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"""
Problem Parser Module
Extracts geometric parameters from problem expressions.
"""
import re
import numpy as np
from typing import Dict, List, Tuple, Optional
class ProblemParser:
"""Parse problem expressions into geometric constraints and SDFs."""
def __init__(self):
pass
def parse_line(self, fact_expr: str) -> Optional[Dict]:
"""Parse line expression."""
# Expression(G) = (x + y - 1 = 0) or similar
match = re.search(r'Expression\(\w+\)\s*=\s*\(([^)]+)\s*=\s*0\)', fact_expr)
if match:
expr = match.group(1)
# Parse ax + by + c = 0 format
# Try to extract coefficients
a, b, c = 0.0, 0.0, 0.0
# Match patterns like "x + y - 1" or "2*x - 3*y + 5"
x_match = re.search(r'([+-]?\s*\d*\.?\d*)\s*\*?\s*x', expr)
y_match = re.search(r'([+-]?\s*\d*\.?\d*)\s*\*?\s*y', expr)
if x_match:
coef = x_match.group(1).replace(' ', '')
if coef in ['', '+']:
a = 1.0
elif coef == '-':
a = -1.0
else:
try:
a = float(coef)
except:
a = 1.0
if y_match:
coef = y_match.group(1).replace(' ', '')
if coef in ['', '+']:
b = 1.0
elif coef == '-':
b = -1.0
else:
try:
b = float(coef)
except:
b = 1.0
# Find constant term
const_match = re.search(r'([+-]\s*\d+\.?\d*)\s*(?:=|$)', expr)
if const_match:
try:
c = float(const_match.group(1).replace(' ', ''))
except:
c = 0.0
if a != 0 or b != 0:
return {
'type': 'line',
'a': a,
'b': b,
'c': c,
'equation': expr
}
# Check for Slope constraint - sqrt format
slope_match = re.search(r'Slope\(\w+\)\s*=\s*sqrt\((\d+)\)', fact_expr)
if slope_match:
slope = np.sqrt(float(slope_match.group(1)))
return {
'type': 'line',
'slope': slope,
'symbolic': True
}
# Check for Slope constraint - numeric format
slope_match = re.search(r'Slope\(\w+\)\s*=\s*([\d.]+)', fact_expr)
if slope_match:
return {
'type': 'line',
'slope': float(slope_match.group(1)),
'symbolic': True
}
return None
def parse_circle(self, fact_expr: str) -> Optional[Dict]:
"""Parse circle expression."""
# Format 1: (x-a)^2 + (y-b)^2 = r^2
match = re.search(r'Expression\(\w+\)\s*=\s*\(\(x-([^)]+)\)\^2\s*\+\s*\(y-([^)]+)\)\^2\s*=\s*(\d+)\)', fact_expr)
if match:
return {
'type': 'circle',
'center': (float(match.group(1)), float(match.group(2))),
'radius': np.sqrt(float(match.group(3)))
}
# Format 2: x^2 + (y-a)^2 = r (center at origin or on axis)
match = re.search(r'Expression\(\w+\)\s*=\s*\(x\^2\s*\+\s*\(([+-]?\s*\d*\.?\d*)\s*[+-]\s*y\)\^2\s*=\s*(\d+)\)', fact_expr)
if match:
cy = -float(match.group(1).replace(' ', '')) if match.group(1) else 0.0
return {
'type': 'circle',
'center': (0.0, cy),
'radius': np.sqrt(float(match.group(2)))
}
# Format 3: y^2 + (x-a)^2 = r or y^2 + (x+a)^2 = r
match = re.search(r'Expression\(\w+\)\s*=\s*\(y\^2\s*\+\s*\(x\s*([+-])\s*(\d+\.?\d*)\)\^2\s*=\s*(\d+\.?\d*)\)', fact_expr)
if match:
sign = -1 if match.group(1) == '-' else 1
cx = sign * float(match.group(2))
return {
'type': 'circle',
'center': (cx, 0.0),
'radius': np.sqrt(float(match.group(3)))
}
# Format 4: x^2 + y^2 = r (center at origin)
match = re.search(r'Expression\(\w+\)\s*=\s*\(x\^2\s*\+\s*y\^2\s*=\s*(\d+\.?\d*)\)', fact_expr)
if match:
return {
'type': 'circle',
'center': (0.0, 0.0),
'radius': np.sqrt(float(match.group(1)))
}
# Format 5: Check if it's explicitly declared as Circle type
if re.search(r'\w+:\s*Circle', fact_expr):
# Try more general patterns
# (x + a)^2 + (y - b)^2 = r
match = re.search(r'\(x\s*([+-])\s*(\d+\.?\d*)\)\^2\s*\+\s*\(y\s*([+-])\s*(\d+\.?\d*)\)\^2\s*=\s*(\d+\.?\d*)', fact_expr)
