Tutorial:Command
reference
Command reference
This page provides an alphabetical list of the TTC commands.
Each item contains a brief description of the corresponding command
and, in most cases, a reference to the sections where more information
can be found. If the command refers to the symbolic/explicit tensors it
is labeled with an S
/ E
.
The essential information about a command can be obtained inside Mathematica
by typing
?command Inside TTC you can also use TTCFunctions[]
and TTCFunctions[char].
In the description of commands, typewrite style denotes fixed
text that you have to type as it is printed, while italic style
is used to denote commands arguments that you fill in.
The commands that perform in an intrinsic way an action which can also
be performed in index notation are indicated by it can be computed using
index notation
Several symbols frequently used in the description of the commands
have a precise meaning:
x ..................a coordinate system name
b...................a basis name (coordinate or not)
g...................a metric tensor name
v...................a vector
t....................a tensor
w................an exterior form
i, j, k..............
E positive integers used to denote index
Sindex
in indexed calculus
n, p, q.............positive integers
AbsoluteD[g][t] computes the covariant
derivative of the tensor t using the metric g. If t
is a (p, q) tensor, the covariant derivative of t is a (p,
q+1) tensor. It can be computed using index notation.
AllIndex
S
AllIndex[t] gives all index, not repeated, used
for all tensors in t.
Antisymmetric[t] gives the antisymmetric part
of the tensor t. If t is not antisymmetrizable then Antisymmetric[t]
returns
Fail.
It can be computed using index notation.
ApplyTensor[t][t1, t2, t3,...]
applies t to t1, t2, t3,... Empty slots are allowed as in ApplyTensor[t][t1,
, t2,..]
Arrange
S
See SimplifyAllIndexIndex
BasicRulesS
BasicRules[n] is the list of essential rules of indexed tensors
introduced by InputTensor and InputSymmetries. n can
be 0,1 or 2 . See examples in TTC tutorial
BasisE
S
Basis[t] gives the name of the basis of t.
E
If t is a scalar and ScalarBasisQ = True then Basis[t]
asks you for the name of the basis.
BasisChangeNamesE
BasisChangeNames prints a list with the names of the basis changes
defined in the present session.
BasisChangeQE
BasisChangeQ[b1, b2] gives True if
there exists BasisVectorChange[b1,b2] and
False otherwise.
BasisFormChange[b1, b2] gives the relation
between the forms of the basis b1 and b2 provided that an
input for the change b1
b2
has been made. Otherwise, TTC asks you for this input.
BasisNamesE
BasisNames gives a list of all the noncoordinate basis defined
in the present session
BasisQE
BasisQ [b] yields True if b is actually
the name of a basis of vectors or a coordinate system, and yields False
otherwise.
BasisSymbolE
BasisSymbol[b][i] gives the symbol used
for the i-th vector of the basis named b.
BasisSymbolsE
BasisSymbols[b]gives a list of the symbols of
the basis b.
BasisFormChange[b1,b2]gives the
relation between the vectors of the basis b1 and b2 provided
that an input for the change b1 
b2
has been made. Otherwise, TTC asks you for this input.
Change [b1, b2][t] changes t from basis b1
to basis b2. Change[b2][t] makes the same
using Basis[t] as b1.
Christoffel[g, b][i, -j, -k] gives the connection
coefficient (or Christoffel symbol of second kind) for the tensor metric
g
expanded in the basis b. The Christoffel symbol of first kind can
be computed by Christoffel[g, b][-i, -j, -k]. It
is computed only the first time it is called.
ChristoffelTensor[g, b] gives the pseudotensor build from
the connection coefficients of the metric g in the basis b.
See also SChristoffelTensorS
ClearBasis
E
ClearBasis[b] removes the basis b and all
objects related to it.
ClearCoordinatesE
ClearCoordinates[x] removes the coordinate system
named x and all objects related to it.
ClearChangeE
ClearChange[b1, b2] removes all things related
to the change b1
b2.
