Clifford
v1.4.0
Installation
API
Predefined Algebras
Changelog
Issues
Tutorials
Quick Start (G2)
The Algebra Of Space (G3)
Rotations in Space: Euler Angles, Matrices, and Quaternions
Space Time Algebra
Interfacing Other Mathematical Systems
Writing high(ish) performance code with Clifford and Numba via Numpy
Conformal Geometric Algebra
Linear transformations
Working with custom algebras
Other resources
Other resources for
clifford
Other resources for Geometric Algebra
Bibliography
Clifford
»
Index
Edit on GitHub
Index
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A
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B
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C
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D
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E
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F
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G
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H
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I
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J
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L
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M
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N
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O
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P
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Q
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R
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S
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T
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U
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V
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X
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__add__() (clifford.MultiVector method)
__and__() (clifford.MultiVector method)
__call__() (clifford.MultiVector method)
(clifford.MVArray method)
__getitem__() (clifford.MultiVector method)
__init__() (clifford.cga.CGA method)
(clifford.cga.CGAThing method)
(clifford.cga.Dilation method)
(clifford.cga.Flat method)
(clifford.cga.Rotation method)
(clifford.cga.Round method)
(clifford.cga.Translation method)
(clifford.cga.Transversion method)
__invert__() (clifford.MultiVector method)
__mul__() (clifford.MultiVector method)
__or__() (clifford.MultiVector method)
__sub__() (clifford.MultiVector method)
__xor__() (clifford.MultiVector method)
A
adjoint (clifford.transformations.LinearMatrix property)
adjoint() (clifford.MultiVector method)
adjoint_func (clifford.Layout attribute)
angle_between_vectors() (in module clifford.tools.g3)
annihilate_k() (in module clifford.tools.g3c)
anticommutator() (clifford.MultiVector method)
apply_rotor() (in module clifford.tools.g3c)
apply_rotor_inv() (in module clifford.tools.g3c)
as_array() (clifford.MultiVector method)
astype() (clifford.MultiVector method)
augmented_with() (clifford.BasisVectorIds method)
average_objects() (in module clifford.tools.g3c)
B
b1 (clifford.BladeMap property)
b2 (clifford.BladeMap property)
base_vector() (clifford.cga.CGA method)
bases() (clifford.Layout method)
basis() (clifford.MultiVector method)
basis_names (clifford.Layout property)
basis_vectors (clifford.Layout property)
basis_vectors_lst (clifford.Layout property)
BasisBladeOrder (class in clifford)
BasisVectorIds (class in clifford)
between_basis_vectors() (in module clifford.transformations)
bitmap_as_tuple() (clifford.BasisVectorIds method)
bitmap_to_indices (clifford.BasisBladeOrder attribute)
Blade (class in clifford.tools.classify)
BladeMap (class in clifford)
blades (clifford.Layout property)
(in module clifford.<predefined>)
blades_list (clifford.Layout property)
(clifford.MultiVector property)
blades_of_grade() (clifford.Layout method)
bladeTupList (clifford.Layout attribute)
C
calculate_S_over_mu() (in module clifford.tools.g3c)
center (clifford.cga.Round property)
center_down (clifford.cga.Round property)
CGA (class in clifford.cga)
CGAThing (class in clifford.cga)
check_infinite_roots() (in module clifford.tools.g3c)
