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- %==========================================================================%
- % GRGdecl.sl Internal Variables, Flags, Properties %
- %==========================================================================%
- % GRG 3.2 Standard Lisp Source Code (C) 1988-2000 Vadim V. Zhytnikov %
- %==========================================================================%
- % This file is distributed without any warranty. You may modify it but you %
- % are not allowed to remove author's name and/or distribute modified file. %
- %==========================================================================%
- %
- % Notation for GRG symbols :
- %
- % !!sym!! - Self-Quoted Symbols
- % ![sys!] - Internal GRG Control or Working System Variables
- % !#id - Internal Variables of Built-in Objects
- % !+flag - GRG Specific Flags
- % !=prop - GRG Specific Properties
- % !*switch - GRG and REDUCE Switches
- % funtion!> - GRG functions
- %
- %========== (1) Internal GRG Control Variables ==========================
- (put 'grg 'stat 'endstat) % Making grg; REDUCE command ...
- %---------- GRG System Variables --------------------------------------
- (global '(
- ![version!] % Version number
- % Start mode :
- ![autostart!] % Run (grg) atomatically during load grg; or not
- % General Status :
- ![dim!] % Current Dimension 4
- ![dim1!] % dim-1
- ![sgn!] % Current Signature (-1 1 1 1)
- ![sigprod!] % prod(-1 1 1 1)
- ![dim0!] % Initial Dimension and
- ![sgn0!] % Signature in the session
- ![umod!] % Current basis mode
- % Metric and Frame Type :
- ![mtype!] % Metric type: nil - unknown
- ![mitype!] % 1 - null 2 - diagonal 3 - general
- ![dtype!] % Metric differentiability: nil - unknown
- ![ditype!] % 1 - constant 2 - general
- ![ftype!] % Frame type: nil - unknown
- ![fitype!] % 1 - holonomic 2 - diagonal 3 - general
- ![nullm!] % Standard Null Metric for -,+,+,+
- ![nullm1!] % Standard Null Metric for +,-,-,-
- % Others working variables :
- ![w!] % General purpose
- ![instr!] % All Commands list
- ![datl!] % All Objects
- ![abbr!] % All User-Defined Objects (Abbreviations)
- ![rconstl!] % List of reserved constants
- ![sublist!] % Substitutions List
- ![rpfl!] % Flags and properties which must be cleared
- ![rpflcr!] % for Coordinates
- ![rpflcn!] % for Constants
- ![rpflap!] % for Affine Parameter
- ![rpflfu!] % for Functions
- ![tlst!] % List of Energy-Momentum tensors
- ![slst!] % List of spin forms
- ![solveq!] % Equations for solve
- ![allprops!] % All Flags and Props
- ![allflags!] % important for Load/Unload
- ![icompos!] % List of Commands allowed in composites
- ![newabbr!] % New object in assignment
- ![wi!] ![wh!] ![wf!] ![ws!]
- ![gfun!] % Generic functions list
- % Session Control :
- ![er!] % Error type
- ![firsti!] % First instruction indicator for Dimension
- ![time!] % Timer
- ![gctime!] % GC Timer
- ![ttime!] % Total Session Time
- ![tgctime!] % Total GC Time
- ![pause!] % Pause regim indicator
- ![origlower!]
- % Switches control :
- ![flaghis!] % Flags On/Off history list
- ![flagl!] % GRG Flags list
- ![flaglo!] % GRG Output-Flags list
- ![iflago!] % Initial mode of output
- ![echo!] % Echo in LISTOK>
- ![flagnil!] % Swithes initailly to nil
- ![flagt!] % Swithes initially t
- ![fldtuned!] % nil tuning of FANCY-LOWER-DIGITS is needded
- % OS scpecific :
- ![dirsep!] % The directories separator. This symbol is
- % added to the end of GRG environ. var. when
- % trying to open files.
- % \ for DOS, / for UNIX, : for VMS (?)
- % if nil then nothing added.
- ![syscall!] % Temporary exit to OS and OS commands
- % 1 - via SYSTEM (UNIX,DOS)
- % 2 - via QUIT (VAX/VMS)
- % nil - forbidden
- ![grgdir!] % Standard Input Didrectory Expanded
- ![grgdir1!] % Standard Input Didrectory
- % Version specific:
- ![lower!] % If t then background lisp internally is in lower case
- % Debugging :
- ![erst1!] % First ERRORSET debuggin parameter
- ![erst2!] % Second ERRORSET debuggin parameter
- % GRG printing:
- ![line!] % Current Line for GPRIN
- ![lline!] % Current Line Length
- ![gptab!] % Tabulation for GPRIN
- ![gpfirst!] % First Line marker for GPRIN
- ![modp!] % Basis mode for write
- ![allzero!] % Zero-Nonzero components indicator for write
- ![idwri!] % Writed Data Identifier
- % Files manipulation :
- ![fromf!] % In file
- ![loa!] % Load file
- ![unl!] % Global Unload file
- ![lunl!] % Local Unload file
- ![wri!] % Global Write file
- ![lwri!] % Local Write file
- % Data evaluation control :
- ![chain!] % Chain of required data in REQUEST
- ![way!] % Way for Find/Calculate
- % Translation control:
- ![cs!] % Chanhe Sign
- ![ch!] % Change Conjugation
- ![lsrs!] % Left or Right side in equation
- ![extvar!] % External variables list
- ![extvara!] % Additional external variables list
- ![idl!] % For T(J) = expr(J)
- ![texpr!] % translation
- ![ivs!] % Iteration vars stack
- % Coordinates transformation:
- ![ocord!] % Old coordinates list
- ![x!] % X
- ![dfx!] % d X
- ![dex!] % @ X
- % Basis mode:
- ![xb!] % d X/\d Y/\...
- ![xf!] % d X = b
- ![xv!] % @ X = e
- ![ccb!] % ~ b
- ![ccbi!] % ~ e
- ![dbas!] % d(b/\...) accumulation
- % Rotations:
- ![l!] % L - frame rotaion matrix
- ![dl!] % det(L) - its det
- ![sdl!] % sgn(det(L)) - the sign of its det
- ![li!] % L^(-1) - its inverse
- ![ls!] % LS - spinor rotation matrix
- ![dens!] % density factor for an object
- % Processor internals:
- ![tlow!] % T_a (lower index a) for Duialisation
- ))
- (setq ![autostart!] t) % By default we start (grg) during load grg;
- %------- Self Quoted Atoms -------------------------------------------
- (global '( !!stop!! !!next!! !!er!! ))
- (setq !!stop!! '!!stop!!) % This is STOP
- (setq !!er!! '!!er!!) % This is ERROR
- (setq !!next!! '!!next!!) % This is NEXT
- %-----------------------------------------------------------------------
- %========== (2) Built-In Objects =======================================
- %---- Flags and Properties for Internal Data variables #ID -------------
- %
- % Prop =type - Type of Component:
- % -1 - vector; 0 - algebraic expression, n - n-form.
- %
- % Prop =idxl - List of Indices. Absent for Scalars. In The List:
- % nil - lower frame, t - upper frame,
- % 0 - lower holonomic, 1 - upper holonomic,
- % (u . n) - un. spinor, (d . n) - do. spinor,
- % (uu . n) - up un. spinor, (ud . n) - up do. spinor,
- % (n . n) - enimerating, (n) - enum. d-dimensional.
- %
- % Prop =sidxl - Symmetries List is (sy1 sy2 ...)
- % sy = (type el1 el2 ...)
- % with type = a | s | h | c which stands for
- % Antisymmetric, Symmetric, Hermitian, Cyclic
- % el = n | (n1 n2 ...) | sy
- % where n is the index number and sy as above.
- %
- % Prop =way - Ways of Calculation is (el1 el2 ...)
- % el = ( (name) (cond) (evfun) data ... )
- % data = id | (cond id1 id2 ...) | (t id)
- % the second form is included iff cond=true
- % the third form defines Main data.
- %
- % Prop =constr - Restriction when data can be used is
- % (fn1 fn2 ...)
- % where fn is function call.
- %
- % Prop =dens - Pseudo-tensor and Density properties
- % List of four elements (a b c d)
- % a=t/nil - Pseudo for coodrinate transform sgnD
- % b=n - Density for coordinate transform D^n
- % c=t/nil - Pseudo for rotations sgnL
- % d=n - Density for rotations L^n
- %
- % Flag +noncov - Marks Noncovariant data types for
- % preventing Dc and Lie calculation.
- % But don't prevent rotations.
- %
- % Flags +fconn +hconn +uconn +dconn
- % types of connection are
- % Frame, Holonomic, Spinorial, Conjugate Spinorial
- %
- % Flag +hold - Prevents rotation or coordinate
- % transformation of the object.
- %
- % Flag +pl - Marks oblects with plural name.
- %
- % Flag +equ - Marks equations.
- %
- % Flag +ivar - Marks all internal variables.
- %
- % Flag +abbr - Marks new user created objects (abbreviations).
- %
- % Prop =unl - Special function call for Unload.
- %
- % Prop =datl - Special function call for Write.
- %
- % Prop =tex - Writre in FANCY/TEX output mode.
- % If ID than ID both in TEX and FANCY mode
- % If (IT . IF) IT for TEX IF for FANCY
- %----- Flags and Prop. for Funs and Vars (Cord, Const, Fun) --------
- %
- % Flag +grg - Already used by GRG (Can't be declared once again).
- %
- % Prop =depend - Dependence List for Functions.
- %
- % Flag +grgvar - Marks Variables: Cord, Const, Implicit Fun.
- % So, can be used as var in any expression.
- %
- % Flag +fun - Marks Functions.
- %
- % Prop =cord - Coordinate number N (0 1 ... dim-1).
- %
- % Prop =conj - Complex Conjugated Object.
- %
- % Prop =subind - Value of Iteration Variable.
- %
- % Flag +redbad - Specially blocks some atoms.
- %
- % Reduce Flags: used!* constant
- %
- % Reduce Flags: subfn symmetric antisymmetric odd even
- %
- % Reduce Props: simpfn kvalue klist narg
- %
- %-----------------------------------------------------------------------
- %------- Data List -------------------------------------------------
- (setq ![datl!] '(
- % Coordinates, Constants, Functions, Solutions ...
- ((Coordinates) ![cord!] )
- ((Functions) ![fun!] )
- ((Constants) ![const!] )
- ((Affine Parameter) ![apar!] )
- ((Solutions) ![sol!] )
- % Metric, Frame, Basis, Volume ...
- ((Frame) !#!T )
- ((Vector Frame) !#!D )
- ((Metric) !#!G )
- ((Inverse Metric) !#!G!I )
- ((Det of Metric) !#!d!e!t!G )
- ((Det of Holonomic Metric) !#!d!e!t!g )
- ((Sqrt Det of Metric) !#!s!d!e!t!G )
- ((Volume) !#!V!O!L )
- ((Basis) !#!b )
- ((Vector Basis) !#!e )
- ((S - forms) !#!S )
- % Rotation Matrices ...
- ((Frame Transformation) !#!L )
- ((Spinorial Transformation) !#!L!S )
- % Connection and related objects ...
- ((Frame Connection) !#!o!m!e!g!a )
- ((Holonomic Connection) !#!G!A!M!M!A )
- ((Undotted Connection) !#!o!m!e!g!a!u )
- ((Dotted Connection) !#!o!m!e!g!a!d )
- ((Spinorial Connection) ( !#!o!m!e!g!a!u !#!o!m!e!g!a!d ))
- ((Riemann Frame Connection) !#!r!o!m!e!g!a )
- ((Riemann Holonomic Connection) !#!R!G!A!M!M!A )
- ((Riemann Undotted Connection) !#!r!o!m!e!g!a!u )
- ((Riemann Dotted Connection) !#!r!o!m!e!g!a!d )
- ((Riemann Spinorial Connection) ( !#!r!o!m!e!g!a!u !#!r!o!m!e!g!a!d ))
- ((Connection Defect) !#!K )
- ((Undotted S - forms) !#!S!U )
- ((Dotted S - forms) !#!S!D )
- ((Spinorial S - forms) ( !#!S!U !#!S!D ))
- % Torsion ...
- ((Torsion) !#!T!H!E!T!A )
- ((Contorsion) !#!K!Q )
- ((Torsion Trace 1 - form) !#!Q!Q )
- ((Antisymmetric Torsion 3 - form) !#!Q!Q!A )
- ((Undotted Contorsion) !#!K!U )
- ((Dotted Contorsion) !#!K!D )
- ((Spinorial Contorsion) ( !#!K!U !#!K!D ))
- ((Torsion Trace) !#!Q!T )
- ((Torsion Pseudo Trace) !#!Q!P )
- ((Traceless Torsion Spinor) !#!Q!C )
- ((Torsion Spinors) ( !#!Q!C !#!Q!T !#!Q!P ))
- ((Torsion Components) ( !#!Q!C !#!Q!T !#!Q!P ))
- ((Traceless Torsion 2 - form) !#!T!H!Q!C )
- ((Torsion Trace 2 - form) !#!T!H!Q!T )
- ((Antisymmetric Torsion 2 - form) !#!T!H!Q!A )
- ((Torsion 2 - forms) ( ((geq ![dim!] 3) !#!T!H!Q!C)
- !#!T!H!Q!T
- ((geq ![dim!] 3) !#!T!H!Q!A) ))
- ((Undotted Torsion Trace 2 - form) !#!T!H!Q!T!U )
- ((Undotted Antisymmetric Torsion 2 - form) !#!T!H!Q!A!U )
- ((Undotted Traceless Torsion 2 - form) !#!T!H!Q!C!U )
- ((Undotted Torsion 2 - forms) ( !#!T!H!Q!C!U !#!T!H!Q!T!U !#!T!H!Q!A!U ))
- % Nonmetricity ...
- ((Nonmetricity) !#!N )
- ((Nonmetricity Defect ) !#!K!N )
- ((Weyl Vector) !#!N!N!W )
- ((Nonmetricity Trace) !#!N!N!T )
- ((Symmetric Nonmetricity 1 - form) !#!N!C )
- ((Antisymmetric Nonmetricity 1 - form) !#!N!A )
- ((Nonmetricity Trace 1 - form) !#!N!T )
- ((Weyl Nonmetricity 1 - form) !#!N!W )
- ((Nonmetricity 1 - forms) ( !#!N!C
- ((geq ![dim!] 3) !#!N!A)
- !#!N!T
- !#!N!W ))
- % Curvature ...
