searchindex.js

Search.setIndex({"alltitles": {"(1) \\Gamma is real": [[25, "gamma-is-real"]], "(1) \\Gamma^{\\mathbf{k}\\alpha} is real": [[25, "gamma-mathbf-k-alpha-is-real"]], "(2, 3) \\Gamma is pseudo-real or not equivalent to \\Gamma^{\\ast}": [[25, "gamma-is-pseudo-real-or-not-equivalent-to-gamma-ast"]], "(2, 3) \\Gamma^{\\mathbf{k}\\alpha} is pseudo-real or not equivalent to \\Gamma^{\\mathbf{k}\\alpha \\ast}": [[25, "gamma-mathbf-k-alpha-is-pseudo-real-or-not-equivalent-to-gamma-mathbf-k-alpha-ast"]], "API Reference": [[0, null]], "Algorithm for enumerating irreps": [[18, null]], "Anti-linear operator": [[23, "anti-linear-operator"]], "Application of space-group irreps to lattice vibration": [[15, null]], "Apply projection operator and block-diagonalize dynamical matrix": [[15, "Apply-projection-operator-and-block-diagonalize-dynamical-matrix"]], "Bloch sphere": [[13, "bloch-sphere"]], "C_{3v} associated with P3m1 (No. 156)": [[21, "c-3v-associated-with-p3m1-no-156"]], "Calculate physically irreducible representation": [[17, "Calculate-physically-irreducible-representation"]], "Calculate symmetry-adapted tensors": [[17, "Calculate-symmetry-adapted-tensors"]], "Case-1: conjugated irreps are mutually inequivalent": [[20, "case-1-conjugated-irreps-are-mutually-inequivalent"]], "Case-2: conjugated irreps are equivalent": [[20, "case-2-conjugated-irreps-are-equivalent"]], "Case: \\xi^{\\alpha} = -1": [[23, "id4"]], "Case: \\xi^{\\alpha} = 0": [[23, "case-xi-alpha-0"]], "Case: \\xi^{\\alpha} = 1": [[23, "case-xi-alpha-1"]], "Change Log": [[11, null]], "Change log": [[30, "change-log"]], "Co-representation for spinor": [[2, null]], "Co-representation of magnetic point and space group": [[23, null]], "Constructing symmetry-adapted basis": [[28, null]], "Convention of anti-linear operators in spgrep": [[23, "convention-of-anti-linear-operators-in-spgrep"]], "Convention of rotations for spinor": [[27, "convention-of-rotations-for-spinor"]], "Core functions": [[1, null]], "Crystallographic point group": [[1, "crystallographic-point-group"], [1, "id2"], [21, "crystallographic-point-group"]], "Decomposition of crystallographic point groups": [[20, "decomposition-of-crystallographic-point-groups"]], "Definition": [[23, "definition"]], "Development": [[12, null]], "Enumerate spin representations from factor system": [[16, "Enumerate-spin-representations-from-factor-system"]], "Examples": [[14, null]], "Factor system for spinor": [[27, "factor-system-for-spinor"]], "Features": [[30, "features"]], "Formulation": [[22, null]], "Formulation of irreducible representations": [[24, null]], "Frobenius-Schur indicator for co-representation": [[23, "frobenius-schur-indicator-for-co-representation"]], "Frobenius-Schur indicator for space-group representations": [[25, "frobenius-schur-indicator-for-space-group-representations"]], "Functions for (magnetic) crystal structure": [[1, "functions-for-magnetic-crystal-structure"]], "Functions for (magnetic) crystallographic point-group symmetry operations": [[1, "functions-for-magnetic-crystallographic-point-group-symmetry-operations"]], "Functions for (magnetic) space-group symmetry operations": [[1, "functions-for-magnetic-space-group-symmetry-operations"]], "Group": [[3, null]], "How to compile JOSS draft": [[12, "how-to-compile-joss-draft"]], "How to compile documents": [[12, "how-to-compile-documents"]], "How to contribute": [[30, "how-to-contribute"]], "How to generate diagram from Mermaid file": [[12, "how-to-generate-diagram-from-mermaid-file"]], "Import modules": [[15, "Import-modules"], [17, "Import-modules"]], "Index": [[29, null]], "Installation": [[12, "installation"], [30, "installation"]], "Intertwiner between two projective representations of finite group": [[19, "intertwiner-between-two-projective-representations-of-finite-group"]], "Intertwiner between two space-group representations of space group \\mathcal{G}": [[19, "intertwiner-between-two-space-group-representations-of-space-group-mathcal-g"]], "Irreps": [[4, null]], "Irreps of space group": [[26, null]], "Irreps of translation subgroup": [[26, "irreps-of-translation-subgroup"]], "License": [[30, "license"]], "Linear representation": [[1, "linear-representation"]], "Little group": [[26, "little-group"]], "Load dynamical matrix from PhononDB": [[15, "Load-dynamical-matrix-from-PhononDB"]], "Memo": [[13, null]], "Numerically obtain intertwiner between equivalent representations": [[19, null]], "Obtaining all irreps from (projective) regular representation": [[21, "obtaining-all-irreps-from-projective-regular-representation"]], "On-the-fly irreps generation from regular representation": [[21, null]], "On-the-fly irreps generation from solvable group chain": [[20, null]], "P4_{2}/mnm (No. 136) at X=(0\\frac{1}{2}0)": [[21, "p4-2-mnm-no-136-at-x-0-frac-1-2-0"]], "PIR of finite group": [[25, "pir-of-finite-group"]], "PIR of space group \\mathcal{G}": [[25, "pir-of-space-group-mathcal-g"]], "Physically irreducible representation (PIR)": [[25, null]], "Pointgroup": [[5, null]], "Prepare point-group operations": [[16, "Prepare-point-group-operations"]], "Prepare point-group operations and representation": [[17, "Prepare-point-group-operations-and-representation"]], "Prepare space-group operations and representation": [[15, "Prepare-space-group-operations-and-representation"]], "Projection operator": [[28, "projection-operator"]], "Projective representation": [[26, "projective-representation"]], "Reciprocal lattice and transformation": [[26, "reciprocal-lattice-and-transformation"]], "References": [[13, "references"], [20, "references"], [21, "references"], [22, "references"], [23, "references"], [25, "references"], [27, "references"], [28, "references"]], "Regular representation": [[21, "regular-representation"]], "Release": [[12, "release"]], "Representation": [[6, null]], "Representation for spinor": [[7, null]], "Small representation": [[26, "small-representation"]], "Space