ClearMetricE
ClearMetric[g, b] removes the metric named g in
basis b and all objects related to it.
ClearTTCE
ClearTTC tries to remove all objects generated by TTC as
Coordinates, Metrics, ... etc .
Compact[] is On or Off depending you have set
Compact[On]or
Compact[Off].
If Compact[] is On TTC works with compacted objects.
The default value is
On . See also
Coordinate[x][i] gives the i-th coordinate
of the coordinate system named x.
CoordinateChange [x1, x2] gives the relation between the
coordinate systems x1 and x2 provided that an input InputCoordinateChange[x1,
x2, change] has been made. Otherwise, TTC asks you for
this input.
CoordinateChangeNamesE
CoordinateChangeNames prints a list with the coordinate changes
defined in the present session.
CoordinateChangeQE
CoordinateChangeQ[x1, x2] yields True if the coordinate
change x1 
x2 has been
defined and yields False otherwise.
CoordinateNamesE
CoordinateNames shows the coordinate systems declared in the present
session.
Coordinates [x] gives a list with the symbols of the coordinate
system named x provided that you have defined it.
CoordinatesQE
CoordinatesQ [x] yields True if x is actually
a name of a coordinate system, and yields False otherwise.
CoordinateTensorE
CoordinateTensor [x] gives the pseudotensor build from
the coordinates of the system named x.
CovariantD [g][v][t] or CovariantD[g][t,
v] computes the covariant derivative of the tensor t with respect to
the vector v using the metric g. If t is a (p,
q) tensor, the covariant derivative of t in the direction of
v
is also a (p, q) tensor.
CovariantToPartialS
expr//Index[g,CovariantToPartial], where g is
the name of the metric used to raise and lower index, transform covariant
derivatives, appearing in expr, to partial ones introducing
the Christoffel symbol when needed.
Curvature [g, b] gives the curvature scalar of the metric
g
in the basis b. It is computed only the first time it is called.
CyclicS
InputSymmetries[R[i,j,k,l],Cyclic[j,k,l][2]] is the way to
define the cyclic propertie of the tensor R for the indexes (j,k,l) adding
the corresponding rules to BasicRules[2]
CyclicApplyS
Obsole function. See SimplifyAllIndex
DimensionE
Dimension[b] gives the dimension of the basis b. It
can be used also to obtain the dimension of coordinate system.
Euclidean is the name of the default metric in the default coordinates
XX.
ExpandDS
expr//Index[g,ExpandD],
where g is the name of the metric used to raise and lower indexes,
expand derivatives over sums apearing in expr
ExpandSAFormRuleS
indexexpr//Index[g,TensorRules[ExpandSAFormRule[g,x]]]
expand products of volume forms SAForm[g,x]
ExteriorDE
ExteriorD[w] computes the exterior derivative of the
form w.
ExteriorProduct[w1, w2, ...] computes the exterior product
of the forms w1, w2, ... Alternatively, w1 *^ w2*^
... can be used.
ExteriorToOuter[w] transforms the exterior products appearing
in w in outer products.
FirstFundamentalForm[g, x1, x2] computes the first fundamental
form of the hypersurface parametrized with coordinates x2. g is
the name of the metric in the background space with coordinates x1.
It is computed only the first time it is called.
FormatFunctionS
FormatFunction[{symbols to be formated}] perfoms
an easy-to-read format for the list of functions required
FormQE
FormQ[w] yields True if w is a form, and yields
False otherwise.
GhostSMetricS
indexexpr//Index[g,GhostSMetric] absorb
metrics contracted with tensors.
Hodge[g][w] gives the dual of w relative
to the metric g.
IdentityTensor[b, p, q] gives the Kronecker delta of type
{p, q} in the basis b.
Index[g][expr] is the function used for doing computations
in index notation . expr means and indexed tensorial expression.
If all tensors in expr are explicit tensors then Index
gives
an explicit tensor as a result. If all tensors in expr
are symbolic tensors then Index gives a symbolic tensor as a result.
