2}^{(b)}(E_{2g},1) = \left[\begin{matrix}\frac{11 \sqrt{3}}{42} & \frac{\sqrt{3}}{21} & - \frac{13 \sqrt{3}}{42} & \frac{13 \sqrt{3}}{42} & - \frac{11 \sqrt{3}}{42} & - \frac{\sqrt{3}}{21}\end{matrix}\right]\]

Atomic SAMB for (bh_rank, bh_idx, kt_rank, kt_idx)

atomic_samb = mm["atomic_samb"]
for am, samb in atomic_samb.items():
    print(f"== {to_tuple(am)} ==")
    for idx, (mat,ex) in samb.items():
        tag = group.tag_multipole(idx,latex=True,superscript="a")
        for e, m in zip(tag,mat):
            d = sp.Eq(sp.Symbol(e),sp.Matrix(m), evaluate=False)
            display(d)

== (1, (2,), 1, (2,)) ==

\[\displaystyle \mathbb{Q}_{0}^{(a)}(A_{1g}) = \left[\begin{matrix}1\end{matrix}\right]\]

Combined SAMB for (head, tail, wyckoff, (bh_rank, bh_idx, kt_rank, kt_idx))

combined_samb = mm["combined_samb"]
for comb, samb in combined_samb.items():
    print(f"== {to_tuple(comb)} ==")
    clustar_str = "b" if comb.wyckoff.count("@")>0 else "s"
    for idx, (cl, ex) in samb.items():
        tag = group.tag_multipole(idx,latex=True,superscript="c")
        for t, m in zip(tag,cl):
            ex = 0
            for cg, t1, c1, t2, c2 in m:
                t1 = group.tag_multipole(t1,c1,latex=True,superscript="a")
                t2 = group.tag_multipole(t2,c2,latex=True,superscript=clustar_str)
                ex += cg * sp.Symbol(t1, commutative=False) * sp.Symbol(t2, commutative=False)
            d = sp.Eq(sp.Symbol(t),ex, evaluate=False)
            display(d)

== ('C', 'C', '2c', (1, (2,), 1, (2,))) ==

\[\displaystyle \mathbb{Q}_{0}^{(c)}(A_{1g}) = \mathbb{Q}_{0}^{(a)}(A_{1g}) \mathbb{Q}_{0}^{(s)}(A_{1g})\]

\[\displaystyle \mathbb{Q}_{3}^{(c)}(B_{1u}) = \mathbb{Q}_{0}^{(a)}(A_{1g}) \mathbb{Q}_{3}^{(s)}(B_{1u})\]

== ('C', 'C', '3a@3f', (1, (2,), 1, (2,))) ==

\[\displaystyle \mathbb{Q}_{0}^{(c)}(A_{1g}) = \mathbb{Q}_{0}^{(a)}(A_{1g}) \mathbb{Q}_{0}^{(b)}(A_{1g})\]

\[\displaystyle \mathbb{Q}_{2,1}^{(c)}(E_{2g}) = \frac{\sqrt{2} \mathbb{Q}_{0}^{(a)}(A_{1g}) \mathbb{Q}_{2,1}^{(b)}(E_{2g})}{2}\]

\[\displaystyle \mathbb{Q}_{2,2}^{(c)}(E_{2g}) = \frac{\sqrt{2} \mathbb{Q}_{0}^{(a)}(A_{1g}) \mathbb{Q}_{2,2}^{(b)}(E_{2g})}{2}\]

== ('C', 'C', '6b@6l', (1, (2,), 1, (2,))) ==

\[\displaystyle \mathbb{Q}_{0}^{(c)}(A_{1g}) = \mathbb{Q}_{0}^{(a)}(A_{1g}) \mathbb{Q}_{0}^{(b)}(A_{1g})\]

\[\displaystyle \mathbb{Q}_{3}^{(c)}(B_{1u}) = \mathbb{Q}_{0}^{(a)}(A_{1g}) \mathbb{Q}_{3}^{(b)}(B_{1u})\]

\[\displaystyle \mathbb{Q}_{1,1}^{(c)}(E_{1u}) = \frac{\sqrt{2} \mathbb{Q}_{0}^{(a)}(A_{1g}) \mathbb{Q}_{1,1}^{(b)}(E_{1u})}{2}\]

\[\displaystyle \mathbb{Q}_{1,2}^{(c)}(E_{1u}) = \frac{\sqrt{2} \mathbb{Q}_{0}^{(a)}(A_{1g}) \mathbb{Q}_{1,2}^{(b)}(E_{1u})}{2}\]

\[\displaystyle \mathbb{Q}_{2,1}^{(c)}(E_{2g}) = \frac{\sqrt{2} \mathbb{Q}_{0}^{(a)}(A_{1g}) \mathbb{Q}_{2,1}^{(b)}(E_{2g})}{2}\]

\[\displaystyle \mathbb{Q}_{2,2}^{(c)}(E_{2g}) = \frac{\sqrt{2} \mathbb{Q}_{0}^{(a)}(A_{1g}) \mathbb{Q}_{2,2}^{(b)}(E_{2g})}{2}\]