group": [[1, "space-group"], [1, "id1"], [21, "space-group"]], "Spgrep": [[30, null]], "Spin representation": [[1, "spin-representation"], [27, null]], "Spin representation for C_{3v}": [[16, null]], "Subduced and induced representations for solvable group": [[20, "subduced-and-induced-representations-for-solvable-group"]], "Subpages": [[12, "subpages"], [18, "subpages"], [22, "subpages"], [24, "subpages"]], "Summary": [[1, "summary"]], "Symmetry operation of the first kind": [[27, "symmetry-operation-of-the-first-kind"]], "Symmetry operation of the second kind": [[27, "symmetry-operation-of-the-second-kind"]], "Symmetry-adapted tensor": [[17, null]], "Symmetry-adapted tensor with intrinsic symmetry": [[13, "symmetry-adapted-tensor-with-intrinsic-symmetry"]], "Tensor": [[8, null]], "Transformation": [[9, null]], "Unitary matrices for spinor": [[16, "Unitary-matrices-for-spinor"]], "Usage": [[30, "usage"]], "Utility functions": [[10, null]], "Working example": [[21, "working-example"]], "\\mathcal{G} = Ia\\overline{3}d (No. 230) at H=(\\frac{1}{2}\\overline{\\frac{1}{2}}\\frac{1}{2})_{\\mathrm{primitive}}": [[21, "mathcal-g-ia-overline-3-d-no-230-at-h-frac-1-2-overline-frac-1-2-frac-1-2-mathrm-primitive"]], "v0.2.11": [[11, "v0-2-11"]], "v0.2.12": [[11, "v0-2-12"]], "v0.2.8": [[11, "v0-2-8"]], "v0.2.9": [[11, "v0-2-9"]], "v0.3.0 (17 Nov. 2022)": [[11, "v0-3-0-17-nov-2022"]], "v0.3.1 (15 Dec. 2022)": [[11, "v0-3-1-15-dec-2022"]], "v0.3.2 (28 Dec. 2022)": [[11, "v0-3-2-28-dec-2022"]], "v0.3.3 (11 Jan. 2023)": [[11, "v0-3-3-11-jan-2023"]], "v0.3.5 (18 Jun. 2024)": [[11, "v0-3-5-18-jun-2024"]], "v0.3.6 (18 Feb. 2025)": [[11, "v0-3-6-18-feb-2025"]]}, "docnames": ["api/api", "api/api_core", "api/api_corep", "api/api_group", "api/api_irreps", "api/api_pointgroup", "api/api_representation", "api/api_spinor", "api/api_tensor", "api/api_transformation", "api/api_utils", "changelog", "development/development", "development/memo", "examples/examples", "examples/lattice_vibration", "examples/spin_representation", "examples/symmetry_adapted_tensor", "formulation/algorithm/algorithm", "formulation/algorithm/intertwiner", "formulation/algorithm/irreps_from_chain", "formulation/algorithm/irreps_from_regular", "formulation/formulation", "formulation/irreps/corep", "formulation/irreps/irreps", "formulation/irreps/reality", "formulation/irreps/spacegroup_irreps", "formulation/irreps/spinor", "formulation/projection", "genindex", "index"], "envversion": {"nbsphinx": 4, "sphinx": 64, "sphinx.domains.c": 3, "sphinx.domains.changeset": 1, "sphinx.domains.citation": 1, "sphinx.domains.cpp": 9, "sphinx.domains.index": 1, "sphinx.domains.javascript": 3, "sphinx.domains.math": 2, "sphinx.domains.python": 4, "sphinx.domains.rst": 2, "sphinx.domains.std": 2, "sphinx.ext.intersphinx": 1, "sphinx.ext.viewcode": 1, "sphinxcontrib.bibtex": 9}, "filenames": ["api/api.md", "api/api_core.md", "api/api_corep.md", "api/api_group.md", "api/api_irreps.md", "api/api_pointgroup.md", "api/api_representation.md", "api/api_spinor.md", "api/api_tensor.md", "api/api_transformation.md", "api/api_utils.md", "changelog.md", "development/development.md", "development/memo.md", "examples/examples.md", "examples/lattice_vibration.ipynb", "examples/spin_representation.ipynb", "examples/symmetry_adapted_tensor.ipynb", "formulation/algorithm/algorithm.md", "formulation/algorithm/intertwiner.md", "formulation/algorithm/irreps_from_chain.md", "formulation/algorithm/irreps_from_regular.md", "formulation/formulation.md", "formulation/irreps/corep.md", "formulation/irreps/irreps.md", "formulation/irreps/reality.md", "formulation/irreps/spacegroup_irreps.md", "formulation/irreps/spinor.md", "formulation/projection.md", "genindex.rst", "index.md"], "indexentries": {"apply_intrinsic_symmetry() (in module spgrep.tensor)": [[8, "spgrep.tensor.apply_intrinsic_symmetry", false]], "check_cocycle_condition() (in module spgrep.group)": [[3, "spgrep.group.check_cocycle_condition", false]], "check_spacegroup_representation() (in module spgrep.representation)": [[6, "spgrep.representation.check_spacegroup_representation", false]], "decompose_by_maximal_space_subgroup() (in module spgrep.group)": [[3, "spgrep.group.decompose_by_maximal_space_subgroup", false]], "decompose_representation() (in module spgrep.irreps)": [[4, "spgrep.irreps.decompose_representation", false]], "enumerate_small_representations() (in module spgrep.irreps)": [[4, "spgrep.irreps.enumerate_small_representations", false]], "enumerate_spinor_small_corepresentations() (in module spgrep.corep)": [[2, "spgrep.corep.enumerate_spinor_small_corepresentations", false]], "enumerate_spinor_small_representations() (in module spgrep.spinor)": [[7, "spgrep.spinor.enumerate_spinor_small_representations", false]], "enumerate_unitary_irreps() (in module spgrep.irreps)": [[4, "spgrep.irreps.enumerate_unitary_irreps", false]], "enumerate_unitary_irreps_from_regular_representation() (in module spgrep.irreps)": [[4, "spgrep.irreps.enumerate_unitary_irreps_from_regular_representation", false]], "enumerate_unitary_irreps_from_solvable_group_chain() (in module spgrep.irreps)": [[4, "spgrep.irreps.enumerate_unitary_irreps_from_solvable_group_chain", false]], "frobenius_schur_indicator() (in module spgrep.representation)": [[6, "spgrep.representation.frobenius_schur_indicator", false]], "get_cayley_table() (in module spgrep.group)": [[3, "spgrep.group.get_cayley_table", false]], "get_character() (in module spgrep.representation)": [[6, "spgrep.representation.get_character", false]], "get_corep_spinor_factor_system() (in module spgrep.corep)": [[2, "spgrep.corep.get_corep_spinor_factor_system", false]], "get_crystallographic_pointgroup_irreps_from_symmetry() (in module spgrep)": [[1, "spgrep.get_crystallographic_pointgroup_irreps_from_symmetry", false]], "get_crystallographic_pointgroup_spinor_irreps_from_symmetry() (in module