IndexFactor
S
polindextensorexpr//Index[g,IndexFactor[factorindex]]
try to factor polindextensorexpr with factorindex. factorindex
must be some subpart of a term of polindextensorexpr using the same
indices.
IndexList S
IndexList, gives the actual list of indexes defined through InputIndex.
IndexSave S
IndexSave[Tsymbol,expr] may be used as a valid argument
in the TTC function TTCSave in In option. The
effect is to save, on the selected file, Tsymbol[index]:=expr
updating the indexes.
IndexTensorBasis
S
expr//Index[gn,IndexTensorBasis[n,a,r]]
sets r to be the polynomial tensor basis of expr with coefficients
a[1]
a[2]...simplified up to n (using SimplifyAllIndex[n]).
See examples in TTC tutorial "
IndexUpdate[Tsymbol,":="( or ":"),expr], where
(:=
or :) makes the corresponding assignement, updating the indexes.
Example: the input IndexUpdate[S,":=",T[-i,j]
Q[-j,k]] will allow you to input
S[a,-b]//Index[] to produce the corresponding expression:
0[a,-b]+T[a,c]Q[c,-b].
IniSimplifyAllIndexSave
S
IniSimplifyAllIndexSave[file] will save all
new rules created by SimplifyAllIndex in the file file
and in compacted form to be reused using TTCGet. You will need
to resume using EndSimplifyAllIndexSave. See examples in TTC tutorial
InputBasis[{cc,bb}] declares the noncoordinate basis
named bb related to the coordinate system named cc. InputBasis[{cc,bb},
{e1, e2,...}] makes the same but the symbols e1, e2, etc.
can be used instead of the indices 1, 2, etc. to label tensors.
In both cases, and assuming that cc is the unic coordinate system related
to the basis bb, you can use bb as a valid symbol to input tensor basis
elements as in bb[1,2,-3]
InputBasisChange[b1, b2, change] sets the relation between
the basis b1 and b2 through change. change is a list
of rules relating vectors or forms of b1 and b2. You can
give elements of b1 in terms of elements of b2 or viceversa.
b1
and b2 must be basis
related to the same coordinate system!
InputCoordinateChange[x1, x2, change] sets the relation
between the coordinate systems x1 and x2 through change.
change
is a list of rules relating the coordinates of x1 and x2.
InputCoordinates[x, {x1, x2,...}] declares the coordinate
system named x with symbols x1, x2,... Once the coordinates
system named x has been declared x[x1,x3,...] can
be used to input tensor basis. InputCoordinates[XX, n],
being n a positive number sets the dimension of the default system
XX
to n.
InputSChristoffelTensor S
InputSChristoffelTensor[metricname,coordinatename ,outputstring,inputsymbol]
Is the way to define a the symbolic Christoffel tensor. metricname is the
name of the metric we want to use, coordinatename is the name of the actual
coordinates, outputstring is the symbol used to display the Christoffel
tensor , inputsymbol is the symbol for the Christoffel tensor used in tensorial
expressions."
InputIndex[{indexes}] is the way to introduce
or to change the indexes you want use in the present session. The list
must to have at least one element, say {i}, then i1, i2, i3, i4,..etc will
be used as indexes if it is needed.
InputMetric[g, b, t] declares the tensor t to be
the metric named g in basis b.
InputMetricSign[g, b, s] sets to positive (if s=+1)
or negative (if s=-1) the sign of the determinant of Metric[g,
b].
InputNormalFormSign[g, x1, x2, s] sets to positive (s=+1)
or negative (s=-1) the sign of the modulus of the normal to the
hypersurface parametrized with coordinates x2. g and x1
are the metric and the coordinates, respectively, of the background space.
InputSimplifyLevel[n], with n an integer between 0 an 4
sets the value of SimplifyLevel.
InputSMetric[metricname,coordinatename,outputstring,inputsymbol].