== ('C', 'C', '3b@1a', (1, (2,), 1, (2,))) ==

\[\displaystyle \mathbb{Q}_{0}^{(c)}(A_{1g}) = \mathbb{Q}_{0}^{(a)}(A_{1g}) \mathbb{Q}_{0}^{(b)}(A_{1g})\]

\[\displaystyle \mathbb{Q}_{2,1}^{(c)}(E_{2g}) = \frac{\sqrt{2} \mathbb{Q}_{0}^{(a)}(A_{1g}) \mathbb{Q}_{2,1}^{(b)}(E_{2g})}{2}\]

\[\displaystyle \mathbb{Q}_{2,2}^{(c)}(E_{2g}) = \frac{\sqrt{2} \mathbb{Q}_{0}^{(a)}(A_{1g}) \mathbb{Q}_{2,2}^{(b)}(E_{2g})}{2}\]

== ('C', 'C', '6d@3f', (1, (2,), 1, (2,))) ==

\[\displaystyle \mathbb{Q}_{0}^{(c)}(A_{1g}) = \mathbb{Q}_{0}^{(a)}(A_{1g}) \mathbb{Q}_{0}^{(b)}(A_{1g})\]

\[\displaystyle \mathbb{Q}_{6}^{(c)}(A_{2g}) = \mathbb{Q}_{0}^{(a)}(A_{1g}) \mathbb{Q}_{6}^{(b)}(A_{2g})\]

\[\displaystyle \mathbb{Q}_{2,1}^{(c)}(E_{2g}) = \frac{\sqrt{2} \mathbb{Q}_{0}^{(a)}(A_{1g}) \mathbb{Q}_{2,1}^{(b)}(E_{2g})}{2}\]

\[\displaystyle \mathbb{Q}_{2,2}^{(c)}(E_{2g}) = \frac{\sqrt{2} \mathbb{Q}_{0}^{(a)}(A_{1g}) \mathbb{Q}_{2,2}^{(b)}(E_{2g})}{2}\]

\[\displaystyle \mathbb{Q}_{4,1}^{(c)}(E_{2g},1) = \frac{\sqrt{2} \mathbb{Q}_{0}^{(a)}(A_{1g}) \mathbb{Q}_{4,1}^{(b)}(E_{2g},1)}{2}\]

\[\displaystyle \mathbb{Q}_{4,2}^{(c)}(E_{2g},1) = \frac{\sqrt{2} \mathbb{Q}_{0}^{(a)}(A_{1g}) \mathbb{Q}_{4,2}^{(b)}(E_{2g},1)}{2}\]

== ('C', 'C', '6a@6l', (1, (2,), 1, (2,))) ==

\[\displaystyle \mathbb{Q}_{0}^{(c)}(A_{1g}) = \mathbb{Q}_{0}^{(a)}(A_{1g}) \mathbb{Q}_{0}^{(b)}(A_{1g})\]

\[\displaystyle \mathbb{Q}_{3}^{(c)}(B_{1u}) = \mathbb{Q}_{0}^{(a)}(A_{1g}) \mathbb{Q}_{3}^{(b)}(B_{1u})\]

\[\displaystyle \mathbb{Q}_{1,1}^{(c)}(E_{1u}) = \frac{\sqrt{2} \mathbb{Q}_{0}^{(a)}(A_{1g}) \mathbb{Q}_{1,1}^{(b)}(E_{1u})}{2}\]

\[\displaystyle \mathbb{Q}_{1,2}^{(c)}(E_{1u}) = \frac{\sqrt{2} \mathbb{Q}_{0}^{(a)}(A_{1g}) \mathbb{Q}_{1,2}^{(b)}(E_{1u})}{2}\]

\[\displaystyle \mathbb{Q}_{2,1}^{(c)}(E_{2g}) = \frac{\sqrt{2} \mathbb{Q}_{0}^{(a)}(A_{1g}) \mathbb{Q}_{2,1}^{(b)}(E_{2g})}{2}\]

\[\displaystyle \mathbb{Q}_{2,2}^{(c)}(E_{2g}) = \frac{\sqrt{2} \mathbb{Q}_{0}^{(a)}(A_{1g}) \mathbb{Q}_{2,2}^{(b)}(E_{2g})}{2}\]