- ((Curvature) !#!O!M!E!G!A )
- ((Undotted Curvature) !#!O!M!E!G!A!U )
- ((Dotted Curvature) !#!O!M!E!G!A!D )
- ((Spinorial Curvature) ( !#!O!M!E!G!A!U !#!O!M!E!G!A!D ))
- ((Riemann Tensor) !#!R!I!M )
- ((Ricci Tensor) !#!R!I!C )
- ((A - Ricci Tensor) !#!R!I!C!A )
- ((S - Ricci Tensor) !#!R!I!C!S )
- ((Homothetic Curvature) !#!O!M!E!G!A!H )
- ((Scalar Curvature) !#!R!R )
- ((Einstein Tensor) !#!G!T )
- ((Weyl Spinor) !#!R!W)
- ((Traceless Ricci Spinor) !#!R!C)
- ((Ricanti Spinor) !#!R!A)
- ((Traceless Deviation Spinor) !#!R!B)
- ((Scalar Deviation) !#!R!D)
- ((Curvature Spinors) ( !#!R!W !#!R!C !#!R!R
- (!*torsion !#!R!B !#!R!A !#!R!D ) ))
- ((Curvature Components) ( !#!R!W !#!R!C !#!R!R
- (!*torsion !#!R!B !#!R!A !#!R!D ) ))
- ((Undotted Weyl 2 - form) !#!O!M!W!U )
- ((Undotted Traceless Ricci 2 - form) !#!O!M!C!U )
- ((Undotted Scalar Curvature 2 - form) !#!O!M!R!U )
- ((Undotted Ricanti 2 - form) !#!O!M!A!U )
- ((Undotted Traceless Deviation 2 - form) !#!O!M!B!U )
- ((Undotted Scalar Deviation 2 - form) !#!O!M!D!U )
- ((Undotted Curvature 2 - forms)
- ( !#!O!M!W!U !#!O!M!C!U !#!O!M!R!U (!*torsion !#!O!M!A!U !#!O!M!B!U !#!O!M!D!U )))
- ((Weyl 2 - form) !#!O!M!W )
- ((Traceless Ricci 2 - form) !#!O!M!C )
- ((Scalar Curvature 2 - form) !#!O!M!R )
- ((Ricanti 2 - form) !#!O!M!A )
- ((Traceless Deviation 2 - form) !#!O!M!B )
- ((Antisymmetric Curvature 2 - form) !#!O!M!D )
- ((Homothetic Curvature 2 - form) !#!O!S!H )
- ((Antisymmetric S - Ricci 2 - form) !#!O!S!A )
- ((Traceless S - Ricci 2 - form) !#!O!S!C )
- ((Antisymmetric S - Curvature 2 - form) !#!O!S!V )
- ((Symmetric S - Curvature 2 - form) !#!O!S!U )
- ((Curvature 2 - forms) (
- ((geq ![dim!] 4) !#!O!M!W )
- ((geq ![dim!] 3) !#!O!M!C )
- !#!O!M!R
- ((and (or !*torsion !*nonmetr) (geq ![dim!] 3)) !#!O!M!A )
- ((and (or !*torsion !*nonmetr) (geq ![dim!] 4)) !#!O!M!B )
- ((and (or !*torsion !*nonmetr) (geq ![dim!] 4)) !#!O!M!D )
- (!*nonmetr !#!O!S!H )
- ((and !*nonmetr (geq ![dim!] 3)) !#!O!S!A )
- (!*nonmetr !#!O!S!C )
- ((and !*nonmetr (geq ![dim!] 4)) !#!O!S!V )
- ((and !*nonmetr (geq ![dim!] 3)) !#!O!S!U )
- ))
- % Various constants ...
- ((A - Constants) !#!A!C!O!N!S!T )
- ((L - Constants) !#!L!C!O!N!S!T )
- ((M - Constants) !#!M!C!O!N!S!T )
- % Scalar field ...
- ((Scalar Equation) !#!S!C!q )
- ((Scalar Field) !#!F!I )
- ((Scalar Action) !#!S!A!C!T )
- ((Minimal Scalar Action) !#!S!A!C!T!M!I!N )
- ((Minimal Scalar Energy - Momentum Tensor) !#!T!S!C!L!M!I!N )
- % EM field ...
- % for all dim ...
- ((EM Potential) !#!A )
- ((Current 1 - form) !#!J )
- ((EM Action) !#!E!M!A!C!T )
- ((EM 2 - form) !#!F!F )
- ((EM Tensor) !#!F!T )
- ((First Maxwell Equation) !#!M!W!F!q )
- ((Second Maxwell Equation) !#!M!W!S!q )
- ((Maxwell Equations) ( !#!M!W!F!q !#!M!W!S!q ))
- ((Continuity Equation) !#!C!O!q )
- ((EM Energy - Momentum Tensor) !#!T!E!M )
- % dim=4 only ...
- ((First EM Scalar) !#!S!C!F )
- ((Second EM Scalar) !#!S!C!S )
- ((EM Scalars) ( !#!S!C!F !#!S!C!S ))
- ((Selfduality Equation) !#!S!D!q )
- ((Complex EM 2 - form) !#!F!F!U )
- ((Complex Maxwell Equation) !#!M!W!U!q )
- ((Undotted EM Spinor) !#!F!I!U )
- ((Complex EM Scalar) !#!S!C!U )
- ((EM Energy - Momentum Spinor) !#!T!E!M!S )
- % YM field ...
- ((YM Potential) !#!A!Y!M )
- ((Structural Constants) !#!S!C!O!N!S!T )
- ((YM Action) !#!Y!M!A!C!T )
- ((YM 2 - form) !#!F!F!Y!M )
- ((YM Tensor) !#!F!T!Y!M )
- ((First YM Equation) !#!Y!M!F!q )
- ((Second YM Equation) !#!Y!M!S!q )
- ((YM Equations) ( !#!Y!M!F!q !#!Y!M!S!q ))
- ((YM Energy - Momentum Tensor) !#!T!Y!M )
- % Dirac field ...
- ((Phi Spinor) !#!P!H!I )
- ((Chi Spinor) !#!C!H!I )
- ((Dirac Spinor) ( !#!P!H!I !#!C!H!I ))
- ((Dirac Action 4 - form) !#!D!A!C!T )
- ((Undotted Dirac Spin 3 - Form) !#!S!P!D!I!U )
- ((Dirac Energy - Momentum Tensor) !#!T!D!I )
- ((Phi Dirac Equation) !#!D!P!q )
- ((Chi Dirac Equation) !#!D!C!q )
- ((Dirac Equation) ( !#!D!P!q !#!D!C!q ))
- % Geodesics and congruences ...
- ((Geodesic Equation) !#!G!E!O!q )
- % Null congruence ...
- ((Congruence) !#!K!V )
- ((Null Congruence Condition) !#!N!C!o )
- ((Geodesics Congruence Condition) !#!G!C!o )
- ((Congruence Expansion) !#!t!h!e!t!a!O )
- ((Congruence Squared Rotation) !#!o!m!e!g!a!S!Q!O )
- ((Congruence Squared Shear) !#!s!i!g!m!a!S!Q!O )
- ((Optical Scalars)
- (!#!t!h!e!t!a!O !#!o!m!e!g!a!S!Q!O !#!s!i!g!m!a!S!Q!O ))
- % Kinematics ...
- ((Velocity Vector) !#!U!V )
- ((Velocity) !#!U!U )
- ((Velocity Square) !#!U!S!Q )
- ((Projector) !#!P!R )
- ((Acceleration) !#!a!c!c!U )
- ((Vorticity) !#!o!m!e!g!a!U )
- ((Volume Expansion) !#!t!h!e!t!a!U )
- ((Shear) !#!s!i!g!m!a!U )
- ((Kinematics)
- ( !#!a!c!c!U !#!o!m!e!g!a!U !#!t!h!e!t!a!U !#!s!i!g!m!a!U ))
- % Ideal Fluid ...
- ((Pressure) !#!P!R!E!S )
- ((Energy Density) !#!E!N!E!R )
- ((Ideal Fluid Energy - Momentum Tensor) !#!T!I!F!L )
- % Spin Fluid ...
- ((Spin Fluid Energy - Momentum Tensor) !#!T!S!F!L )
- ((Spin Density) !#!S!P!F!L!T )
- ((Spin Density 2 - form) !#!S!P!F!L )
- ((Undotted Fluid Spin 3 - form) !#!S!P!F!L!U )
- ((Frenkel Condition) !#!F!C!o )
- % Total Energy-Momentum and Spin ...
- ((Total Energy - Momentum Tensor) !#!T!E!N!M!O!M )
- ((Total Energy - Momentum Spinor) !#!T!E!N!M!O!M!S )
- ((Total Energy - Momentum Trace) !#!T!E!N!M!O!M!T )
- ((Total Undotted Spin 3 - form) !#!S!P!I!N!U )
- % Einstein Equations ...
- ((Einstein Equation) !#!E!E!q )
- ((Traceless Einstein Equation) !#!C!E!E!q )
- ((Trace of Einstein Equation) !#!T!E!E!q )
- ((Spinor Einstein Equations) ( !#!C!E!E!q !#!T!E!E!q ))
- % Gravitational Equations ...
- ((Action) !#!L!A!C!T )
- ((Undotted Curvature Momentum) !#!P!O!M!E!G!A!U )
- ((Torsion Momentum) !#!P!T!H!E!T!A )
- ((Metric Equation) !#!M!E!T!R!q )
- ((Torsion Equation) !#!T!O!R!S!q )
- ((Gravitational Equations) ( !#!M!E!T!R!q
- (!*torsion !#!T!O!R!S!q )))
- ))
- (prog ( ![idatl!] )
- (foreach!> ![www!] in ![datl!] do
- (cond ((atom (cadr ![www!]))
- (setq ![idatl!] (cons (cadr ![www!]) ![idatl!] )))))
- (global ![idatl!])
- (flag ![idatl!] '!+ivar))
- %------- Plural ----------------------------------------------------
- (flag '(
- ![cord!] ![const!] ![fun!]
- !#!T !#!b !#!S !#!S!U !#!S!D
- !#!A!C!O!N!S!T !#!M!C!O!N!S!T !#!L!C!O!N!S!T
- ) '!+pl)
- %-------- Equations ----------------------------------------------------
- (flag '(
- ![sol!]
- !#!S!C!q
- !#!D!P!q !#!D!C!q
- !#!Y!M!F!q !#!Y!M!S!q
- !#!M!W!F!q !#!M!W!S!q !#!C!O!q !#!S!D!q !#!M!W!U!q
- !#!G!E!O!q
- !#!N!C!o !#!G!C!o !#!F!C!o
- !#!E!E!q !#!T!E!E!q !#!C!E!E!q
- !#!M!E!T!R!q !#!T!O!R!S!q
- ) '!+equ)
- %-------- Total Enargy-Momentum and Spin -------------------------------
- (setq ![tlst!] '( !#!T!D!I !#!T!E!M !#!T!Y!M !#!T!S!C!L!M!I!N
- !#!T!I!F!L !#!T!S!F!L ))
- (setq ![slst!] '( !#!S!P!D!I!U !#!S!P!F!L!U ))
- %-------- Properties of the Built-In Objects ---------------------------
- (put '![sol!] '!=type 0)
- % word!!! in =way
- % Metric, Farame, Volume ...
- (put '!#!T '!=type 1)
- (put '!#!T '!=idxl '(t))
- (put '!#!T '!=way '( ((By Default) nil (frame0!>) )
- ((From Vector Frame) nil (frame1!>) (t !#!D) ) ))
- (put '!#!T '!=tex "\theta")
- (put '!#!D '!=type -1)
- (put '!#!D '!=idxl '(nil))
- (put '!#!D '!=way '( ((From Frame)
- nil (iframe1!>) !#!V!O!L !#!T ) ))
- (put '!#!D '!=tex '("\partial" . 182))
- (put '!#!G '!=type 0)
- (put '!#!G '!=idxl '(nil nil))
- (put '!#!G '!=sidxl '((s 1 2)))
- (put '!#!G '!=way '( ((By Default) nil (metr0!>) )
- ((From Inverse Metric) nil (metr1!>) (t !#!G!I) ) ))
- (put '!#!G '!=tex '!g)
- (put '!#!G!I '!=type 0)
- (put '!#!G!I '!=idxl '(t t))
- (put '!#!G!I '!=sidxl '((s 1 2)))
- (put '!#!G!I '!=way '( ((From Metric) nil (imetr1!>) !#!G ) ))
- (put '!#!G!I '!=tex '!g)
- (put '!#!d!e!t!G '!=type 0)
- (put '!#!d!e!t!G '!=way '( (nil nil (detg1!>) !#!G ) ))
- (put '!#!d!e!t!G '!=dens '(nil nil nil -2))
- (put '!#!d!e!t!G '!=tex '!g)
- (put '!#!d!e!t!g '!=type 0)
- (put '!#!d!e!t!g '!=way '( (nil nil (dethg1!>) !#!G !#!T ) ))
- (put '!#!d!e!t!g '!=dens '(nil -2 nil nil))
- (put '!#!d!e!t!g '!=tex '!g)
- (put '!#!s!d!e!t!G '!=type 0)
- (put '!#!s!d!e!t!G '!=way '((nil nil (sdetg1!>) !#!G ) ))
- (put '!#!s!d!e!t!G '!=dens '(nil nil t -1))
- (put '!#!s!d!e!t!G '!=tex "\sqrt{-g}")
- (put '!#!V!O!L '!=type '![dim!]) % Variable Type !!!
- (put '!#!V!O!L '!=way '((nil nil (vol0!>) !#!s!d!e!t!G !#!T ) ))
- (put '!#!V!O!L '!=dens '(t nil t nil))
- (put '!#!V!O!L '!=tex "\upsilon")
- (put '!#!b '!=type 1)
- (put '!#!b '!=idxl '((n)))
- (put '!#!b '!=way '(((From Frame) nil (base!>) !#!V!O!L !#!T )
- ((From Vector Basis) nil (base1!>) (t !#!e) ) ))
- (put '!#!e '!=type -1)
- (put '!#!e '!=idxl '((n)))
- (put '!#!e '!=way '(((From Basis) nil (ibase!>) !#!b ) ))
- (put '!#!S '!=type 2)
- (put '!#!S '!=idxl '(t t))
- (put '!#!S '!=sidxl '((a 1 2)))
- (put '!#!S '!=way '((nil nil (makesforms!>) !#!T)))
- % Rotation matrices ...
- (put '!#!L '!=type 0)
- (put '!#!L '!=idxl '(t nil))
- (put '!#!L '!=tex '!L)
- (put '!#!L!S '!=type 0)
- (put '!#!L!S '!=idxl '((u . 1) (uu . 1)))
- (put '!#!L!S '!=tex '("\Lambda" . 76))
- % Spinorial S-forms ...
- (put '!#!S!U '!=type 2)
- (put '!#!S!U '!=idxl '((u . 2)))
- (put '!#!S!U '!=way '( (nil nil (ssform!> '!#!S!U 2 3) !#!T ) ))
- (put '!#!S!U '!=constr '((sp!>)))
- (put '!#!S!D '!=type 2)
- (put '!#!S!D '!=idxl '((d . 2)))
- (put '!#!S!D '!=way '( (nil nil (ssform!> '!#!S!D 3 2) !#!T ) ))
- (put '!#!S!D '!=constr '((sp!>)))
- % Connection and related objects ...
