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from .explainer_types import ExplainerResult, ExplainerScaffold
_ALGEBRA_PATTERNS = [
r"=",
r"\bsolve\b",
r"\bequation\b",
r"\bexpression\b",
r"\bvalue of\b",
r"\bwhat is x\b",
r"\bwhat is y\b",
r"\bvariable\b",
]
def _looks_like_algebra_question(text: str) -> bool:
low = (text or "").lower()
if re.search(r"\b[xyzab]\b", low) and "=" in low:
return True
if any(re.search(p, low) for p in _ALGEBRA_PATTERNS):
return True
return False
def _infer_algebra_subtype(text: str) -> str:
low = (text or "").lower()
if any(k in low for k in ["system", "simultaneous", "x and y", "two equations"]):
return "system"
if any(k in low for k in ["inequality", "<", ">", "at least", "at most", "no more than"]):
return "inequality"
if any(k in low for k in ["quadratic", "squared", "^2", "x2", "root", "factor"]):
return "quadratic"
if any(k in low for k in ["expression", "value of 2x", "value of x +", "in terms of"]):
return "expression_evaluation"
if "=" in low:
return "linear_equation"
return "generic_algebra"
def explain_algebra_question(text: str):
if not _looks_like_algebra_question(text):
return None
subtype = _infer_algebra_subtype(text)
low = (text or "").lower()
result = ExplainerResult(
understood=True,
topic="algebra",
summary="This is an algebra problem. The main goal is to translate the wording into a clean symbolic relationship and isolate the requested quantity step by step.",
asks_for="the value of the variable or the requested expression built from it",
plain_english="Algebra questions usually become easier once you write one clean equation and then reverse the operations in order.",
)
scaffold = ExplainerScaffold(
concept="Algebra represents unknown quantities symbolically, then uses valid transformations to isolate or compare them.",
ask="Identify the unknown, identify the governing relationship, and check whether the question wants the variable itself or an expression built from it.",
target="Set up the simplest correct equation or relation before manipulating it.",
answer_hidden=True,
solution_path_type=subtype,
)
result.givens = [
"A symbolic relationship or equation is implied by the wording.",
]
if "=" in low:
result.givens.append("An equals sign or equation structure is present.")
result.relationships = [
"Both sides of an equation must stay balanced.",
"Each algebra step should simplify or isolate the target quantity.",
]
result.needed_concepts = [
"equation balancing",
"inverse operations",
"checking what the question actually asks for",
]
result.trap_notes = [
"Moving terms across the equals sign incorrectly.",
"Trying to isolate the variable before simplifying.",
"Finding x and forgetting the question asks for something like 2x or x + 3.",
]
result.strategy_hint = "Rewrite the relationship as one clean equation before doing any manipulation."
result.teaching_points = [
"Most algebra errors happen before the solving starts: either the variable is misdefined, or the equation is set up incorrectly.",
"A clean equation makes the solving steps much easier.",
"You should always check whether the question asks for x itself or for something derived from x.",
]
if subtype == "linear_equation":
scaffold.setup_actions = [
"Identify the unknown and write the equation cleanly.",
"Simplify each side if needed.",
"Undo operations in a logical order to isolate the variable.",
]
scaffold.intermediate_steps = [
"Combine like terms first when possible.",
"Move variable terms and constant terms carefully.",
"Check whether the final result should be the variable or a substituted expression.",
]
scaffold.first_move = "Rewrite the relationship as one clean equation if it is not already in that form."
scaffold.next_hint = "Simplify both sides before isolating the variable."
scaffold.variables_to_define = [
"Let the unknown quantity be x if the question has not already named it.",
]
scaffold.equations_to_form = [
"Build one equation from the stated relationship.",
]
scaffold.key_operations = [
"Simplify",
"undo addition/subtraction",
"undo multiplication/division",
]
scaffold.hint_ladder = [
"What operation is attached to the variable?",
"What inverse operation would undo it?",
"Apply that same operation to both sides.",
]
elif subtype == "system":
scaffold.setup_actions = [
"Identify the separate equations and unknowns.",
"Decide whether substitution or elimination is the cleaner method.",
"Reduce the system to one variable before solving completely.",
]
scaffold.intermediate_steps = [
"Make one variable easy to substitute, or align coefficients for elimination.",
"After finding one variable, substitute back carefully.",
"Check whether the question asks for one variable, both variables, or a combination of them.",
]
scaffold.first_move = "Choose one variable to eliminate or substitute."
