code: def generate_rotated_translated_paraboloid(
      range_coeffs: Range,
  ) -> Polynomial:
      """Unused."""
      do_sample = True
      while do_sample:
          coeffs_0 = generate_plane(range_coeffs).coeffs
          coeffs_1 = generate_plane(range_coeffs).coeffs
          mat = np.array(
              [
                  coeffs_0,
                  coeffs_1,
              ]
          )
          if np.linalg.matrix_rank(mat) == 2:
              do_sample = False
      x = Symbol("x")
      y = Symbol("y")
      xprime = coeffs_0[0] * x + coeffs_0[1] * y + coeffs_0[2]
      yprime = coeffs_1[0] * x + coeffs_1[1] * y + coeffs_1[2]
      expr = xprime**2 + yprime**2
      poly = Poly(expr, [x, y])
      return sympy_poly_to_poly(poly, 2, 2)
  
imports: from collections import defaultdict
  from dataclasses import dataclass, field
  from itertools import combinations_with_replacement, product
  import math
  from math import comb
  import numpy
  import numpy.typing
  import random
  import sympy
  from sympy import Symbol, Poly, diff
  from sympy.parsing.sympy_parser import standard_transformations, implicit_multiplication_application
  from typing import List, Optional, Tuple, Dict
  from helm.benchmark.adaptation.adapters.adapter_factory import ADAPT_GENERATION
  from helm.benchmark.adaptation.adapter_spec import AdapterSpec
  from helm.benchmark.window_services.tokenizer_service import TokenizerService
  from helm.common.authentication import Authentication
  from helm.proxy.services.server_service import ServerService
  from .scenario import Scenario, Instance, Reference, TRAIN_SPLIT, TEST_SPLIT, CORRECT_TAG, Input, Output
label_desc: Use image node_id 12 for calling a global function with example usage: generate_rotated_translated_paraboloid(range_coeffs) and returns: sympy_poly_to_poly