This function give the way to define a symbolic metric. metricname
is the name of the metric we want to use, coordinatename is the
name of the actual coordinates, outputstring is the string used
to display the metric, inputsymbol is the symbol for the
metric used to make inputs in tensorial expressions.
InputSAForm
S
InputSAForm[metricname,coordinatename,outputstring,inputsymbol]
This function give the way to define a symbolic volume form. metricname
is
the name of the metric we want to use, coordinatename is the name
of the actual coordinates, outputstring is the string used to display
the volume form, inputsymbol is the symbol for the volume
form used to make inputs in tensorial expressions.
InputSRiemann[metricname,coordinatename,outputstring,
symbolinputriemann,symbolinputricci,symbolinputcurvature]
This function gives the way to define the symbolic Riemann and Ricci tensors
and the curvature. metricname is the name of the metric we want
to use, coordinatename is the name of the actual coordinates, outputstring
is the string used to display the Riemann and Ricci tensors and the curvature
scalar. symbolinputriemann and symbolinputricci
are the symbols for the Riemann and Ricci tensors and symbolinputcurvature
the symbol for the curvature used to make inputs in tensorial expressions.
InputSymmetries[tensorname[indexlist],symmetrieslist] This
function enables you to input the symmetry properties (symmetrieslist)
of the indexes (indexlist) of one tensor (tensorname).
Example: InputSymmetries[T[i,j,k,l,m],{{i,m}}[1],{i,k,l}[2],{{i,j},{k,l}}[1]]
The symmetries of the indexes in the tensor T are:
{{i, m,l,...}} i, m ,l,...antysimmetrics.
{i, k, l} i, k, l symmetrics.
{{i,j},{k,l}} (i, j),(k, l) pairsymmetrics.
Cyclic[i,j,k...] i,j,k,...cyclic symmetrics
The
list of symmetries can be as long as you want and the mathematical correctness
allows you . The numbers [1] [2]...[n]..indicates that the property will
be used with BasicRules[n]. See examples in TTC tutorial.
Example the Levi Civita like symmetries: InputSymmetries[s[i,j,k,l],{{i,j,k,l}}]
Example: the riemann like symmetries :
InputSymmetries[R[i,j,k,l],{{i,j}}[1],{{k,l}}[1],{{i,j},{k,l}}[2],
Cyclic[j,k,l][2]]
InputSymmetries[R[i,j,k,l,.;m],Cyclic[k,l,m][2]]
InputTensorS
InputTensor[tensorname,basisname,tensortype],
is the way to define a symbolic tensor. tensorname is the
name of the tensor, basisname is the name of the basis
used to define the components of the tensor, tensortype
is the TensorType of the tensor.
Example: InputTensor[T,XX,{1,1}] , this input define a tensor
T with two indexes .
InputTTCSimplifyE
InputTTCSimplify[list] sets TTCSimplify=list
cheking that list are (possible) simplificators
InteriorContractionE
InteriorContraction[t1, t2] computes the interior product
of t1 and t2. It can be computed using index notation.
InverseHodgeE
InverseHodge[g][w] is the inverse Hodge star
operator applied to the form w.
InverseMetricE
InverseMetric[g, b] gives the contravariant version
of the metric tensor Metric[g,b]. It is computed only the
first time it is called.
JacobianMatrixE
JacobianMatrix[b1, b2] gives the jacobian matrix of
the change b1
b2, being
b1
and b2 natural basis.
LeibnizS
expr//Index[g,Leibniz], where g is the metric
used to raise and lower indexes, applies Leibniz rule on derivatives appearing
in expr
LieD[v][T] or LieD[v, T]
computes the Lie derivative of the tensor T with respect to the
vector v.
