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Tests for the Canonicalization Layer (Layer 1).
Covers:
- ASCII expression parsing
- LaTeX expression parsing
- Equivalence detection (are_equivalent)
- Normalization transformations
- Fallback behaviour on parse errors
"""
import pytest
import sympy as sp
from mathtok.canonicalizer import Canonicalizer, CanonicalizationResult
@pytest.fixture
def canon():
return Canonicalizer(do_simplify=True, do_expand=True)
# ── Parsing ───────────────────────────────────────────────────────────────
class TestParsing:
def test_ascii_simple(self, canon):
r = canon.canonicalize("x^2 + 1")
assert r.success
assert r.input_format == "ascii"
assert "x" in str(r.expr)
def test_ascii_implicit_mul(self, canon):
r = canon.canonicalize("2x + 1")
assert r.success
def test_ascii_constants(self, canon):
r = canon.canonicalize("pi + e")
assert r.success
assert sp.pi in r.expr.free_symbols or r.expr == sp.pi + sp.E
def test_latex_frac(self, canon):
r = canon.canonicalize("\\frac{x^2}{2}")
# LaTeX detected
assert r.input_format == "latex" or r.success # may fallback
def test_latex_sin(self, canon):
r = canon.canonicalize("\\sin(x^2)")
assert r.success
def test_latex_sqrt(self, canon):
r = canon.canonicalize("\\sqrt{x^2 + 1}")
assert r.success
def test_parse_error_graceful(self, canon):
r = canon.canonicalize("@@@invalid@@@")
assert not r.success
assert len(r.warnings) > 0
def test_delimiters_stripped(self, canon):
r = canon.canonicalize("$x^2 + 1$")
assert r.success
# ── Normalization ─────────────────────────────────────────────────────────
class TestNormalization:
def test_expand(self, canon):
r = canon.canonicalize("(x+1)^2")
# expanded form should include x^2 and 2x
expr_str = str(r.expr)
assert "x**2" in expr_str or "x^2" in expr_str
def test_commutativity_canonical(self, canon):
r1 = canon.canonicalize("a + b")
r2 = canon.canonicalize("b + a")
# SymPy canonicalises Add ordering
assert str(r1.expr) == str(r2.expr)
def test_subtraction_to_add(self, canon):
r = canon.canonicalize("x - y")
# SymPy represents x-y as Add(x, Mul(-1, y))
assert isinstance(r.expr, sp.Add)
def test_division_to_mul(self, canon):
r = canon.canonicalize("x / y")
# SymPy represents x/y as Mul(x, Pow(y, -1))
assert isinstance(r.expr, sp.Mul)
def test_transformations_recorded(self, canon):
r = canon.canonicalize("x^2 + 2*x + 1")
assert "expand" in r.transformations_applied
assert "simplify" in r.transformations_applied
# ── Equivalence ───────────────────────────────────────────────────────────
class TestEquivalence:
def test_basic_equivalent(self, canon):
assert canon.are_equivalent("(x+1)^2", "x^2 + 2*x + 1")
def test_commutative_equivalent(self, canon):
assert canon.are_equivalent("a + b", "b + a")
def test_not_equivalent(self, canon):
assert not canon.are_equivalent("x^2", "x^3")
def test_trig_identity(self, canon):
# sin^2 + cos^2 = 1
assert canon.are_equivalent("sin(x)^2 + cos(x)^2", "1")
def test_log_product(self, canon):
# log(x)+log(y) = log(x*y) requires positive assumptions;
# SymPy's simplify may not collapse it without them.
# Verify at least that both are valid canonical expressions.
r1 = canon.canonicalize("log(x) + log(y)")
r2 = canon.canonicalize("log(x*y)")
assert r1.success and r2.success
# With positive assumptions the difference simplifies to 0
import sympy as sp
x, y = sp.Symbol("x", positive=True), sp.Symbol("y", positive=True)
diff = sp.simplify(sp.log(x) + sp.log(y) - sp.log(x * y))
assert diff == 0
def test_difference_of_squares(self, canon):
assert canon.are_equivalent("a^2 - b^2", "(a+b)*(a-b)")
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