- (flag '( !#!G!A!M!M!A !#!o!m!e!g!a !#!o!m!e!g!a!u !#!o!m!e!g!a!d )
- '!+noncov)
- (flag '( !#!R!G!A!M!M!A !#!r!o!m!e!g!a !#!r!o!m!e!g!a!u !#!r!o!m!e!g!a!d )
- '!+noncov)
- (put '!#!G!A!M!M!A '!=type 1)
- (put '!#!G!A!M!M!A '!=idxl '(1 0))
- (put '!#!G!A!M!M!A '!=way '(
- ((From Frame Connection) nil
- (gfromo!>) !#!T !#!D !#!o!m!e!g!a )
- ))
- (flag '(!#!G!A!M!M!A) '!+hconn)
- (put '!#!G!A!M!M!A '!=tex '("\Gamma" . 71))
- (put '!#!R!G!A!M!M!A '!=type 1)
- (put '!#!R!G!A!M!M!A '!=idxl '(1 0))
- (put '!#!R!G!A!M!M!A '!=way '(
- ((From Riemann Frame Connection) nil
- (rgfromro!>) !#!T !#!D !#!r!o!m!e!g!a )
- ))
- (flag '(!#!R!G!A!M!M!A) '!+hconn)
- (put '!#!o!m!e!g!a '!=type 1)
- (put '!#!o!m!e!g!a '!=idxl '(t nil))
- (put '!#!o!m!e!g!a '!=way '(
- (nil nil (connec!>) !#!T !#!D !#!G !#!G!I
- (!*torsion !#!T!H!E!T!A)
- (!*nonmetr !#!N))
- ((From Spinorial Connection) (sp!-n!>)
- (ofromos!> '!#!o!m!e!g!a !#!o!m!e!g!a!u !#!o!m!e!g!a!d)
- (t !#!o!m!e!g!a!u) !#!o!m!e!g!a!d )
- ((From Connection Defect) (tttqandn!>)
- (connecplus!> !#!K) !#!T !#!D !#!G !#!G!I (t !#!K))
- ((From Contorsion) (tttq!>)
- (connecplus!> !#!K!Q) !#!T !#!D !#!G !#!G!I (t !#!K!Q))
- ((From Nonmetricity Defect) (tttn!>)
- (connecplus!> !#!K!N) !#!T !#!D !#!G !#!G!I (t !#!K!N))
- ((From Holonomic Connection) nil
- (ofromg!>) !#!T !#!D !#!G!A!M!M!A )
- ))
- (flag '(!#!o!m!e!g!a) '!+fconn)
- (put '!#!r!o!m!e!g!a '!=type 1)
- (put '!#!r!o!m!e!g!a '!=idxl '(t nil))
- (put '!#!r!o!m!e!g!a '!=way '(
- (nil nil (connecplus!> nil) !#!T !#!D !#!G !#!G!I) ))
- (put '!#!r!o!m!e!g!a '!=constr '((tttqorn!>)))
- (flag '(!#!r!o!m!e!g!a) '!+fconn)
- (put '!#!o!m!e!g!a!u '!=type 1)
- (put '!#!o!m!e!g!a!u '!=idxl '((u . 2)))
- (put '!#!o!m!e!g!a!u '!=way '(
- (nil nil (uconnec!>) !#!T !#!S!U !#!V!O!L (!*torsion !#!K!U))
- ((By Conjugation) nil
- (conj3!> '!#!o!m!e!g!a!u !#!o!m!e!g!a!d) !#!o!m!e!g!a!d)
- ((From Frame Connection) nil
- (oufromo!> '!#!o!m!e!g!a!u !#!o!m!e!g!a) !#!o!m!e!g!a )
- ))
- (put '!#!o!m!e!g!a!u '!=tex "\omega")
- (put '!#!o!m!e!g!a!u '!=constr '((sp!-n!>)))
- (flag '(!#!o!m!e!g!a!u) '!+uconn)
- (put '!#!o!m!e!g!a!d '!=type 1)
- (put '!#!o!m!e!g!a!d '!=idxl '((d . 2)))
- (put '!#!o!m!e!g!a!d '!=way '(
- (nil nil (dconnec!>) !#!T !#!S!D !#!V!O!L (!*torsion !#!K!D))
- ((By Conjugation) nil
- (conj3!> '!#!o!m!e!g!a!d !#!o!m!e!g!a!u) !#!o!m!e!g!a!u)
- ((From Frame Connection) nil
- (odfromo!> '!#!o!m!e!g!a!d !#!o!m!e!g!a) !#!o!m!e!g!a )
- ))
- (put '!#!o!m!e!g!a!d '!=tex "\omega")
- (put '!#!o!m!e!g!a!d '!=constr '((sp!-n!>)))
- (flag '(!#!o!m!e!g!a!d) '!+dconn)
- (put '!#!r!o!m!e!g!a!u '!=type 1)
- (put '!#!r!o!m!e!g!a!u '!=idxl '((u . 2)))
- (put '!#!r!o!m!e!g!a!u '!=way '(
- (nil nil (ruconnec!>) !#!T !#!S!U !#!V!O!L) ))
- (put '!#!r!o!m!e!g!a!u '!=constr '((tttqorn!>) (sp!>)))
- (flag '(!#!r!o!m!e!g!a!u) '!+uconn)
- (put '!#!r!o!m!e!g!a!d '!=type 1)
- (put '!#!r!o!m!e!g!a!d '!=idxl '((d . 2)))
- (put '!#!r!o!m!e!g!a!d '!=way '(
- (nil nil (rdconnec!>) !#!T !#!S!D !#!V!O!L) ))
- (put '!#!r!o!m!e!g!a!d '!=constr '((tttqorn!>) (sp!>)))
- (flag '(!#!r!o!m!e!g!a!d) '!+dconn)
- % Torsion ...
- (put '!#!T!H!E!T!A '!=type 2)
- (put '!#!T!H!E!T!A '!=idxl '(t))
- (put '!#!T!H!E!T!A '!=constr '((tttq!>)))
- (put '!#!T!H!E!T!A '!=way '(
- ((From Connection Defect) (tttqandn!>) (qfromk!> '!#!K) !#!T !#!K )
- ((From Contorsion) (tttq!>) (qfromk!> '!#!K!Q) !#!T !#!K!Q )
- ))
- (put '!#!T!H!E!T!A '!=tex '("\Theta" . 81))
- (put '!#!Q!Q '!=type 1)
- (put '!#!Q!Q '!=way '((nil nil (qqq!>) !#!T!H!E!T!A !#!D )))
- (put '!#!Q!Q '!=constr '((tttq!>)))
- (put '!#!Q!Q!A '!=type 1)
- (put '!#!Q!Q!A '!=way '((nil nil (qqqa!>) !#!T!H!E!T!A !#!T )))
- (put '!#!Q!Q!A '!=constr '((dg2!>)(tttq!>)))
- (put '!#!K!Q '!=type 1)
- (put '!#!K!Q '!=idxl '(t nil))
- (put '!#!K!Q '!=way '(
- ((From Torsion) nil (contor!>) !#!T !#!D !#!G !#!G!I !#!T!H!E!T!A )
- ((From Spinorial Contorsion) (sp!>)
- (ofromos!> '!#!K!Q !#!K!U !#!K!D) (t !#!K!U) (t !#!K!D) )
- ))
- (put '!#!K!Q '!=constr '((tttq!>)))
- (put '!#!K!U '!=type 1)
- (put '!#!K!U '!=idxl '((u . 2)))
- (put '!#!K!U '!=way '(
- ((From Contorsion) (sp!>) (oufromo!> '!#!K!U !#!K!Q) !#!K!Q)
- ((By Conjugation) nil (conj3!> '!#!K!U !#!K!D) (t !#!K!D))
- ))
- (put '!#!K!U '!=constr '((tttq!>)(sp!>)))
- (put '!#!K!D '!=type 1)
- (put '!#!K!D '!=idxl '((d . 2)))
- (put '!#!K!D '!=way '(
- ((From Contorsion) (sp!>) (odfromo!> '!#!K!D !#!K!Q) !#!K!Q)
- ((By Conjugation) nil (conj3!> '!#!K!D !#!K!U) (t !#!K!U))
- ))
- (put '!#!K!D '!=constr '((tttq!>)(sp!>)))
- (put '!#!Q!T '!=type 0)
- (put '!#!Q!T '!=idxl '(t))
- (put '!#!Q!T '!=way '(
- ((From Torsion using Spinors) (sp!>) (qtfromthsp!>)
- !#!T!H!E!T!A !#!S!U !#!S!D !#!V!O!L )
- ((From Torsion Trace 1 - form) nil (qtfromqq!>)
- !#!Q!Q !#!D !#!G!I )
- ))
- (put '!#!Q!T '!=constr '((tttq!>)))
- (put '!#!Q!P '!=type 0)
- (put '!#!Q!P '!=idxl '(t))
- (put '!#!Q!P '!=way '(
- ((From Torsion using Spinors) (sp!>) (qpfromthsp!>)
- !#!T!H!E!T!A !#!S!U !#!S!D !#!V!O!L )
- ((From Antisymmetric Torsion 3 - form) (ttt4!>) (qpfromqqa!>)
- !#!Q!Q!A !#!D !#!G!I !#!T !#!G )
- ))
- (put '!#!Q!P '!=constr '((tttq!>)(ttt4!>)))
- (put '!#!Q!C '!=type 0)
- (put '!#!Q!C '!=idxl '((u . 3)(d . 1)))
- (put '!#!Q!C '!=way '(
- ((From Torsion) (sp!>) (qcfromth!>) !#!T!H!E!T!A !#!S!U !#!V!O!L) ))
- (put '!#!Q!C '!=constr '((tttq!>)(sp!>)))
- (put '!#!T!H!Q!C '!=type 2)
- (put '!#!T!H!Q!C '!=idxl '(t))
- (put '!#!T!H!Q!C '!=way '(
- (nil nil (qcfcomp!>) !#!T!H!E!T!A !#!T!H!Q!T !#!T!H!Q!A )))
- (put '!#!T!H!Q!C '!=constr '((tttq!>)(dg2!>)))
- (put '!#!T!H!Q!T '!=type 2)
- (put '!#!T!H!Q!T '!=idxl '(t))
- (put '!#!T!H!Q!T '!=way '(
- (nil nil (qtfcomp!>) !#!Q!Q !#!T )))
- (put '!#!T!H!Q!T '!=constr '((tttq!>)))
- (put '!#!T!H!Q!A '!=type 2)
- (put '!#!T!H!Q!A '!=idxl '(t))
- (put '!#!T!H!Q!A '!=way '(
- (nil nil (qafcomp!>) !#!Q!Q!A !#!D !#!G!I )))
- (put '!#!T!H!Q!A '!=constr '((tttq!>)(dg2!>)))
- (put '!#!T!H!Q!C!U '!=type 2)
- (put '!#!T!H!Q!C!U '!=idxl '(t))
- (put '!#!T!H!Q!C!U '!=way '(
- (nil (sp!>) (trfr!> '!#!T!H!Q!C!U 'gcf!> '!#!S!U) !#!S!U !#!Q!C ) ))
- (put '!#!T!H!Q!C!U '!=constr '((sp!>)(tttq!>)))
- (put '!#!T!H!Q!T!U '!=type 2)
- (put '!#!T!H!Q!T!U '!=idxl '(t))
- (put '!#!T!H!Q!T!U '!=way '(
- (nil (sp!>) (trfr!> '!#!T!H!Q!T!U 'gqf!> '!#!S!U) !#!S!U !#!Q!T ) ))
- (put '!#!T!H!Q!T!U '!=constr '((sp!>)(tttq!>)))
- (put '!#!T!H!Q!A!U '!=type 2)
- (put '!#!T!H!Q!A!U '!=idxl '(t))
- (put '!#!T!H!Q!A!U '!=way '(
- (nil (sp!>) (trfr!> '!#!T!H!Q!A!U 'gpf!> '!#!S!U) !#!S!U !#!Q!P ) ))
- (put '!#!T!H!Q!A!U '!=constr '((sp!>)(tttq!>)))
- % Nonmetricity ...
- (put '!#!N '!=type 1)
- (put '!#!N '!=idxl '(nil nil))
- (put '!#!N '!=sidxl '((s 1 2)))
- (put '!#!N '!=way '(
- ((From Connection Defect) (tttqandn!>) (nfromk!> '!#!K) !#!G !#!K )
- ((From Nonmetricity Defect) (tttn!>) (nfromk!> '!#!K!N) !#!G !#!K!N )
- ))
- (put '!#!N '!=constr '((tttn!>)))
- (put '!#!K!N '!=type 1)
- (put '!#!K!N '!=idxl '(t nil))
- (put '!#!K!N '!=way '(
- ((From Nonmetricity) nil (nondef!>) !#!T !#!D !#!G !#!G!I !#!N )
- ))
- (put '!#!K!N '!=constr '((tttn!>)))
- (put '!#!K '!=type 1)
- (put '!#!K '!=idxl '(t nil))
- (put '!#!K '!=way '(
- (nil nil (conndef!>) !#!T !#!D !#!G !#!G!I !#!T!H!E!T!A !#!N )
- ))
- (put '!#!K '!=constr '((tttqandn!>)))
- (put '!#!N!N!W '!=type 1)
- (put '!#!N!N!W '!=way '( (nil nil (compnnw!>) !#!N !#!G!I )) )
- (put '!#!N!N!W '!=constr '((tttn!>)))
- (put '!#!N!N!T '!=type 1)
- (put '!#!N!N!T '!=way '(
- (nil nil (compnnt!>) !#!N !#!G!I !#!D !#!T !#!N!N!W )) )
- (put '!#!N!N!T '!=constr '((tttn!>)))
- (put '!#!N!W '!=type 1)
- (put '!#!N!W '!=idxl '(nil nil))
- (put '!#!N!W '!=sidxl '((s 1 2)))
- (put '!#!N!W '!=way '(
- (nil nil (compnw!>) !#!G !#!N!N!W )) )
- (put '!#!N!W '!=constr '((tttn!>)))
- (put '!#!N!T '!=type 1)
- (put '!#!N!T '!=idxl '(nil nil))
- (put '!#!N!T '!=sidxl '((s 1 2)))
- (put '!#!N!T '!=way '(
- (nil nil (compnt!>) !#!G !#!T !#!N!N!T )) )
- (put '!#!N!T '!=constr '((tttn!>)))
- (put '!#!N!A '!=type 1)
- (put '!#!N!A '!=idxl '(nil nil))
- (put '!#!N!A '!=sidxl '((s 1 2)))
- (put '!#!N!A '!=way '(
- (nil nil (compna!>) !#!D !#!T !#!N !#!N!W !#!N!T )))
- (put '!#!N!A '!=constr '((tttn!>)(dg2!>)))
- (put '!#!N!C '!=type 1)
- (put '!#!N!C '!=idxl '(nil nil))
- (put '!#!N!C '!=sidxl '((s 1 2)))
- (put '!#!N!C '!=way '(
- (nil nil (compnc!>) !#!N ((geq ![dim!] 3) !#!N!A) !#!N!T !#!N!W )))
- (put '!#!N!C '!=constr '((tttn!>)))
- % Curvature ...