spgrep)": [[1, "spgrep.get_crystallographic_pointgroup_spinor_irreps_from_symmetry", false]], "get_direct_product() (in module spgrep.representation)": [[6, "spgrep.representation.get_direct_product", false]], "get_factor_system_from_little_group() (in module spgrep.group)": [[3, "spgrep.group.get_factor_system_from_little_group", false]], "get_identity_index() (in module spgrep.group)": [[3, "spgrep.group.get_identity_index", false]], "get_intertwiner() (in module spgrep.representation)": [[6, "spgrep.representation.get_intertwiner", false]], "get_inverse_index() (in module spgrep.group)": [[3, "spgrep.group.get_inverse_index", false]], "get_little_group() (in module spgrep.group)": [[3, "spgrep.group.get_little_group", false]], "get_order() (in module spgrep.group)": [[3, "spgrep.group.get_order", false]], "get_physically_irrep() (in module spgrep.irreps)": [[4, "spgrep.irreps.get_physically_irrep", false]], "get_pointgroup_chain_generators() (in module spgrep.pointgroup)": [[5, "spgrep.pointgroup.get_pointgroup_chain_generators", false]], "get_primitive_transformation_matrix() (in module spgrep.transform)": [[9, "spgrep.transform.get_primitive_transformation_matrix", false]], "get_projective_regular_representation() (in module spgrep.representation)": [[6, "spgrep.representation.get_projective_regular_representation", false]], "get_regular_representation() (in module spgrep.representation)": [[6, "spgrep.representation.get_regular_representation", false]], "get_spacegroup_irreps() (in module spgrep)": [[1, "spgrep.get_spacegroup_irreps", false]], "get_spacegroup_irreps_from_primitive_symmetry() (in module spgrep)": [[1, "spgrep.get_spacegroup_irreps_from_primitive_symmetry", false]], "get_spacegroup_spinor_irreps() (in module spgrep)": [[1, "spgrep.get_spacegroup_spinor_irreps", false]], "get_spacegroup_spinor_irreps_from_primitive_symmetry() (in module spgrep)": [[1, "spgrep.get_spacegroup_spinor_irreps_from_primitive_symmetry", false]], "get_spinor_factor_system() (in module spgrep.spinor)": [[7, "spgrep.spinor.get_spinor_factor_system", false]], "get_spinor_unitary_rotation() (in module spgrep.spinor)": [[7, "spgrep.spinor.get_spinor_unitary_rotation", false]], "get_symmetry_adapted_tensors() (in module spgrep.tensor)": [[8, "spgrep.tensor.get_symmetry_adapted_tensors", false]], "grassmann_distance() (in module spgrep.utils)": [[10, "spgrep.utils.grassmann_distance", false]], "is_equivalent_irrep() (in module spgrep.irreps)": [[4, "spgrep.irreps.is_equivalent_irrep", false]], "is_matrix_group() (in module spgrep.group)": [[3, "spgrep.group.is_matrix_group", false]], "is_representation() (in module spgrep.representation)": [[6, "spgrep.representation.is_representation", false]], "is_unitary() (in module spgrep.representation)": [[6, "spgrep.representation.is_unitary", false]], "project_to_irrep() (in module spgrep.representation)": [[6, "spgrep.representation.project_to_irrep", false]], "transform_symmetry_and_kpoint() (in module spgrep.transform)": [[9, "spgrep.transform.transform_symmetry_and_kpoint", false]]}, "objects": {"spgrep": [[1, 0, 1, "", "get_crystallographic_pointgroup_irreps_from_symmetry"], [1, 0, 1, "", "get_crystallographic_pointgroup_spinor_irreps_from_symmetry"], [1, 0, 1, "", "get_spacegroup_irreps"], [1, 0, 1, "", "get_spacegroup_irreps_from_primitive_symmetry"], [1, 0, 1, "", "get_spacegroup_spinor_irreps"], [1, 0, 1, "", "get_spacegroup_spinor_irreps_from_primitive_symmetry"]], "spgrep.corep": [[2, 0, 1, "", "enumerate_spinor_small_corepresentations"], [2, 0, 1, "", "get_corep_spinor_factor_system"]], "spgrep.group": [[3, 0, 1, "", "check_cocycle_condition"], [3, 0, 1, "", "decompose_by_maximal_space_subgroup"], [3, 0, 1, "", "get_cayley_table"], [3, 0, 1, "", "get_factor_system_from_little_group"], [3, 0, 1, "", "get_identity_index"], [3, 0, 1, "", "get_inverse_index"], [3, 0, 1, "", "get_little_group"], [3, 0, 1, "", "get_order"], [3, 0, 1, "", "is_matrix_group"]], "spgrep.irreps": [[4, 0, 1, "", "decompose_representation"], [4, 0, 1, "", "enumerate_small_representations"], [4, 0, 1, "", "enumerate_unitary_irreps"], [4, 0, 1, "", "enumerate_unitary_irreps_from_regular_representation"], [4, 0, 1, "", "enumerate_unitary_irreps_from_solvable_group_chain"], [4, 0, 1, "", "get_physically_irrep"], [4, 0, 1, "", "is_equivalent_irrep"]], "spgrep.pointgroup": [[5, 0, 1, "", "get_pointgroup_chain_generators"]], "spgrep.representation": [[6, 0, 1, "", "check_spacegroup_representation"], [6, 0, 1, "", "frobenius_schur_indicator"], [6, 0, 1, "", "get_character"], [6, 0, 1, "", "get_direct_product"], [6, 0, 1, "", "get_intertwiner"], [6, 0, 1, "", "get_projective_regular_representation"], [6, 0, 1, "", "get_regular_representation"], [6, 0, 1, "", "is_representation"], [6, 0, 1, "", "is_unitary"], [6, 0, 1, "", "project_to_irrep"]], "spgrep.spinor": [[7, 0, 1, "", "enumerate_spinor_small_representations"], [7, 0, 1, "", "get_spinor_factor_system"], [7, 0, 1, "", "get_spinor_unitary_rotation"]], "spgrep.tensor": [[8, 0, 1, "", "apply_intrinsic_symmetry"], [8, 0, 1, "", "get_symmetry_adapted_tensors"]], "spgrep.transform": [[9, 0, 1, "", "get_primitive_transformation_matrix"], [9, 0, 1, "", "transform_symmetry_and_kpoint"]], "spgrep.utils": [[10, 0, 1, "", "grassmann_distance"]]}, "objnames": {"0": ["py", "function", "Python function"]}, "objtypes": {"0": "py:function"}, "terms": {"": [1, 2, 6, 7, 9, 13, 15, 19, 20, 21, 23, 25, 26, 27, 28, 30], "0": [3, 4, 5, 9, 15, 16, 17, 18, 19, 20, 25, 26, 27, 28, 30], "00133": 21, "009": 21, "017": 21, "05": [1, 2, 4, 6, 7], "06": [6, 8, 21], "08": [1, 2, 3, 4, 6, 7, 8, 10], "090779966": 21, "0j": 16, "1": [1, 2, 3, 4, 5, 6, 7, 9, 10, 13, 15, 16, 17, 18, 19, 26, 27, 28, 30], "10": [6, 10, 12, 13, 15, 20, 21, 23, 25, 28, 30], "1002": 28, "1016": 21, "1038": 21, "107": 21, "11": 17, "11010": 25, "11018": 25, "1103": [13, 25], "1107": [20, 25], "1126": 23, "1137": 21, "1145": 10, "11556": 13, "11570": 13, "1176": 10, "1197": 