1 (cond (($get
'$cartan
'$version
) (merror "CARTAN already loaded"))
2 (t ($put
'$cartan
'$v20041209
'$version
))
10 (ADD2LNC (QUOTE "|") $PROPS
)
11 (DEFPROP $\| DIMENSION-infix DIMENSION
)
12 (DEFPROP $\|
(#\Space
#\|
#\Space
) DISSYM
)
15 (DEFPROP $\| PARSE-INFIX LED
)
16 (DEFPROP $\| MSIZE-INFIX GRIND
)
17 (DEFPROP %\| DIMENSION-infix DIMENSION
)
18 (DEFPROP %\|
(#\Space
#\|
#\Space
) DISSYM
)
19 (MDEFPROP $\|
((LAMBDA) ((MLIST) $V $F
) ((MPROG SIMP
) ((MLIST SIMP
)
20 $I $J $EXT101 $EXT102 $EXT103 $EXT104
) ((MSETQ SIMP
) $EXT103
21 (($EXPAND SIMP
) $F
)) ((MSETQ SIMP
) $EXT102
((MTIMES SIMP
)
22 (($V SIMP ARRAY
) 1) (($COEFF SIMP
) $EXT103
(($CARTAN_BASIS SIMP ARRAY
) 1))))
23 ((MDO SIMP
) $I
2 NIL NIL $CARTAN_DIM NIL
((MPROGN SIMP
) ((MSETQ SIMP
)
24 $EXT101
(($COEFF SIMP
) $EXT103
(($CARTAN_BASIS SIMP ARRAY
) $I
)))
25 ((MCOND SIMP
) ((MNOTEQUAL SIMP
) $EXT101
0) ((MSETQ SIMP
) $EXT101
26 (($SUBSTITUTE SIMP
) (($EXTSUB SIMP ARRAY
) $I
) $EXT101
)) T $FALSE
)
27 ((MSETQ SIMP
) $EXT102
((MPLUS SIMP
) $EXT102
((MTIMES SIMP
) $EXT101
28 (($V SIMP ARRAY
) $I
)))))) ((MRETURN SIMP
) (($EXPAND SIMP
) $EXT102
))))
30 (ADD2LNC (QUOTE (($\|
) $V $F
)) $FUNCTIONS
)
31 (DEFPROP %\| $\| NOUN
)
35 (ADD2LNC (QUOTE "~") $PROPS
)
36 (DEFPROP $~ DIMENSION-infix DIMENSION
)
37 (DEFPROP $~
(#\Space
#\~
#\Space
) DISSYM
)
40 (DEFPROP $~ PARSE-INFIX LED
)
41 (DEFPROP $~ MSIZE-INFIX GRIND
)
42 (DEFPROP %~ DIMENSION-infix DIMENSION
)
43 (DEFPROP %~
(#\Space
#\~
#\Space
) DISSYM
)
44 (MDEFPROP $~
((LAMBDA) ((MLIST) $F $G
) ((MPROG SIMP
) ((MLIST SIMP
) $I $J $EXT101 $EXT102 $EXT103 $EXT104 $EXT105
) ((MSETQ SIMP
) $EXT101
0) ((MSETQ SIMP
) $EXT102 $TRUE
) ((MSETQ SIMP
) $EXT103
(($EXPAND SIMP
) $F
)) ((MDO SIMP
) $I $CARTAN_DIM -
1 NIL
1 NIL
((MPROGN SIMP
) ((MSETQ SIMP
) $EXT104
(($EXPAND SIMP
) (($BOTHCOEF SIMP
) $EXT103
(($CARTAN_BASIS SIMP ARRAY
) $I
)))) ((MSETQ SIMP
) $EXT105
(($FIRST SIMP
) $EXT104
)) ((MCOND SIMP
) ((MNOTEQUAL SIMP
) $EXT105
0) ((MPROGN SIMP
) ((MSETQ SIMP
) $EXT103
(($LAST SIMP
) $EXT104
)) ((MSETQ SIMP
) $CARTAN_DIM
((MPLUS SIMP
) -
1 $I
)) ((MSETQ SIMP
) $EXT101
((MPLUS SIMP
) $EXT101
(($~ SIMP
) $EXT105
((MTIMES SIMP
) (($CARTAN_BASIS SIMP ARRAY
) $I
) (($SUBSTITUTE SIMP
) (($EXTSUBB SIMP ARRAY
) $I
) $G
))))) ((MSETQ SIMP
) $CARTAN_DIM $EXTDIM
) ((MSETQ SIMP
) $EXT102 $FALSE
)) T $FALSE
))) ((MCOND SIMP
) $EXT102
((MRETURN SIMP
) (($EXPAND SIMP
) ((MTIMES SIMP
) $F $G
))) T
((MRETURN SIMP