== ('C', 'C', '6c@2c', (1, (2,), 1, (2,))) ==

\[\displaystyle \mathbb{Q}_{0}^{(c)}(A_{1g}) = \mathbb{Q}_{0}^{(a)}(A_{1g}) \mathbb{Q}_{0}^{(b)}(A_{1g})\]

\[\displaystyle \mathbb{Q}_{3}^{(c)}(B_{1u}) = \mathbb{Q}_{0}^{(a)}(A_{1g}) \mathbb{Q}_{3}^{(b)}(B_{1u})\]

\[\displaystyle \mathbb{Q}_{1,1}^{(c)}(E_{1u}) = \frac{\sqrt{2} \mathbb{Q}_{0}^{(a)}(A_{1g}) \mathbb{Q}_{1,1}^{(b)}(E_{1u})}{2}\]

\[\displaystyle \mathbb{Q}_{1,2}^{(c)}(E_{1u}) = \frac{\sqrt{2} \mathbb{Q}_{0}^{(a)}(A_{1g}) \mathbb{Q}_{1,2}^{(b)}(E_{1u})}{2}\]

\[\displaystyle \mathbb{Q}_{2,1}^{(c)}(E_{2g}) = \frac{\sqrt{2} \mathbb{Q}_{0}^{(a)}(A_{1g}) \mathbb{Q}_{2,1}^{(b)}(E_{2g})}{2}\]

\[\displaystyle \mathbb{Q}_{2,2}^{(c)}(E_{2g}) = \frac{\sqrt{2} \mathbb{Q}_{0}^{(a)}(A_{1g}) \mathbb{Q}_{2,2}^{(b)}(E_{2g})}{2}\]

Symmetry of multipoles

for idx, ex in mm.get_multipole_expression().items():
    X, Gamma, l, n = idx
    idx = (X,l,Gamma,n,-1,0,0,"q")
    tag = group.tag_multipole(idx, latex=True)
    for t, e in zip(tag, ex):
        d = sp.Eq(sp.Symbol(t),e,evaluate=False)
        display(d)

\[\displaystyle \mathbb{Q}_{0}(A_{1g}) = 1\]

\[\displaystyle \mathbb{G}_{1}(A_{2g}) = z\]

\[\displaystyle \mathbb{Q}_{6}(A_{2g}) = \frac{\sqrt{462} x y \left(x^{2} - 3 y^{2}\right) \left(3 x^{2} - y^{2}\right)}{16}\]

\[\displaystyle \mathbb{Q}_{3}(B_{1u}) = \frac{\sqrt{10} y \left(3 x^{2} - y^{2}\right)}{4}\]

\[\displaystyle \mathbb{Q}_{3}(B_{2u}) = \frac{\sqrt{10} x \left(x^{2} - 3 y^{2}\right)}{4}\]

\[\displaystyle \mathbb{Q}_{1,1}(E_{1u}) = x\]

\[\displaystyle \mathbb{Q}_{1,2}(E_{1u}) = y\]

\[\displaystyle \mathbb{Q}_{2,1}(E_{2g}) = \frac{\sqrt{3} \left(x - y\right) \left(x + y\right)}{2}\]

\[\displaystyle \mathbb{Q}_{2,2}(E_{2g}) = - \sqrt{3} x y\]

\[\displaystyle \mathbb{Q}_{4,1}(E_{2g},1) = \frac{\sqrt{35} \left(x^{2} - 2 x y - y^{2}\right) \left(x^{2} + 2 x y - y^{2}\right)}{8}\]

\[\displaystyle \mathbb{Q}_{4,2}(E_{2g},1) = \frac{\sqrt{35} x y \left(x - y\right) \left(x + y\right)}{2}\]

Combined ID: (head, tail, wyckoff, (bh_rank, bh_idx, kt_rank, kt_idx), neighbor, n)

for z, (tag, samb_info, idx, comp) in mm["combined_id"].items():
    d = sp.Eq(sp.Symbol("z_{"+z[1:]+"}"),sp.Symbol(tag),evaluate=False)
    print("info = ", to_tuple(samb_info), "index =", idx, "comp =", comp)
    display(d)

info =  (('C', 'C', '2c', (1, (2,), 1, (2,))), 0, -1) index = ('Q', 0, 'A1g', -1, -1, 0, 0, 'q') comp = 0

\[\displaystyle z_{1} = \mathbb{Q}_{0}^{(c)}(A_{1g})\]