LlistaMonomisS
LlistaMonomis[g,x,nfreeindex,nsym,ncounter]
is the ncounter-th list of tensor index monomials generated by indexpr//Index[g,SimplifyAllIndex[nsym]]
and in codified version. LlistaMonomis[g,x,{i,j,k...n},nsym,ncounter]
will
show LlistaMonomis[g,x,nfreeindex,nsym,ncounter]
using (i,j,k..n) as free indices. See examples in TTC tutorial
LlistaRulesS
LlistaRules[g,x,nfreeindex,nsym,ncounter] is
the ncounter-th list of rules of tensor index monomials generated
by indexpr//Index[g,SimplifyAllIndex[nsym]]
and in codified version. LlistaRules[g,x,{i,j,k...n},nsym,ncounter]
will show LlistaRules[g,x,nfreeindex,nsym,ncounter]
using (i,j,k..n) as free indices. See examples in TTC tutorial.
MakeDE
MakeD[expr] makes again all derivatives
MatrixToTensor[m, tp, b] gives a tensor of type
tp,
expanded in the basis b and built with the components of the matrix
m.
Metric[g, b] gives the expression of the metric named g
in the basis b provided you have entered it using InputMetric.
If not, TTC asks you to make the input.
MetricDet[g, b] computes the determinant of the metric
Metric[g,
b]. It is computed only the first time it is called.
MetricNamesE
MetricNames shows the names of the metric tensors defined in the
present session.
MetricQE
MetricQ[g, x] gives True if g is the name of a
metric in the coordinate system named x and gives False otherwise.
MetricSignE
MetricSign[g, b] gives the sign of MetricDet[g,
x] if you have established it with InputMetricSign[g, b,
s]. Otherwise TTC asks you for the input.
NormalForm[g, x1, x2] computes the normal form to the hypersurface
parametrized with the coordinates x2. g is the name of the
metric in the background space with coordinates x1. It is computed
only the first time it is called.
NormalFormSign[g, x1 ,x2] gives the sign of the modulus of
the normal to the hypersurface parametrized with the coordinates x2 provided
that it has been stated with InputNormalFormSign. Otherwise, TTC
asks you for the input.
OuterProduct[t1, t2, ...] computes the outer or tensor
product of t1, t2, ... Alternatively, t1*.t2*.
... can be used.
OuterToExterior[t] antisymmetrizes t and then gives
the result in exterior notation.
PartialToCovariant
S
expr//Index[g,PartialToCovariant],
where g is the metric used to raise and lower indexes, convert all partial
derivatives appearing in expr to covariant introducing, when needed,
Christoffel symbols.
ReduceE
You can use Reduce (Mathematica
build-in function) over TTC-tensor
equations. TTC convert tensor equation into a equation system.
Ricci[g, b] computes the Ricci tensor of the metric named
g
in the basis b. It is computed only the first time it is called.
RicciApply
S
Obsolete function. See SimplifyAllIndex
RicciToCurvatureRule
S
Obsolete function. See SimplifyAllIndex
Riemann[g, b] computes the full covariant version of the
Riemann tensor of the metric named g in the basis b. It is
computed only the first time it is called.
RiemannToRicciRuleS
Obsolete function. See SimplifyAllIndex
ScalarBasisE
ScalarBasis = b sets b as the basis that will be
assigned to the scalars if ScalarBasisQ = False. The default is
ScalarBasis
= XX.
ScalarBasisQE
ScalarBasisQ can be set to True or False. If
ScalarBasisQ
= True then Basis[s], with s an scalar, asks
you for the name of the basis of s. If ScalarBasisQ = False
then Basis[s] has the value stored in ScalarBasis.
ScalarProduct[g][v1, v2] gives the contraction or
scalar product of the vectors (or 1-forms) v1 and v2. It
can be computed using index notation.
ScalarQE
ScalarQ[s] yields True if s is a scalar, and yields
False
otherwise.
SChristoffelTensorS
SChristoffelTensor[g,basisname], is the symbolic
Christoffel tensor. g is the metric used to raise and lower indexes
and basisname is the name of the basis used.
SCurvature
S
SCurvature[g,basisname], is the symbolic Curvature
of scalar of the Riemann tensor SRiemann[g,basisname].
g
is the metric used to raise and lower indexes and basisname is the
name of the basis used.