check_infinite_roots_val() (in module clifford.tools.g3c)
check_sigma_for_negative_root() (in module clifford.tools.g3c)
check_sigma_for_negative_root_val() (in module clifford.tools.g3c)
check_sigma_for_positive_root() (in module clifford.tools.g3c)
check_sigma_for_positive_root_val() (in module clifford.tools.g3c)
Circle (class in clifford.tools.classify)
circle_to_sphere() (in module clifford.tools.g3c)
Cl() (in module clifford)
classify() (in module clifford.tools.classify)
clean() (clifford.MultiVector method)
clifford
module
clifford.cga
module
clifford.dg3c
module
clifford.dpga
module
clifford.g2
module
clifford.g2c
module
clifford.g3
module
clifford.g3c
module
clifford.g4
module
clifford.gac
module
clifford.numba
module
clifford.operator
module
clifford.pga
module
clifford.taylor_expansions
module
clifford.tools
module
clifford.tools.classify
module
clifford.tools.g3
module
clifford.tools.g3c
module
clifford.tools.g3c.object_fitting
module
clifford.transformations
module
closest_point_on_circle_from_line() (in module clifford.tools.g3c)
closest_point_on_line_from_circle() (in module clifford.tools.g3c)
commutator() (clifford.MultiVector method)
conformalize() (in module clifford)
ConformalLayout (class in clifford)
conjugate() (clifford.MultiVector method)
convert_2D_point_to_conformal() (in module clifford.tools.g3c)
convert_2D_polar_line_to_conformal_line() (in module clifford.tools.g3c)
correlation_matrix() (in module clifford.tools.g3)
cos() (clifford.MultiVector method)
(in module clifford.taylor_expansions)
cosh() (clifford.MultiVector method)
(in module clifford.taylor_expansions)
D
Dilation (class in clifford.cga)
dilation() (clifford.cga.CGA method)
dim (clifford.cga.Round property)
dims (clifford.Layout attribute)
Direction (class in clifford.tools.classify)
direction (clifford.tools.classify.Direction attribute)
(clifford.tools.classify.Flat attribute)
(clifford.tools.classify.Round attribute)
distance_polar_line_to_euc_point_2d() (in module clifford.tools.g3c)
disturb_object() (in module clifford.tools.g3c)
dorst_norm_val() (in module clifford.tools.g3c)
down() (clifford.ConformalLayout method)
dual (clifford.cga.Round property)
dual() (clifford.MultiVector method)
(clifford.MVArray method)
dual_func (clifford.Layout attribute)
dual_func() (in module clifford.tools.g3c)
DualFlat (class in clifford.tools.classify)
E
E0 (clifford.ConformalLayout attribute)
einf (clifford.ConformalLayout attribute)
en (clifford.ConformalLayout attribute)
En (clifford.Frame property)
eo (clifford.ConformalLayout attribute)
ep (clifford.ConformalLayout attribute)
eps() (in module clifford)
euc_cross_prod() (in module clifford.tools.g3)
euc_dist() (in module clifford.tools.g3c)
euc_mv_to_np() (in module clifford.tools.g3)
even (clifford.MultiVector property)
exp() (clifford.MultiVector method)
(in module clifford.taylor_expansions)
F
factorise() (clifford.MultiVector method)
fast_down() (in module clifford.tools.g3c)
fast_dual() (in module clifford.tools.g3c)
fast_up() (in module clifford.tools.g3c)
firstIdx (clifford.Layout property)
fit_circle() (in module clifford.tools.g3c.object_fitting)
fit_line() (in module clifford.tools.g3c.object_fitting)
fit_plane() (in module clifford.tools.g3c.object_fitting)
fit_sphere() (in module clifford.tools.g3c.object_fitting)
FixedLayout (class in clifford.transformations)
Flat (class in clifford.cga)
(class in clifford.tools.classify)
flat (clifford.tools.classify.DualFlat attribute)
flat() (clifford.cga.CGA method)
Frame (class in clifford)
from_center_radius() (clifford.cga.Round method)
from_function() (clifford.transformations.LinearMatrix class method)
from_rotor() (clifford.transformations.LinearMatrix class method)
from_value_array() (clifford.MVArray static method)
G
GA_SVD() (in module clifford.tools.g3)
gaDims (clifford.Layout attribute)
general_object_interpolation() (in module clifford.tools.g3c)
general_root() (in module clifford.tools.g3c)
general_root_val() (in module clifford.tools.g3c)
generate_dilation_rotor() (in module clifford.tools.g3c)
generate_n_clusters() (in module clifford.tools.g3c)