info =  (('C', 'C', '3a@3f', (1, (2,), 1, (2,))), 1, 1) index = ('Q', 0, 'A1g', -1, -1, 0, 0, 'q') comp = 0

\[\displaystyle z_{2} = \mathbb{Q}_{0}^{(c)}(A_{1g})\]

info =  (('C', 'C', '6b@6l', (1, (2,), 1, (2,))), 2, 1) index = ('Q', 0, 'A1g', -1, -1, 0, 0, 'q') comp = 0

\[\displaystyle z_{3} = \mathbb{Q}_{0}^{(c)}(A_{1g})\]

info =  (('C', 'C', '3b@1a', (1, (2,), 1, (2,))), 3, 1) index = ('Q', 0, 'A1g', -1, -1, 0, 0, 'q') comp = 0

\[\displaystyle z_{4} = \mathbb{Q}_{0}^{(c)}(A_{1g})\]

info =  (('C', 'C', '6d@3f', (1, (2,), 1, (2,))), 4, 1) index = ('Q', 0, 'A1g', -1, -1, 0, 0, 'q') comp = 0

\[\displaystyle z_{5} = \mathbb{Q}_{0}^{(c)}(A_{1g})\]

info =  (('C', 'C', '6a@6l', (1, (2,), 1, (2,))), 5, 1) index = ('Q', 0, 'A1g', -1, -1, 0, 0, 'q') comp = 0

\[\displaystyle z_{6} = \mathbb{Q}_{0}^{(c)}(A_{1g})\]

info =  (('C', 'C', '6c@2c', (1, (2,), 1, (2,))), 6, 1) index = ('Q', 0, 'A1g', -1, -1, 0, 0, 'q') comp = 0

\[\displaystyle z_{7} = \mathbb{Q}_{0}^{(c)}(A_{1g})\]

info =  (('C', 'C', '6d@3f', (1, (2,), 1, (2,))), 4, 1) index = ('Q', 6, 'A2g', -1, -1, 0, 0, 'q') comp = 0

\[\displaystyle z_{8} = \mathbb{Q}_{6}^{(c)}(A_{2g})\]

info =  (('C', 'C', '3a@3f', (1, (2,), 1, (2,))), 1, 1) index = ('Q', 2, 'E2g', -1, -1, 0, 0, 'q') comp = 0

\[\displaystyle z_{9} = \mathbb{Q}_{2,1}^{(c)}(E_{2g})\]

info =  (('C', 'C', '3a@3f', (1, (2,), 1, (2,))), 1, 1) index = ('Q', 2, 'E2g', -1, -1, 0, 0, 'q') comp = 1

\[\displaystyle z_{10} = \mathbb{Q}_{2,2}^{(c)}(E_{2g})\]

info =  (('C', 'C', '6b@6l', (1, (2,), 1, (2,))), 2, 1) index = ('Q', 2, 'E2g', -1, -1, 0, 0, 'q') comp = 0

\[\displaystyle z_{11} = \mathbb{Q}_{2,1}^{(c)}(E_{2g})\]

info =  (('C', 'C', '6b@6l', (1, (2,), 1, (2,))), 2, 1) index = ('Q', 2, 'E2g', -1, -1, 0, 0, 'q') comp = 1

\[\displaystyle z_{12} = \mathbb{Q}_{2,2}^{(c)}(E_{2g})\]

info =  (('C', 'C', '3b@1a', (1, (2,), 1, (2,))), 3, 1) index = ('Q', 2, 'E2g', -1, -1, 0, 0, 'q') comp = 0

\[\displaystyle z_{13} = \mathbb{Q}_{2,1}^{(c)}(E_{2g})\]

info =  (('C', 'C', '3b@1a', (1, (2,), 1, (2,))), 3, 1) index = ('Q', 2, 'E2g', -1, -1, 0, 0, 'q') comp = 1

\[\displaystyle z_{14} = \mathbb{Q}_{2,2}^{(c)}(E_{2g})\]

info =  (('C', 'C', '6d@3f', (1, (2,), 1, (2,))), 4, 1) index = ('Q', 2, 'E2g', -1, -1, 0, 0, 'q') comp = 0

\[\displaystyle z_{15} = \mathbb{Q}_{2,1}^{(c)}(E_{2g})\]

info =  (('C', 'C', '6d@3f', (1, (2,), 1, (2,))), 4, 1) index = ('Q', 2, 'E2g', -1, -1, 0, 0, 'q') comp = 1

\[\displaystyle z_{16} = \mathbb{Q}_{2,2}^{(c)}(E_{2g})\]