if match:
cx = float(match.group(2)) * (-1 if match.group(1) == '+' else 1)
cy = float(match.group(4)) * (-1 if match.group(3) == '+' else 1)
return {
'type': 'circle',
'center': (cx, cy),
'radius': np.sqrt(float(match.group(5)))
}
# Check for circle defined by diameter
if 'IsDiameter' in fact_expr:
return {
'type': 'circle',
'from_diameter': True
}
# Check for circle defined by slope product = -1 (perpendicular)
# Pattern: Slope(LineSegmentOf(P, A)) * Slope(LineSegmentOf(P, B)) = -1
# This means angle APB = 90°, so P lies on circle with diameter AB
slope_match = re.search(r'Slope\(LineSegmentOf\(\w+,\s*(\w+)\)\)\s*\*\s*Slope\(LineSegmentOf\(\w+,\s*(\w+)\)\)\s*=\s*-1', fact_expr)
if slope_match:
pt1_name = slope_match.group(1)
pt2_name = slope_match.group(2)
coords = self.parse_coordinates(fact_expr)
if pt1_name in coords and pt2_name in coords:
x1, y1 = coords[pt1_name]
x2, y2 = coords[pt2_name]
# Circle with diameter AB: center = midpoint, radius = |AB|/2
cx = (x1 + x2) / 2
cy = (y1 + y2) / 2
radius = np.sqrt((x2 - x1)**2 + (y2 - y1)**2) / 2
return {
'type': 'circle',
'center': (cx, cy),
'radius': radius,
'from_constraints': True
}
# General circle equation: x^2 + y^2 + Dx + Ey + F = 0
# Center: (-D/2, -E/2), Radius: sqrt(D²/4 + E²/4 - F)
# Pattern: ax^2 + by^2 + Dx + Ey + F = 0 where coefficients can vary
general_match = re.search(r'Expression\(\w+\)\s*=\s*\(([^)]+x\^2[^)]+y\^2[^)]+)\s*=\s*0\)', fact_expr)
if general_match and 'Circle' in fact_expr:
expr = general_match.group(1)
# Parse coefficients: D*x, E*y, F (constant)
D = E = F = 0.0
# Find coefficient of x (not x^2)
d_match = re.search(r'([+-]?\s*\d*\.?\d*)\s*\*?\s*x(?!\^)', expr)
if d_match:
d_str = d_match.group(1).replace(' ', '')
D = float(d_str) if d_str and d_str not in ['+', '-'] else (1.0 if d_str == '+' or d_str == '' else -1.0)
# Find coefficient of y (not y^2)
e_match = re.search(r'([+-]?\s*\d*\.?\d*)\s*\*?\s*y(?!\^)', expr)
if e_match:
e_str = e_match.group(1).replace(' ', '')
E = float(e_str) if e_str and e_str not in ['+', '-'] else (1.0 if e_str == '+' or e_str == '' else -1.0)
# Find constant term
const_match = re.search(r'([+-]\s*\d+\.?\d*)\s*(?:=|$)', expr)
if const_match:
f_str = const_match.group(1).replace(' ', '')
F = float(f_str)
cx = -D / 2
cy = -E / 2
r_sq = D**2 / 4 + E**2 / 4 - F
if r_sq > 0:
return {
'type': 'circle',
'center': (cx, cy),
'radius': np.sqrt(r_sq),
'from_constraints': True
}
# Shifted center circle: (x+h)^2 + y^2 = r^2 or (x-h)^2 + y^2 = r^2
shifted_match = re.search(r'Expression\(\w+\)\s*=\s*\(\(x([+-])(\d+\.?\d*)\)\^2\s*\+\s*y\^2\s*=\s*(\d+\.?\d*)\)', fact_expr)
if shifted_match:
sign = shifted_match.group(1)
h = float(shifted_match.group(2))
r_sq = float(shifted_match.group(3))
cx = -h if sign == '+' else h
return {
'type': 'circle',
'center': (cx, 0.0),
'radius': np.sqrt(r_sq),
}
# (x±h)^2 + (y±k)^2 = r^2
shifted_match2 = re.search(r'Expression\(\w+\)\s*=\s*\(\(x([+-])(\d+\.?\d*)\)\^2\s*\+\s*\(y([+-])(\d+\.?\d*)\)\^2\s*=\s*(\d+\.?\d*)\)', fact_expr)
if shifted_match2:
sign_x = shifted_match2.group(1)
h = float(shifted_match2.group(2))
sign_y = shifted_match2.group(3)
k = float(shifted_match2.group(4))
r_sq = float(shifted_match2.group(5))
cx = -h if sign_x == '+' else h
cy = -k if sign_y == '+' else k
return {
'type': 'circle',
'center': (cx, cy),
'radius': np.sqrt(r_sq),
}
return None
def parse_ellipse(self, fact_expr: str) -> Optional[Dict]:
"""Parse ellipse expression and return parameters."""