generate_random_object_cluster() (in module clifford.tools.g3c)
generate_rotation_rotor() (in module clifford.tools.g3)
generate_translation_rotor() (in module clifford.tools.g3c)
get_center_from_sphere() (in module clifford.tools.g3c)
get_circle_in_euc() (in module clifford.tools.g3c)
get_grade_projection_matrix() (clifford.Layout method)
get_left_gmt_matrix() (clifford.Layout method)
get_line_intersection() (in module clifford.tools.g3c)
get_line_reflection_matrix() (in module clifford.tools.g3c)
get_nearest_plane_point() (in module clifford.tools.g3c)
get_plane_normal() (in module clifford.tools.g3c)
get_plane_origin_distance() (in module clifford.tools.g3c)
get_radius_from_sphere() (in module clifford.tools.g3c)
get_right_gmt_matrix() (clifford.Layout method)
gmt (clifford.Layout attribute)
gmt_func (clifford.Layout attribute)
gmt_func_generator() (clifford.Layout method)
gp() (clifford.MVArray method)
(in module clifford.operator)
grade_mask() (clifford.Layout method)
grade_obj() (in module clifford)
gradeInvol() (clifford.MultiVector method)
gradeList (clifford.Layout property)
grades (clifford.BasisBladeOrder attribute)
grades() (clifford.MultiVector method)
H
hitzer_inverse() (clifford.MultiVector method)
homo() (clifford.ConformalLayout method)
I
I (clifford.Layout property)
(clifford.MultiVector property)
I_base (clifford.ConformalLayout attribute)
id_as_bitmap() (clifford.BasisVectorIds method)
imt (clifford.Layout attribute)
imt_func (clifford.Layout attribute)
imt_func_generator() (clifford.Layout method)
index_to_bitmap (clifford.BasisBladeOrder attribute)
InfinitePoint (class in clifford.tools.classify)
interp_objects_root() (in module clifford.tools.g3c)
interpret_multivector_as_object() (in module clifford.tools.g3c)
intersect_line_and_plane_to_point() (in module clifford.tools.g3c)
inv (clifford.Frame property)
inv() (clifford.MultiVector method)
inv_func (clifford.Layout attribute)
inverted() (clifford.cga.CGAThing method)
(clifford.cga.Dilation method)
(clifford.cga.Flat method)
(clifford.cga.Rotation method)
(clifford.cga.Round method)
(clifford.cga.Translation method)
(clifford.cga.Transversion method)
involuted() (clifford.cga.CGAThing method)
(clifford.cga.Dilation method)
(clifford.cga.Flat method)
(clifford.cga.Rotation method)
(clifford.cga.Round method)
(clifford.cga.Translation method)
(clifford.cga.Transversion method)
invPS() (clifford.MultiVector method)
ip() (in module clifford.operator)
is_innermorphic_to() (clifford.Frame method)
isBlade() (clifford.MultiVector method)
isScalar() (clifford.MultiVector method)
isVersor() (clifford.MultiVector method)
iterative_closest_points_circle_line() (in module clifford.tools.g3c)
iterative_closest_points_on_circles() (in module clifford.tools.g3c)
iterative_furthest_points_on_circles() (in module clifford.tools.g3c)
J
join() (clifford.MultiVector method)
L
Layout (class in clifford)
layout (clifford.tools.classify.Blade attribute)
(in module clifford.<predefined>)
layout1 (clifford.BladeMap property)
layout2 (clifford.BladeMap property)
lc() (clifford.MultiVector method)
lcmt (clifford.Layout attribute)
lcmt_func (clifford.Layout attribute)
lcmt_func_generator() (clifford.Layout method)
left_complement() (clifford.MultiVector method)
left_complement_func (clifford.Layout attribute)
leftInv() (clifford.MultiVector method)
leftLaInv() (clifford.MultiVector method)
Line (class in clifford.tools.classify)
line_to_point_and_direction() (in module clifford.tools.g3c)
Linear (class in clifford.transformations)
LinearMatrix (class in clifford.transformations)
load_ga_file() (clifford.Layout method)
location (clifford.tools.classify.Flat attribute)
(clifford.tools.classify.Round attribute)
M
mag2() (clifford.MultiVector method)
mat2Frame() (in module clifford.tools)
meet() (clifford.MultiVector method)
(in module clifford.tools.g3c)
meet_val() (in module clifford.tools.g3c)
metric (clifford.Layout property)
midpoint_between_lines() (in module clifford.tools.g3c)
midpoint_of_line_cluster() (in module clifford.tools.g3c)
module
clifford
