## [Maxima-commits] CVS: maxima/doc/info/de Polynomials.de.texi, 1.5, 1.6

 [Maxima-commits] CVS: maxima/doc/info/de Polynomials.de.texi, 1.5, 1.6 From: Dieter Kaiser - 2010-12-11 00:07:34 ```Update of /cvsroot/maxima/maxima/doc/info/de In directory sfp-cvsdas-4.v30.ch3.sourceforge.com:/tmp/cvs-serv26504/doc/info/de Modified Files: Polynomials.de.texi Log Message: Moving the function dontfactor from Matrices.de.texi in this chapter. Index: Polynomials.de.texi =================================================================== RCS file: /cvsroot/maxima/maxima/doc/info/de/Polynomials.de.texi,v retrieving revision 1.5 retrieving revision 1.6 diff -u -d -r1.5 -r1.6 --- Polynomials.de.texi 6 Dec 2010 00:07:04 -0000 1.5 +++ Polynomials.de.texi 11 Dec 2010 00:07:25 -0000 1.6 @@ -2,6 +2,7 @@ @c File : Polynomials.de.texi @c License : GNU General Public License (GPL) @c Language : German +@c Original : Polynomials.texi revision 1.34 @c Date : 15.10.2010 @c @c This file is part of Maxima -- GPL CAS based on DOE-MACSYMA @@ -68,79 +69,10 @@ @node Functions and Variables for Polynomials, , Introduction to Polynomials, Polynome @section Functions and Variables for Polynomials -@... ----------------------------------------------------------------------------- -@... {Funktion} lopow (@var{expr}, @var{x}) - -@... Returns the lowest exponent of @var{x} which explicitly appears in -@... @var{expr}. Thus - -gibt den kleinsten Exponenten von @var{x} zur@"uck, der im Ausdruck @var{expr} -auftritt. Treten symbolische Exponententen auf, wird ein Ausdruck mit @code{min} -zur@"uckgegeben. - -@... -(%i1) lopow ((x+y)^2 + (x+y)^a, x+y); -(%o1) min(a, 2) -@... example - -@... @opencatbox -@... @category{Ausdr@"ucke} -@... @closecatbox -@... deffn - @c ISN'T THERE AN EQUIVALENT FUNCTION SOMEWHERE ?? @c NEEDS WORK (IF KEPT) @c ----------------------------------------------------------------------------- -@... {Funktion} polymod (@var{p}) -@... {Function} polymod (@var{p}, @var{m}) - -@... Converts the polynomial @var{p} to a modular representation with respect to -@... the current modulus which is the value of the variable @code{modulus}. - -Konvertiert das Polynom @var{p} in eine modulare Darstellung bez@"uglich dem -aktuellen Modul. Das Modul ist der Wert der Variablen @code{modulus}. - -@... @code{polymod (@var{p}, @var{m})} specifies a modulus @var{m} to be used -@... instead of the current value of @code{modulus}. - -@...{polymod(@var{p}, @var{m}} konvertiert das Polynom bez@"uglich dem Modul -@...{m}, anstatt dem aktuellen Modul @code{modulus}. - -@... See @code{modulus}. - -Siehe @code{modulus}. - -@... @opencatbox -@... @category{Polynome} -@... @closecatbox -@... deffn - -@... ----------------------------------------------------------------------------- -@... {Function} powers (@var{expr}, @var{x}) -Gives the powers of @var{x} occuring in @var{expr}. - -@...{load (powers)} loads this function. -@... HMM, THERE'S A BUNCH OF MAXIMA FUNCTIONS IN src/powers.lisp ... -@... FOR SOME REASON src/powers.lisp IS NOT PART OF THE USUAL BUILD -- STRANGE - -@... HERE IS THE TEXT FROM archive/share/unknown/powers.usg -- MERGE !!! -@... THIS FUNCTION IS A GENERALISATION OF "HIPOW" AND "LOPOW" -@... IN THAT IT RETURNS A LIST OF ALL THE POWERS OF VAR OCCURING -@... IN EXPR. IT IS STILL NECESSARY TO EXPAND EXPR BEFORE APPLYING -@... POWERS (ON PAIN OF GETTING THE WRONG ANSWER). -@... -@... THIS FUNCTION HAS MANY USES, E.G. IF YOU WANT TO FIND ALL -@... THE COEFFICIENTS OF X IN A POLYNOMIAL POLY YOU CAN USE -@... MAP(LAMBDA([POW],COEFF(POLY,X,POW)),POWERS(POLY,X)); -@... AND MANY OTHER SIMILAR USEFUL HACKS. - -@... @opencatbox -@... @category{Expressions} @category{Polynomials} -@... @closecatbox -@... deffn - -@... ----------------------------------------------------------------------------- @defvr {Option variable} algebraic Default value: @code{false} @@ -423,6 +355,22 @@ @c @closecatbox @end deffn +@c --- 09.12.2010 DK ----------------------------------------------------------- +@anchor{dontfactor} +@defvr {Optionsvariable} dontfactor +Standardwert: @code{[]} + +@code{dontfactor} may be set to a list of variables with respect to which +factoring is not to occur. (The list is initially empty.) Factoring also +will not take place with respect to any variables which are less important, +according the variable ordering assumed for canonical rational expression +(CRE) form, than those on the @code{dontfactor} list. + +@c @opencatbox +@c @category{Expressions} +@c @closecatbox +@end defvr + @c ----------------------------------------------------------------------------- @deffn {Function} eliminate ([@var{eqn_1}, ..., @var{eqn_n}], [@var{x_1}, ..., @var{x_k}]) @@ -1109,6 +1057,26 @@ @c @closecatbox @end defvr +@c ----------------------------------------------------------------------------- +@deffn {Funktion} lopow (@var{expr}, @var{x}) + +@c Returns the lowest exponent of @var{x} which explicitly appears in +@c @var{expr}. Thus + +gibt den kleinsten Exponenten von @var{x} zur@"uck, der im Ausdruck @var{expr} +auftritt. Treten symbolische Exponententen auf, wird ein Ausdruck mit @code{min} +zur@"uckgegeben. + +@example +(%i1) lopow ((x+y)^2 + (x+y)^a, x+y); +(%o1) min(a, 2) +@end example + +@c @opencatbox +@c @category{Ausdr@"ucke} +@c @closecatbox +@end deffn + @c DESCRIBE lratsubst INDEPENDENTLY OF subst @c THIS ITEM NEEDS MORE WORK @@ -1336,6 +1304,55 @@ @end deffn @c ----------------------------------------------------------------------------- +@deffn {Funktion} polymod (@var{p}) +@deffnx {Function} polymod (@var{p}, @var{m}) + +@c Converts the polynomial @var{p} to a modular representation with respect to +@c the current modulus which is the value of the variable @code{modulus}. + +Konvertiert das Polynom @var{p} in eine modulare Darstellung bez@"uglich dem +aktuellen Modul. Das Modul ist der Wert der Variablen @code{modulus}. + +@c @code{polymod (@var{p}, @var{m})} specifies a modulus @var{m} to be used +@c instead of the current value of @code{modulus}. + +@code{polymod(@var{p}, @var{m}} konvertiert das Polynom bez@"uglich dem Modul +@var{m}, anstatt dem aktuellen Modul @code{modulus}. + +@c See @code{modulus}. + +Siehe @code{modulus}. + +@c @opencatbox +@c @category{Polynome} +@c @closecatbox +@end deffn + +@c ----------------------------------------------------------------------------- +@deffn {Function} powers (@var{expr}, @var{x}) +Gives the powers of @var{x} occuring in @var{expr}. + +@code{load (powers)} loads this function. +@c HMM, THERE'S A BUNCH OF MAXIMA FUNCTIONS IN src/powers.lisp ... +@c FOR SOME REASON src/powers.lisp IS NOT PART OF THE USUAL BUILD -- STRANGE + +@c HERE IS THE TEXT FROM archive/share/unknown/powers.usg -- MERGE !!! +@c THIS FUNCTION IS A GENERALISATION OF "HIPOW" AND "LOPOW" +@c IN THAT IT RETURNS A LIST OF ALL THE POWERS OF VAR OCCURING +@c IN EXPR. IT IS STILL NECESSARY TO EXPAND EXPR BEFORE APPLYING +@c POWERS (ON PAIN OF GETTING THE WRONG ANSWER). +@c +@c THIS FUNCTION HAS MANY USES, E.G. IF YOU WANT TO FIND ALL +@c THE COEFFICIENTS OF X IN A POLYNOMIAL POLY YOU CAN USE +@c MAP(LAMBDA([POW],COEFF(POLY,X,POW)),POWERS(POLY,X)); +@c AND MANY OTHER SIMILAR USEFUL HACKS. + +@c @opencatbox +@c @category{Expressions} @category{Polynomials} +@c @closecatbox +@end deffn + +@c ----------------------------------------------------------------------------- @deffn {Function} quotient (@var{p_1}, @var{p_2}) @deffnx {Function} quotient (@var{p_1}, @var{p_2}, @var{x_1}, ..., @var{x_n}) ```