SecondFundamentalForm[g, x1, x2] computes the second fundamental
form of the hypersurface parametrized with coordinates x2. g
is the name of the metric in the background space with coordinates x1.
It is computed only the first time it is called.
SetCompactTensor[T,expr] or T=>expr
is the way to define a compacted tensor T as expr.
ShowChristoffel[g, b] shows all nonnull connection coefficients
of the Metric[g,b]
ShowStructureCoefficient[b] shows all nonnull structure
coefficients of the basis b.
SimplifyLevel is a variable that determines the frequency of internally
simplifications. It can take values from 0 to 4. It is established with
InputSimplifyLevel.
SimplifyAllIndex
S
expr//Index[gn,SimplifyAllIndex[num]]
is the way to simplify the symbolic tensor expr using:
num=0 uses BasicRules[0] and dummy indices.
num=1 uses BasicRules[0], dummy indices and index symmetry
properties stored in BasicRules[1].
num=2 uses BasicRules[0], dummy indices and index symmetry
properties stored in BasicRules[1] and 2.
num=3 uses BasicRules[0], dummy indices and index symmetry
properties stored in BasicRules[1] and 2 and dimensional index properties.
num=SymmApply uses SymmApply which does not
work making rules and only uses symmetry, antisymmetry and pairsymmetry
of indices. See examples .
SinTosin is useful in order to simplify some exepressions. Example
InputTTCSimplify[
{SinTosin,Together,sinToSin}]
See SinTosin
SMetricS
SMetric[g,basisname], is the symbolic Metric tensor
named g and labeled with basisname.
SolveE
You can use Solve (Mathematica
build-in function) over TTC-tensor equations. TTC convert tensor equation into
a equation system.
SRicci S
SRicci[g,basisname], is the symbolic Ricci tensor
of the Riemann tensor SRiemann[g,basisname]. g
is the metric used to raise and lower indexes and basisname is the
name of the basis used.
SRiemann
S
SRiemann[g,basisname] is the symbolic Riemann
tensor. g is the metric used to raise and lower indexes and basisname
is the name of the basis used.
StructureCoefficient[b][-i, -j, k] is the structure
coefficient of the basis b labeled by the index i, j, k.
It is computed only the first time it is called.
StructureCoefficientTensor[b] gives the pseudotensor build
from the structure coefficients of the basis b.
expr//Index[g,SuperIndexExpand] where g
is the metric used to raise and lower indexes, expand expr using Leibniz,
ExpandDand
ExpandAll
SymbolicTensorNamesS
SymbolicTensorNames give the list of the
actual symbolic tensors.
Symmetric[t] gives the symmetric part of the tensor t.
If t is not symmetrizable then Symmetric[t] returns Fail.
It can be computed using index notation.
polytensorexpr//Index[g,SimplifyAllIndex[SymmApply]]apply
index symmetric rules of tensors defined through the InputSymmetries
function, appearing in polytensorexpr and gives it's canonical
form . SymmApply suport symetry antisymmetry, pairsymmetry and
anti pairsymmetry but not cyclic and Ricci like rules. See SimplifyAllIndex.
TangentVector[x1, x2][-i] gives the i-th
vector of the basis of the tangent space to the hypersurface parametrized
by the coordinates x2 in the manifold with coordinates x1.
TensorComponent[t][i, j, k,...] gives the component
of the tensor t labeled by the (positive or negative) integers i,
j, k, ... TensorComponent[w][{i, j, k,...}]
gives the
component of the form w labeled by the (negative) integers i,
j, k.
TTCTensorQE
TTCTensorQ[t] yields True if t is a tensor, and yields
False otherwise.