10, "12": [17, 27, 30], "126": 9, "13": [15, 27, 30], "136": 30, "137": 9, "1390156": 10, "1390204": 10, "15": 15, "16": [15, 30], "1651": 23, "1959": 23, "1968": 15, "1973": 20, "1989": 28, "1991": 25, "1996": [22, 25], "1a": 15, "1b": 15, "1e": [1, 2, 3, 4, 6, 7, 8], "2": [1, 2, 4, 6, 7, 9, 10, 12, 13, 15, 16, 17, 23, 26, 27, 28, 30], "2000": 13, "2005": [13, 27], "2008": [10, 13, 22], "2009": [21, 22], "2011": 21, "2013": 25, "2014": 9, "2016": [1, 10, 13, 20], "2017": 21, "2018": 23, "21": 27, "221": [15, 17], "224425": 13, "23": 27, "25th": 10, "2657": 30, "29": 20, "2998": 15, "2a": 30, "2i": 25, "2j": 15, "3": [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 15, 16, 17, 23, 26, 27, 28, 30], "3046": 30, "31": 27, "32": [21, 27], "35": 28, "37": [10, 15], "376": 10, "383": 10, "388": 25, "395": 25, "3c": 15, "3m": [15, 16, 17], "3m1": 16, "4": [1, 2, 4, 6, 7, 15, 16, 17, 20, 21, 23, 25, 30], "40": 15, "41": 11, "43": 25, "441": 28, "456": 28, "464": 20, "47": 11, "472": 20, "48": [17, 21], "4f": 30, "5": [6, 15, 16, 17, 21, 30], "50": [11, 21], "517": 17, "53": 11, "560350309": 28, "6": [15, 16, 17, 21], "603": 30, "605": 21, "62": 13, "620": 21, "69": 25, "7": [15, 16, 17, 21], "76": 21, "8": [12, 15, 16, 17, 21, 23, 30], "8000": 12, "9": [12, 15, 16, 17, 30], "93": 13, "95": 21, "96": 21, "969": 30, "97809553602060000114": 20, "986": 15, "A": [1, 15, 17, 18, 20, 23, 25, 26, 27, 28], "At": [12, 25, 30], "Be": [16, 21, 23, 26], "For": [1, 4, 16, 17, 20, 21, 25, 26, 27], "If": [1, 2, 3, 4, 6, 10, 26], "In": [10, 19, 20, 23, 25, 27], "No": [15, 17, 30], "Of": 17, "On": 18, "Such": 16, "The": [1, 5, 6, 9, 13, 15, 16, 17, 19, 20, 21, 22, 23, 25, 27, 28], "Then": [3, 4, 5, 17, 21, 23, 25, 26, 27, 28], "There": [20, 25], "These": [13, 25], "_": [1, 2, 3, 4, 7, 13, 15, 16, 17, 19, 20, 23, 25, 26, 27, 28], "__future__": [16, 17], "__version__": [15, 16, 17], "a0_idx": 3, "a70": 9, "a_": [3, 21, 23], "aa": 23, "aat8685": 23, "ab": [15, 23, 28], "abelian": [4, 5], "abov": [19, 21], "absolut": [1, 4, 6, 21], "ac": [13, 15], "act": [17, 23, 27], "acta": [9, 20, 25], "action": [13, 17, 27, 28], "activ": [12, 30], "adapt": [8, 14, 20, 22, 27, 30], "add": 11, "addition": 25, "adjoint": 6, "adv": 23, "after": 9, "ainv": 15, "algorithm": [20, 21, 22], "all": [1, 2, 4, 5, 7, 12, 17, 20], "all_basi": [15, 17], "allclos": [15, 16], "alloi": 13, "alpha": [1, 2, 7, 13, 21, 27, 28], "also": [13, 17, 20, 21, 23, 25, 27], "alt05": [13, 27], "alt89": 28, "altmann": [13, 27, 28], "alwai": 20, "am": 23, "ambigu": [16, 27], "an": [2, 16, 19, 20, 21, 23, 25, 26, 27, 28, 30], "anal": 21, "analysi": 10, "angl": 27, "angular": 27, "ani": [19, 21, 26, 30], "anisotropi": 13, "annot": [16, 17], "anoth": 16, "anti": [1, 2], "anti_linear": [1, 2], "antisymmetri": [2, 23], "anton": 21, "ap": [13, 25, 26], "api": 30, "appear": [1, 20], "append": 17, "appl": 21, "appli": [8, 9, 11, 17, 28], "applic": [10, 14, 22, 23, 25], "apply_intrinsic_symmetri": [0, 8, 11, 17], "approach": [13, 22], "ar": [1, 4, 5, 6, 9, 15, 17, 18, 19, 21, 23, 25, 27, 28], "aro16": 20, "around": 16, "aroyo": [9, 20], "arrai": [1, 2, 3, 4, 6, 7, 8, 9, 10, 15, 16, 17], "arthur": [21, 22], "articl": 21, "arxiv": 21, "ashvin": [21, 23], "aspect": 17, "assert": [15, 16, 17, 30], "associ": 10, "assum": [1, 25, 27, 28], "ast": [2, 13, 21, 23, 26, 28], "atol": [1, 2, 3, 4, 6, 7, 8], "atom": [1, 15, 23], "au": 23, "augment": 13, "autobuild": 12, "ax": [15, 17], "axi": 27, "b": [13, 18, 19, 25, 26], "ba": 15, "band": [21, 23], "base": [10, 21, 25], "basi": [1, 2, 5, 6, 7, 10, 13, 15, 17, 22, 23, 25, 26, 30], "basis1": 10, "basis2": 10, "batanouni": [13, 22], "batio3": 15, "bc09": [21, 22], "becaus": [20, 25, 26, 27, 28], "beforehand": 19, "begin": [1, 4, 13, 17, 20, 21, 23, 25, 27], "belong": [1, 3], "berlin": [22, 25], "beta": 21, "between": [6, 10, 11, 20, 23], "bi": 17, "bigoplus_": 13, "bin": 12, "bj": 17, "bloch": [26, 27], "block": [17, 21], "blocked_dynamical_matrix": 15, "boil": 26, "bool": [1, 2, 4, 8, 10], "bradlei": [21, 22], "branton": 25, "break": 15, "browser": 12, "bsd": 30, "bwr": [15, 17], "c": [10, 13, 16, 19, 21, 23, 25, 30], "c3v": 16, "c_": 23, "calcul": [1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 13, 15, 18, 26], "call": [1, 4, 17, 25, 26], "cambridg": [13, 22], "campbel": 25, "can": [16, 17, 19, 20, 21, 23, 25, 26, 27, 28, 30], "care": [16, 21, 23, 26], "cartesian": [15, 16], "case": [1, 4, 13, 19, 25, 30], "caylei": 4, "cd": [12, 30], "cdot": [1, 2, 3, 4, 7, 15, 20, 21, 23, 25, 26, 27, 28], "cell": [1, 6, 9, 15, 26, 28, 30], "chain": [1, 2, 4, 7, 18], "changelog": 12, "charact": [6, 21], "character1": 4, "character2": 4, "check": [6, 15, 17, 21, 23], "check_cocycle_condit": [0, 3], "check_spacegroup_represent": [0, 6, 15], "chem": 28, "chi": [6, 21, 23, 25], "choos": [19, 20, 23, 25, 26, 27], "chosen": [1, 4, 28], "christoph": [21, 22], "chun": [21, 23], "clariti": 16, "classic": [21, 22], "classifi": 25, "claus": 30, "clean": 11, "clebsch": 28, "cli": 12, "clone": [12, 30], "cmap": [15, 17], "co": [0, 1, 3, 4, 7, 11, 13, 15, 18, 21, 24, 25, 26, 27, 30], "cocycl": [3, 23, 26], "coeffici": [9, 20, 26, 28], "col": [15, 17], "collinear": 1, "column": 15, "com": [12, 21, 28, 30], "combin": [1, 6], "commit": 12, "commun": 21, "commut": [1, 2, 4, 7, 18, 21], "compar": [1, 2, 4, 6, 7], "comparison": 11, "compat": 11, "complex": [4, 19, 23], "complex128": 15, "compon": 15, "compos": 4, "comput": [1, 4, 10, 11, 13, 15, 22, 25, 28], "concaten": [15, 17], "conda": [12, 30], "condens": [13, 22], "condit": [3, 13, 21, 23, 25, 26], "condon": 27, "confer": 10, "confin": 26, "confirm": [12, 17], "cong": [20, 21], "conj": 15, "conjug": [4, 23, 25], "conjugaci": 25, "consid": [13, 15, 17, 19, 20, 21, 23, 25, 26, 27], "consist": 9, "constant": 17, "construct": [1, 2, 4, 6, 7, 13, 15, 17, 18, 25], "contain": 21, "contain_spac": 11, "control": 21, "convent": [1, 2, 6, 7, 9, 16, 22], "convert": 