 [Maxima-commits] CVS: maxima/doc/info/de Polynomials.de.texi, 1.5, 1.6 From: Dieter Kaiser - 2010-12-11 00:07:34 ```Update of /cvsroot/maxima/maxima/doc/info/de In directory sfp-cvsdas-4.v30.ch3.sourceforge.com:/tmp/cvs-serv26504/doc/info/de Modified Files: Polynomials.de.texi Log Message: Moving the function dontfactor from Matrices.de.texi in this chapter. Index: Polynomials.de.texi =================================================================== RCS file: /cvsroot/maxima/maxima/doc/info/de/Polynomials.de.texi,v retrieving revision 1.5 retrieving revision 1.6 diff -u -d -r1.5 -r1.6 --- Polynomials.de.texi 6 Dec 2010 00:07:04 -0000 1.5 +++ Polynomials.de.texi 11 Dec 2010 00:07:25 -0000 1.6 @@ -2,6 +2,7 @@ @c File : Polynomials.de.texi @c License : GNU General Public License (GPL) @c Language : German +@c Original : Polynomials.texi revision 1.34 @c Date : 15.10.2010 @c @c This file is part of Maxima -- GPL CAS based on DOE-MACSYMA @@ -68,79 +69,10 @@ @node Functions and Variables for Polynomials, , Introduction to Polynomials, Polynome @section Functions and Variables for Polynomials -@... ----------------------------------------------------------------------------- -@... {Funktion} lopow (@var{expr}, @var{x}) - -@... Returns the lowest exponent of @var{x} which explicitly appears in -@... @var{expr}. Thus - -gibt den kleinsten Exponenten von @var{x} zur@"uck, der im Ausdruck @var{expr} -auftritt. Treten symbolische Exponententen auf, wird ein Ausdruck mit @code{min} -zur@"uckgegeben. - -@... -(%i1) lopow ((x+y)^2 + (x+y)^a, x+y); -(%o1) min(a, 2) -@... example - -@... @opencatbox -@... @category{Ausdr@"ucke} -@... @closecatbox -@... deffn - @c ISN'T THERE AN EQUIVALENT FUNCTION SOMEWHERE ?? @c NEEDS WORK (IF KEPT) @c ----------------------------------------------------------------------------- -@... {Funktion} polymod (@var{p}) -@... {Function} polymod (@var{p}, @var{m}) - -@... Converts the polynomial @var{p} to a modular representation with respect to -@... the current modulus which is the value of the variable @code{modulus}. - -Konvertiert das Polynom @var{p} in eine modulare Darstellung bez@"uglich dem -aktuellen Modul. Das Modul ist der Wert der Variablen @code{modulus}. - -@... @code{polymod (@var{p}, @var{m})} specifies a modulus @var{m} to be used -@... instead of the current value of @code{modulus}. - -@...{polymod(@var{p}, @var{m}} konvertiert das Polynom bez@"uglich dem Modul -@...{m}, anstatt dem aktuellen Modul @code{modulus}. - -@... See @code{modulus}. - -Siehe @code{modulus}. - -@... @opencatbox -@... @category{Polynome} -@... @closecatbox -@... deffn - -@... ----------------------------------------------------------------------------- -@... {Function} powers (@var{expr}, @var{x}) -Gives the powers of @var{x} occuring in @var{expr}. - -@...{load (powers)} loads this function. -@... HMM, THERE'S A BUNCH OF MAXIMA FUNCTIONS IN src/powers.lisp ... -@... FOR SOME REASON src/powers.lisp IS NOT PART OF THE USUAL BUILD -- STRANGE - -@... HERE IS THE TEXT FROM archive/share/unknown/powers.usg -- MERGE !!! -@... THIS FUNCTION IS A GENERALISATION OF "HIPOW" AND "LOPOW" -@... IN THAT IT RETURNS A LIST OF ALL THE POWERS OF VAR OCCURING -@... IN EXPR. IT IS STILL NECESSARY TO EXPAND EXPR BEFORE APPLYING -@... POWERS (ON PAIN OF GETTING THE WRONG ANSWER). -@... -@... THIS FUNCTION HAS MANY USES, E.G. IF YOU WANT TO FIND ALL -@... THE COEFFICIENTS OF X IN A POLYNOMIAL POLY YOU CAN USE -@... MAP(LAMBDA([POW],COEFF(POLY,X,POW)),POWERS(POLY,X)); -@... AND MANY OTHER SIMILAR USEFUL HACKS. - -@... @opencatbox -@... @category{Expressions} @category{Polynomials} -@... @closecatbox -@... deffn - -@... ----------------------------------------------------------------------------- @defvr {Option variable} algebraic Default value: @code{false} @@ -423,6 +355,22 @@ @c @closecatbox @end deffn +@c --- 09.12.2010 DK ----------------------------------------------------------- +@anchor{dontfactor} +@defvr {Optionsvariable} dontfactor +Standardwert: @code{[]} + +@code{dontfactor} may be set to a list of variables with respect to which +factoring is not to occur. (The list is initially empty.) Factoring also +will not take place with respect to any variables which are less important, +according the variable ordering assumed for canonical rational expression +(CRE) form, than those on the @code{dontfactor} list. + +@c @opencatbox +@c @category{Expressions} +@c @closecatbox +@end defvr + @c ----------------------------------------------------------------------------- @deffn {Function} eliminate ([@var{eqn_1}, ..., @var{eqn_n}], [@var{x_1}, ..., @var{x_k}]) @@ -1109,6 +1057,26 @@ @c @closecatbox @end defvr +@c ----------------------------------------------------------------------------- +@deffn {Funktion} lopow (@var{expr}, @var{x}) + +@c Returns the lowest exponent of @var{x} which explicitly appears in +@c @var{expr}. Thus + +gibt den kleinsten Exponenten von @var{x} zur@"uck, der im Ausdruck @var{expr} +auftritt. Treten symbolische Exponententen auf, wird ein Ausdruck mit @code{min} +zur@"uckgegeben. + +@example +(%i1) lopow ((x+y)^2 + (x+y)^a, x+y); +(%o1) min(a, 2) +@end example + +@c @opencatbox +@c @category{Ausdr@"ucke} +@c @closecatbox +@end deffn + @c DESCRIBE lratsubst INDEPENDENTLY OF subst @c THIS ITEM NEEDS MORE WORK @@ -1336,6 +1304,55 @@ @end deffn @c ----------------------------------------------------------------------------- +@deffn {Funktion} polymod (@var{p}) +@deffnx {Function} polymod (@var{p}, @var{m}) + +@c Converts the polynomial @var{p} to a modular representation with respect to +@c the current modulus which is the value of the variable @code{modulus}. + +Konvertiert das Polynom @var{p} in eine modulare Darstellung bez@"uglich dem +aktuellen Modul. Das Modul ist der Wert der Variablen @code{modulus}. + +@c @code{polymod (@var{p}, @var{m})} specifies a modulus @var{m} to be used +@c instead of the current value of @code{modulus}. + +@code{polymod(@var{p}, @var{m}} konvertiert das Polynom bez@"uglich dem Modul +@var{m}, anstatt dem aktuellen Modul @code{modulus}. + +@c See @code{modulus}. + +Siehe @code{modulus}. + +@c @opencatbox +@c @category{Polynome} +@c @closecatbox +@end deffn + +@c ----------------------------------------------------------------------------- +@deffn {Function} powers (@var{expr}, @var{x}) +Gives the powers of @var{x} occuring in @var{expr}. + +@code{load (powers)} loads this function. +@c HMM, THERE'S A BUNCH OF MAXIMA FUNCTIONS IN src/powers.lisp ... +@c FOR SOME REASON src/powers.lisp IS NOT PART OF THE USUAL BUILD -- STRANGE + +@c HERE IS THE TEXT FROM archive/share/unknown/powers.usg -- MERGE !!! +@c THIS FUNCTION IS A GENERALISATION OF "HIPOW" AND "LOPOW" +@c IN THAT IT RETURNS A LIST OF ALL THE POWERS OF VAR OCCURING +@c IN EXPR. IT IS STILL NECESSARY TO EXPAND EXPR BEFORE APPLYING +@c POWERS (ON PAIN OF GETTING THE WRONG ANSWER). +@c +@c THIS FUNCTION HAS MANY USES, E.G. IF YOU WANT TO FIND ALL +@c THE COEFFICIENTS OF X IN A POLYNOMIAL POLY YOU CAN USE +@c MAP(LAMBDA([POW],COEFF(POLY,X,POW)),POWERS(POLY,X)); +@c AND MANY OTHER SIMILAR USEFUL HACKS. + +@c @opencatbox +@c @category{Expressions} @category{Polynomials} +@c @closecatbox +@end deffn + +@c ----------------------------------------------------------------------------- @deffn {Function} quotient (@var{p_1}, @var{p_2}) @deffnx {Function} quotient (@var{p_1}, @var{p_2}, @var{x_1}, ..., @var{x_n}) ```