info =  (('C', 'C', '6d@3f', (1, (2,), 1, (2,))), 4, 1) index = ('Q', 4, 'E2g', 1, -1, 0, 0, 'q') comp = 0

\[\displaystyle z_{17} = \mathbb{Q}_{4,1}^{(c)}(E_{2g},1)\]

info =  (('C', 'C', '6d@3f', (1, (2,), 1, (2,))), 4, 1) index = ('Q', 4, 'E2g', 1, -1, 0, 0, 'q') comp = 1

\[\displaystyle z_{18} = \mathbb{Q}_{4,2}^{(c)}(E_{2g},1)\]

info =  (('C', 'C', '6a@6l', (1, (2,), 1, (2,))), 5, 1) index = ('Q', 2, 'E2g', -1, -1, 0, 0, 'q') comp = 0

\[\displaystyle z_{19} = \mathbb{Q}_{2,1}^{(c)}(E_{2g})\]

info =  (('C', 'C', '6a@6l', (1, (2,), 1, (2,))), 5, 1) index = ('Q', 2, 'E2g', -1, -1, 0, 0, 'q') comp = 1

\[\displaystyle z_{20} = \mathbb{Q}_{2,2}^{(c)}(E_{2g})\]

info =  (('C', 'C', '6c@2c', (1, (2,), 1, (2,))), 6, 1) index = ('Q', 2, 'E2g', -1, -1, 0, 0, 'q') comp = 0

\[\displaystyle z_{21} = \mathbb{Q}_{2,1}^{(c)}(E_{2g})\]

info =  (('C', 'C', '6c@2c', (1, (2,), 1, (2,))), 6, 1) index = ('Q', 2, 'E2g', -1, -1, 0, 0, 'q') comp = 1

\[\displaystyle z_{22} = \mathbb{Q}_{2,2}^{(c)}(E_{2g})\]

info =  (('C', 'C', '2c', (1, (2,), 1, (2,))), 0, -1) index = ('Q', 3, 'B1u', -1, -1, 0, 0, 'q') comp = 0

\[\displaystyle z_{23} = \mathbb{Q}_{3}^{(c)}(B_{1u})\]

info =  (('C', 'C', '6b@6l', (1, (2,), 1, (2,))), 2, 1) index = ('Q', 3, 'B1u', -1, -1, 0, 0, 'q') comp = 0

\[\displaystyle z_{24} = \mathbb{Q}_{3}^{(c)}(B_{1u})\]

info =  (('C', 'C', '6a@6l', (1, (2,), 1, (2,))), 5, 1) index = ('Q', 3, 'B1u', -1, -1, 0, 0, 'q') comp = 0

\[\displaystyle z_{25} = \mathbb{Q}_{3}^{(c)}(B_{1u})\]

info =  (('C', 'C', '6c@2c', (1, (2,), 1, (2,))), 6, 1) index = ('Q', 3, 'B1u', -1, -1, 0, 0, 'q') comp = 0

\[\displaystyle z_{26} = \mathbb{Q}_{3}^{(c)}(B_{1u})\]

info =  (('C', 'C', '6b@6l', (1, (2,), 1, (2,))), 2, 1) index = ('Q', 1, 'E1u', -1, -1, 0, 0, 'q') comp = 0

\[\displaystyle z_{27} = \mathbb{Q}_{1,1}^{(c)}(E_{1u})\]

info =  (('C', 'C', '6b@6l', (1, (2,), 1, (2,))), 2, 1) index = ('Q', 1, 'E1u', -1, -1, 0, 0, 'q') comp = 1

\[\displaystyle z_{28} = \mathbb{Q}_{1,2}^{(c)}(E_{1u})\]

info =  (('C', 'C', '6a@6l', (1, (2,), 1, (2,))), 5, 1) index = ('Q', 1, 'E1u', -1, -1, 0, 0, 'q') comp = 0

\[\displaystyle z_{29} = \mathbb{Q}_{1,1}^{(c)}(E_{1u})\]

info =  (('C', 'C', '6a@6l', (1, (2,), 1, (2,))), 5, 1) index = ('Q', 1, 'E1u', -1, -1, 0, 0, 'q') comp = 1

\[\displaystyle z_{30} = \mathbb{Q}_{1,2}^{(c)}(E_{1u})\]

info =  (('C', 'C', '6c@2c', (1, (2,), 1, (2,))), 6, 1) index = ('Q', 1, 'E1u', -1, -1, 0, 0, 'q') comp = 0

\[\displaystyle z_{31} = \mathbb{Q}_{1,1}^{(c)}(E_{1u})\]

info =  (('C', 'C', '6c@2c', (1, (2,), 1, (2,))), 6, 1) index = ('Q', 1, 'E1u', -1, -1, 0, 0, 'q') comp = 1

\[\displaystyle z_{32} = \mathbb{Q}_{1,2}^{(c)}(E_{1u})\]