16, "coordin": [1, 9, 16, 26], "coprod_": [19, 20, 25, 26, 27], "cord": 25, "core": 0, "corep": [1, 2], "corep_spinor_factor_system": 2, "corpor": [13, 27], "correl": 10, "correspond": [3, 16, 21, 27], "coset": [3, 4, 19, 25], "coupl": 13, "courier": [13, 27], "cours": 17, "cracknel": [21, 22], "creat": [12, 30], "cryst": [9, 20, 25], "crystal": [0, 25], "crystallin": 21, "crystallograph": [0, 5, 11, 17, 18, 25, 26, 30], "crystallographi": [1, 20], "current": 8, "d": [1, 2, 3, 4, 7, 9, 10, 13, 20, 23, 25, 26, 27], "d_": [13, 21, 27, 28], "dagger": [21, 23, 25, 28], "daniel": 10, "data": 12, "ddot": 20, "de": 9, "decemb": [20, 21, 22], "decompos": [3, 4, 17, 18, 20, 23, 26], "decompose_by_maximal_space_subgroup": [0, 3], "decompose_represent": [0, 4], "decomposit": [11, 21], "def": [15, 17], "default": [1, 4, 6, 10], "defin": [13, 17, 21, 23, 26, 27, 28], "definit": [6, 9, 13], "delta": [18, 19, 20, 21, 26, 28], "delta_": [15, 20, 21, 26, 28], "denot": 26, "depend": [11, 30], "der": 21, "deriv": [1, 2, 7, 21, 28], "describ": [20, 21], "det": 25, "detail": [1, 30], "determin": [6, 20], "dev": 12, "dev177": [15, 17], "dev5": 16, "develop": 30, "diag": 21, "diagon": [1, 2, 4, 7, 17, 18, 21, 25], "differ": [1, 2, 4, 6, 7, 10, 27], "dim": [1, 4, 6, 7, 8], "dim0": 4, "dim1": 6, "dim2": [4, 6], "dim_irrep": 6, "dimens": [10, 21], "dimension": [10, 17, 26, 30], "direct": [6, 15], "directori": 12, "discrimin": 10, "disord": 13, "displac": 15, "distanc": [10, 11], "distinguish": [1, 2, 4, 6, 7], "distort": 25, "doc": 12, "docker": 12, "docs_build": 12, "document": [11, 30], "doe": 9, "doi": [10, 13, 20, 21, 23, 25, 28], "dorian": 25, "dot": [1, 6, 13, 15, 18, 20, 21, 26], "doubl": [13, 27], "down": 26, "downarrow": [13, 20, 27], "draft": 11, "drop": 11, "dtype": [15, 17], "dual": 26, "duplic": 9, "dynamical_matrix": 15, "e": [1, 2, 4, 6, 7, 9, 12, 15, 17, 19, 20, 21, 25, 26, 27, 28, 30], "e_": 17, "eaat8685": 23, "each": [1, 2, 4, 6, 17, 23, 26, 27], "ebw08": [13, 22], "editor": 20, "effici": 21, "eigenvalu": [1, 2, 4, 6, 7], "eigenvector": 25, "einsum": 15, "either": 27, "el": [13, 22], "elast": [17, 21], "element": [3, 21, 23], "elsevi": 23, "end": [1, 4, 13, 17, 20, 21, 23, 25, 27], "england": [21, 22], "enough": 21, "ensuremath": 13, "enumer": [1, 2, 4, 7, 15, 17, 22, 26, 27, 30], "enumerate_small_represent": [0, 4, 11], "enumerate_spinor_small_corepresent": [0, 2], "enumerate_spinor_small_represent": [0, 7], "enumerate_unitary_irrep": [0, 4, 11], "enumerate_unitary_irreps_from_regular_represent": [0, 4, 18], "enumerate_unitary_irreps_from_solvable_group_chain": [0, 4, 18], "env": 12, "environ": 30, "eq": [20, 21, 26], "equal": [15, 17, 21], "equilibrium": 15, "equiv": [3, 20, 25, 26], "equival": [4, 6, 23], "erd\u00f6": 11, "error": 21, "eugen": 23, "exampl": [11, 15, 16, 17, 30], "exhaust": 21, "exist": [23, 25, 26], "exp": [3, 15, 20, 26, 27], "expect": 17, "explicitli": 27, "explor": 21, "extend": 15, "extens": 25, "f": [13, 15, 16, 17, 26, 27], "fact": 27, "factor": [1, 2, 3, 4, 5, 6, 7, 20, 21, 23, 26, 28], "factor_system": [1, 2, 3, 4, 6, 7, 16], "fail": 6, "fals": [1, 4, 8, 10], "fe": 13, "fig": [15, 17], "figsiz": [15, 17], "file": 15, "find": [25, 30], "finit": 21, "first": [25, 26], "fix": [1, 2, 4, 7, 11], "float": [1, 2, 4, 6, 7, 10], "float64": 17, "flor": 9, "fly": [18, 30], "follow": [1, 13, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 30], "foral": [19, 20, 27], "form": [3, 15, 21, 23, 26, 27, 28, 30], "formul": 26, "fourier": [15, 28], "frac": [6, 15, 17, 19, 20, 23, 25, 27, 28], "fraction": 1, "frederick": [13, 22], "frobeniu": [1, 2, 4, 11, 20], "frobenius_schur_ind": [0, 6], "from": [1, 2, 4, 7, 9, 11, 17, 18, 19, 25, 26, 27, 30], "fulli": 13, "function": [0, 6, 9, 11, 17, 24, 26, 27, 30], "g": [2, 3, 4, 5, 6, 7, 9, 12, 13, 15, 17, 18, 20, 26, 27, 28], "g_": [4, 5, 18, 21, 26, 27], "g_0": 21, "g_1": 21, "g_2": 21, "g_3": 21, "g_4": 21, "g_5": 21, "ga44d231": 16, "gamma": [1, 13, 17, 19, 20, 21, 23, 26, 27, 28], "gamma_": [15, 17], "gaug": 27, "gd763494": [15, 17], "gener": [1, 2, 4, 5, 6, 7, 11, 18, 22, 30], "georg": 13, "germani": [22, 25], "get_cayley_t": [0, 3, 17], "get_charact": [0, 6, 16, 30], "get_corep_spinor_factor_system": [0, 2], "get_crystallographic_pointgroup_irreps_from_symmetri": [0, 1, 11, 17], "get_crystallographic_pointgroup_spinor_irreps_from_symmetri": [0, 1, 11, 16], "get_direct_product": [0, 6], "get_displacements_represent": 15, "get_factor_system_from_little_group": [0, 3], "get_identity_index": [0, 3], "get_intertwin": [0, 6], "get_inverse_index": [0, 3], "get_little_group": [0, 3], "get_ord": [0, 3], "get_physically_irrep": [0, 4], "get_pointgroup_chain_gener": [0, 5, 11], "get_primitive_transformation_matrix": [0, 9], "get_projective_regular_represent": [0, 6], "get_regular_represent": [0, 6], "get_representation_on_symmetric_matrix": 17, "get_spacegroup_irrep": [0, 1, 11, 15, 30], "get_spacegroup_irreps_from_primitive_symmetri": [0, 1, 11, 28], "get_spacegroup_spinor_irrep": [0, 1, 11], "get_spacegroup_spinor_irreps_from_primitive_symmetri": [0, 1, 11], "get_spinor_factor_system": [0, 7], "get_spinor_unitary_rot": [0, 7], "get_standard_basi": 17, "get_symmetry_adapted_tensor": [0, 8, 11, 17], "get_symmetry_from_databas": 17, "git": [12, 30], "github": [9, 12, 30], "give": [5, 16, 22, 23, 24, 27], "given": [1, 3, 4, 5, 6, 7, 9, 16, 21, 30], "gordan": 28, "grassmann": [10, 11], "grassmann_dist": [0, 10, 11], "greedi": 15, "grid": [15, 17], "group": [0, 2, 4, 5, 6, 7, 8, 11, 13, 14, 18, 22, 24, 27, 28, 30], "h": [9, 15, 19, 20], "h_": 21, "hafner": 13, "hall_numb": [9, 17], "hamm": 10, "harmon": 15, "harold": 25, "haruki": [21, 23], "hat": 27, "hatch": 25, "have": 3, "heng": 10, "here": [12, 23, 25, 26, 27, 28], "hermit": 21, "hexagon": 16, "higher": 8, "hkh00": 13, "hobb": 13, "hoi": [21, 23], "hold": [21, 26], "how": [15, 17], "howev": 27, "html": 9, "http": [9, 10, 12, 13, 15, 20, 21, 23, 25, 28, 