## maxima-commits

 [Maxima-commits] CVS: maxima/doc/info/de Matrices.de.texi,1.2,1.3 From: Dieter Kaiser - 2010-11-28 20:26:20 Update of /cvsroot/maxima/maxima/doc/info/de In directory sfp-cvsdas-4.v30.ch3.sourceforge.com:/tmp/cvs-serv16068/doc/info/de Modified Files: Matrices.de.texi Log Message: Moving two functions from the chapter Calculus to this file. Index: Matrices.de.texi =================================================================== RCS file: /cvsroot/maxima/maxima/doc/info/de/Matrices.de.texi,v retrieving revision 1.2 retrieving revision 1.3 diff -u -d -r1.2 -r1.3 --- Matrices.de.texi 20 Nov 2010 13:06:09 -0000 1.2 +++ Matrices.de.texi 28 Nov 2010 20:26:11 -0000 1.3 @@ -909,9 +909,107 @@ @c @closecatbox @end deffn -@... {Function} genmatrix (@var{a}, @var{i_2}, @var{j_2}, @var{i_1}, @var{j_1}) +@c --- 20.11.2010 DK ----------------------------------------------------------- +@anchor{express} +@deffn {Funktion} express (@var{expr}) + +@c HERE IS THE PREVIOUS TEXT. WHAT IS THE POINT ABOUT depends ?? +@c I'M NOT GETTING IT +@c The result uses the noun form of any +@c derivatives arising from expansion of the vector differential +@c operators. To force evaluation of these derivatives, the built-in @code{ev} +@c function can be used together with the @code{diff} evflag, after using the +@c built-in @code{depends} function to establish any new implicit dependencies. + +Expands differential operator nouns into expressions in terms of partial +derivatives. @code{express} recognizes the operators @code{grad}, @code{div}, +@code{curl}, @code{laplacian}. @code{express} also expands the cross product +@code{~}. + +Symbolic derivatives (that is, @code{diff} nouns) in the return value of express +may be evaluated by including @code{diff} in the @code{ev} function call or +command line. In this context, @code{diff} acts as an @code{evfun}. + +@code{load ("vect")} loads this function. +@c IN POINT OF FACT, express IS A SIMPLIFICATION RULE, AND express1 IS THE FCN +@c WHICH DOES ALL THE WORK + +Beispiele: + +@c ===beg=== +@c load ("vect")\$ +@c grad (x^2 + y^2 + z^2); +@c express (%); +@c ev (%, diff); +@c div ([x^2, y^2, z^2]); +@c express (%); +@c ev (%, diff); +@c curl ([x^2, y^2, z^2]); +@c express (%); +@c ev (%, diff); +@c laplacian (x^2 * y^2 * z^2); +@c express (%); +@c ev (%, diff); +@c [a, b, c] ~ [x, y, z]; +@c express (%); +@c ===end=== +@example +(%i1) load ("vect")\$ +(%i2) grad (x^2 + y^2 + z^2); + 2 2 2 +(%o2) grad (z + y + x ) +(%i3) express (%); + d 2 2 2 d 2 2 2 d 2 2 2 +(%o3) [-- (z + y + x ), -- (z + y + x ), -- (z + y + x )] + dx dy dz +(%i4) ev (%, diff); +(%o4) [2 x, 2 y, 2 z] +(%i5) div ([x^2, y^2, z^2]); + 2 2 2 +(%o5) div [x , y , z ] +(%i6) express (%); + d 2 d 2 d 2 +(%o6) -- (z ) + -- (y ) + -- (x ) + dz dy dx +(%i7) ev (%, diff); +(%o7) 2 z + 2 y + 2 x +(%i8) curl ([x^2, y^2, z^2]); + 2 2 2 +(%o8) curl [x , y , z ] +(%i9) express (%); + d 2 d 2 d 2 d 2 d 2 d 2 +(%o9) [-- (z ) - -- (y ), -- (x ) - -- (z ), -- (y ) - -- (x )] + dy dz dz dx dx dy +(%i10) ev (%, diff); +(%o10) [0, 0, 0] +(%i11) laplacian (x^2 * y^2 * z^2); + 2 2 2 +(%o11) laplacian (x y z ) +(%i12) express (%); + 2 2 2 + d 2 2 2 d 2 2 2 d 2 2 2 +(%o12) --- (x y z ) + --- (x y z ) + --- (x y z ) + 2 2 2 + dz dy dx +(%i13) ev (%, diff); + 2 2 2 2 2 2 +(%o13) 2 y z + 2 x z + 2 x y +(%i14) [a, b, c] ~ [x, y, z]; +(%o14) [a, b, c] ~ [x, y, z] +(%i15) express (%); +(%o15) [b z - c y, c x - a z, a y - b x] +@end example + +@c @opencatbox +@c @category{Differential calculus} @category{Vectors} @category{Operators} +@c @closecatbox +@end deffn + +@c ----------------------------------------------------------------------------- +@deffn {Function} genmatrix (@var{a}, @var{i_2}, @var{j_2}, @var{i_1}, @var{j_1}) @deffnx {Function} genmatrix (@var{a}, @var{i_2}, @var{j_2}, @var{i_1}) @deffnx {Function} genmatrix (@var{a}, @var{i_2}, @var{j_2}) + Returns a matrix generated from @var{a}, taking element @code{@var{a}[@var{i_1},@var{j_1}]} as the upper-left element and @code{@var{a}[@var{i_2},@var{j_2}]} @@ -987,7 +1085,8 @@ @c @closecatbox @end deffn -@... {Function} gramschmidt (@var{x}) +@c ----------------------------------------------------------------------------- +@deffn {Function} gramschmidt (@var{x}) @deffnx {Function} gramschmidt (@var{x}, @var{F}) Carries out the Gram-Schmidt orthogonalization algorithm on @var{x}, @@ -1608,6 +1707,26 @@ @c @closecatbox @end deffn +@c ----------------------------------------------------------------------------- +@deffn {Function} potential (@var{givengradient}) + +The calculation makes use of the global variable @code{potentialzeroloc[0]} +which must be @code{nonlist} or of the form + +@example +[indeterminatej=expressionj, indeterminatek=expressionk, ...] +@end example + +the +former being equivalent to the nonlist expression for all right-hand +sides in the latter. The indicated right-hand sides are used as the +lower limit of integration. The success of the integrations may +depend upon their values and order. @code{potentialzeroloc} is initially set +to 0. + +@end deffn + +@c ----------------------------------------------------------------------------- @defvr {Option variable} ratmx Default value: @code{false} @@ -1625,7 +1744,6 @@ @c @opencatbox @c @category{Matrices} @c @category{Rational expressions} @c @closecatbox - @end defvr @c --- 28.08.2010 DK -----------------------------------------------------------