Common SAMB (head, tail, wyckoff, (bh_rank, bh_idx, kt_rank, kt_idx)): combined_id

for info, lst in mm["common_id"].items():
    print(to_tuple(info), lst)

('C', 'C', '2c', (1, (2,), 1, (2,))) ([['z1', 'z23']], ['C'])
('C', 'C', '3a@3f', (1, (2,), 1, (2,))) ([['z2', 'z9', 'z10']], ['C;C_001_1'])
('C', 'C', '6b@6l', (1, (2,), 1, (2,))) ([['z3', 'z11', 'z12', 'z24', 'z27', 'z28']], ['C;C_002_1'])
('C', 'C', '3b@1a', (1, (2,), 1, (2,))) ([['z4', 'z13', 'z14']], ['C;C_003_1'])
('C', 'C', '6d@3f', (1, (2,), 1, (2,))) ([['z5', 'z8', 'z15', 'z16', 'z17', 'z18']], ['C;C_004_1'])
('C', 'C', '6a@6l', (1, (2,), 1, (2,))) ([['z6', 'z19', 'z20', 'z25', 'z29', 'z30']], ['C;C_005_1'])
('C', 'C', '6c@2c', (1, (2,), 1, (2,))) ([['z7', 'z21', 'z22', 'z26', 'z31', 'z32']], ['C;C_006_1'])

Cluster info.

for site_bond, dic in mm["cluster_info"].items():
    print(site_bond)
    for bk_block, (wyckoff, z_list) in dic.items():
        print(bk_block, wyckoff, z_list)

C
(1, 1) 2c ['z1', 'z23']
C;C_001_1
(1, 1) 3a@3f ['z2', 'z9', 'z10']
C;C_002_1
(1, 1) 6b@6l ['z3', 'z11', 'z12', 'z24', 'z27', 'z28']
C;C_003_1
(1, 1) 3b@1a ['z4', 'z13', 'z14']
C;C_004_1
(1, 1) 6d@3f ['z5', 'z8', 'z15', 'z16', 'z17', 'z18']
C;C_005_1
(1, 1) 6a@6l ['z6', 'z19', 'z20', 'z25', 'z29', 'z30']
C;C_006_1
(1, 1) 6c@2c ['z7', 'z21', 'z22', 'z26', 'z31', 'z32']

Contents in mm[“site”][“representative”] or mm[“site”][“cell”]

mm._write_site()

--- representative site ---
C: #1, wyckoff = 2c, symmetry = -6m2, 1st = [0.3333333333333333, 0.6666666666666666, 0.0], orbital = [[], ['pz'], [], []]
--- cell site ---
tag = C
#1: position = [0.3333333333333333, 0.6666666666666666, 0.0], mapping = [1, 2, 3, 10, 11, 12, 16, 17, 18, 19, 20, 21], sublattice = 1, plus set = 1
#2: position = [0.6666666666666666, 0.3333333333333333, 0.0], mapping = [4, 5, 6, 7, 8, 9, 13, 14, 15, 22, 23, 24], sublattice = 2, plus set = 1

Contents in mm[“bond”][“representative”] or mm[“bond”][“cell”]

mm._write_bond()