- (put '!#!O!M!E!G!A '!=type 2)
- (put '!#!O!M!E!G!A '!=idxl '(t nil))
- (put '!#!O!M!E!G!A '!=way '(
- (nil nil (curvature!>) !#!o!m!e!g!a )
- ((From Spinorial Curvature) (sp!-n!>)
- (ofromos!> '!#!O!M!E!G!A !#!O!M!E!G!A!U !#!O!M!E!G!A!D)
- (t !#!O!M!E!G!A!U) !#!O!M!E!G!A!D )
- ))
- (put '!#!O!M!E!G!A '!=tex '("\Omega" . 87))
- (put '!#!O!M!E!G!A!U '!=type 2)
- (put '!#!O!M!E!G!A!U '!=idxl '((u . 2)))
- (put '!#!O!M!E!G!A!U '!=way '(
- (nil nil (scurvature!> '!#!O!M!E!G!A!U !#!o!m!e!g!a!u)
- !#!o!m!e!g!a!u )
- ((By Conjugation) nil
- (conj3!> '!#!O!M!E!G!A!U !#!O!M!E!G!A!D) !#!O!M!E!G!A!D)
- ((From Curvature) nil
- (oufromo!> '!#!O!M!E!G!A!U !#!O!M!E!G!A) !#!O!M!E!G!A )
- ))
- (put '!#!O!M!E!G!A!U '!=constr '((sp!-n!>)))
- (put '!#!O!M!E!G!A!U '!=tex '("\Omega" . 87))
- (put '!#!O!M!E!G!A!D '!=type 2)
- (put '!#!O!M!E!G!A!D '!=idxl '((d . 2)))
- (put '!#!O!M!E!G!A!D '!=way '(
- (nil nil (scurvature!> '!#!O!M!E!G!A!D !#!o!m!e!g!a!d)
- !#!o!m!e!g!a!d )
- ((By Conjugation) nil
- (conj3!> '!#!O!M!E!G!A!D !#!O!M!E!G!A!U) !#!O!M!E!G!A!U)
- ((From Curvature) nil
- (odfromo!> '!#!O!M!E!G!A!D !#!O!M!E!G!A) !#!O!M!E!G!A )
- ))
- (put '!#!O!M!E!G!A!D '!=constr '((sp!-n!>)))
- (put '!#!O!M!E!G!A!D '!=tex '("\Omega" . 87))
- (put '!#!R!I!M '!=type 0)
- (put '!#!R!I!M '!=idxl '(t nil nil nil))
- (put '!#!R!I!M '!=sidxl '((a 3 4)))
- (put '!#!R!I!M '!=way '(
- (nil nil (riemm!>) !#!D !#!O!M!E!G!A ) ))
- (put '!#!R!I!M '!=tex '!R)
- (put '!#!R!I!C '!=type 0)
- (put '!#!R!I!C '!=idxl '( nil nil))
- (put '!#!R!I!C '!=sidxl '((s 1 2)))
- (put '!#!R!I!C '!=way '(
- ((From Curvature) nil (riccio!>) !#!D !#!G !#!G!I !#!O!M!E!G!A )
- ((From Riemann Tensor) nil (ricci!>) !#!R!I!M ) ))
- (put '!#!R!I!C '!=tex '!R)
- (put '!#!R!I!C!A '!=type 0)
- (put '!#!R!I!C!A '!=idxl '( nil nil))
- (put '!#!R!I!C!A '!=way '(
- ((From Curvature) nil (riccioa!>) !#!D !#!G !#!G!I !#!O!M!E!G!A )))
- (put '!#!R!I!C!A '!=constr '((tttn!>)))
- (put '!#!R!R '!=type 0)
- (put '!#!R!R '!=way '(
- ((From A - Ricci Tensor) (tttn!>) (rscalara!>) !#!G!I (t !#!R!I!C!A) )
- ((From Ricci Tensor) nil (rscalar!>) !#!G!I !#!R!I!C )
- ((From Spinor Curvature) (sp!-n!>)
- (rrsp!>) (t !#!O!M!E!G!A!U) !#!S!U !#!V!O!L )
- ))
- (put '!#!R!R '!=tex '!R)
- (put '!#!G!T '!=type 0)
- (put '!#!G!T '!=idxl '( nil nil))
- (put '!#!G!T '!=sidxl '((s 1 2)))
- (put '!#!G!T '!=way '(
- (nil nil (gtensor!>) !#!G !#!R!R !#!R!I!C ) ))
- (put '!#!R!W '!=type 0)
- (put '!#!R!W '!=idxl '((u . 4)))
- (put '!#!R!W '!=way '(
- ((From Spinor Curvature) nil (rwsp!>) !#!O!M!E!G!A!U !#!S!U !#!V!O!L)))
- (put '!#!R!W '!=tex '!C)
- (put '!#!R!W '!=constr '((sp!-n!>)))
- (put '!#!R!C '!=type 0)
- (put '!#!R!C '!=idxl '((u . 2)(d . 2)))
- (put '!#!R!C '!=sidxl '((h 1 2)))
- (put '!#!R!C '!=way '(
- ((From Spinor Curvature) nil (rcsp!>)
- !#!O!M!E!G!A!U !#!S!D !#!V!O!L
- (!*torsion !#!O!M!E!G!A!D !#!S!U))))
- (put '!#!R!C '!=tex '!C)
- (put '!#!R!C '!=constr '((sp!-n!>)))
- (put '!#!R!A '!=type 0)
- (put '!#!R!A '!=idxl '((u . 2)))
- (put '!#!R!A '!=way '(
- ((From Spinor Curvature) nil (rasp!>) !#!O!M!E!G!A!U !#!S!U !#!V!O!L)))
- (put '!#!R!A '!=tex '!A)
- (put '!#!R!A '!=constr '((tttq!>)(sp!-n!>)))
- (put '!#!R!B '!=type 0)
- (put '!#!R!B '!=idxl '((u . 2)(d . 2)))
- (put '!#!R!B '!=sidxl '((h 1 2)))
- (put '!#!R!B '!=way '(
- ((From Spinor Curvature) nil
- (rbsp!>) !#!O!M!E!G!A!U !#!O!M!E!G!A!D !#!S!U !#!S!D !#!V!O!L)))
- (put '!#!R!B '!=tex '!B)
- (put '!#!R!B '!=constr '((tttq!>)(sp!-n!>)))
- (put '!#!R!D '!=type 0)
- (put '!#!R!D '!=way '(
- ((From Spinor Curvature) (sp!-n!>)
- (rdsp!>) !#!O!M!E!G!A!U !#!S!U !#!V!O!L)))
- (put '!#!R!D '!=tex '!D)
- (put '!#!R!D '!=constr '((tttq!>)(ttt4!>)))
- (put '!#!O!M!W!U '!=type 2)
- (put '!#!O!M!W!U '!=idxl '((u . 2)))
- (put '!#!O!M!W!U '!=way '(
- (nil nil (crfr!> '!#!O!M!W!U 'gwf!> '!#!S!U) !#!S!U !#!R!W ) ))
- (put '!#!O!M!W!U '!=constr '((sp!-n!>)))
- (put '!#!O!M!C!U '!=type 2)
- (put '!#!O!M!C!U '!=idxl '((u . 2)))
- (put '!#!O!M!C!U '!=way '(
- (nil nil (crfr!> '!#!O!M!C!U 'gtf!> '!#!S!D) !#!S!D !#!R!C ) ))
- (put '!#!O!M!C!U '!=constr '((sp!-n!>)))
- (put '!#!O!M!R!U '!=type 2)
- (put '!#!O!M!R!U '!=idxl '((u . 2)))
- (put '!#!O!M!R!U '!=way '(
- (nil nil (crfr!> '!#!O!M!R!U 'gsf!> '!#!S!U) !#!S!U !#!R!R ) ))
- (put '!#!O!M!R!U '!=constr '((sp!-n!>)))
- (put '!#!O!M!A!U '!=type 2)
- (put '!#!O!M!A!U '!=idxl '((u . 2)))
- (put '!#!O!M!A!U '!=way '(
- (nil nil (crfr!> '!#!O!M!A!U 'gaf!> '!#!S!U) !#!S!U !#!R!A ) ))
- (put '!#!O!M!A!U '!=constr '((sp!-n!>)(tttqnotn!>)))
- (put '!#!O!M!B!U '!=type 2)
- (put '!#!O!M!B!U '!=idxl '((u . 2)))
- (put '!#!O!M!B!U '!=way '(
- (nil nil (crfr!> '!#!O!M!B!U 'gbf!> '!#!S!D) !#!S!D !#!R!B ) ))
- (put '!#!O!M!B!U '!=constr '((sp!-n!>)(tttqnotn!>)))
- (put '!#!O!M!D!U '!=type 2)
- (put '!#!O!M!D!U '!=idxl '((u . 2)))
- (put '!#!O!M!D!U '!=way '(
- (nil nil (crfr!> '!#!O!M!D!U 'gdf!> '!#!S!U) !#!S!U !#!R!D ) ))
- (put '!#!O!M!D!U '!=constr '((sp!-n!>)(tttqnotn!>)))
- (put '!#!O!M!W '!=type 2)
- (put '!#!O!M!W '!=idxl '(nil nil))
- (put '!#!O!M!W '!=sidxl '((a 1 2)))
- (put '!#!O!M!W '!=way '(
- (nil nil (mkrwf!>) !#!G !#!O!M!E!G!A !#!O!M!C !#!O!M!R
- ((or !*torsion !*nonmetr) !#!O!M!A !#!O!M!B !#!O!M!D )
- )))
- (put '!#!O!M!W '!=constr '((dg3!>)))
- (put '!#!O!M!C '!=type 2)
- (put '!#!O!M!C '!=idxl '(nil nil))
- (put '!#!O!M!C '!=sidxl '((a 1 2)))
- (put '!#!O!M!C '!=way '(
- (nil nil (mkrcf!>) !#!G !#!T (!*nonmetr !#!R!I!C!A)
- ((not !*nonmetr) !#!R!I!C) !#!R!R )))
- (put '!#!O!M!C '!=constr '((dg2!>)))
- (put '!#!O!M!R '!=type 2)
- (put '!#!O!M!R '!=idxl '(nil nil))
- (put '!#!O!M!R '!=sidxl '((a 1 2)))
- (put '!#!O!M!R '!=way '(
- (nil nil (mkrrf!>) !#!G !#!S !#!R!R )))
- (put '!#!O!M!R '!=sidxl '((a 1 2)))
- (put '!#!O!M!A '!=type 2)
- (put '!#!O!M!A '!=idxl '(nil nil))
- (put '!#!O!M!A '!=sidxl '((a 1 2)))
- (put '!#!O!M!A '!=way '(
- (nil nil (mkraf!>) !#!G !#!T (!*nonmetr !#!R!I!C!A)
- ((not !*nonmetr) !#!R!I!C) )))
- (put '!#!O!M!A '!=constr '((tttqorn!>)(dg2!>)))
- (put '!#!O!M!B '!=type 2)
- (put '!#!O!M!B '!=idxl '(nil nil))
- (put '!#!O!M!B '!=sidxl '((a 1 2)))
- (put '!#!O!M!B '!=way '(
- (nil nil (mkrbf!>) !#!G !#!T !#!D !#!O!M!E!G!A
- !#!O!M!R !#!O!M!C !#!O!M!A !#!O!M!D )))
- (put '!#!O!M!B '!=constr '((tttqorn!>)(dg3!>)))
- (put '!#!O!M!D '!=type 2)
- (put '!#!O!M!D '!=idxl '(nil nil))
- (put '!#!O!M!D '!=sidxl '((a 1 2)))
- (put '!#!O!M!D '!=way '(
- (nil nil (mkrdf!>) !#!G !#!D !#!S !#!T !#!O!M!E!G!A )))
- (put '!#!O!M!D '!=constr '((tttqorn!>)(dg3!>)))
- (put '!#!R!I!C!S '!=type 0)
- (put '!#!R!I!C!S '!=idxl '(nil nil))
- (put '!#!R!I!C!S '!=way '(
- ((From Curvature) nil (riccios!>) !#!D !#!G !#!G!I !#!O!M!E!G!A )))
- (put '!#!R!I!C!S '!=constr '((tttn!>)))
- (put '!#!O!M!E!G!A!H '!=type 2)
- (put '!#!O!M!E!G!A!H '!=way '(
- (nil nil (mkomegah!>) !#!O!M!E!G!A )))
- (put '!#!O!M!E!G!A!H '!=constr '((tttn!>)))
- (put '!#!O!S!H '!=type 2)
- (put '!#!O!S!H '!=idxl '(nil nil))
- (put '!#!O!S!H '!=sidxl '((s 1 2)))
- (put '!#!O!S!H '!=way '(
- (nil (deq2!>) (mkrshf2!>) !#!G !#!T !#!O!M!E!G!A #!O!S!C )
- (nil (dg2!>) (mkrshf!>) !#!G !#!O!M!E!G!A!H )
- % (nil (dg2!>) (mkrshf!>) !#!G !#!T !#!O!M!E!G!A!H )
- ))
- (put '!#!O!S!H '!=constr '((tttn!>)))
- (put '!#!O!S!A '!=type 2)
- (put '!#!O!S!A '!=idxl '(nil nil))
- (put '!#!O!S!A '!=sidxl '((s 1 2)))
- (put '!#!O!S!A '!=way '(
- (nil nil (mkrsaf!>) !#!G !#!T !#!S !#!D !#!R!I!C!S !#!O!M!E!G!A!H )
- % (nil nil (mkrsaf!>) !#!G !#!T !#!S !#!R!I!C!S )
- ))
- (put '!#!O!S!A '!=constr '((tttn!>)(dg2!>)))
- (put '!#!O!S!C '!=type 2)
- (put '!#!O!S!C '!=idxl '(nil nil))
- (put '!#!O!S!C '!=sidxl '((s 1 2)))
- (put '!#!O!S!C '!=way '(
- (nil nil (mkrscf!>) !#!G !#!T !#!S !#!R!I!C!S )))
- (put '!#!O!S!C '!=constr '((tttn!>)))
- (put '!#!O!S!V '!=type 2)
- (put '!#!O!S!V '!=idxl '(nil nil))
- (put '!#!O!S!V '!=sidxl '((s 1 2)))
- (put '!#!O!S!V '!=way '(
- (nil nil (mkrsvf!>) !#!T !#!D !#!G !#!O!S!H !#!O!S!A !#!O!S!C )))
- (put '!#!O!S!V '!=constr '((tttn!>)(dg3!>)))
- (put '!#!O!S!U '!=type 2)
- (put '!#!O!S!U '!=idxl '(nil nil))
- (put '!#!O!S!U '!=sidxl '((s 1 2)))
- (put '!#!O!S!U '!=way '(
- (nil nil (mkrsuf!>) !#!G !#!O!M!E!G!A
- ((geq ![dim!] 4) !#!O!S!V )
- !#!O!S!H !#!O!S!A !#!O!S!C )))
- (put '!#!O!S!U '!=constr '((tttn!>)(dg2!>)))
- % Dirac field ...
