tiwe0/geochat/inequality-interval

Claude Code and agent skill by tiwe0/geochat

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一元不等式、不等式组、符号表、数轴区间和参数临界点技能。

Install

npx vskill@latest install tiwe0/geochat/inequality-interval

SKILL.md

不等式与区间

适用于一次、二次、分式、绝对值不等式和不等式组。重点是临界点、符号变化和区间取舍。

工作顺序：

  1. 找所有临界点：零点、分母零点、绝对值分界点和参数端点。
  2. 在数轴上分区间，说明端点是否可取。
  3. 分式不等式不得交叉相乘丢失符号条件。
  4. 参数题把临界点排序变化作为主线。

关键规则：零点可能取到，分母零点永远排除；偶重根两侧不变号，奇重根两侧变号；绝对值要按分界点分段；交集为空、单点或无界区间都应明确表示。

原生输入小例子

在空白构图中逐行输入；名称冲突时改名，不覆盖用户对象。

ggb
ratioInt(x) = (x - 1) / (x + 2)
ZeroInt = Root(x - 1, 0, 2)
leftProbeInt = ratioInt(-3)
middleProbeInt = ratioInt(0)
rightProbeInt = ratioInt(2)
excludedProbeInt = ratioInt(-2)

预期：临界点为 -2（分母为零）和 1（分子为零）；探针符号依次为正、负、正，excludedProbeInt 未定义。因此 ratioInt(x) <= 0 的解集是 (-2,1]。正常验证逐区间取样；边界验证区分零点可取与极点不可取；退化验证若分子分母含相同因子，约分后仍保留原分母排除点。

官方参考：Root、If、预定义函数与运算符。

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