\( \DeclareMathOperator{\abs}{abs} \newcommand{\ensuremath}[1]{\mbox{$#1$}} \)
| (%i1) | load ( linearalgebra ) ; |
\[\operatorname{ }"/usr/share/maxima/5.43.2/share/linearalgebra/linearalgebra.mac"\]
| (%i2) |
LieCovector
(
[
l
]
)
:
=
block
(
[
f
,
w
,
x
,
k
,
Df
,
Dw
,
Lfw
]
,
if ( length ( l ) < 3 ) or ( length ( l ) > 4 ) then error ( "Aufruf mit 3 oder 4 Argumenten." ) , f : l [ 1 ] , w : l [ 2 ] , x : l [ 3 ] , if length ( l ) = 3 then k : 1 else k : l [ 4 ] , if not ( nonnegintegerp ( k ) ) then error ( "Ordnung k muss natürliche Zahl sein." ) , if k = 0 then return ( w ) else Df : jacobian ( f , x ) , Dw : jacobian ( w , x ) , Lfw : list_matrix_entries ( w . Df + f . transpose ( Dw ) ) , return ( LieCovector ( f , Lfw , x , k − 1 ) ) ) $ |
| (%i5) |
f
:
[
sin
(
x3
)
,
cos
(
x3
)
,
0
]
;
h : x1 ^ 2 + x2 ^ 2 ; x : [ x1 , x2 , x3 ] ; |
\[\operatorname{(f) }\left[ \sin{\left( \ensuremath{\mathrm{x3}}\right) }\operatorname{,}\cos{\left( \ensuremath{\mathrm{x3}}\right) }\operatorname{,}0\right] \]
\[\operatorname{(h) }{{\ensuremath{\mathrm{x2}}}^{2}}+{{\ensuremath{\mathrm{x1}}}^{2}}\]
\[\operatorname{(x) }\left[ \ensuremath{\mathrm{x1}}\operatorname{,}\ensuremath{\mathrm{x2}}\operatorname{,}\ensuremath{\mathrm{x3}}\right] \]
| (%i6) | dh : list_matrix_entries ( jacobian ( [ h ] , x ) ) ; |
\[\operatorname{(dh) }\left[ 2 \ensuremath{\mathrm{x1}}\operatorname{,}2 \ensuremath{\mathrm{x2}}\operatorname{,}0\right] \]
| (%i7) | LieCovector ( f , dh , x ) ; |
\[\operatorname{ }\left[ 2 \sin{\left( \ensuremath{\mathrm{x3}}\right) }\operatorname{,}2 \cos{\left( \ensuremath{\mathrm{x3}}\right) }\operatorname{,}2 \ensuremath{\mathrm{x1}} \cos{\left( \ensuremath{\mathrm{x3}}\right) }-2 \ensuremath{\mathrm{x2}} \sin{\left( \ensuremath{\mathrm{x3}}\right) }\right] \]
Created with wxMaxima.