30], "i": [1, 2, 3, 4, 5, 6, 7, 9, 10, 13, 15, 16, 17, 18, 19, 20, 21, 23, 26, 27, 28, 30], "iab": 15, "icml": 10, "id": 12, "ident": [3, 16, 17, 27], "idx": [1, 3, 15, 17], "iff": [3, 21], "ii": [1, 4, 28], "iii": [1, 4], "ij": [13, 17, 20, 21, 23, 26, 28], "il": 21, "im": [13, 25], "imaginari": 25, "implement": 8, "import": [16, 30], "impos": 25, "improv": [11, 30], "imshow": [15, 17], "inara": 12, "index": 3, "indic": [1, 2, 3, 4, 6, 11, 21], "induc": [11, 18], "infinit": 21, "initi": 11, "inner": 26, "input": [1, 12], "inspect": 6, "instead": 25, "int": [1, 2, 3, 4, 5, 6, 7, 8, 15, 28], "integ": [1, 3], "interchang": 26, "interest": 28, "intern": [1, 10, 20], "interpret": 27, "intertwin": [6, 18, 20, 23, 25], "inui": [22, 25], "inv": [1, 15], "invari": [20, 26], "invers": [3, 27], "invert": 23, "io": [9, 30], "ipaqb": 15, "ipq": 15, "ir": 27, "irreduc": [1, 4, 11, 20, 22, 26, 30], "irrep": [0, 1, 2, 6, 7, 11, 13, 14, 16, 17, 19, 22, 23, 24, 25, 27, 28, 30], "irrep_dim": 6, "is_equivalent_irrep": [0, 4], "is_matrix_group": [0, 3], "is_represent": [0, 6, 17], "is_unitari": [0, 6], "isomorph": 30, "issu": 30, "ito96": [22, 25], "its": [1, 3, 4, 13, 21, 22, 23, 25, 26], "j": [1, 2, 3, 6, 7, 9, 12, 13, 16, 17, 20, 21, 23, 25, 26, 27, 28, 30], "jame": 25, "ji": [23, 28], "jihun": 10, "jj": 28, "jk": 23, "jl": 21, "jmp": 21, "john": 21, "joss": 11, "journal": [10, 12], "jp": 15, "jul": [20, 25], "jun": [13, 21], "k": [1, 2, 3, 4, 6, 7, 9, 10, 13, 18, 19, 21, 23, 26, 27, 28], "kappa": 15, "kappa2": 15, "kazuo": 21, "ke": 10, "ket": [13, 27], "khmelevskyi": 13, "ki": 23, "kind": [10, 26], "kj": 23, "knocker": 6, "known": 27, "kpoint": [1, 2, 3, 4, 6, 7, 9, 30], "kress": 13, "kvec": 9, "kyoto": 15, "l": [10, 13, 15, 21, 27, 28], "l_": [26, 27], "la": 9, "label": 21, "lambda": 21, "lambda_": 21, "langl": [4, 5], "lattic": [1, 2, 7, 14, 16, 19, 27, 30], "learn": 10, "lee": 10, "left": [3, 13, 15, 19, 20, 21, 23, 25, 26, 27], "lek": 10, "lemma": 19, "len": [15, 17, 30], "let": [1, 3, 4, 5, 9, 15, 19, 20, 23, 25, 26, 27, 28], "li": 28, "lim": 10, "linalg": [1, 15], "linear": [0, 2, 3, 6, 10, 11, 30], "linewidth": [15, 17], "link": [13, 25], "list": [1, 2, 3, 4, 5, 6, 7, 8, 17], "list_basi": [15, 17], "littl": [1, 2, 3, 4, 7, 15, 18, 19, 21, 25, 27, 28, 30], "little_group_ord": [1, 3], "little_ord": 15, "little_rot": [1, 2, 3, 4, 6, 7, 15], "little_spinor_factor_system": 1, "little_time_revers": 2, "little_transl": [1, 2, 3, 4, 6, 7, 15], "little_unitary_rot": 1, "live": 16, "lj": 28, "local": 30, "localhost": 12, "london": [21, 22], "longleftrightarrow": 26, "m": [3, 9, 12, 13, 15, 17, 18, 20, 21, 23, 25], "m_": [13, 15], "machin": 10, "machineri": 10, "maehara": 21, "magmom": 1, "magnet": [0, 2, 3, 13, 24], "mai": [8, 25], "make": 11, "manual": 12, "map": [2, 7, 13, 27], "mapping_little_group": [1, 3, 15, 30], "mapsto": [23, 27], "maradudin": 15, "march": [22, 25], "marsmann": 13, "martijn": 13, "mass": 15, "mat": 13, "materi": [21, 30], "materialsproject": 30, "math": 15, "mathbb": [10, 13, 17, 20, 21, 23, 25, 26], "mathbf": [1, 2, 3, 4, 7, 9, 13, 15, 16, 17, 18, 19, 20, 21, 23, 26, 27, 28], "mathcal": [15, 17, 18, 26, 27, 28], "mathemat": [21, 22], "mathrm": [6, 13, 16, 23, 25, 26, 27], "mathsf": 13, "matic": 27, "mato": 9, "matplotlib": [15, 17], "matric": [3, 8, 17, 21, 23, 25, 27], "matrix": [1, 2, 4, 6, 7, 9, 10, 17, 18, 19, 21, 23, 25, 26, 27], "matter": [13, 22], "max_num_random_gener": [1, 2, 4, 6, 7], "max_num_tri": 6, "maxim": [3, 23], "maximum": [1, 2, 4, 6, 7], "mbox": [21, 25, 26], "md": 12, "measur": 11, "mech": 21, "mechan": 23, "memo": 12, "method": [1, 2, 4, 7, 11, 13, 18, 25], "methodologi": 13, "metric": 10, "michael": [13, 22], "mid": [19, 25, 26, 27], "min": 10, "minim": 30, "minor": [15, 17], "mm": 23, "mm11": 21, "mmd": 12, "mmdc": 12, "mmm": [21, 30], "mnm": 30, "mod": 15, "mode": 25, "moment": 1, "momentum": 27, "more": 30, "move": 15, "mp": 30, "mtl": 15, "mu": [6, 15, 20, 21, 26, 27, 28], "mu_": [26, 27], "multipl": [3, 19], "multipli": 16, "murota": 21, "mutual": 28, "n": [10, 12, 15, 19, 20, 21, 25, 27, 28, 30], "n_": 27, "nat": 21, "ncol": [15, 17], "ndarrai": 17, "need": [16, 17, 25], "neq": 28, "net73": 20, "neto": [1, 2, 4, 7, 20], "new": [10, 11, 23, 25], "new_po": 15, "newer": 11, "newli": 11, "next": [12, 15, 25], "ni": [23, 27], "node_modul": 12, "non": 26, "noncollinear": 13, "none": [1, 3, 4, 6, 7, 15], "nonlinear": 21, "nonumb": 26, "normal": [4, 5], "note": [1, 21], "notebook": 11, "nov": 13, "now": 26, "np": [1, 6, 15, 16, 17], "npm": 12, "npmj": 12, "nrow": [15, 17], "nu": 27, "num_atom": [1, 15], "num_sym": [1, 9], "number": [1, 2, 4, 6, 7, 8, 11, 12, 15, 17, 19, 30], "numer": [1, 2, 4, 7, 20, 25], "numpi": [11, 15, 16, 17, 30], "ny": 10, "o": [6, 7, 15, 23, 26, 30], "object": 28, "obtain": [4, 15, 16, 17, 18, 20, 25, 26], "omega": [2, 23, 25], "omega_": 20, "onc": 20, "one": [3, 17, 20, 21, 23, 25, 26], "ones": 17, "onli": [6, 15, 20], "onlinelibrari": 28, "onodera": [22, 25], "open": [12, 30], "openjourn": 12, "oper": [0, 2, 4, 9, 11, 26, 30], "opposit": 27, "optim": 15, "option": [1, 3], "orbit": 13, "ord": 10, "order": [1, 2, 3, 4, 5, 6, 7, 8, 15, 17, 30], "ordinari": [2, 4, 28], "org": [10, 13, 20, 21, 23, 25, 28, 30], "origin": [12, 26], "orobengoa": 9, "orthogon": [7, 21, 25, 28], "orthonorm": [6, 10], "other": 23, "otherwis": [6, 25], "otim": 13, "our": [16, 26, 27], "over": [1, 4, 11, 13, 17, 19, 20, 21, 23, 25, 30], "overlin": [2, 15, 17, 18, 19, 23, 25, 26, 27], "oxford": [21, 22], "p": [3, 9, 13, 17, 20, 21, 22, 26, 27, 28], "p4_2": 30, "packag": [12, 30], "page": [20, 21, 26, 30], "pair": 25, "paper": 12, "paramet": [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], "parameter": 21, "parent": 15, "part": [1, 2, 3, 15, 25], "particular": [19, 25, 27], "path": 15, "pathlib": 15, "pauli": [23, 27], "pdf": 13, "perez": 9, "period": [26, 27], "perm_i": 15, "perm_rep": 15, "permut": 15, "perovskit": 