- (put '!#!P!H!I '!=type 0)
- (put '!#!P!H!I '!=idxl '((u . 1)))
- (put '!#!C!H!I '!=type 0)
- (put '!#!C!H!I '!=idxl '((u . 1)))
- (put '!#!P!H!I '!=tex "\phi")
- (put '!#!C!H!I '!=tex "\chi")
- (put '!#!P!H!I '!=constr '((sp!-n!>)))
- (put '!#!C!H!I '!=constr '((sp!-n!>)))
- (put '!#!D!A!C!T '!=type 4)
- (put '!#!D!A!C!T '!=way '(
- (nil (sp!-n!>) (dact!>)
- !#!P!H!I !#!C!H!I !#!D !#!T !#!o!m!e!g!a!u !#!G
- !#!V!O!L !#!s!d!e!t!G !#!G!I (!*torsion !#!Q!Q)) ))
- (put '!#!D!A!C!T '!=dens '(t nil t nil))
- (put '!#!T!D!I '!=type 0)
- (put '!#!T!D!I '!=idxl '(nil nil))
- (put '!#!T!D!I '!=sidxl '((s 1 2)))
- (put '!#!T!D!I '!=way '(
- (nil (sp!-n!>) (tdi!>)
- !#!T !#!D !#!G !#!G!I !#!s!d!e!t!G !#!V!O!L
- !#!D!A!C!T !#!P!H!I !#!C!H!I !#!o!m!e!g!a!u ) ))
- (put '!#!T!D!I '!=constr '((tttnotn!>)))
- (put '!#!S!P!D!I!U '!=type 3)
- (put '!#!S!P!D!I!U '!=idxl '((u . 2)))
- (put '!#!S!P!D!I!U '!=way '(
- (nil nil (spinsd!>)
- !#!C!H!I !#!P!H!I !#!T !#!s!d!e!t!G !#!G !#!V!O!L ) ))
- (put '!#!S!P!D!I!U '!=constr '((sp!-n!>)))
- (put '!#!D!P!q '!=type 0)
- (put '!#!D!P!q '!=idxl '((d . 1)))
- (put '!#!D!P!q '!=way '(
- (nil nil (dequ!> !#!P!H!I !#!C!H!I '!#!D!P!q t)
- !#!P!H!I !#!C!H!I !#!D !#!o!m!e!g!a!u (!*torsion !#!Q!Q)) ))
- (put '!#!D!P!q '!=constr '((sp!-n!>)))
- (put '!#!D!C!q '!=type 0)
- (put '!#!D!C!q '!=idxl '((d . 1)))
- (put '!#!D!C!q '!=way '(
- (nil nil (dequ!> !#!C!H!I !#!P!H!I '!#!D!C!q nil)
- !#!P!H!I !#!C!H!I !#!D !#!o!m!e!g!a!u (!*torsion !#!Q!Q)) ))
- (put '!#!D!C!q '!=constr '((sp!-n!>)))
- % EM field ...
- (put '!#!A '!=type 1)
- (put '!#!A '!=constr '((dg2!>)))
- (put '!#!F!F '!=type 2)
- (put '!#!F!F '!=way '(
- ((From EM Potential) nil (fffroma!>) !#!A)
- ((From EM Tensor) nil (fffromft!>) !#!S (t !#!F!T))
- ((From Complex EM 2 - form) (sp!>) (fffromffu!>) (t !#!F!F!U))
- ))
- (put '!#!F!F '!=constr '((dg2!>)))
- (put '!#!J '!=type 1)
- (put '!#!J '!=way '(
- ((From Dirac Spinor) (sp!>) (dcurr!>) !#!P!H!I !#!C!H!I !#!T ) ))
- (put '!#!J '!=constr '((dg2!>)))
- (put '!#!F!T '!=type 0)
- (put '!#!F!T '!=idxl '(nil nil))
- (put '!#!F!T '!=sidxl '((a 1 2)))
- (put '!#!F!T '!=way '(
- (nil nil (ftfromff!>) !#!D !#!F!F) ))
- (put '!#!F!T '!=constr '((dg2!>)))
- (put '!#!E!M!A!C!T '!=type '![dim!])
- (put '!#!E!M!A!C!T '!=way '(
- (nil nil (emact!>) !#!F!F !#!V!O!L !#!s!d!e!t!G !#!T !#!G )
- ))
- (put '!#!E!M!A!C!T '!=constr '((dg2!>)))
- (put '!#!E!M!A!C!T '!=dens '(t nil t nil))
- (put '!#!T!E!M '!=type 0)
- (put '!#!T!E!M '!=idxl '(nil nil))
- (put '!#!T!E!M '!=sidxl '((s 1 2)))
- (put '!#!T!E!M '!=way '(
- (nil nil (tembydef!>)
- !#!G!I !#!G !#!V!O!L !#!F!T !#!E!M!A!C!T )
- ))
- (put '!#!T!E!M '!=constr '((dg2!>)))
- (put '!#!M!W!F!q '!=type '![dim1!])
- (put '!#!M!W!F!q '!=way '(
- (nil nil (firstmw!>) !#!T !#!G !#!s!d!e!t!G !#!V!O!L !#!F!F ) ))
- (put '!#!M!W!F!q '!=constr '((dg2!>)))
- (put '!#!M!W!S!q '!=type 3)
- (put '!#!M!W!S!q '!=way '(
- (nil nil (secondmw!>) !#!F!F )))
- (put '!#!M!W!S!q '!=constr '((dg2!>)))
- (put '!#!C!O!q '!=type '![dim!])
- (put '!#!C!O!q '!=way '(
- (nil nil (contineq!>) !#!T !#!G !#!s!d!e!t!G !#!V!O!L !#!J ) ))
- (put '!#!C!O!q '!=constr '((dg2!>)))
- (put '!#!S!C!F '!=type 0)
- (put '!#!S!C!F '!=way '(
- (nil (ttt4!>) (firstscal!>)
- !#!T !#!G !#!s!d!e!t!G !#!V!O!L !#!F!F ) ))
- (put '!#!S!C!F '!=constr '((ttt4!>)))
- (put '!#!S!C!S '!=type 0)
- (put '!#!S!C!S '!=way '(
- (nil (ttt4!>) (secondscal!>)
- !#!T !#!G !#!s!d!e!t!G !#!V!O!L !#!F!F ) ))
- (put '!#!S!C!F '!=constr '((ttt4!>)))
- (put '!#!F!I!U '!=type 0)
- (put '!#!F!I!U '!=idxl '((u . 2)))
- (put '!#!F!I!U '!=way '(
- ((From Complex EM 2 - form) nil (fiufromffu!>) !#!S!U !#!V!O!L !#!F!F!U )
- ((From EM 2 - form) nil (fiufromff!>) !#!S!U !#!V!O!L !#!F!F )
- ))
- (put '!#!F!I!U '!=constr '((sp!>)))
- (put '!#!F!I!U '!=tex '("\Phi" . 70))
- (put '!#!S!D!q '!=type 4)
- (put '!#!S!D!q '!=idxl '((d . 2)))
- (put '!#!S!D!q '!=way '(
- (nil nil (sduality!>) !#!S!D !#!F!F!U )
- ))
- (put '!#!S!D!q '!=constr '((sp!>)))
- (put '!#!F!F!U '!=type 2)
- (put '!#!F!F!U '!=way '(
- ((From EM 2 - form) nil (ffufromff!>)
- !#!V!O!L !#!T !#!G !#!s!d!e!t!G !#!F!F )
- ((From EM Spinor) (sp!>) (ffufromfiu!>)
- !#!S!U !#!F!I!U )
- ))
- (put '!#!F!F!U '!=constr '((sp!>)))
- (put '!#!F!F!U '!=tex '("\Phi" . 70))
- (put '!#!S!C!U '!=type 0)
- (put '!#!S!C!U '!=way '(
- ((From EM Spinor) nil (scufromfiu!>) !#!F!I!U )
- ((From Complex EM 2 - form) nil (scufromffu!>) !#!V!O!L !#!F!F!U )
- ))
- (put '!#!S!C!U '!=constr '((sp!>)))
- (put '!#!M!W!U!q '!=type 3)
- (put '!#!M!W!U!q '!=way '(
- (nil nil (complexmw!>)
- !#!T !#!G !#!s!d!e!t!G !#!V!O!L !#!F!F!U ) ))
- (put '!#!M!W!U!q '!=constr '((sp!>)))
- (put '!#!T!E!M!S '!=type 0)
- (put '!#!T!E!M!S '!=idxl '((u . 2)(d . 2)))
- (put '!#!T!E!M!S '!=sidxl '((h 1 2)))
- (put '!#!T!E!M!S '!=way '(
- (nil nil (tems!>) !#!F!I!U )))
- (put '!#!T!E!M!S '!=constr '((sp!>)))
- % YM field ...
- (put '!#!A!Y!M '!=type 1)
- (put '!#!A!Y!M '!=idxl '((n . 9)))
- (put '!#!A!Y!M '!=constr '((dg2!>)))
- (put '!#!S!C!O!N!S!T '!=type 0)
- (put '!#!S!C!O!N!S!T '!=idxl '((n . 9)(n . 9)(n . 9)))
- (put '!#!S!C!O!N!S!T '!=sidxl '((a 1 2 3)))
- (put '!#!S!C!O!N!S!T '!=constr '((dg2!>)))
- (put '!#!F!F!Y!M '!=type 2)
- (put '!#!F!F!Y!M '!=idxl '((n . 9)))
- (put '!#!F!F!Y!M '!=way '(
- ((From YM Potential) nil (ffymfromaym!>) !#!A!Y!M !#!S!C!O!N!S!T )
- ((From YM Tensor) nil (ffymfromftym!>) !#!S (t !#!F!T!Y!M))
- ))
- (put '!#!F!F!Y!M '!=constr '((dg2!>)))
- (put '!#!F!T!Y!M '!=type 0)
- (put '!#!F!T!Y!M '!=idxl '((n . 9) nil nil))
- (put '!#!F!T!Y!M '!=sidxl '((a 2 3)))
- (put '!#!F!T!Y!M '!=way '(
- (nil nil (ftymfromffym!>) !#!D !#!F!F!Y!M) ))
- (put '!#!F!T!Y!M '!=constr '((dg2!>)))
- (put '!#!Y!M!A!C!T '!=type '![dim!])
- (put '!#!Y!M!A!C!T '!=way '(
- (nil nil (ymact!>) !#!F!F!Y!M !#!V!O!L !#!s!d!e!t!G !#!T !#!G )
- ))
- (put '!#!Y!M!A!C!T '!=constr '((dg2!>)))
- (put '!#!Y!M!A!C!T '!=dens '(t nil t nil))
- (put '!#!T!Y!M '!=type 0)
- (put '!#!T!Y!M '!=idxl '(nil nil))
- (put '!#!T!Y!M '!=sidxl '((s 1 2)))
- (put '!#!T!Y!M '!=way '(
- (nil nil (tymbydef!>)
- !#!G!I !#!G !#!V!O!L !#!F!T!Y!M !#!Y!M!A!C!T )
- ))
- (put '!#!T!Y!M '!=constr '((dg2!>)))
- (put '!#!Y!M!F!q '!=type '![dim1!])
- (put '!#!Y!M!F!q '!=idxl '((n . 9)))
- (put '!#!Y!M!F!q '!=way '(
- (nil nil (firstym!>)
- !#!T !#!G !#!s!d!e!t!G !#!V!O!L !#!F!F!Y!M !#!S!C!O!N!S!T ) ))
- (put '!#!Y!M!F!q '!=constr '((dg2!>)))
- (put '!#!Y!M!S!q '!=type 3)
- (put '!#!Y!M!S!q '!=idxl '((n . 9)))
- (put '!#!Y!M!S!q '!=way '(
- (nil nil (secondym!>) !#!F!F!Y!M !#!S!C!O!N!S!T ) ))
- (put '!#!Y!M!S!q '!=constr '((dg2!>)))
- % Scalar field ...
- (put '!#!F!I '!=type 0)
- (put '!#!S!A!C!T!M!I!N '!=type '![dim!])
- (put '!#!S!A!C!T!M!I!N '!=way '(
- (nil nil (sactmin!>) !#!F!I !#!V!O!L !#!G!I !#!D )))
- (put '!#!S!A!C!T!M!I!N '!=dens '(t nil t nil))
- (put '!#!S!A!C!T '!=type '![dim!])
- (put '!#!S!A!C!T '!=way '(
- (nil nil (sact!>) !#!F!I !#!V!O!L !#!G!I !#!D
- (!*nonmin !#!R!R !#!A!C!O!N!S!T ) )))
- (put '!#!S!A!C!T '!=dens '(t nil t nil))
- (put '!#!S!C!q '!=type 0)
- (put '!#!S!C!q '!=way '(
- (nil nil (kgeq!>) !#!V!O!L !#!s!d!e!t!G !#!D !#!T !#!F!I
- (!*nonmin !#!A!C!O!N!S!T !#!R!R ))))
- (put '!#!T!S!C!L!M!I!N '!=type 0)
- (put '!#!T!S!C!L!M!I!N '!=idxl '(nil nil))
- (put '!#!T!S!C!L!M!I!N '!=sidxl '((s 1 2)))
- (put '!#!T!S!C!L!M!I!N '!=way '(
- (nil nil (tsclmin!>)
- !#!F!I !#!V!O!L !#!G !#!D !#!S!A!C!T!M!I!N )))
- % Constants ...
- (put '!#!A!C!O!N!S!T '!=type 0)
- (put '!#!A!C!O!N!S!T '!=idxl '((n . 2)))
- (put '!#!A!C!O!N!S!T '!=way '((nil nil (aconst!>))))
- (put '!#!M!C!O!N!S!T '!=type 0)
- (put '!#!M!C!O!N!S!T '!=idxl '((n . 3)))
- (put '!#!M!C!O!N!S!T '!=way '((nil nil (mconst!>))))
- (put '!#!L!C!O!N!S!T '!=type 0)
- (put '!#!L!C!O!N!S!T '!=idxl '((n . 6)))
- (put '!#!L!C!O!N!S!T '!=way '((nil nil (lconst!>))))
- % Einstein Equations ...
- (put '!#!E!E!q '!=type 0)
- (put '!#!E!E!q '!=idxl '(nil nil))
- (put '!#!E!E!q '!=sidxl '((s 1 2)))
- (put '!#!E!E!q '!=way '(
- (nil nil (einstein!>) !#!G !#!R!I!C !#!R!R !#!T!E!N!M!O!M )))
- (put '!#!E!E!q '!=constr '((tttnotqn!>)))
- (put '!#!T!E!E!q '!=type 0)
- (put '!#!T!E!E!q '!=way '(
- (nil nil (einsteint!>) !#!R!R !#!T!E!N!M!O!M!T )))
- (put '!#!T!E!E!q '!=constr '((sp!>)(tttnotqn!>)))
- (put '!#!C!E!E!q '!=type 0)
- (put '!#!C!E!E!q '!=idxl '((u . 2)(d . 2)))
- (put '!#!C!E!E!q '!=sidxl '((h 1 2)))
- (put '!#!C!E!E!q '!=way '(
- (nil nil (einsteinc!>) !#!R!C !#!T!E!N!M!O!M!S )))
- (put '!#!C!E!E!q '!=constr '((sp!>)(tttnotqn!>)))
- % Gravitational Equations ...