--- info ---
C-C: neighbor=[1, 2, 3, 4, 5, 6], head rank=[1], tail rank=[1]
--- representative bond ---
C;C_001_1: #1, 1th, directional = False, wyckoff = 3a@3f, 1st = [0.33333333, 0.66666666, 0.0]@[0.5, 0.0, 0.0], distance = 0.5773502595671213
C;C_002_1: #2, 2th, directional = False, wyckoff = 6b@6l, 1st = [1.0, 0.0, 0.0]@[0.83333333, 0.66666666, 0.0], distance = 1.0
C;C_003_1: #3, 3th, directional = False, wyckoff = 3b@1a, 1st = [-0.66666667, -1.33333334, 0.0]@[0.0, 0.0, 0.0], distance = 1.1547005364547505
C;C_004_1: #4, 4th, directional = False, wyckoff = 6d@3f, 1st = [-1.66666667, -1.33333333, 0.0]@[0.5, 0.0, 0.0], distance = 1.5275252269238924
C;C_005_1: #5, 5th, directional = True, wyckoff = 6a@6l, 1st = [1.0, 2.0, 0.0]@[0.83333333, 0.66666666, 0.0], distance = 1.7320507960218718
C;C_006_1: #6, 6th, directional = False, wyckoff = 6c@2c, 1st = [2.0, 0.0, 0.0]@[0.3333333333333333, 0.6666666666666666, 0.0], distance = 2.0
--- cell bond ---
tag = C;C_001_1
#1: bond = [0.33333333, 0.66666666, 0.0]@[0.5, 0.0, 0.0], mapping = [1, -4, -8, 11, -13, 16, 20, -23], sublattice = 1, plus set = 1, head(sublattice,plus_set) = (2, 1), tail(sublattice,plus_set) = (1, 1)
#2: bond = [-0.66666666, -0.33333333, 0.0]@[0.0, 0.5, 0.0], mapping = [2, -5, -7, 10, -14, 17, 19, -22], sublattice = 2, plus set = 1, head(sublattice,plus_set) = (2, 1), tail(sublattice,plus_set) = (1, 1)
#3: bond = [0.33333333, -0.33333333, 0.0]@[0.5, 0.5, 0.0], mapping = [3, -6, -9, 12, -15, 18, 21, -24], sublattice = 3, plus set = 1, head(sublattice,plus_set) = (2, 1), tail(sublattice,plus_set) = (1, 1)
tag = C;C_002_1
#1: bond = [1.0, 0.0, 0.0]@[0.83333333, 0.66666666, 0.0], mapping = [1, -11, 16, -20], sublattice = 1, plus set = 1, head(sublattice,plus_set) = (1, 1), tail(sublattice,plus_set) = (1, 1)
#2: bond = [0.0, 1.0, 0.0]@[0.33333334000000003, 0.16666667000000002, 0.0], mapping = [2, -10, 17, -19], sublattice = 2, plus set = 1, head(sublattice,plus_set) = (1, 1), tail(sublattice,plus_set) = (1, 1)
#3: bond = [-1.0, -1.0, 0.0]@[0.83333333, 0.16666667000000002, 0.0], mapping = [3, -12, 18, -21], sublattice = 3, plus set = 1, head(sublattice,plus_set) = (1, 1), tail(sublattice,plus_set) = (1, 1)
#4: bond = [-1.0, 0.0, 0.0]@[0.16666667000000002, 0.33333334000000003, 0.0], mapping = [4, -8, 13, -23], sublattice = 4, plus set = 1, head(sublattice,plus_set) = (2, 1), tail(sublattice,plus_set) = (2, 1)
#5: bond = [0.0, -1.0, 0.0]@[0.66666666, 0.83333333, 0.0], mapping = [5, -7, 14, -22], sublattice = 5, plus set = 1, head(sublattice,plus_set) = (2, 1), tail(sublattice,plus_set) = (2, 1)
#6: bond = [1.0, 1.0, 0.0]@[0.16666667000000002, 0.83333333, 0.0], mapping = [6, -9, 15, -24], sublattice = 6, plus set = 1, head(sublattice,plus_set) = (2, 1), tail(sublattice,plus_set) = (2, 1)
tag = C;C_003_1
#1: bond = [-0.66666667, -1.33333334, 0.0]@[0.0, 0.0, 0.0], mapping = [1, -4, -8, 11, -13, 16, 20, -23], sublattice = 1, plus set = 1, head(sublattice,plus_set) = (2, 1), tail(sublattice,plus_set) = (1, 1)
#2: bond = [1.33333334, 0.66666667, 0.0]@[0.0, 0.0, 0.0], mapping = [2, -5, -7, 10, -14, 17, 19, -22], sublattice = 2, plus set = 1, head(sublattice,plus_set) = (2, 1), tail(sublattice,plus_set) = (1, 1)
#3: bond = [-0.66666667, 0.66666667, 0.0]@[0.0, 0.0, 0.0], mapping = [3, -6, -9, 12, -15, 18, 21, -24], sublattice = 3, plus set = 1, head(sublattice,plus_set) = (2, 1), tail(sublattice,plus_set) = (1, 1)
tag = C;C_004_1