15, "pg_dataset": 16, "ph": 15, "phase": [25, 27], "phi": [23, 28], "phi_": 23, "phonon": 15, "phonopi": 15, "phonopy_mp": 15, "phy": [13, 15, 21, 25], "physic": [1, 4, 11, 13, 21, 22, 24, 30], "physrevb": [13, 25], "pi": [1, 15, 20, 26, 27], "pii": 21, "pip": [12, 30], "pir": 1, "pleas": 30, "plt": [15, 17], "pm": [15, 17], "pmatrix": [1, 4, 13, 17, 20, 21, 23, 25, 27], "po": [17, 21, 23], "point": [0, 2, 5, 6, 11, 13, 15, 18, 19, 26, 30], "point_group_chain": 12, "pointgroup": [11, 16], "posit": [1, 15, 30], "position2": 15, "poster": [15, 17], "power": 16, "pre": 12, "prepar": 30, "press": [13, 21, 22], "prim_rot": 5, "prime": 20, "primit": [1, 5, 6, 9, 15, 26, 28], "print": [15, 16, 17, 30], "procedur": [21, 28], "proceed": 10, "prod_": 20, "produc": 21, "product": [6, 26], "project": [1, 3, 4, 6, 10, 11, 13, 17, 18, 20, 25, 27, 30], "project_to_irrep": [0, 6, 11, 15, 17, 28], "projector": 13, "properti": 17, "provid": 1, "psedu": 6, "pseudo": 6, "psi": [23, 27], "psi_": [13, 20, 23, 26], "pull": 30, "pure": 1, "push": 12, "pvw17": 21, "pwd": 12, "pypi": [11, 30], "pyplot": [15, 17], "python": [11, 12, 30], "python3": 30, "q": [15, 20, 26], "qpoint": 15, "qua": 28, "quad": [13, 15, 17, 19, 20, 21, 23, 25, 26, 27, 28], "quantum": [23, 28], "quaternion": [13, 27], "r": [9, 13, 15, 16, 17, 20, 21, 25, 26, 27, 28], "r_": [21, 27], "random": [1, 2, 4, 6, 7, 18, 21], "rang": [15, 17], "rangl": [4, 5], "rank": [8, 13, 17], "re": [13, 25], "real": [1, 4, 6, 8, 11, 17, 30], "real_irrep": 4, "recent": 30, "reciproc": [1, 20], "reciprocal_lattic": 1, "recommend": 22, "reduc": 20, "ref": [1, 13, 21, 22, 23, 25], "refer": 10, "reflect": 16, "reg": [4, 6, 21], "regular": [1, 2, 4, 6, 7, 18], "rel": [1, 2, 4, 7], "relat": 27, "releas": [11, 30], "remaind": 15, "rep": [1, 6, 8, 15, 17], "rep1": 6, "rep2": 6, "rep_transform": 17, "replac": 21, "repres": [15, 19, 25, 27], "represent": [0, 3, 4, 8, 11, 14, 18, 22, 28, 30], "request": 30, "requir": 11, "reshap": 15, "resolv": 15, "respect": 1, "restrict": 25, "retri": 6, "return": [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 17], "rev": [13, 15, 25], "revers": 2, "ri": 15, "right": [3, 13, 15, 19, 20, 21, 23, 25, 26, 27], "rightarrow": [26, 27], "rk": [26, 27], "rm": 12, "root": [12, 25], "rotat": [1, 2, 3, 4, 6, 7, 8, 9, 13, 15, 16, 17, 30], "rotation_rep": 15, "row": [1, 2, 7, 15, 17], "rp": 26, "rr": 28, "rtol": [1, 2, 4, 6, 7], "run": [12, 15], "rutil": 30, "ryan": 25, "s0022509616309309": 21, "s0108767313007538": 25, "s0567739473001129": 20, "s41467": 21, "s_": [3, 7, 20, 26, 27], "same": 28, "saniti": [15, 17], "satisfi": [1, 3, 17, 19, 20, 21, 23, 26], "scalar": [19, 26], "scale": [6, 20], "scc13": 25, "schubert": 10, "schur": [1, 2, 4, 11, 19], "sci": 23, "sciadv": 23, "scienc": [21, 22, 23, 25], "sciencedirect": 21, "scm": 12, "seaborn": [15, 17], "search": 1, "see": [1, 2, 7, 20, 30], "select": [6, 28], "sergii": 13, "seri": [5, 18, 22, 25], "set": 1, "set_aspect": [15, 17], "set_context": [15, 17], "set_xtick": [15, 17], "set_ytick": [15, 17], "setuptool": 12, "setuptools_scm": 12, "shape": 15, "shift": 15, "shortlei": 27, "should": [1, 19, 23], "show": [15, 17], "shown": [1, 25], "shw91": 25, "siam": [10, 21], "sigma": [13, 27], "sigma_": 23, "sign": 27, "similar": 19, "simon": [13, 27], "simplifi": [26, 27], "simultan": 21, "sin": [1, 4, 25, 27], "sinc": 25, "singl": 4, "singular": 26, "site": 1, "skip": 10, "skip_orthonorm": 10, "skmk16": 13, "sl": [26, 27], "small": [1, 2, 3, 4, 7, 25, 28], "small_corep": 2, "sn": [15, 17], "so": [1, 4, 13, 27], "so3su2": 13, "solid": [21, 22, 25], "solvabl": [4, 18], "solvable_chain_gener": [4, 5], "solvable_group_chain": 4, "some": 19, "sometim": 25, "soner": 13, "sourc": [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], "sp": 21, "space": [0, 3, 4, 6, 11, 13, 14, 18, 20, 22, 24, 27, 28, 30], "span": [10, 23, 25], "speci": 1, "specifi": [1, 4, 9, 25], "spectra": 23, "spectral": 21, "spglib": [1, 9, 11, 12, 17, 30], "spgrep": [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 17, 18, 20, 22, 27, 28], "sphinx": 12, "spin": [0, 2, 7, 13, 14, 24], "spinor": [0, 1, 11, 13, 24, 30], "spinor_factor_system": [1, 6, 7], "spnior": 30, "springer": [22, 25], "sqcup": [3, 23], "sqrt": [15, 16, 17, 23, 25], "squar": 25, "stabil": 3, "stand": [1, 2, 7], "standard": [1, 9], "star": 26, "state": [22, 25], "steiner": 13, "step": 18, "stoke": 25, "str": [1, 2, 4, 7, 10], "strain": 17, "structur": [0, 15, 23, 30], "studi": 13, "su": [1, 2, 7, 13, 16, 23, 27], "subgroup": [1, 2, 3, 4, 5, 7, 19, 20, 23, 25, 27], "subplot": [15, 17], "subspac": [10, 11], "suffici": 26, "sum": [17, 25], "sum_": [6, 13, 15, 17, 19, 20, 21, 23, 25, 27, 28], "summar": 1, "summari": [0, 30], "summat": [19, 21], "supercel": 15, "superspac": 25, "support": 11, "surfac": 26, "surject": 27, "sym_tensor": 17, "symmetr": [4, 8, 11, 17, 25], "symmetri": [0, 2, 3, 8, 9, 14, 15, 21, 22, 26, 30], "symprec": 1, "system": [1, 2, 3, 6, 7, 20, 21, 23, 26, 28], "t": [1, 4, 6, 9, 13, 15, 17, 19, 23, 25, 26, 27, 28], "tabl": [1, 3, 4, 6, 17, 20], "tabul": 25, "tag": 12, "takanori": 21, "take": [1, 6, 17, 19, 21, 23, 25], "taken": [21, 25, 26], "tanab": [22, 25], "tasci": 9, "task": [1, 26], "tensor": [0, 11, 14], "teturo": [22, 25], "text": [21, 22], "th": [1, 2, 4, 7, 10, 15], "than": 23, "thei": [6, 20, 23, 27], "theorem": [20, 21], "theoret": 25, "theori": [21, 22, 23, 25], "therefor": [13, 20], "theta": 27, "theta_": 2, "thi": [6, 9, 15, 17, 20, 21, 23, 25, 26, 27], "third": 16, "thoma": 21, "three": [17, 25], "thu": [15, 20, 21, 25, 26], "ti": [15, 30], "tight_layout": 17, "tild": [21, 23, 25], "time": [2, 21], "time_revers": [1, 2, 3], "time_reversal_indic": 3, "toler": [1, 2, 4, 6, 7], "top": [17, 25, 26], "topologi": [21, 23], "tr": [23, 27], "transform": [0, 1, 15, 21, 23, 25, 27, 28], "transform_symmetry_and_kpoint": [0, 9], "transformation_matrix": 9, "transformed_kpoint": 9, "transformed_rot": 