The Exterior Calculus

Documentation for package ‘stokes’ version 1.2-0

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The Exterior Calculus

-- A --

Alt	Alternating multilinear forms
as.1form	Coerce vectors to 1-forms
as.function.kform	k-forms
as.function.ktensor	k-tensors
as.kform	k-forms
as.ktensor	k-tensors
as.spray	Extract and manipulate coefficients
as.symbolic	Symbolic form

-- C --

coeff	Extract and manipulate coefficients
coeffs	Extract and manipulate coefficients
coeffs-method	Extract and manipulate coefficients
coeffs.kform	Extract and manipulate coefficients
coeffs.ktensor	Extract and manipulate coefficients
coeffs<-	Extract and manipulate coefficients
coeffs<--method	Extract and manipulate coefficients
coeffs<-.kform	Extract and manipulate coefficients
coeffs<-.ktensor	Extract and manipulate coefficients
coeffs<-.spray	Extract and manipulate coefficients
consolidate	Various low-level helper functions
contract	Contractions of k-forms
contract_elementary	Contractions of k-forms

-- D --

d	k-forms
discard	Keep or drop variables
dovs	Dimension of the underlying vector space
drop	Scalars and losing attributes
drop.free	Keep or drop variables
dx	Elementary forms in three-dimensional space
dy	Elementary forms in three-dimensional space
dz	Elementary forms in three-dimensional space

-- E --

e	k-forms
ex	Basis vectors in three-dimensional space
ey	Basis vectors in three-dimensional space
ez	Basis vectors in three-dimensional space

-- G --

general_kform	k-forms
grad	Coerce vectors to 1-forms

-- H --

Hodge	Hodge star operator
hodge	Hodge star operator

-- I --

include_perms	Various low-level helper functions
inner	Inner product operator
inner.product	Inner product operator
inner_product	Inner product operator
is.empty	Zero tensors and zero forms
is.form	k-forms
is.kform	k-forms
is.ktensor	k-tensors
is.scalar	Scalars and losing attributes
is.tensor	k-tensors
is.volume	The volume element
is.zero	Zero tensors and zero forms
issmall	Is a form zero to within numerical precision?

-- K --

keep	Keep or drop variables
kform	k-forms
kform_basis	k-forms
kform_general	k-forms
kform_symbolic_print	Print methods for k-tensors and k-forms
kform_to_ktensor	Various low-level helper functions
kill_trivial_rows	Various low-level helper functions
kinner	Inner product of two kforms
ktensor	k-tensors
ktensor_symbolic_print	Print methods for k-tensors and k-forms

-- L --

lose	Scalars and losing attributes
lose.kform	Scalars and losing attributes
lose.ktensor	Scalars and losing attributes
lose_repeats	Various low-level helper functions

-- N --

Extract and manipulate coefficients

-- O --

Ops	Arithmetic Ops Group Methods for 'kform' and 'ktensor' objects
Ops.kform	Arithmetic Ops Group Methods for 'kform' and 'ktensor' objects
Ops.ktensor	Arithmetic Ops Group Methods for 'kform' and 'ktensor' objects
Ops.stokes	Arithmetic Ops Group Methods for 'kform' and 'ktensor' objects

-- P --

polyform	Print methods for k-tensors and k-forms
print.kform	Print methods for k-tensors and k-forms
print.ktensor	Print methods for k-tensors and k-forms
print.stokes	Print methods for k-tensors and k-forms
print.summary.kform	Summaries of tensors and alternating forms
print.summary.ktensor	Summaries of tensors and alternating forms
print.summary.spray	Summaries of tensors and alternating forms
pull-back	Linear transforms of k-forms
pullback	Linear transforms of k-forms
push-forward	Linear transforms of k-forms
pushforward	Linear transforms of k-forms

-- R --

-- S --

scalar	Scalars and losing attributes
spray	Extract and manipulate coefficients
star	Hodge star operator
stokes	The Exterior Calculus
stokes_symbolic_print	Print methods for k-tensors and k-forms
stretch	Linear transforms of k-forms
summary	Summaries of tensors and alternating forms
summary.kform	Summaries of tensors and alternating forms
summary.ktensor	Summaries of tensors and alternating forms
summary.stokes	Summaries of tensors and alternating forms
symbolic	Symbolic form

-- T --

-- V --

value<-	Extract and manipulate coefficients
vcp3	The Vector cross product
vector_cross_product	The Vector cross product
volume	The volume element

-- W --

wedge	Wedge products
wedge2	Wedge products

-- Z --

zap	Zap small values in k-forms and k-tensors
zap.kform	Zap small values in k-forms and k-tensors
zap.ktensor	Zap small values in k-forms and k-tensors
zap.spray	Zap small values in k-forms and k-tensors
zapsmall	Zap small values in k-forms and k-tensors
zaptiny	Zap small values in k-forms and k-tensors
zero	Zero tensors and zero forms
zeroform	Zero tensors and zero forms
zerotensor	Zero tensors and zero forms

-- misc --

%X%	Tensor products of k-tensors
%^%	Wedge products
0form	Scalars and losing attributes
0tensor	Scalars and losing attributes