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nnss 見易い式を求めて

次の不等式を簡約します.

(%i86) f:(x^2-1)*(x^2-4)*(x^2-9)<0;
Evaluation took 0.0000 seconds (0.0000 elapsed) using 1.344 KB.
(%o86) (x^2-9)*(x^2-4)*(x^2-1) < 0

まずは,qepmax + nns です.悪くはありませんが,ちょっと解り難いですね.

(%i87) qe([],f);
Evaluation took 0.1000 seconds (0.3300 elapsed) using 2.794 MB.
(%o87) (x-3 < 0) %and (x-2 # 0) %and (x-1 # 0) %and (x+1 # 0) %and (x+2 # 0)
                 %and (x+3 > 0)
                 %and ((x-2 > 0) %or (x+2 < 0) %or ((x-1 < 0) %and (x+1 > 0)))
(%i88) nns(%);
Evaluation took 4.9000 seconds (6.1500 elapsed) using 232.032 MB.
(%o88) (x-3 < 0) %and (x+3 > 0)
                 %and ((x-2 > 0) %or (x+2 < 0) %or ((x-1 < 0) %and (x+1 > 0)))

ということで,nnss の出番です.

(%i89) nnss(f);
Evaluation took 4.4000 seconds (7.2900 elapsed) using 194.955 MB.
(%o89) ((x-3 < 0) %and (x-2 > 0)) %or ((x-1 < 0) %and (x+1 > 0))
                                  %or ((x+2 < 0) %and (x+3 > 0))