clifford.cga
clifford.dg3c
clifford.dpga
clifford.g2
clifford.g2c
clifford.g3
clifford.g3c
clifford.g4
clifford.gac
clifford.numba
clifford.operator
clifford.pga
clifford.taylor_expansions
clifford.tools
clifford.tools.classify
clifford.tools.g3
clifford.tools.g3c
clifford.tools.g3c.object_fitting
clifford.transformations
mult_with_ninf() (in module clifford.tools.g3c)
MultiVector (class in clifford)
MultiVector() (clifford.Layout method)
mv (clifford.tools.classify.Blade property)
MVArray (class in clifford)
N
n_th_rotor_root() (in module clifford.tools.g3c)
names (clifford.Layout attribute)
neg_twiddle_root() (in module clifford.tools.g3c)
neg_twiddle_root_val() (in module clifford.tools.g3c)
negative_root() (in module clifford.tools.g3c)
negative_root_val() (in module clifford.tools.g3c)
norm() (in module clifford.tools.g3c)
normal() (clifford.MultiVector method)
(clifford.MVArray method)
normalInv() (clifford.MultiVector method)
normalise_n_minus_1() (in module clifford.tools.g3c)
normalise_TR_to_unit_T() (in module clifford.tools.g3c)
normalised() (in module clifford.tools.g3c)
np_to_euc_mv() (in module clifford.tools.g3)
null_vector() (clifford.cga.CGA method)
O
odd (clifford.MultiVector property)
omoh() (in module clifford.tools)
omt (clifford.Layout attribute)
omt_func (clifford.Layout attribute)
omt_func_generator() (clifford.Layout method)
op() (clifford.MVArray method)
(in module clifford.operator)
order_as_tuples() (clifford.BasisVectorIds method)
order_from_tuples() (clifford.BasisVectorIds method)
ordered_integers() (clifford.BasisVectorIds class method)
orthoFrames2Versor() (in module clifford.tools)
orthoMat2Versor() (in module clifford.tools)
OutermorphismMatrix (class in clifford.transformations)
P
parse_multivector() (clifford.Layout method)
Plane (class in clifford.tools.classify)
Point (class in clifford.tools.classify)
point_pair_to_end_points() (in module clifford.tools.g3c)
PointFlat (class in clifford.tools.classify)
PointPair (class in clifford.tools.classify)
pos_twiddle_root() (in module clifford.tools.g3c)
pos_twiddle_root_val() (in module clifford.tools.g3c)
positive_root() (in module clifford.tools.g3c)
positive_root_val() (in module clifford.tools.g3c)
pretty() (in module clifford)
print_precision() (in module clifford)
project() (clifford.MultiVector method)
project_points_to_circle() (in module clifford.tools.g3c)
project_points_to_line() (in module clifford.tools.g3c)
project_points_to_plane() (in module clifford.tools.g3c)
project_points_to_sphere() (in module clifford.tools.g3c)
project_val() (in module clifford.tools.g3c)
pseudoScalar (clifford.Layout property)
(clifford.MultiVector property)
Q
quaternion_and_vector_to_rotor() (in module clifford.tools.g3c)
quaternion_to_matrix() (in module clifford.tools.g3)
quaternion_to_rotor() (in module clifford.tools.g3)
R
radius (clifford.cga.Round property)
(clifford.tools.classify.Round attribute)
random_bivector() (in module clifford.tools.g3c)
random_circle() (in module clifford.tools.g3c)
random_circle_at_origin() (in module clifford.tools.g3c)
random_conformal_point() (in module clifford.tools.g3c)
random_euc_mv() (in module clifford.tools.g3)
random_line() (in module clifford.tools.g3c)
random_line_at_origin() (in module clifford.tools.g3c)
random_plane() (in module clifford.tools.g3c)
random_plane_at_origin() (in module clifford.tools.g3c)
random_point_pair() (in module clifford.tools.g3c)
random_point_pair_at_origin() (in module clifford.tools.g3c)
random_rotation_rotor() (in module clifford.tools.g3)
random_rotation_translation_rotor() (in module clifford.tools.g3c)
random_sphere() (in module clifford.tools.g3c)
random_sphere_at_origin() (in module clifford.tools.g3c)
random_translation_rotor() (in module clifford.tools.g3c)
random_unit_vector() (in module clifford.tools.g3)
randomMV() (clifford.Layout method)
(in module clifford)
randomRotor() (clifford.Layout method)
randomV() (clifford.Layout method)
right_complement() (clifford.MultiVector method)
right_complement_func (clifford.Layout attribute)
rightInv() (clifford.MultiVector method)