9, "transformed_transl": 9, "transit": 25, "translat": [1, 3, 4, 9, 15, 19, 25, 27, 30], "transpos": 15, "treat": 4, "trial": [1, 2, 4, 6, 7], "triangleleft": 18, "true": [1, 2, 3, 4, 6, 10, 15, 17, 25], "tvandven17": 21, "two": [4, 6, 10, 17, 20, 21, 26, 30], "type": [1, 3, 4, 5, 6, 8, 10, 23], "typic": 28, "u": [2, 7, 12, 15, 16, 19, 20, 21, 23, 25, 27], "u_": [15, 23, 26], "ua": 23, "um": 23, "unconstrain": 13, "under": [3, 25, 30], "unifi": 10, "union": 20, "uniqu": [9, 11, 19, 25], "unit": [9, 15], "unitari": [1, 2, 4, 6, 7, 17, 19, 21, 23, 25, 27, 28], "unitarili": 19, "unitary_rot": [1, 2, 7, 16], "uniti": 6, "univers": [13, 21, 22], "univi": 13, "up": [1, 19, 21, 26], "uparrow": [13, 18, 20, 27], "updat": 12, "url": [13, 20, 21, 23, 25, 28], "us": [11, 15, 18, 25, 26, 28, 30], "usa": 10, "user": 12, "util": [0, 11], "uu": 23, "v": [9, 12, 13, 21, 23, 25, 26, 27], "valu": 1, "van": 21, "varieti": 10, "vasp": 13, "vdot": 20, "vector": [1, 2, 4, 6, 7, 9, 10, 13, 15, 19, 23, 25, 26, 28], "ven": 21, "version": 12, "vi": 15, "via": [12, 30], "vibrat": [14, 25], "view": 10, "vim": 12, "vishwanath": [21, 23], "vmax": [15, 17], "vmin": [15, 17], "voigt": 17, "vol": 1, "volum": [12, 20], "vosko": 15, "w": [1, 2, 3, 7, 13, 19, 25, 26, 27], "wai": 20, "watanab": [21, 23], "wave": [13, 24, 27], "we": [13, 15, 16, 17, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30], "welcom": 30, "well": [25, 30], "westra": 13, "when": [1, 4, 6, 19, 21, 26], "where": [1, 3, 4, 7, 13, 15, 17, 19, 21, 23, 25, 26, 27], "which": [3, 15, 17, 25, 26, 27], "while": [16, 23], "whose": 5, "wig59": 23, "wigner": 23, "wilei": 28, "wise": [1, 2, 7, 15], "within": [13, 26], "without": 1, "wondratschek": 9, "wooten": [13, 22], "work": [6, 30], "wpv18": 23, "write": [16, 26], "written": [19, 26, 27], "wrong": 8, "www": [12, 13, 21, 23], "x": [1, 13, 15, 26, 27, 30], "x_": 21, "x_4f": 30, "xsg": 3, "xsg_indic": 3, "xx": 17, "xy": 17, "xz": 15, "y": [13, 15, 23, 27], "yaml": 15, "ye": 10, "york": 10, "yositaka": [22, 25], "you": 26, "your": [12, 28], "yukito": [22, 25], "yy": 17, "yz": 17, "z": [1, 7, 13, 15, 16, 20, 25, 26, 27], "zero": [15, 17, 25], "zip": [15, 17], "zx": 17, "zz": 17}, "titles": ["API Reference", "Core functions", "Co-representation for spinor", "Group", "Irreps", "Pointgroup", "Representation", "Representation for spinor", "Tensor", "Transformation", "Utility functions", "Change Log", "Development", "Memo", "Examples", "Application of space-group irreps to lattice vibration", "Spin representation for <span class=\"math notranslate nohighlight\">\\(C_{3v}\\)</span>", "Symmetry-adapted tensor", "Algorithm for enumerating irreps", "Numerically obtain intertwiner between equivalent representations", "On-the-fly irreps generation from solvable group chain", "On-the-fly irreps generation from regular representation", "Formulation", "Co-representation of magnetic point and space group", "Formulation of irreducible representations", "Physically irreducible representation (PIR)", "Irreps of space group", "Spin representation", "Constructing symmetry-adapted basis", "Index", "Spgrep"], "titleterms": {"0": [11, 21, 23], "1": [11, 20, 21, 23, 25], "11": 11, "12": 11, "136": 21, "15": 11, "156": 21, "17": 11, "18": 11, "2": [11, 20, 21, 25], "2022": 11, "2023": 11, "2024": 11, "2025": 11, "230": 21, "28": 11, "3": [11, 21, 25], "3v": [16, 21], "5": 11, "6": 11, "8": 11, "9": 11, "No": 21, "On": [20, 21], "_": 21, "adapt": [13, 17, 28], "algorithm": 18, "all": 21, "alpha": [23, 25], "anti": 23, "api": 0, "appli": 15, "applic": 15, "ar": 20, "associ": 21, "ast": 25, "basi": 28, "between": 19, "bloch": 13, "block": 15, "c_": [16, 21], "calcul": 17, "case": [20, 23], "chain": 20, "chang": [11, 30], "co": [2, 23], "compil": 12, "conjug": 20, "construct": 28, "contribut": 30, "convent": [23, 27], "core": 1, "crystal": 1, "crystallograph": [1, 20, 21], "d": 21, "dec": 11, "decomposit": 20, "definit": 23, "develop": 12, "diagon": 15, "diagram": 12, "document": 12, "draft": 12, "dynam": 15, "enumer": [16, 18], "equival": [19, 20, 25], "exampl": [14, 21], "factor": [16, 27], "featur": 30, "feb": 11, "file": 12, "finit": [19, 25], "first": 27, "fly": [20, 21], "formul": [22, 24], "frac": 21, "frobeniu": [23, 25], "from": [12, 15, 16, 20, 21], "function": [1, 10], "g": [19, 21, 25], "gamma": 25, "gener": [12, 20, 21], "group": [1, 3, 15, 16, 17, 19, 20, 21, 23, 25, 26], "h": 21, "how": [12, 30], "i": 25, "ia": 21, "import": [15, 17], "index": 29, "indic": [23, 25], "induc": 20, "inequival": 20, "instal": [12, 30], "intertwin": 19, "intrins": 13, "irreduc": [17, 24, 25], "irrep": [4, 15, 18, 20, 21, 26], "jan": 11, "joss": 12, "jun": 11, "k": 25, "kind": 27, "lattic": [15, 26], "licens": 30, "linear": [1, 23], "littl": 26, "load": 15, "log": [11, 30], "magnet": [1, 23], "mathbf": 25, "mathcal": [19, 21, 25], "mathrm": 21, "matric": 16, "matrix": 15, "memo": 13, "mermaid": 12, "mnm": 21, "modul": [15, 17], "mutual": 20, "nov": 11, "numer": 19, "obtain": [19, 21], "oper": [1, 15, 16, 17, 23, 27, 28], "overlin": 21, "p3m1": 21, "p4_": 21, "phonondb": 15, "physic": [17, 25], "pir": 25, "point": [1, 16, 17, 20, 21, 23], "pointgroup": 5, "prepar": [15, 16, 17], "primit": 21, "project": [15, 19, 21, 26, 28], "pseudo": 25, "real": 25, "reciproc": 26, "refer": [0, 13, 20, 21, 22, 23, 25, 27, 28], "regular": 21, "releas": 12, "represent": [1, 2, 6, 7, 15, 16, 17, 19, 20, 21, 23, 24, 25, 26, 27], "rotat": 27, "schur": [23, 25], "second": 27, "small": 26, "solvabl": 20, "space": [1, 15, 19, 21, 23, 25, 26], "spgrep": [23, 30], "sphere": 13, "spin": [1, 16, 27], "spinor": [2, 7, 16, 27], "structur": 1, "subduc": 20, "subgroup": 26, "subpag": [12, 18, 22, 24], "summari": 1, "symmetri": [1, 13, 17, 27, 28], "system": [16, 27], "tensor": [8, 13, 17], "transform": [9, 26], "translat": 26, "two": 19, "unitari": 16, "usag": 30, "util": 10, "v0": 11, "vibrat": 15, "work": 21, "x": 21, "xi": 23}})