Create solver_absolute_value.py

solver_absolute_value.py

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+from __future__ import annotations
+
+import re
+from typing import Optional
+
+from models import SolverResult
+
+
+def solve_absolute_value(text: str) -> Optional[SolverResult]:
+    lower = (text or "").lower()
+
+    if "|" not in text and "absolute value" not in lower and "abs" not in lower:
+        return None
+
+    # |x| = a
+    m = re.search(r"\|?\s*x\s*\|?\s*=\s*(-?\d+(?:\.\d+)?)", text.replace(" ", ""))
+    if m:
+        a = float(m.group(1))
+        if a < 0:
+            return SolverResult(
+                domain="quant",
+                solved=True,
+                topic="absolute_value",
+                answer_value="no solution",
+                internal_answer="no solution",
+                steps=[
+                    "Absolute value cannot equal a negative number.",
+                ],
+            )
+        return SolverResult(
+            domain="quant",
+            solved=True,
+            topic="absolute_value",
+            answer_value=f"{a:g} and {-a:g}",
+            internal_answer=f"{a:g} and {-a:g}",
+            steps=[
+                "For |x| = a with a ≥ 0, x = a or x = -a.",
+            ],
+        )
+
+    # |x - a| = b
+    m = re.search(r"\|x-(-?\d+(?:\.\d+)?)\|=(-?\d+(?:\.\d+)?)", text.replace(" ", ""))
+    if m:
+        a = float(m.group(1))
+        b = float(m.group(2))
+        if b < 0:
+            return SolverResult(
+                domain="quant",
+                solved=True,
+                topic="absolute_value",
+                answer_value="no solution",
+                internal_answer="no solution",
+                steps=["Absolute value cannot equal a negative number."],
+            )
+        x1 = a + b
+        x2 = a - b
+        return SolverResult(
+            domain="quant",
+            solved=True,
+            topic="absolute_value",
+            answer_value=f"{x1:g} and {x2:g}",
+            internal_answer=f"{x1:g} and {x2:g}",
+            steps=[
+                "Split the absolute value equation into two cases.",
+                "Solve x − a = b and x − a = -b.",
+            ],
+        )
+
+    return None