) (($EXPAND SIMP
) $EXT101
))))) MEXPR
)
45 (ADD2LNC (QUOTE (($~
) $F $G
)) $FUNCTIONS
)
47 (MDEFPROP $EXT_DIFF
((LAMBDA) ((MLIST) $F
) (($SUM SIMP
) (($~ SIMP
)
48 (($CARTAN_BASIS SIMP ARRAY
) $I
) (($DIFF SIMP
) $F
(($CARTAN_COORDS SIMP ARRAY
) $I
)))
49 $I
1 $CARTAN_DIM
)) MEXPR
)
50 (ADD2LNC (QUOTE (($EXT_DIFF
) $F
)) $FUNCTIONS
)
51 (MDEFPROP $LIE_DIFF_F
((LAMBDA) ((MLIST) $V $F
) ((MPLUS SIMP
) (($\| SIMP
) $V
52 (($EXT_DIFF SIMP
) $F
)) (($EXT_DIFF SIMP
) (($\| SIMP
) $V $F
)))) MEXPR
)
53 (ADD2LNC (QUOTE (($LIE_DIFF_F
) $V $F
)) $FUNCTIONS
)
54 (MDEFPROP $LIE_DIFF_V
((LAMBDA) ((MLIST) $V $W
) ((MPROG SIMP
) ((MLIST SIMP
)
55 $I $J $EXT101
) ((MSETQ SIMP
) $EXT101
((MLIST SIMP
))) ((MDO SIMP
)
56 $I
1 NIL NIL $CARTAN_DIM NIL
((MSETQ SIMP
) $EXT101
(($ENDCONS SIMP
)
57 (($SUM SIMP
) ((MPLUS SIMP
) ((MTIMES SIMP
) (($DIFF SIMP
)
58 (($W SIMP ARRAY
) $I
) (($CARTAN_COORDS SIMP ARRAY
) $J
)) (($V SIMP ARRAY
) $J
))
59 ((MTIMES SIMP
) -
1 (($DIFF SIMP
) (($V SIMP ARRAY
) $I
)
60 (($CARTAN_COORDS SIMP ARRAY
) $J
)) (($W SIMP ARRAY
) $J
))) $J
1 $CARTAN_DIM
) $EXT101
)))
61 ((MRETURN SIMP
) (($EXPAND SIMP
) $EXT101
)))) MEXPR
)
62 (ADD2LNC (QUOTE (($LIE_DIFF_V
) $V $W
)) $FUNCTIONS
)
63 (MDEFPROP $EDIT
((LAMBDA) ((MLIST) $F
) ((MPROG SIMP
) ((MLIST SIMP
) $I
64 $EXT101 $EXT102 $EXT103 $EXT104 $EXT105
) ((MSETQ SIMP
) $EXT101
0)
65 ((MSETQ SIMP
) $EXT102
(($EXPAND SIMP
) $F
)) ((MDO SIMP
) $I $CARTAN_DIM -
1
66 NIL
1 NIL
((MPROGN SIMP
) ((MSETQ SIMP
) $EXT103
(($EXPAND SIMP
)
67 (($BOTHCOEF SIMP
) $EXT102
(($CARTAN_BASIS SIMP ARRAY
) $I
)))) ((MSETQ SIMP
)
68 $EXT104
(($FIRST SIMP
) $EXT103
)) ((MCOND SIMP
) ((MNOTEQUAL SIMP
)
69 $EXT104
0) ((MPROGN SIMP
) ((MSETQ SIMP
) $EXT102
(($LAST SIMP
) $EXT103
))
70 ((MSETQ SIMP
) $CARTAN_DIM
((MPLUS SIMP
) -
1 $I
)) ((MSETQ SIMP
) $EXT105
71 (($EDIT SIMP
) $EXT104
)) ((MSETQ SIMP
) $CARTAN_DIM $EXTDIM
) ((MCOND SIMP
)
72 ((MEQUAL SIMP
) $EXT105
0) ((MSETQ SIMP
) $EXT101
((MPLUS SIMP
) $EXT101
73 ((MTIMES SIMP
) $EXT104
(($CARTAN_BASIS SIMP ARRAY
) $I
)))) T
((MCOND SIMP
)
74 ((MEQUAL SIMP
) (($INPART SIMP
) $EXT105
0) "+") ((MSETQ SIMP
) $EXT101
75 ((MPLUS SIMP
) $EXT101
(($MULTTHRU SIMP
) ((MTIMES SIMP
) $EXT105
76 (($CARTAN_BASIS SIMP ARRAY
) $I
))))) T
((MSETQ SIMP
) $EXT101
((MPLUS SIMP
)
77 $EXT101
((MTIMES SIMP
) $EXT105
(($CARTAN_BASIS SIMP ARRAY
) $I
)))))))
78 T $FALSE
))) ((MRETURN SIMP
) $EXT101
))) MEXPR
)
79 (ADD2LNC (QUOTE (($EDIT
) $F
)) $FUNCTIONS
