# cineqs4 使用例

Maxima 5.39.0
using Lisp CMU Common Lisp 21b (21B Unicode)

(%i1) ep(1,0)$cineqs4('( (x-1)*(x^2-2)*(x^3-3)*(x^2+4)<=0 )); Evaluation took 0.0000 seconds (0.0000 elapsed) using 856 bytes. Evaluation took 0.0600 seconds (0.0600 elapsed) using 1.337 MB. (%o2) [[-sqrt(2) <= x,x <= 1],[sqrt(2) <= x,x <= 3^(1/3)]] 代数的な表示が出来ない場合は，近似値（内部では小数第6位以下を切り捨てています）で答えます． (%i3) ep(1,0)$cineqs4('(   (x-1)*(x^2-2)*(x^3-3)*(x^2+4)<=1/10   ));
Evaluation took 0.0000 seconds (0.0100 elapsed) using 720 bytes.
Evaluation took 0.0100 seconds (0.0100 elapsed) using 1.091 MB.
(%o4) [[-1.414631932468004 <= x,x <= 1.010331702011963],
[1.374072765807135 <= x,x <= 1.473559962228517]]

(%i5) ep(1,0)$cineqs4('( (x-1)/x<2 )); Evaluation took 0.0000 seconds (0.0000 elapsed) using 720 bytes. Evaluation took 0.0000 seconds (0.0100 elapsed) using 520.242 KB. (%o6) [[x < -1],[0 < x]] 連言． (%i7) ep(1,0)$cineqs4('(   (x-1)*(x^2-2)*(x^3-3)<=0 and (x-1)/x<2 ));
Evaluation took 0.0000 seconds (0.0000 elapsed) using 720 bytes.
Evaluation took 0.0400 seconds (0.0500 elapsed) using 2.571 MB.
(%o8) [[-sqrt(2) <= x,x < -1],[0 < x,x <= 1],[sqrt(2) <= x,x <= 3^(1/3)]]

(%i9) ep(1,0)$cineqs4('( (x-1)*(x^2-2)*(x^3-3)<=0 or (x-1)/x<2 )); Evaluation took 0.0000 seconds (0.0000 elapsed) using 720 bytes. Evaluation took 0.0300 seconds (0.0300 elapsed) using 2.804 MB. (%o10) [[true]] こんな場合は．．． (%i11) ep(1,0)$cineqs4('(   x^4-x-1<=0   ));
Evaluation took 0.0000 seconds (0.0000 elapsed) using 720 bytes.
Evaluation took 0.2500 seconds (0.2500 elapsed) using 24.248 MB.
(%o12) [[-(sqrt(sqrt(6)*sqrt((sqrt(849)+9)^(1/3)*(3*sqrt(849)+155)^(1/3)
*(2^(8/3)*18^(2/3)*sqrt(849)
-9*2^(8/3)*18^(2/3))
+(sqrt(849)+9)^(1/3)*(3*sqrt(849)+155)^(2/3)
*(2^(1/3)*18^(2/3)*sqrt(849)
-9*2^(1/3)*18^(2/3))
+(sqrt(849)+9)^(1/3)
*(32*18^(2/3)*sqrt(849)-16*18^(5/3)))
+3*2^(11/3)*(3^(3/2)*sqrt(283)-27)^(1/3)
-8*18^(2/3)*(sqrt(3)*sqrt(283)+9)^(1/3))
-sqrt(6)*sqrt(2^(1/3)*(3*sqrt(849)-27)^(1/3)*(3*sqrt(849)+155)^(1/3)
-2^(8/3)*(3*sqrt(849)-27)^(1/3)))
/24
<= x,
x <= (sqrt(sqrt(6)*sqrt((sqrt(849)+9)^(1/3)*(3*sqrt(849)+155)^(1/3)
*(2^(8/3)*18^(2/3)
*sqrt(849)
-9*2^(8/3)*18^(2/3))
+(sqrt(849)+9)^(1/3)*(3*sqrt(849)+155)^(2/3)
*(2^(1/3)*18^(2/3)
*sqrt(849)
-9*2^(1/3)*18^(2/3))
+(sqrt(849)+9)^(1/3)
*(32*18^(2/3)*sqrt(849)-16*18^(5/3)))
+3*2^(11/3)*(3^(3/2)*sqrt(283)-27)^(1/3)
-8*18^(2/3)*(sqrt(3)*sqrt(283)+9)^(1/3))
+sqrt(6)*sqrt(2^(1/3)*(3*sqrt(849)-27)^(1/3)
*(3*sqrt(849)+155)^(1/3)
-2^(8/3)*(3*sqrt(849)-27)^(1/3)))
/24]]

コントローラー ep の第一引数を 0 にすると，近似値で答えます．

(%i13) ep(0,0)$cineqs4('( x^4-x-1<=0 )); Evaluation took 0.0000 seconds (0.0000 elapsed) using 736 bytes. Evaluation took 0.0000 seconds (0.0100 elapsed) using 175.711 KB. (%o14) [[-0.7244919786096257 <= x,x <= 1.220744081172491]] 無理関数で表された不等式． (%i15) ep(1,0)$cineqs4('(   sqrt(x)<x-1  ));
Evaluation took 0.0000 seconds (0.0000 elapsed) using 720 bytes.
Evaluation took 0.0100 seconds (0.0100 elapsed) using 674.156 KB.
(%o16) [[(sqrt(5)+3)/2 < x]]

(%i17) ep(1,0)$cineqs4('( 1<sqrt(x) implies 1<x )); Evaluation took 0.0000 seconds (0.0000 elapsed) using 720 bytes. Evaluation took 0.0100 seconds (0.0100 elapsed) using 428.797 KB. (%o18) [[true]] 根号が複数あっても． (%i19) ep(1,0)$cineqs4('(   sqrt(x)+sqrt(3-x)<2  ));
Evaluation took 0.0000 seconds (0.0000 elapsed) using 720 bytes.
Evaluation took 0.0300 seconds (0.0200 elapsed) using 1.524 MB.
(%o20) [[0 <= x,x < -(2^(3/2)-3)/2],[(2^(3/2)+3)/2 < x,x <= 3]]
(%i21) ep(0,0)$cineqs4('( sqrt(x)+sqrt(3-x)+sqrt(3+x)<22/5 )); Evaluation took 0.0000 seconds (0.0000 elapsed) using 736 bytes. Evaluation took 0.0200 seconds (0.0200 elapsed) using 2.500 MB. (%o22) [[0 <= x,x < 0.9647335423197492],[2.937906564163217 < x,x <= 3]] ネストされても． (%i23) ep(1,0)$cineqs4('(   1/sqrt(sqrt(1+x)-x)<2   ));
Evaluation took 0.0000 seconds (0.0000 elapsed) using 720 bytes.
Evaluation took 0.0700 seconds (0.0800 elapsed) using 4.835 MB.
(%o24) [[-1 <= x,x < 5/4]]

(%i25) ep(1,0)\$cineqs4('(   x^4-x^(1/3)-1>0   ));
Evaluation took 0.0000 seconds (0.0000 elapsed) using 720 bytes.
Evaluation took 0.0300 seconds (0.0400 elapsed) using 1.039 MB.
(%o26) [[x < -0.6196702671972711],[1.198342827550492 < x]]