- (put '!#!P!O!M!E!G!A!U '!=type 2)
- (put '!#!P!O!M!E!G!A!U '!=idxl '((u . 2)))
- (put '!#!P!O!M!E!G!A!U '!=way '(
- (nil nil (pomegau!>) !#!L!C!O!N!S!T !#!S!U
- (!*nonmin !#!A!C!O!N!S!T !#!F!I) )))
- (put '!#!P!O!M!E!G!A!U '!=constr '((sp!-n!>)))
- (put '!#!P!T!H!E!T!A '!=type 2)
- (put '!#!P!T!H!E!T!A '!=idxl '(t))
- (put '!#!P!T!H!E!T!A '!=way '(
- (nil nil (ptheta!>) !#!M!C!O!N!S!T )))
- (put '!#!P!T!H!E!T!A '!=constr '((sp!-n!>)(tttq!>)))
- (put '!#!L!A!C!T '!=type 4)
- (put '!#!L!A!C!T '!=way '(
- (nil (sp!-n!>) (lact!>)
- !#!V!O!L !#!R!R !#!L!C!O!N!S!T
- !#!P!O!M!E!G!A!U !#!O!M!E!G!A!U
- (!*torsion !#!P!T!H!E!T!A !#!T!H!E!T!A)
- (!*nonmin !#!A!C!O!N!S!T !#!F!I) )
- ))
- (put '!#!L!A!C!T '!=constr '((ttt4!>)))
- (put '!#!L!A!C!T '!=dens '(t nil t nil))
- (put '!#!M!E!T!R!q '!=type 0)
- (put '!#!M!E!T!R!q '!=idxl '(nil nil))
- (put '!#!M!E!T!R!q '!=sidxl '((s 1 2)))
- (put '!#!M!E!T!R!q '!=way '(
- (nil nil (metrequation!>)
- !#!D !#!T !#!S!U !#!V!O!L !#!L!A!C!T !#!T!E!N!M!O!M
- !#!o!m!e!g!a!u !#!o!m!e!g!a!d
- !#!O!M!E!G!A!U !#!P!O!M!E!G!A!U
- (!*torsion !#!T!H!E!T!A !#!P!T!H!E!T!A ) )
- ))
- (put '!#!M!E!T!R!q '!=constr '((sp!-n!>)))
- (put '!#!T!O!R!S!q '!=type 3)
- (put '!#!T!O!R!S!q '!=idxl '((u . 2)))
- (put '!#!T!O!R!S!q '!=way '(
- (nil nil (torsequation!>)
- !#!T !#!S!U !#!o!m!e!g!a!u !#!P!O!M!E!G!A!U !#!P!T!H!E!T!A
- !#!S!P!I!N!U )
- ))
- (put '!#!T!O!R!S!q '!=constr '((sp!-n!>)(tttq!>)))
- % Geodesics and congruences ...
- (put '!#!G!E!O!q '!=type 0)
- (put '!#!G!E!O!q '!=idxl '(1))
- (put '!#!G!E!O!q '!=way '(
- (nil (tttapar!>) (geodesics!>) !#!G !#!G!I !#!T !#!D )))
- (put '!#!G!E!O!q '!=constr '((tttapar!>)))
- % Null congruence ...
- (put '!#!K!V '!=type -1)
- (put '!#!N!C!o '!=type 0)
- (put '!#!N!C!o '!=way '(
- (nil nil (ncnq!>) !#!T !#!D !#!G !#!G!I !#!K!V )))
- (put '!#!G!C!o '!=type 0)
- (put '!#!G!C!o '!=idxl '(t))
- (put '!#!G!C!o '!=way '(
- (nil nil (ncgq!>)
- !#!T !#!D !#!G !#!G!I !#!K!V
- ((or !*torsion !*nonmetr) !#!r!o!m!e!g!a)
- ((and (null !*torsion) (null !*nonmetr)) !#!o!m!e!g!a) )
- ))
- (put '!#!t!h!e!t!a!O '!=type 0)
- (put '!#!t!h!e!t!a!O '!=way '(
- (nil nil (nctheta!>)
- !#!T !#!D !#!G !#!G!I !#!K!V !#!N!C!o !#!G!C!o
- ((or !*torsion !*nonmetr) !#!r!o!m!e!g!a)
- ((and (null !*torsion) (null !*nonmetr)) !#!o!m!e!g!a) )
- ))
- (put '!#!t!h!e!t!a!O '!=constr '((ttt4!>)))
- (put '!#!o!m!e!g!a!S!Q!O '!=type 0)
- (put '!#!o!m!e!g!a!S!Q!O '!=way '(
- (nil nil (ncomega!>)
- !#!T !#!D !#!G !#!G!I !#!K!V !#!N!C!o !#!G!C!o
- ((or !*torsion !*nonmetr) !#!r!o!m!e!g!a)
- ((and (null !*torsion) (null !*nonmetr)) !#!o!m!e!g!a) )
- ))
- (put '!#!o!m!e!g!a!S!Q!O '!=constr '((ttt4!>)))
- (put '!#!s!i!g!m!a!S!Q!O '!=type 0)
- (put '!#!s!i!g!m!a!S!Q!O '!=way '(
- (nil nil (ncsigma!>)
- !#!T !#!D !#!G !#!G!I !#!K!V !#!t!h!e!t!a!O
- !#!N!C!o !#!G!C!o
- ((or !*torsion !*nonmetr) !#!r!o!m!e!g!a)
- ((and (null !*torsion) (null !*nonmetr)) !#!o!m!e!g!a) )
- ))
- (put '!#!s!i!g!m!a!S!Q!O '!=constr '((ttt4!>)))
- % Kinematics ...
- (put '!#!U!V '!=type -1)
- (put '!#!U!V '!=way '((nil nil (uvfromuup!>) !#!D !#!U!U )))
- (put '!#!U!U '!=type 0)
- (put '!#!U!U '!=idxl '(t))
- (put '!#!U!U '!=way '(
- ((By Default) (tttdiag!>) (uudefault!>) )
- ((From Velocity Vector) nil (uupfromuv!>) !#!T (t !#!U!V) )
- ))
- (put '!#!U!S!Q '!=type 0)
- (put '!#!U!S!Q '!=way '((nil nil (usquare!>) !#!U!U !#!G )))
- (put '!#!P!R '!=type 0)
- (put '!#!P!R '!=idxl '(t nil))
- (put '!#!P!R '!=way '((nil nil (projector!>) !#!U!U !#!U!S!Q )))
- (put '!#!a!c!c!U '!=type 0)
- (put '!#!a!c!c!U '!=idxl '(t))
- (put '!#!a!c!c!U '!=way '(
- (nil nil (accelerat!>)
- !#!T !#!D !#!G !#!G!I !#!U!U
- ((or !*torsion !*nonmetr) !#!r!o!m!e!g!a)
- ((and (null !*torsion) (null !*nonmetr)) !#!o!m!e!g!a) )
- ))
- (put '!#!o!m!e!g!a!U '!=type 0)
- (put '!#!o!m!e!g!a!U '!=idxl '(nil nil))
- (put '!#!o!m!e!g!a!U '!=sidxl '((a 1 2)))
- (put '!#!o!m!e!g!a!U '!=way '(
- (nil nil (uomega!>)
- !#!T !#!D !#!G !#!G!I !#!U!U !#!P!R
- ((or !*torsion !*nonmetr) !#!r!o!m!e!g!a)
- ((and (null !*torsion) (null !*nonmetr)) !#!o!m!e!g!a) )
- ))
- (put '!#!s!i!g!m!a!U '!=type 0)
- (put '!#!s!i!g!m!a!U '!=idxl '(nil nil))
- (put '!#!s!i!g!m!a!U '!=sidxl '((s 1 2)))
- (put '!#!s!i!g!m!a!U '!=way '(
- (nil nil (usigma!>)
- !#!T !#!D !#!G !#!G!I !#!U!U !#!P!R !#!t!h!e!t!a!U
- ((or !*torsion !*nonmetr) !#!r!o!m!e!g!a)
- ((and (null !*torsion) (null !*nonmetr)) !#!o!m!e!g!a) )
- ))
- (put '!#!t!h!e!t!a!U '!=type 0)
- (put '!#!t!h!e!t!a!U '!=way '(
- (nil nil (utheta!>)
- !#!T !#!D !#!G !#!G!I !#!U!U
- ((or !*torsion !*nonmetr) !#!r!o!m!e!g!a)
- ((and (null !*torsion) (null !*nonmetr)) !#!o!m!e!g!a) )
- ))
- % Ideal Fluid ...
- (put '!#!P!R!E!S '!=type 0)
- (put '!#!E!N!E!R '!=type 0)
- (put '!#!T!I!F!L '!=type 0)
- (put '!#!T!I!F!L '!=idxl '(nil nil))
- (put '!#!T!I!F!L '!=sidxl '((s 1 2)))
- (put '!#!T!I!F!L '!=way '(
- (nil nil (tfli!>) !#!G !#!U!S!Q !#!U!U !#!E!N!E!R !#!P!R!E!S )))
- % Spin Fluid ...
- (put '!#!T!S!F!L '!=type 0)
- (put '!#!T!S!F!L '!=idxl '(nil nil))
- (put '!#!T!S!F!L '!=sidxl '((s 1 2)))
- (put '!#!T!S!F!L '!=way '(
- (nil nil (tsfluid!>) !#!T !#!D !#!G !#!G!I
- !#!U!S!Q !#!U!U !#!U!V !#!E!N!E!R !#!P!R!E!S
- !#!S!P!F!L!T !#!F!C!o !#!o!m!e!g!a )))
- (put '!#!T!S!F!L '!=constr '((tttnotn!>)))
- (put '!#!S!P!F!L '!=type 2)
- (put '!#!S!P!F!L '!=way '(
- ((From Spin Density) nil (spfl!>) !#!S !#!S!P!F!L!T )))
- (put '!#!S!P!F!L!T '!=type 0)
- (put '!#!S!P!F!L!T '!=idxl '(nil nil))
- (put '!#!S!P!F!L!T '!=sidxl '((a 1 2)))
- (put '!#!S!P!F!L!T '!=way '(
- ((From Spin Density 2 - form) nil (spflt!>) !#!D !#!S!P!F!L )))
- (put '!#!S!P!F!L!U '!=type 3)
- (put '!#!S!P!F!L!U '!=idxl '((u . 2)))
- (put '!#!S!P!F!L!U '!=way '(
- (nil nil (spflu!>) !#!D !#!T !#!G !#!G!I !#!S!P!F!L!T !#!U!U !#!F!C!o )))
- (put '!#!S!P!F!L!U '!=constr '((sp!>)))
- (put '!#!F!C!o '!=type 1)
- (put '!#!F!C!o '!=way '(
- (nil nil (frenkel!>) !#!U!V !#!S!P!F!L )))
- % Total Energy-Momentum and Spin ...
- (put '!#!T!E!N!M!O!M '!=type 0)
- (put '!#!T!E!N!M!O!M '!=idxl '(nil nil))
- (put '!#!T!E!N!M!O!M '!=sidxl '((s 1 2)))
- (put '!#!T!E!N!M!O!M '!=way '((nil nil (tenmom!>) )))
- (put '!#!T!E!N!M!O!M!T '!=type 0)
- (put '!#!T!E!N!M!O!M!T '!=way '(
- (nil nil (tenmomt!>) !#!G!I !#!T!E!N!M!O!M )))
- (put '!#!T!E!N!M!O!M!S '!=type 0)
- (put '!#!T!E!N!M!O!M!S '!=idxl '((u . 2)(d . 2)))
- (put '!#!T!E!N!M!O!M!S '!=sidxl '((h 1 2)))
- (put '!#!T!E!N!M!O!M!S '!=way '(
- (nil nil (tenmoms!>) !#!G !#!T!E!N!M!O!M !#!T!E!N!M!O!M!T )))
- (put '!#!T!E!N!M!O!M!S '!=constr '((sp!>)))
- (put '!#!S!P!I!N!U '!=type 3)
- (put '!#!S!P!I!N!U '!=idxl '((u . 2)))
- (put '!#!S!P!I!N!U '!=way '((nil nil (spinu!>) )))
- (put '!#!S!P!I!N!U '!=constr '((sp!>)))
- %------ Macros ---------------------------------------------------------
- % Macro Functions. Work like functions. Recognized by property =MACROS
- % its value is the evaluator function. Additional flags:
- % +MACROS - marks corresponding evaluating functions
- % +grgmac - protect external names from additional usage
- (flag '(
- ima!> re!> getsoln!>
- ) '!+macros)
- (flag '(
- !I!m !R!e !S!o!l !E!R!R!O!R
- ) '!+grgmac)
- (put '!I!m '!=macros 'ima!>)
- (put '!R!e '!=macros 're!>)
- (put '!S!o!l '!=macros 'getsoln!>)
- %--- Macros 2 and 3 ----------------------------------------------------
- % Macro Tensor. Work in expressions like tensors.