scaffold.next_hint = "Turn the system into a single-variable equation before solving."
scaffold.equations_to_form = [
"Use the two given equations together to reduce to one unknown.",
]
scaffold.key_operations = [
"substitute",
"eliminate",
"back-substitute",
]
scaffold.hint_ladder = [
"Which variable looks easier to isolate?",
"Can you align coefficients for elimination?",
"After finding one variable, plug it back into the other equation.",
]
elif subtype == "inequality":
scaffold.setup_actions = [
"Translate the condition into an inequality.",
"Manipulate it like an equation, but track the inequality direction carefully.",
"Reverse the sign only if multiplying or dividing by a negative number.",
]
scaffold.intermediate_steps = [
"Simplify both sides first if possible.",
"Isolate the variable systematically.",
"Interpret the final solution set in the form the question wants.",
]
scaffold.first_move = "Set up the inequality carefully from the wording."
scaffold.next_hint = "Solve it step by step, watching for any operation that would reverse the sign."
scaffold.key_operations = [
"translate wording to an inequality",
"simplify",
"watch for sign reversal with negatives",
]
scaffold.hint_ladder = [
"What phrase tells you the direction of the inequality?",
"Can you simplify both sides first?",
"Did you divide or multiply by a negative at any point?",
]
elif subtype == "quadratic":
scaffold.setup_actions = [
"Rewrite the equation so one side is zero if needed.",
"Look for factoring, structure, or another simplifying method.",
"Treat each factor or case carefully once the equation is structured properly.",
]
scaffold.intermediate_steps = [
"Factor if the form allows it.",
"Otherwise identify another clean solving route.",
"Check whether all resulting values are allowed in the original context.",
]
scaffold.first_move = "Put the expression into a standard structured form before solving."
scaffold.next_hint = "Then look for a factorable pattern or another clean route."
scaffold.key_operations = [
"standardize the expression",
"factor or use structure",
"check all roots back in context",
]
scaffold.hint_ladder = [
"Can you move everything to one side first?",
"Does the expression factor neatly?",
"Do all candidate solutions actually fit the original question?",
]
elif subtype == "expression_evaluation":
scaffold.setup_actions = [
"Find the variable or relationship first.",
"Only then substitute into the requested expression.",
"Simplify the final expression carefully.",
]
scaffold.intermediate_steps = [
"Do not stop when you find the variable unless that is exactly what the question asks.",
"Preserve parentheses during substitution.",
"Check whether there is a shortcut using the given relationship directly.",
]
scaffold.first_move = "Work out whether you need to solve for the variable first or can rewrite the target expression directly."
scaffold.next_hint = "Once the relationship is clear, substitute only into the exact expression the question asks for."
scaffold.key_operations = [
"solve or rewrite the relationship",
"substitute carefully",
"simplify the requested expression",
]
scaffold.hint_ladder = [
"What expression does the question actually want?",
"Do you already have enough information to rewrite that expression?",
"Only substitute after the target expression is clear.",
]
else:
scaffold.setup_actions = [
"Define the unknown clearly.",
"Translate the wording into a symbolic relationship.",
"Manipulate the relationship only after the setup is clean.",
]
scaffold.intermediate_steps = [
"Simplify before isolating.",
"Keep track of what the question actually asks for.",
"Check the final quantity against the prompt.",
]
scaffold.first_move = "Start by translating the words into one clean symbolic statement."
scaffold.next_hint = "Then simplify the structure before solving."
scaffold.key_operations = [
"translate",
"simplify",
"isolate",
]
scaffold.hint_ladder = [
"What is the unknown?",
"What relationship connects the quantities?",
"What is the cleanest first algebra step?",
]
result.scaffold = scaffold
result.meta = {
"intent": "explain_question",
"bridge_ready": True,
"hint_style": "step_ready",
"subtype": subtype,
}
return result |