Negligible terms in polynomials

Maybe it is really handy to have a special version of
freeof(x_1,...,x_n, expr) which compares x_1,...,x_n only
with non-dummy variables in expr.

Here's a code which could be used in addition to nrat4.lisp
stuff:

------------------------------------------------------------

(defun lfreeof-var (x expr)
  (let*
    (($listdummyvars nil)
     (v ($listofvars expr)))
    (loop while x do
      (if (member (car x) v :test 'equal)
        (return-from lfreeof-var nil))
      (setf x (cdr x)))
    t))

(defun $lfreeof_var (x expr)
  (if ($listp x)
    (lfreeof-var (margs x) expr)
    (merror "First argument must be a list")))

(defun $freeof_var (&rest xe)
  (let ((ex (reverse xe)))
    (lfreeof-var (cdr ex) (car ex))))

------------------------------------------------------------

Examples:

freeof_var (x,y,z, x^n + y^n = z^n)           => false
freeof     (x,y,z, x^n + y^n = z^n)           => false

Dummy variables:
freeof_var (i, 'sum(i,i,0,1000))              => true
freeof     (i, 'sum(i,i,0,1000))              => true

Useless for operators or constants:
freeof_var (cos, cos(x))                      => true
freeof     (cos, cos(x))                      => false
freeof_var (23, 23*x)                         => true
freeof     (23, 23*x)                         => false

But may be useful for subscripted names:
freeof_var (x,y,z, x[0]^n + y[0]^n = z[0]^n)  => true
freeof     (x,y,z, x[0]^n + y[0]^n = z[0]^n)  => false

-- 
Setting Orange, Chaos 10 YOLD 3175
Alexey Beshenov  http://beshenov.ru/