- % They are flagged by +MACROS2 falg. They have their properties:
- % =type =idxl - as usual, and in addition properties:
- % =evf - function evaluator for the component
- % =ndl - list of required data
- (flag '(
- !#!x !#!X !#!d!i!m !#!s!i!g!n !#!s!g!n!t !#!s!d!i!a!g
- !#!p!m!s!g!n !#!m!p!s!g!n
- !#!h !#!h!i !#!g !#!g!i
- !#!d!e!l !#!d!e!l!h !#!e!p!s !#!e!p!s!i !#!e!p!s!h !#!e!p!s!i!h
- !#!E!P!S !#!E!P!S!I !#!D!E!L !#!s!i!g!m!a !#!s!i!g!m!a!i
- !#!C!H!R !#!C!H!R!F !#!C!H!R!T !#!S!P!C!O!E!F !#!c!c!i
- !#!P!H!I!N!P !#!P!S!I!N!P
- !#!a!l!p!h!a!n!p !#!b!e!t!a!n!p !#!g!a!m!m!a!n!p !#!e!p!s!i!l!o!n!n!p
- !#!k!a!p!p!a!n!p !#!r!h!o!n!p !#!s!i!g!m!a!n!p !#!t!a!u!n!p
- !#!m!u!n!p !#!n!u!n!p !#!l!a!m!b!d!a!n!p !#!p!i!n!p
- !#!D!D !#!D!T !#!d!d !#!d!u
- ) '!+macros2)
- % Coordinates
- (put '!#!x '!=type 0)
- (put '!#!x '!=idxl '(1))
- (put '!#!x '!=evf 'x!>)
- (put '!#!X '!=type 0)
- (put '!#!X '!=idxl '(1))
- (put '!#!X '!=evf 'x!>)
- % Conjugate spinorial index
- (put '!#!c!c!i '!=type 0)
- (put '!#!c!c!i '!=idxl '((n . 3)))
- (put '!#!c!c!i '!=evf 'ccin!>)
- % Signature
- (put '!#!s!d!i!a!g '!=type 0)
- (put '!#!s!d!i!a!g '!=idxl '((n)))
- (put '!#!s!d!i!a!g '!=evf 'diagonal!>)
- % Frame components
- (put '!#!h '!=type 0)
- (put '!#!h '!=idxl '(t 0))
- (put '!#!h '!=ndl '(!#!T))
- (put '!#!h '!=evf 'ham!>)
- (put '!#!h!i '!=type 0)
- (put '!#!h!i '!=idxl '(nil 1))
- (put '!#!h!i '!=ndl '(!#!D))
- (put '!#!h!i '!=evf 'hiam!>)
- % Holonomic metric
- (put '!#!g '!=type 0)
- (put '!#!g '!=idxl '(0 0))
- (put '!#!g '!=sidxl '((s 1 2)))
- (put '!#!g '!=ndl '(!#!G !#!T))
- (put '!#!g '!=evf 'gmetr!>)
- (put '!#!g '!=tex '!g)
- (put '!#!g!i '!=type 0)
- (put '!#!g!i '!=idxl '(1 1))
- (put '!#!g!i '!=sidxl '((s 1 2)))
- (put '!#!g!i '!=ndl '(!#!G!I !#!D))
- (put '!#!g!i '!=evf 'gimetr!>)
- (put '!#!g!i '!=tex '!g)
- % Delta symbols
- (put '!#!d!e!l '!=type 0)
- (put '!#!d!e!l '!=idxl '(t nil))
- (put '!#!d!e!l '!=evf 'delta!>)
- (put '!#!d!e!l '!=tex "\delta")
- (put '!#!d!e!l!h '!=type 0)
- (put '!#!d!e!l!h '!=idxl '(1 0))
- (put '!#!d!e!l!h '!=evf 'delta!>)
- (put '!#!d!e!l!h '!=tex "\delta")
- (put '!#!D!E!L '!=type 0)
- (put '!#!D!E!L '!=idxl '((uu . 1) (u . 1)))
- (put '!#!D!E!L '!=evf 'delta!>)
- (put '!#!D!E!L '!=tex "\delta")
- % Antysymmetric tensors
- (put '!#!e!p!s '!=type 0)
- (put '!#!e!p!s '!=idxl '(nil nil nil nil))
- (put '!#!e!p!s '!=sidxl '((a 1 2 3 4)))
- (put '!#!e!p!s '!=ndl '(!#!s!d!e!t!G))
- (put '!#!e!p!s '!=evf 'epsilf!>)
- (put '!#!e!p!s '!=tex '!E)
- (put '!#!e!p!s!i '!=type 0)
- (put '!#!e!p!s!i '!=idxl '(t t t t))
- (put '!#!e!p!s!i '!=sidxl '((a 1 2 3 4)))
- (put '!#!e!p!s!i '!=ndl '(!#!s!d!e!t!G))
- (put '!#!e!p!s!i '!=evf 'epsiuf!>)
- (put '!#!e!p!s!i '!=tex '!E)
- (put '!#!e!p!s!h '!=type 0)
- (put '!#!e!p!s!h '!=idxl '(0 0 0 0))
- (put '!#!e!p!s!h '!=sidxl '((a 1 2 3 4)))
- (put '!#!e!p!s!h '!=ndl '(!#!d!e!t!g))
- (put '!#!e!p!s!h '!=evf 'epsilh!>)
- (put '!#!e!p!s!h '!=tex '!E)
- (put '!#!e!p!s!i!h '!=type 0)
- (put '!#!e!p!s!i!h '!=idxl '(1 1 1 1))
- (put '!#!e!p!s!i!h '!=sidxl '((a 1 2 3 4)))
- (put '!#!e!p!s!i!h '!=ndl '(!#!d!e!t!g))
- (put '!#!e!p!s!i!h '!=evf 'epsiuh!>)
- (put '!#!e!p!s!i!h '!=tex '!E)
- (put '!#!E!P!S '!=type 0)
- (put '!#!E!P!S '!=idxl '((u . 1) (u . 1)))
- (put '!#!E!P!S '!=sidxl '((a 1 2)))
- (put '!#!E!P!S '!=evf 'epss!>)
- (put '!#!E!P!S '!=constr '((sp!>)))
- (put '!#!E!P!S '!=tex "\epsilon")
- (put '!#!E!P!S!I '!=type 0)
- (put '!#!E!P!S!I '!=idxl '((uu . 1) (uu . 1)))
- (put '!#!E!P!S!I '!=sidxl '((a 1 2)))
- (put '!#!E!P!S!I '!=evf 'epss!>)
- (put '!#!E!P!S!I '!=constr '((sp!>)))
- (put '!#!E!P!S!I '!=tex "\epsilon")
- % Sigma matrices
- (put '!#!s!i!g!m!a '!=type 0)
- (put '!#!s!i!g!m!a '!=idxl '(t (u . 1) (d . 1)))
- (put '!#!s!i!g!m!a '!=evf 'sigma!>)
- (put '!#!s!i!g!m!a '!=constr '((sp!>)))
- (put '!#!s!i!g!m!a '!=tex '"\sigma")
- (put '!#!s!i!g!m!a!i '!=type 0)
- (put '!#!s!i!g!m!a!i '!=idxl '(nil (uu . 1) (ud . 1)))
- (put '!#!s!i!g!m!a!i '!=evf 'sigmai!>)
- (put '!#!s!i!g!m!a!i '!=constr '((sp!>)))
- (put '!#!s!i!g!m!a!i '!=tex '"\sigma")
- % Christoffel symbols
- % of first kind
- (put '!#!C!H!R!F '!=type 0)
- (put '!#!C!H!R!F '!=idxl '(0 0 0))
- (put '!#!C!H!R!F '!=sidxl '((s 2 3)))
- (put '!#!C!H!R!F '!=evf 'chrf!>)
- (put '!#!C!H!R!F '!=ndl '( !#!G !#!D ))
- % of second kind
- (put '!#!C!H!R '!=type 0)
- (put '!#!C!H!R '!=idxl '(1 0 0))
- (put '!#!C!H!R '!=sidxl '((s 2 3)))
- (put '!#!C!H!R '!=evf 'chr!>)
- (put '!#!C!H!R '!=ndl '( !#!G !#!D !#!G!I !#!T ))
- % trace
- (put '!#!C!H!R!T '!=type 0)
- (put '!#!C!H!R!T '!=idxl '(0))
- (put '!#!C!H!R!T '!=evf 'chrt!>)
- (put '!#!C!H!R!T '!=ndl '( !#!d!e!t!g ))
- (put '!#!S!P!C!O!E!F '!=type 0)
- (put '!#!S!P!C!O!E!F '!=idxl '((u . 2) nil))
- (put '!#!S!P!C!O!E!F '!=constr '((sp!-n!>)))
- (put '!#!S!P!C!O!E!F '!=evf 'spcoef!>)
- (put '!#!S!P!C!O!E!F '!=ndl '( !#!D !#!o!m!e!g!a!u ))
- (put '!#!P!H!I!N!P '!=type 0)
- (put '!#!P!H!I!N!P '!=idxl '((u . 2)(d . 2)))
- (put '!#!P!H!I!N!P '!=evf 'phinp!>)
- (put '!#!P!H!I!N!P '!=ndl '( !#!R!C ))
- (put '!#!P!S!I!N!P '!=type 0)
- (put '!#!P!S!I!N!P '!=idxl '((u . 4)))
- (put '!#!P!S!I!N!P '!=evf 'psinp!>)
- (put '!#!P!S!I!N!P '!=ndl '( !#!R!W ))
- % Macros 3 extension of Macros 2. For quantities without indices.
- (flag '(
- !#!d!i!m !#!s!i!g!n !#!s!g!n!t
- !#!p!m!s!g!n !#!m!p!s!g!n
- !#!a!l!p!h!a!n!p !#!b!e!t!a!n!p !#!g!a!m!m!a!n!p !#!e!p!s!i!l!o!n!n!p
- !#!k!a!p!p!a!n!p !#!r!h!o!n!p !#!s!i!g!m!a!n!p !#!t!a!u!n!p
- !#!m!u!n!p !#!n!u!n!p !#!l!a!m!b!d!a!n!p !#!p!i!n!p
- !#!D!D !#!D!T !#!d!d !#!d!u
- ) '!+macros3)
- (flag '( !d!i!m !s!i!g!n !s!g!n!t ) '!+grgmac)
- % Dimension
- (put '!#!d!i!m '!=type 0)
- (put '!#!d!i!m '!=evf 'dim!>)
- % Signature
- (put '!#!s!i!g!n '!=type 0)
- (put '!#!s!i!g!n '!=evf 'sigprod!>)
- (put '!#!s!g!n!t '!=type 0)
- (put '!#!s!g!n!t '!=evf 'sigprod!>)
- (put '!#!p!m!s!g!n '!=type 0)
- (put '!#!p!m!s!g!n '!=evf 'pmsgn!>)
- (put '!#!m!p!s!g!n '!=type 0)
- (put '!#!m!p!s!g!n '!=evf 'mpsgn!>)
- % NP spin coefficients
- (put '!#!a!l!p!h!a!n!p '!=type 0)
- (put '!#!b!e!t!a!n!p '!=type 0)
- (put '!#!g!a!m!m!a!n!p '!=type 0)
- (put '!#!e!p!s!i!l!o!n!n!p '!=type 0)
- (put '!#!k!a!p!p!a!n!p '!=type 0)
- (put '!#!r!h!o!n!p '!=type 0)
- (put '!#!s!i!g!m!a!n!p '!=type 0)
- (put '!#!t!a!u!n!p '!=type 0)
- (put '!#!m!u!n!p '!=type 0)
- (put '!#!n!u!n!p '!=type 0)
- (put '!#!l!a!m!b!d!a!n!p '!=type 0)
- (put '!#!p!i!n!p '!=type 0)
- (put '!#!a!l!p!h!a!n!p '!=evf 'alphanp!>)
- (put '!#!b!e!t!a!n!p '!=evf 'betanp!>)
- (put '!#!g!a!m!m!a!n!p '!=evf 'gammanp!>)
- (put '!#!e!p!s!i!l!o!n!n!p '!=evf 'epsilonnp!>)
- (put '!#!k!a!p!p!a!n!p '!=evf 'kappanp!>)
- (put '!#!r!h!o!n!p '!=evf 'rhonp!>)
- (put '!#!s!i!g!m!a!n!p '!=evf 'sigmanp!>)
- (put '!#!t!a!u!n!p '!=evf 'taunp!>)
- (put '!#!m!u!n!p '!=evf 'munp!>)
- (put '!#!n!u!n!p '!=evf 'nunp!>)
- (put '!#!l!a!m!b!d!a!n!p '!=evf 'lambdanp!>)
- (put '!#!p!i!n!p '!=evf 'pinp!>)
- (put '!#!a!l!p!h!a!n!p '!=ndl '( !#!D !#!o!m!e!g!a!u ))
- (put '!#!b!e!t!a!n!p '!=ndl '( !#!D !#!o!m!e!g!a!u ))
- (put '!#!g!a!m!m!a!n!p '!=ndl '( !#!D !#!o!m!e!g!a!u ))
- (put '!#!e!p!s!i!l!o!n!n!p '!=ndl '( !#!D !#!o!m!e!g!a!u ))
- (put '!#!k!a!p!p!a!n!p '!=ndl '( !#!D !#!o!m!e!g!a!u ))
- (put '!#!r!h!o!n!p '!=ndl '( !#!D !#!o!m!e!g!a!u ))
- (put '!#!s!i!g!m!a!n!p '!=ndl '( !#!D !#!o!m!e!g!a!u ))
- (put '!#!t!a!u!n!p '!=ndl '( !#!D !#!o!m!e!g!a!u ))
- (put '!#!m!u!n!p '!=ndl '( !#!D !#!o!m!e!g!a!u ))
- (put '!#!n!u!n!p '!=ndl '( !#!D !#!o!m!e!g!a!u ))
- (put '!#!l!a!m!b!d!a!n!p '!=ndl '( !#!D !#!o!m!e!g!a!u ))
- (put '!#!p!i!n!p '!=ndl '( !#!D !#!o!m!e!g!a!u ))
- (put '!#!D!D '!=type -1)
- (put '!#!D!T '!=type -1)
- (put '!#!d!d '!=type -1)
- (put '!#!d!u '!=type -1)
- (put '!#!D!D '!=ndl '( !#!D ))
- (put '!#!D!T '!=ndl '( !#!D ))
- (put '!#!d!d '!=ndl '( !#!D ))
- (put '!#!d!u '!=ndl '( !#!D ))
- (put '!#!D!D '!=evf 'dddop!>)
- (put '!#!D!T '!=evf 'dtop!>)
- (put '!#!d!d '!=evf 'ddop!>)
- (put '!#!d!u '!=evf 'duop!>)
- %-----------------------------------------------------------------------
- %====== (3) Other Internals =============================================
- %--------- Properties for Scaner -----------------------------------
- (flag '( !/ !* !_ !~ !< !> !- !| !. ) '!=fc)
- %%-------- Properties for Translator -------------------------------
- (put '!* '!=op2 'times2!>)
- (put '!/ '!=op2 'quoti!>)
- (put '!/!\ '!=op2 'dfpr2!>)
- (put '!_!| '!=op2 'inpr!>)
- (put '!| '!=op2 'vef!>)
- (put '!. '!=op2 'vpr!>)
- (flag '(times2!> quoti!> dfpr2!> inpr!> vef!> vpr!>) '!+multop2)
- (put '!@ '!=sysfun 'bvec!>)
- (put '!# '!=sysfun 'dualis!>)
- (put '!d '!=sysfun 'dx!>)
- (put '!~ '!=sysfun 'co!>)
- (put '!S!u!m '!=spectr 'sumtr!>)
- (put '!P!r!o!d '!=spectr 'prodtr!>)
- (put '!L!i!e '!=spectr 'lietr!>)
- (put '!D!c '!=spectr 'dctran!>)
- (put '!D!f!c '!=spectr 'dfctran!>)
- %(put '!L!i!m '!=spectr 'limtr!>)
- %(put '!L!i!m!M '!=spectr 'limtrm!>)
- %(put '!L!i!m!P '!=spectr 'limtrp!>)
- (put '!L!H!S '!=spectr 'lhs0!>)
- (put '!R!H!S '!=spectr 'rhs0!>)
- (put 'sub '!=spectr 'subtr!>)
- (put '!I!f '!=spectr 'iftran!>)
- %(put '!D!f '!=spectr 'pdftra!>)
- %(put '!D!f!p '!=spectr 'dfptra!>)
- (put '!E!R!R!O!R '!=spectr 'errortr!>)
- (flag '(
- funapply!> sumexec!> prodexec!> lhs!> rhs!> dummyvar!>
- subexec!> ifexec!> lieexec!> dcexec!> dfcexec!> error!>
- % limexec!>
- ) '!+specexec)
- %------- Boollean Expressions --------------------------------------
- (put '!O!B!J!E!C!T '!=boolmac 'objexe!>)
- (put '!O!N '!=boolmac 'onexe!>)
- (put '!O!F!F '!=boolmac 'offexe!>)
- (put '!Z!E!R!O '!=boolmac 'zeroexe!>)
- (put '!H!A!S!V!A!L!U!E '!=boolmac 'valexe!>)
- (put '!N!U!L!L!M '!=boolmac 'nullexe!>)
- (flag '(objexe!> onexe!> offexe!> zeroexe!> valexe!> nullexe!>)
- '!+specbexe)
- %------- Flags and properties which must be cleared ----------------
- (setq ![rpfl!] '(
- ((![const!]) (!+grg !+grgvar used!* constant)
- !=conj )
- ((![fun!]) ( !+grg subfn !+grgvar !+fun used!*
- symmetric antisymmetric odd even)
- simpfn kvalue klist narg !=conj !=depend)
- ((![cord!]) (!+grg !+grgvar used!*)
- !=cord !=conj)
- ((![ocord!]) (!+grg !+grgvar used!*)
- !=cord !=conj)
- ((![apar!]) (!+grg !+grgvar used!*) )
- ))
- (setq ![rpflcr!] '(
- ((![cord!]) (!+grg !+grgvar used!*) !=cord !=conj)
- ))
- (setq ![rpflcn!] '(
- ((![const!]) (!+grg !+grgvar used!* constant) !=conj)
- ))
- (setq ![rpflap!] '(
- ((![apar!]) (!+grg !+grgvar used!* constant) )
- ))
- (setq ![rpflfu!] '(
- ((![fun!]) ( !+grg subfn !+grgvar !+fun used!*
- symmetric antisymmetric odd even dfp!_commute )
- subfunc generic!_function
- simpfn kvalue klist narg !=conj !=depend)
- ))
- %------- List of Flags and Props important for Load/Unload ------
- (setq ![allflags!]
