(maxima.info)Package ineq

---

Next: Package rducon Prev: Package functs Up: simplification-pkg

---

Enter node , (file) or (file)node

81.5 Package ineq
=================

The 'ineq' package contains simplification rules for inequalities.

   Example session:

     (%i1) load(ineq)$
     tellsimp: warning: rule will treat '+
                               ' as noncommutative and nonassociative.
     tellsimp: warning: rule will treat '+
                               ' as noncommutative and nonassociative.
     tellsimp: warning: rule will treat '+
                               ' as noncommutative and nonassociative.
     tellsimp: warning: rule will treat '+
                               ' as noncommutative and nonassociative.
     tellsimp: warning: rule will treat '+
                               ' as noncommutative and nonassociative.
     tellsimp: warning: rule will treat '+
                               ' as noncommutative and nonassociative.
     tellsimp: warning: rule will treat '+
                               ' as noncommutative and nonassociative.
     tellsimp: warning: rule will treat '+
                               ' as noncommutative and nonassociative.
     (%i2) a>=4;  /* a sample inequality */
     (%o2)                        a >= 4
     (%o3)                     b + a > c + 4
     (%o4)                       7 x < 7 y
     (%o5)                    - 2 x <= - 6 z
                                      2
     (%o6)                      1 <= a  + 1
     (%o8)                       2 x < 3 x
     (%o9)                        a >= b
     (%o10)                   a + 3 >= b + 3
     (%o11)                       a >= b
     (%o12)                     a >= c - b
     (%o13)                     b + a >= c
     (%o14)                 (- c) + b + a >= 0
     (%o15)                   c - b - a <= 0
                                    2
     (%o16)                  (z - 1)  > - 2 z
                                 2
     (%o17)                     z  + 1 > 0
     (%o18)                        true
     (%i19) (b>c)+%; /* add a second, strict inequality */

   Be careful about using parentheses around the inequalities: when the
user types in '(A > B) + (C = 5)' the result is 'A + C > B + 5', but 'A
> B + C = 5' is a syntax error, and '(A > B + C) = 5' is something else
entirely.

   Do 'disprule (all)' to see a complete listing of the rule
definitions.

   The user will be queried if Maxima is unable to decide the sign of a
quantity multiplying an inequality.

   The most common mis-feature is illustrated by:

     (%i1) eq: a > b;
     (%o1)                         a > b
     (%i2) 2*eq;
     (%o2)                       2 (a > b)
     (%i3) % - eq;
     (%o3)                         a > b

   Another problem is 0 times an inequality; the default to have this
turn into 0 has been left alone.  However, if you type
'X*<some_inequality>' and Maxima asks about the sign of 'X' and you
respond 'zero' (or 'z'), the program returns 'X*<some_inequality>' and
not use the information that 'X' is 0.  You should do 'ev (%, x: 0)' in
such a case, as the database will only be used for comparison purposes
in decisions, and not for the purpose of evaluating 'X'.

   The user may note a slower response when this package is loaded, as
the simplifier is forced to examine more rules than without the package,
so you might wish to remove the rules after making use of them.  Do
'kill (rules)' to eliminate all of the rules (including any that you
might have defined); or you may be more selective by killing only some
of them; or use 'remrule' on a specific rule.

   Note that if you load this package after defining your own rules you
will clobber your rules that have the same name.  The rules in this
package are: '*rule1', ..., '*rule8', '+rule1', ..., '+rule18', and you
must enclose the rulename in quotes to refer to it, as in 'remrule ("+",
"+rule1")' to specifically remove the first rule on '"+"' or 'disprule
("*rule2")' to display the definition of the second multiplicative rule.