In version < 4.3.1 TTCTensorQ
was TensorQ. It has been renamed
to be compatible with Mathematica 5.x
TensorRules
S
expr//Index[g,TensorRules[rules]],
apply
rules
on expr.
expr//Index[g,TensorRules[rules,Repeated]],
apply
rules
on expression repeadly until expr don't change
TensorSimplify[simp][t] simplifies every component
of t using the simplification commands given in the list simp.
TensorToMatrix[t] gives a matrix whose components are those
of t.
TensorType[t] gives the type of the tensor t. TensorType[t]
= {} if TTCTensorQ[t] = False.
ToTTCExpressionE
ToTTCExpression[string] converts any string containing
special symbols used in TTC into a valid Mathematica
expression.
TTC[n], where n it's a number, is a compacted object
when you have set Compact[On]. When Compact[] is Off
TTC[n] it's just TTCR[n]
TTCActualSettings
TTCActualSettings prints de actual setting in TTC
TTCFunctionsE
TTCFunctions[] prints all TTC functions. TTCFunctions[abc..]
prints all TTC functions begining with abc...
TTCGet[file] loads a file where the TTC notation
( *. , *^ , =...etc) has been employed or when file
has
been saved in Compact[ ] = On switch.
TTCInFormatE
TTCInFormat restores the standards outputs after TTCOutFormat
has been activated.
TTCListE
TTCList[T] Give the list of all necesary TTC[n]
objects to define T.
TTCOutFormatE
TTCOutFormat starts the textbook-like format for the outputs.
It is the default format.
TTCPrintTime
TTCPrintTime[On/Off] prints CPU Time and Memory in use after
each output
TTCR[n], where n it's a number, is the expression
compacted by TTC[n]
TTCSave[file.ext, In, e1, e2,...] appends
expressions e1, e2,... to file.ext in such a format that
can be read in from Mathematica. TTCSave[file.ext,
Out,
e1,
e2,...] appends expressions e1, e2,... to file.ext in
a format readable by humans. TTCSave[file,
e1, e2,...]
appends expressions e1, e2,... to files file.in and file.out
in In and Out formats, respectively
Note:If Compact[Off] TTCSave saves objects uncompacted.
If Compact[On] TTCSave uses the compact utilities to save objects.
See examples.
TTCSimplify is a variable that stores the chain of conversion
operators used in internal simplifications. Its default value is TTCSimplify
= {Simplify}. Can be chnaged usin InputTTCSimplify.
UncompactTensor[T] is the tensor T uncompacted
UnformatFunction
UnformatFunction[{symbols to be unformated}]
returns FormatFunction to standard outptut form for
the list of functions required
Unitary[g][s, v] gives the s-normalized version
of the vector (or 1-form) v respect to the metric g. s
must be the sign (1 or -1) of ScalarProduct[g][v, v].
When s=+1 it can be omitted.
UpdateTTC
E
UpdateTTC resets all TTC[n] symbols in order to incorporate
news setting (such as a=0, b=0, ..etc)
UpDownQS
UpDownQ[i,j] is True if the symbolic
index i,j are up-down or down-up
UpQ
S
UpQ[i] is True/False if the symbolic
index i is up/down "
AForm[g, b] gives the volume form associated to Metric[g,
b] in exterior notation. It is computed only the first time it is called.
XX is the name of the default coordinate and also the name of
the coordinate basis associated to it.
ZZ is the symbol used to express the basis elements of tensors,
vectors and forms.
Internal and special use TTC symbols
AbsSymbol
ActualIfPBMonomial
AntiPList
AppendNewIndexList
BasisInUse
FabricaRules
IndexF
IndexD
InverseMetricComponent
MetricInUse
New
RepeatedIndex
ReplaceAllIndex
RiemannComponent |
$SChistoffelTensor
SecondFundamentalFormComponent
SequenceHold
SignSymbol
SingleTensorQ
SymbolicIndexTensorExpression
TensorSymmetries
TTCBracket
TTCCPUTime
TTCIndexD
TTCIndexS
TTCPartialD
TTCPrintDate
TTCTryingToReloadQ
TTCVNotes
ZZX |
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