#1: bond = [-1.66666667, -1.33333333, 0.0]@[0.5, 0.0, 0.0], mapping = [1, -4, -13, 16], sublattice = 1, plus set = 1, head(sublattice,plus_set) = (2, 1), tail(sublattice,plus_set) = (1, 1)
#2: bond = [1.33333333, -0.3333333399999998, 0.0]@[0.0, 0.5, 0.0], mapping = [2, -5, -14, 17], sublattice = 2, plus set = 1, head(sublattice,plus_set) = (2, 1), tail(sublattice,plus_set) = (1, 1)
#3: bond = [0.3333333399999998, 1.66666667, 0.0]@[0.5, 0.5, 0.0], mapping = [3, -6, -15, 18], sublattice = 3, plus set = 1, head(sublattice,plus_set) = (2, 1), tail(sublattice,plus_set) = (1, 1)
#4: bond = [-1.33333333, -1.66666667, 0.0]@[0.0, 0.5, 0.0], mapping = [7, -10, -19, 22], sublattice = 4, plus set = 1, head(sublattice,plus_set) = (1, 1), tail(sublattice,plus_set) = (2, 1)
#5: bond = [-0.3333333399999998, 1.33333333, 0.0]@[0.5, 0.0, 0.0], mapping = [8, -11, -20, 23], sublattice = 5, plus set = 1, head(sublattice,plus_set) = (1, 1), tail(sublattice,plus_set) = (2, 1)
#6: bond = [1.66666667, 0.3333333399999998, 0.0]@[0.5, 0.5, 0.0], mapping = [9, -12, -21, 24], sublattice = 6, plus set = 1, head(sublattice,plus_set) = (1, 1), tail(sublattice,plus_set) = (2, 1)
tag = C;C_005_1
#1: bond = [1.0, 2.0, 0.0]@[0.83333333, 0.66666666, 0.0], mapping = [1, 11, 16, 20], sublattice = 1, plus set = 1, head(sublattice,plus_set) = (1, 1), tail(sublattice,plus_set) = (1, 1)
#2: bond = [-2.0, -1.0, 0.0]@[0.33333334, 0.16666667, 0.0], mapping = [2, 10, 17, 19], sublattice = 2, plus set = 1, head(sublattice,plus_set) = (1, 1), tail(sublattice,plus_set) = (1, 1)
#3: bond = [1.0, -1.0, 0.0]@[0.83333333, 0.16666667, 0.0], mapping = [3, 12, 18, 21], sublattice = 3, plus set = 1, head(sublattice,plus_set) = (1, 1), tail(sublattice,plus_set) = (1, 1)
#4: bond = [-1.0, -2.0, 0.0]@[0.16666667, 0.33333334, 0.0], mapping = [4, 8, 13, 23], sublattice = 4, plus set = 1, head(sublattice,plus_set) = (2, 1), tail(sublattice,plus_set) = (2, 1)
#5: bond = [2.0, 1.0, 0.0]@[0.66666666, 0.83333333, 0.0], mapping = [5, 7, 14, 22], sublattice = 5, plus set = 1, head(sublattice,plus_set) = (2, 1), tail(sublattice,plus_set) = (2, 1)
#6: bond = [-1.0, 1.0, 0.0]@[0.16666667, 0.83333333, 0.0], mapping = [6, 9, 15, 24], sublattice = 6, plus set = 1, head(sublattice,plus_set) = (2, 1), tail(sublattice,plus_set) = (2, 1)
tag = C;C_006_1
#1: bond = [2.0, 0.0, 0.0]@[0.3333333333333333, 0.6666666666666666, 0.0], mapping = [1, -11, 16, -20], sublattice = 1, plus set = 1, head(sublattice,plus_set) = (1, 1), tail(sublattice,plus_set) = (1, 1)
#2: bond = [0.0, 2.0, 0.0]@[0.3333333333333333, 0.6666666666666666, 0.0], mapping = [2, -10, 17, -19], sublattice = 2, plus set = 1, head(sublattice,plus_set) = (1, 1), tail(sublattice,plus_set) = (1, 1)
#3: bond = [-2.0, -2.0, 0.0]@[0.3333333333333333, 0.6666666666666666, 0.0], mapping = [3, -12, 18, -21], sublattice = 3, plus set = 1, head(sublattice,plus_set) = (1, 1), tail(sublattice,plus_set) = (1, 1)
#4: bond = [-2.0, 0.0, 0.0]@[0.6666666666666666, 0.3333333333333333, 0.0], mapping = [4, -8, 13, -23], sublattice = 4, plus set = 1, head(sublattice,plus_set) = (2, 1), tail(sublattice,plus_set) = (2, 1)
#5: bond = [0.0, -2.0, 0.0]@[0.6666666666666666, 0.3333333333333333, 0.0], mapping = [5, -7, 14, -22], sublattice = 5, plus set = 1, head(sublattice,plus_set) = (2, 1), tail(sublattice,plus_set) = (2, 1)
#6: bond = [2.0, 2.0, 0.0]@[0.6666666666666666, 0.3333333333333333, 0.0], mapping = [6, -9, 15, -24], sublattice = 6, plus set = 1, head(sublattice,plus_set) = (2, 1), tail(sublattice,plus_set) = (2, 1)