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from __future__ import annotations
import copy
import pytest
from gap_pipeline.models import CanonicalItem
@pytest.fixture
def item() -> CanonicalItem:
return CanonicalItem(
item_id="demo-A-1",
problem=r"Let \(a>0\). Prove that \(a+1/a\ge 2\).",
solution=(
r"Since \((a-1)^2\ge0\), expanding gives \(a^2-2a+1\ge0\). "
r"Divide by \(a>0\) to obtain \(a+1/a\ge2\)."
),
variables=["a"],
problem_type="proof",
)
@pytest.fixture
def plan_dict() -> dict:
return {
"core_steps": [
"use nonnegativity of a square",
"expand and divide by a positive quantity",
],
"mutable_slots": {
"slot1": {
"description": "the positive reference value",
"original": "1",
}
},
}
@pytest.fixture
def candidate_dict() -> dict:
return {
"question": "Let x>0. Prove that x+4/x >= 4.",
"solution": (
"Since (x-2)^2 >= 0, expand and divide by x>0 "
"to get x+4/x >= 4."
),
}
def changed_candidate(candidate: dict, suffix: str) -> dict:
value = copy.deepcopy(candidate)
value["question"] = value["question"] + f" [{suffix}]"
value["solution"] = value["solution"] + f" Repair {suffix}."
return value
|
