en bilinear

Alternatively, try something like:

(setq opers (cons '$multioutative opers)
      *opers-list (cons '($multioutative . multioutative) *opers-list))

(defun multioutative (e z)
  (let ((op (car e))
	(args (margs e))
	(w 1))
    (setq args (mapcar #'(lambda (s) 
			   (let ((k ($numfactor s)))
			     (setq w (mul w k))
			     (div s k))) args))

    (if (or (eq w 1) ($subvarp e)) (protected-oper-apply e z) 
      (mul w (protected-oper-apply (simplifya (cons op args)) z)))))

 (%i2) declare(g,multiadditive,g,multioutative);
 (%o2) done

 (%i15) g(5*x+4*z,2*u+3*v);
 (%o15) 12*g(z,v)+8*g(z,u)+15*g(x,v)+10*g(x,u)

 (%i16) g(-v);
 (%o16) -g(v)

The Maxima outative property looks for factors that are declared constants, but my
code only extracts numerical constants.

--Barton

-----maxima-bounces at math.utexas.edu wrote: -----


>/*?bilinear?*/
>
>(%i11)?en_bioutative(g);
>(%i14)?load("multiadditive");
>(%i15)?declare(g,multiadditive);
>(%i16)?g(5*x+4*z,2*u+3*v);
>(%o16)?????????12?g(z,?v)?+?8?g(z,?u)?+?15?g(x,?v)?+?10?g(x,?u)
>
>
>
>----------------
>
>swap_function_in_expr(f_from,f_to,expr):=scanmap(??lambda([x],if
>atom(x)?then?x?else?if?op(x)?=?f_from?then?substpart(f_to,x,0)?else
>x),expr);
>/*usage
>(%i2)?swap_function_in_expr(f,k,?h(f(x+a)+a)+f(f(x))*c);
>(%o2)?????????????????????h(k(x?+?a)?+?a)?+?c?k(k(x))
>
>*/
>
>
>:lisp?(defun?$tellsimp_func_name_swap??(expr_from?expr_to?fname_from
>fname_to?)??(proc-$tellsimp????(list??????(mfuncall
>'$swap_function_in_expr?fname_from??fname_to??expr_from?)
>(mfuncall?'$swap_function_in_expr?fname_from??fname_to??expr_to?)
>)))
>
>
>/*usage
>is_op_p(expr,op_):=if?atom(expr)?then?false?else?operatorp(expr,op_);
>neg_expr_p(expr):=is_op_p(expr,"-");
>matchdeclare([negexpr],neg_expr_p);
>
>tellsimp_func_name_swap(f(negexpr),-f(-negexpr),f,h);
>tellsimp_func_name_swap(f(negexpr),-f(-negexpr),f,g);
>
>f(-x)
>g(-x)
>h(-x)
>
>(%i7)?f(-x);
>(%o7)???????????????????????????????f(-?x)
>(%i8)?g(-x);
>(%o8)???????????????????????????????-?g(x)
>(%i9)?h(-x);
>(%o9)???????????????????????????????-?h(x)
>
>*/
>
>
>
>en_bioutative(func):=block(
>??matchdeclare?(xx,?all),
>??matchdeclare?(bb,?lambda?([e],?scalarp(e)?and?e?#?1)),
>??matchdeclare?(uu,?lambda?([e],?not?scalarp(e))),
>??tellsimp_func_name_swap(_func_(xx,?bb*uu),?bb?*?_func_(xx,
>uu),_func_,func),
>??tellsimp_func_name_swap(_func_(bb*uu,?xx),?bb?*?_func_(uu,
>xx),_func_,func)
>);
>
>
>/*usage
>(%i11)?en_bioutative(g);
>(%o11)??????????????????[grule5,?grule4,?grule3,?false]
>(%i12)?g(5*x,y);
>(%o12)?????????????????????????????5?g(x,?y)
>(%i13)?g(5*x,10*y);
>(%o13)????????????????????????????50?g(x,?y)
>*/
>
>---------------
>_______________________________________________
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