- '( !+equ !+pl !+ivar !+abbr !+noncov !+hconn !+fconn !+uconn !+dconn ))
- (setq ![allprops!]
- '( !=type !=idxl !=sidxl !=constr !=tex !=dens ))
- %------- Commands ----------------------------------------------
- % word!!!
- (setq ![instr!] '(
- (On !!!! onoff!> t)
- (Off !!!! onoff!> nil)
- (Quit !! grgquit!>)
- (System !!!! grgsystem!>)
- (Stop !! stop!>)
- (Find !!!! find!>)
- % (Calculate !!!! find!>)
- (Write !!!! write!>)
- (Zero !!!! zero!>)
- % (Nullify !!!! zero!>)
- (Print !!!! printi!>)
- (Evaluate !!!! evalcomm!> (function evel!>))
- % (Simplify !!!! evalcomm!> (function evel!>))
- (Erase !!!! erase!>)
- % (Delete !!!! erase!>)
- (Let !!!! leti!> t)
- (Match !!!! matchi!> t)
- (Clear !!!! cleri!> t)
- (For !!!! forinstrs!>)
- (Input !!!! from!>)
- (Dimension !!!! dimension!>)
- (!% !!!! comment!>)
- (Comment !!!! comment!>)
- (File !!!! showfil!>)
- (Factor !!!! orfare!> 'factor)
- (RemFac !!!! orfare!> 'remfac)
- (Order !!!! orfare!> 'order)
- (Holonomic !! turnbg!> nil)
- (Anholonomic !! turnbg!> t)
- (Show !!!! shcommands!>)
- (ds2 !! showlinel!>)
- (Time !! timei!>)
- (GC
- (Time !! gctime!>))
- (Switch !!!! sflag!>)
- (Status !! shstatus!>)
- (Load !!!! loa!>)
- % (Restore !!!! loa!>)
- (Unload !!!! unl!>)
- % (Save !!!! unl!>)
- (Next !! next!>)
- (Pause !! pause!>)
- (Normalize !!!! evalcomm!> (function normel!>))
- (Classify !!!! classify!>)
- (Output !!!! grgout!>)
- (Symmetric !!!! funsym!> 0)
- (Antisymmetric
- !!!! funsym!> 1)
- (Odd !!!! funsym!> 2)
- (Even !!!! funsym!> 3)
- (Coordinates
- !!!! datrc!> '![cord!] ![dim!])
- (Constants !!!! datrc!> '![const!] nil)
- (Functions !!!! fun!>)
- (Generic
- (Functions
- !!!! genfun!>))
- (New !!!! newcommands!>)
- (Object !!!! obdec!> 0)
- (Equation !!!! obdec!> 1)
- (Connection
- !!!! obdec!> 2)
- (Line
- (!-
- (Element
- !! showlinel!>))
- (Length !!!! setlinel!>) )
- (Make
- (Spinorial
- (Rotation
- !!!! rotas!>))
- (Rotation
- !!!! rotat!> nil))
- (Spinorial
- (Rotation
- !!!! rotas!>))
- (Rotation !!!! rotat!> nil)
- (Change
- (Metric !!!! rotat!> t))
- (Forget !!!! forget!>)
- (Solve !!!! solvei!>)
- (EndO !! closewrite!>)
- (EndW !! closewrite!>)
- (EndU !! closeunload!>)
- (End (of
- (Output !! closewrite!>)
- (Write !! closewrite!>)
- (Unload !! closeunload!>) ))
- (Inverse !!!! invi!>)
- (Null
- (Metric !! nullmetric!>))
- (Package !!!! loadpack!> t)
- (Hold !!!! hold!> t)
- (Release !!!! hold!> nil)
- (Affine
- (Parameter
- !!!! affpar!>))
- (copyright !! copyrzw!>)
- (lisp !! lisp!>)
- (debug !! otladka!>)
- ))
- %------- Commands allowed as composites ------------------------------
- % word!!!
- (setq ![icompos!] '(
- Find Write Calculate Nullify Zero Save Unload Forget
- Erase Delete Simplify Evaluate Normalize Hold Release
- ))
- %------- Unlocked Commands when coordinates are undefined ------------
- (flag '(
- onoff!> grgquit!> stop!> pause!> next!> from!> showfil!>
- erase!> zero!> comment!> timei!> datrc!> fun!> copyrzw!>
- loa!> sflag!> shobj!> obdec!> gctime!> shstatus!> shall!>
- forget!> grgsystem!> grgout!> setlinel!> hold!>
- lisp!> loadpack!> closewrite!> closeunload!>
- shcommands!> dimension!> otladka!>
- ) '!+unloc)
- %------- Reserved Variables ------------------------------------------
- (setq ![rconstl!] '(
- e i pi infinity failed
- !E!C!O!N!S!T !D!M!A!S!S !S!M!A!S!S !G!C!O!N!S!T !C!C!O!N!S!T
- !L!C0 !L!C1 !L!C2 !L!C3 !L!C4 !L!C5 !L!C6
- !A!C0 !M!C1 !M!C2 !M!C3
- ))
- (operator '(arbcomplex!~))
- (put 'arbcomplex '!=conj 'arbcomplex!~)
- (put 'arbcomplex!~ '!=conj 'arbcomplex)
- % These can not be used in new declarations ...
- (flag '( df nil sub
- !d !L!H!S !R!H!S !S!u!m !P!r!o!d
- !L!i!e !D!c !I!f !D!f !D!f!p !E!R!R!O!R
- % !L!i!m !L!i!m!M !L!i!m!P
- ) '!+grg)
- (flag ![rconstl!] '!+grg)
- (flag ![rconstl!] 'used!*)
- (flag ![rconstl!] '!+grgvar)
- (flag ![rconstl!] 'constant)
- %---- Specially Prohibiting the usage of some symbols in GRG ---------
- (flag '( conj repart impart fix floor round interpol
- ceiling set ws evenp list factorize ) '!+redbad )
- %------- GRG Switches ----------------------------------------------
- % GRG switches :
- (global '(
- !*aeval % If On REVAL(AEVAL()) else REVAL() (Off)
- !*wrs % Evaluate expression before Write if On (On)
- !*wmatr % Print 2-index scalars as matrices (Off)
- !*torsion % Torsion (Off)
- !*nonmetr % Nonmetricity (Off)
- !*unlcord % Saves coordinates in Save/Unload (On)
- !*auto % Automatical data calculation in expr (On)
- !*trace % Tracing evaluation process (On)
- !*showcommands % Show composite commands expansion (Off)
- !*expandsym % Sym Asym and othre in expr (Off)
- !*dfpcommute % Commutativity ofr DFP (On)
- !*nonmin % Nonminimal Interaction (Off)
- !*nofreevars % Prohibites free vars. in Print command (Off)
- !*cconst % Include cosm.-const. in equation or not (Off)
- !*full % Control number of components in Metr.Eq.(Off)
- !*latex % O
- !*grg % u
- !*reduce % t
- !*maple % p
- !*math % u
- !*macsyma % t
- !*dfindexed % DF in indexed form (Off)
- !*batch % Batch mode (Off)
- !*holonomic % Keeps farme holonomic during cord. (On)
- % and frame transformations
- !*showexpr % If On then values of nonzero expr is (Off)
- % shown in the process of classification
- ))
- % oftenly this is already fluid
- (cond ((not (or (fluidp '!*debug) (globalp '!*debug)))
- (global '(
- !*debug % Otladka
- ))))
- (setq ![flagl!] '(
- aeval % If On REVAL(AEVAL()) else REVAL() (Off)
- wrs % Evaluate expression before Write if On (On)
- wmatr % Print 2-index scalars as matrices (Off)
- torsion % Torsion (Off)
- nonmetr % Nonmetricity (Off)
- unlcord % Saves coordinates in Save/Unload (On)
- auto % Automatical data calculation in expr (On)
- trace % Tracing evaluation process (On)
- showcommands % Show composite commands expansion (Off)
- expandsym % Sym Asym and othre in expr (Off)
- dfpcommute % Commutativity ofr DFP (On)
- nonmin % Nonminimal Interaction (Off)
- nofreevars % Prohibites free vars. in Print command (Off)
- cconst % Include cosm.-const. in equation or not (Off)
- full % Control number of components in Metr.Eq.(Off)
- latex % O
- grg % u
- reduce % t
- maple % p
- math % u
- macsyma % t
- dfindexed % DF in indexed form (Off)
- batch % Batch mode (Off)
- holonomic % Keeps farme holonomic during cord. (On)
- % and frame transformations
- showexpr % If On then values of nonzero expr is (Off)
- % shown in the process of classification
- debug % Otladka (Off)
- ))
- (flag ![flagl!] '!+switch)
- % Set these initially to Off position ...
- (setq ![flagnil!]
- '( !*torsion !*nonmetr !*gc !*echo !*batch !*showcommands
- !*expandsym !*dfindexed !*aeval !*wmatr !*showexpr
- !*nonmin !*nofreevars !*cconst !*full
- !*debug ))
- % Set these initially to On position ...
- (setq ![flagt!]
- '( !*unlcord !*wrs !*trace !*auto !*holonomic
- !*dfpcommute ))
- % Output switches ...
- (setq ![flaglo!] '(
- grg reduce maple math macsyma
- ))
- % Switches tuning ...
- (put 'torsion '!=tuning 'tunetorsion!>)
- (put 'nonmetr '!=tuning 'tunenonmetr!>)
- (put 'fancy '!=tuning 'tunefancy!>)
- (put 'latex '!=tuning 'tunetex!>)
- (put 'grg '!=tuning 'tunegrg!>)
- (put 'reduce '!=tuning 'tunereduce!>)
- (put 'maple '!=tuning 'tunemaple!>)
- (put 'math '!=tuning 'tunemath!>)
- (put 'macsyma '!=tuning 'tunemacsyma!>)
- (put 'dfindexed '!=tuning 'tunedfindexed!>)
- (put 'debug '!=tuning 'swotladka!>)
- %---------- Special Treatment for Write ----------------------------
- (put '![cord!] '!=datl '((datlc!> ![cord!] "Coordinates" t)))
- (put '![const!] '!=datl '((datlc!> ![const!] "Constants" t)))
- (put '![apar!] '!=datl '((datlc!> ![apar!] "Affine Parameter" nil)))
- (put '![fun!] '!=datl '((funl!>)))
- (put '![sol!] '!=datl '((solwri!>)))
- %---------- Special Actions For Load/Unload ------------------------
- (put '![cord!] '!=unl
- '((putpnu!> nil ![cord!] (used!* !+grgvar !+grg) !=cord 1)))
- (put '![const!] '!=unl
- '((putpnu!> nil ![const!] (used!* !+grgvar !+grg) nil 2)))
- (put '![apar!] '!=unl
- '((putpnu!> nil ![apar!] (used!* !+grgvar !+grg) nil 4)))
- (put '![fun!] '!=unl
- '((putpnu!> (putfndp!>) ![fun!] (used!* !+fun !+grg) nil 3)))
- %---------- Standard Null Metric -----------------------------------
- % Signature (-,+,+,+)
- (setq ![nullm!] '( ( nil -1 nil nil )
- ( nil nil nil nil )
- ( nil nil nil 1 )
- ( nil nil nil nil ) ))
- % Signature (+,-,-,-)
- (setq ![nullm1!] '( ( nil 1 nil nil )
- ( nil nil nil nil )
- ( nil nil nil -1 )
- ( nil nil nil nil ) ))
- %---------- For Nice Printing --------------------------------------
- (flag '( !. !, !; !_ !/!\ !* !** !+ !- !_!| ![ !:!\! !=
- !#! !] !^ !/ !' !.!. !'!' !# !| !@ !> !< !~
- !>!= !<!= !:
- ) '!+nonsp)
- (put 'em '!=printas '!E!M)
- (put 'ym '!=printas '!Y!M)
- %---------- Indices Manipulations ----------------------------------
- (flag '( !' !^ !. !_ ) '!+indexman)
- %-----------------------------------------------------------------------
- (put '!a '!=uc '!A) (put '!A '!=lc '!a)
- (put '!b '!=uc '!B) (put '!B '!=lc '!b)
- (put '!c '!=uc '!C) (put '!C '!=lc '!c)
- (put '!d '!=uc '!D) (put '!D '!=lc '!d)
- (put '!e '!=uc '!E) (put '!E '!=lc '!e)
- (put '!f '!=uc '!F) (put '!F '!=lc '!f)
- (put '!g '!=uc '!G) (put '!G '!=lc '!g)
- (put '!h '!=uc '!H) (put '!H '!=lc '!h)
- (put '!i '!=uc '!I) (put '!I '!=lc '!i)
- (put '!j '!=uc '!J) (put '!J '!=lc '!j)
- (put '!k '!=uc '!K) (put '!K '!=lc '!k)
- (put '!l '!=uc '!L) (put '!L '!=lc '!l)
- (put '!m '!=uc '!M) (put '!M '!=lc '!m)
- (put '!n '!=uc '!N) (put '!N '!=lc '!n)
- (put '!o '!=uc '!O) (put '!O '!=lc '!o)
- (put '!p '!=uc '!P) (put '!P '!=lc '!p)
- (put '!q '!=uc '!Q) (put '!Q '!=lc '!q)
- (put '!r '!=uc '!R) (put '!R '!=lc '!r)
- (put '!s '!=uc '!S) (put '!S '!=lc '!s)
- (put '!t '!=uc '!T) (put '!T '!=lc '!t)
- (put '!u '!=uc '!U) (put '!U '!=lc '!u)
- (put '!v '!=uc '!V) (put '!V '!=lc '!v)
- (put '!w '!=uc '!W) (put '!W '!=lc '!w)
- (put '!x '!=uc '!X) (put '!X '!=lc '!x)
- (put '!y '!=uc '!Y) (put '!Y '!=lc '!y)
- (put '!z '!=uc '!Z) (put '!Z '!=lc '!z)
- %------- Trigonometric Functions ---------------------------------------
- (flag '( sin cos tan cot sec csc
- sinh cosh tanh coth sech csch
- asin acos atan acot asec acsc
- asinh acosh atanh acoth asech acsch ) '!+trig)
- %============ End of GRGdecl.sl =========================================%
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