)
80 (MDEFPROP $BASUB
((LAMBDA) ((MLIST) $F $G $H
) ((MPROG SIMP
)
81 ((MLIST SIMP
) $I $EXT101 $EXT102 $EXT103 $EXT104
) ((MSETQ SIMP
)
82 $EXT101
(($EXPAND SIMP
) $H
)) ((MSETQ SIMP
) $EXT102
(($EXPAND SIMP
)
83 (($BOTHCOEF SIMP
) $EXT101 $G
))) ((MSETQ SIMP
) $EXT103
(($FIRST SIMP
)
84 $EXT102
)) ((MCOND SIMP
) ((MEQUAL SIMP
) $EXT103
0) ((MRETURN SIMP
) $H
)
85 T $FALSE
) ((MCOND SIMP
) ((MEQUAL SIMP
) $G
(($CARTAN_BASIS SIMP ARRAY
) 1))
86 ((MRETURN SIMP
) ((MPLUS SIMP
) (($LAST SIMP
) $EXT102
) (($~ SIMP
) $F
87 $EXT103
))) T $FALSE
) ((MDO SIMP
) $I
2 NIL NIL $CARTAN_DIM NIL
((MCOND SIMP
)
88 ((MEQUAL SIMP
) $G
(($CARTAN_BASIS SIMP ARRAY
) $I
)) ((MRETURN SIMP
)
89 ((MSETQ SIMP
) $EXT104
((MPLUS SIMP
) (($LAST SIMP
) $EXT102
) (($~ SIMP
)
90 $F
(($SUBSTITUTE SIMP
) (($EXTSUB SIMP ARRAY
) $I
) $EXT103
)))))
91 T $FALSE
)) ((MRETURN SIMP
) $EXT104
))) MEXPR
)
92 (ADD2LNC (QUOTE (($BASUB
) $F $G $H
)) $FUNCTIONS
)
95 (meval '((MDEFINE) (($LIE_DIFF
) $V $X
)
96 ((MCOND) (($LISTP
) $X
) (($LIE_DIFF_V
) $V $X
) T
97 (($LIE_DIFF_F
) $V $X
))))
101 (defmvar $cartan_coords
)
102 (defmvar $cartan_basis
)
104 ; The following is a hand translation (more or less) of this MAXIMA code:
106 ; init_cartan(coords):=block
109 ; cartan_coords:coords,
110 ; cartan_dim:extdim:length(cartan_coords),
111 ; cartan_basis:extsubb[1]:[],
112 ; for i thru cartan_dim do
115 ; cartan_basis:endcons(ci,cartan_basis),
116 ; extsub[i+1]:cons(ci=-ci,extsub[i]),
117 ; extsubb[i]:cons(ci=0,extsub[i]),
118 ; apply('alias,[concat(d,cartan_coords[i]),ci])
122 (defun $init_cartan
(c)
123 (setq $cartan_coords c
)
124 (setq $cartan_dim
($length $cartan_coords
))
125 (setq $extdim $cartan_dim
)
126 (setq $cartan_basis nil
)
127 (meval (list '(msetq) '(($extsub array
) 1) '((mlist simp
))))
128 (meval (list '(msetq) '(($extsubb array
) 1) '((mlist simp
))))
131 ((c (cdr $cartan_coords
) (cdr c
)) (i 1 (1+ i
)) (ci))
132 ((null c
) (setq $cartan_basis
(cons '(mlist simp
) (reverse $cartan_basis
))))
133 (setq ci
($concat
'zzz
(car c
)))
134 (setq $cartan_basis
(cons ci $cartan_basis
))
136 (meval (list '(msetq) (list '($extsub array
) (1+ i
))
137 ($cons
(list '(mequal simp
) ci
(list '(mtimes simp
) -
1 ci
))
138 (meval (list '($extsub array
) i
))
141 (meval (list '(msetq) (list '($extsubb array
) i
)
142 ($cons
(list '(mequal simp
) ci
0)
143 (meval (list '($extsub array
) i
))
146 (meval (list '(alias) ($concat
'd
(car c
)) ci
))