Rotation (class in clifford.cga)
rotation() (clifford.cga.CGA method)
rotation_matrix_align_vecs() (in module clifford.tools.g3)
rotation_matrix_to_quaternion() (in module clifford.tools.g3)
rotor_align_vecs() (in module clifford.tools.g3)
rotor_between_lines() (in module clifford.tools.g3c)
rotor_between_objects() (in module clifford.tools.g3c)
rotor_between_planes() (in module clifford.tools.g3c)
rotor_mask (clifford.Layout property)
rotor_to_quaternion() (in module clifford.tools.g3)
rotor_vector_to_vector() (in module clifford.tools.g3)
Round (class in clifford.cga)
(class in clifford.tools.classify)
round() (clifford.cga.CGA method)
(clifford.MultiVector method)
S
save() (clifford.MVArray method)
scalar (clifford.Layout property)
scale_TR_translation() (in module clifford.tools.g3c)
shirokov_inverse() (clifford.MultiVector method)
shortlex() (clifford.BasisBladeOrder class method)
sig (clifford.Layout attribute)
sin() (clifford.MultiVector method)
(in module clifford.taylor_expansions)
sinh() (clifford.MultiVector method)
(in module clifford.taylor_expansions)
Sphere (class in clifford.tools.classify)
sphere_behind_plane() (in module clifford.tools.g3c)
sphere_beyond_plane() (in module clifford.tools.g3c)
square_roots_of_rotor() (in module clifford.tools.g3c)
standard_line_at_origin() (in module clifford.tools.g3c)
standard_point_pair_at_origin() (in module clifford.tools.g3c)
straight_up() (clifford.cga.CGA method)
sum() (clifford.MVArray method)
T
tan() (clifford.MultiVector method)
(in module clifford.taylor_expansions)
Tangent (class in clifford.tools.classify)
tanh() (clifford.MultiVector method)
(in module clifford.taylor_expansions)
Transformation (in module clifford.transformations)
Translation (class in clifford.cga)
translation() (clifford.cga.CGA method)
Transversion (class in clifford.cga)
transversion() (clifford.cga.CGA method)
tuple_as_sign_and_bitmap() (clifford.BasisVectorIds method)
U
ugly() (in module clifford)
up() (clifford.ConformalLayout method)
V
val_annihilate_k() (in module clifford.tools.g3c)
val_apply_rotor() (in module clifford.tools.g3c)
val_apply_rotor_inv() (in module clifford.tools.g3c)
val_average_objects() (in module clifford.tools.g3c)
val_average_objects_with_weights() (in module clifford.tools.g3c)
val_convert_2D_point_to_conformal() (in module clifford.tools.g3c)
val_convert_2D_polar_line_to_conformal_line() (in module clifford.tools.g3c)
val_distance_point_to_line() (in module clifford.tools.g3c)
val_down() (in module clifford.tools.g3c)
val_fit_circle() (in module clifford.tools.g3c.object_fitting)
val_fit_line() (in module clifford.tools.g3c.object_fitting)
val_fit_plane() (in module clifford.tools.g3c.object_fitting)
val_fit_sphere() (in module clifford.tools.g3c.object_fitting)
val_get_line_intersection() (in module clifford.tools.g3c)
val_get_line_reflection_matrix() (in module clifford.tools.g3c)
val_homo() (in module clifford.tools.g3c)
val_intersect_line_and_plane_to_point() (in module clifford.tools.g3c)
val_midpoint_between_lines() (in module clifford.tools.g3c)
val_midpoint_of_line_cluster() (in module clifford.tools.g3c)
val_midpoint_of_line_cluster_grad() (in module clifford.tools.g3c)
val_norm() (in module clifford.tools.g3c)
val_normalInv() (in module clifford.tools.g3c)
val_normalise_n_minus_1() (in module clifford.tools.g3c)
val_normalised() (in module clifford.tools.g3c)
val_point_pair_to_end_points() (in module clifford.tools.g3c)
val_rotor_between_lines() (in module clifford.tools.g3c)
val_rotor_between_objects_explicit() (in module clifford.tools.g3c)
val_rotor_between_objects_root() (in module clifford.tools.g3c)
val_rotor_rotor_between_planes() (in module clifford.tools.g3c)
val_truncated_get_line_reflection_matrix() (in module clifford.tools.g3c)
val_unsign_sphere() (in module clifford.tools.g3c)
val_up() (in module clifford.tools.g3c)
value (clifford.MVArray property)
vee() (clifford.MultiVector method)
vee_func (clifford.Layout attribute)
X
x() (clifford.MultiVector method)
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