# x^2/a + y^2/b = 1
match = re.search(r'Expression\(\w+\)\s*=\s*\(x\^2/(\d+)\s*\+\s*y\^2/(\d+)\s*=\s*1\)', fact_expr)
if match:
x_coef = float(match.group(1))
y_coef = float(match.group(2))
return {
'type': 'ellipse',
'x_coef': x_coef,
'y_coef': y_coef,
'a': np.sqrt(max(x_coef, y_coef)),
'b': np.sqrt(min(x_coef, y_coef)),
'major_axis': 'x' if x_coef > y_coef else 'y'
}
# y^2/b + x^2/a = 1
match = re.search(r'Expression\(\w+\)\s*=\s*\(y\^2/(\d+)\s*\+\s*x\^2/(\d+)\s*=\s*1\)', fact_expr)
if match:
y_coef = float(match.group(1))
x_coef = float(match.group(2))
return {
'type': 'ellipse',
'x_coef': x_coef,
'y_coef': y_coef,
'a': np.sqrt(max(x_coef, y_coef)),
'b': np.sqrt(min(x_coef, y_coef)),
'major_axis': 'x' if x_coef > y_coef else 'y'
}
# x^2/a + y^2 = 1 (y has coefficient 1, x has numeric denominator)
match = re.search(r'Expression\(\w+\)\s*=\s*\(x\^2/(\d+)\s*\+\s*y\^2\s*=\s*1\)', fact_expr)
if match:
x_coef = float(match.group(1))
y_coef = 1.0
return {
'type': 'ellipse',
'x_coef': x_coef,
'y_coef': y_coef,
'a': np.sqrt(x_coef), # a > b since x_coef > 1
'b': 1.0,
'major_axis': 'x'
}
# y^2/a + x^2 = 1 (x has coefficient 1, y has numeric denominator)
match = re.search(r'Expression\(\w+\)\s*=\s*\(y\^2/(\d+)\s*\+\s*x\^2\s*=\s*1\)', fact_expr)
if match:
y_coef = float(match.group(1))
x_coef = 1.0
return {
'type': 'ellipse',
'x_coef': x_coef,
'y_coef': y_coef,
'a': np.sqrt(y_coef), # a > b since y_coef > 1
'b': 1.0,
'major_axis': 'y'
}
# y^2 + x^2/k^2 = 1 (y has coefficient 1)
match = re.search(r'Expression\(\w+\)\s*=\s*\(y\^2\s*\+\s*x\^2/\w+\^?2?\s*=\s*1\)', fact_expr)
if match:
return {
'type': 'ellipse',
'x_coef': 4.0, # default
'y_coef': 1.0,
'a': 2.0,
'b': 1.0,
'major_axis': 'x',
'symbolic': True
}
# x^2 + y^2/k^2 = 1
match = re.search(r'Expression\(\w+\)\s*=\s*\(x\^2\s*\+\s*y\^2/\w+\^?2?\s*=\s*1\)', fact_expr)
if match:
return {
'type': 'ellipse',
'x_coef': 1.0,
'y_coef': 4.0, # default
'a': 2.0,
'b': 1.0,
'major_axis': 'y',
'symbolic': True
}
# Ellipse with symbolic: y^2/b^2 + x^2/a^2 = 1 or x^2/a^2 + y^2/b^2 = 1
if re.search(r'Expression\(\w+\)\s*=\s*\([xy]\^2/\w+\^?2?\s*\+\s*[xy]\^2/\w+\^?2?\s*=\s*1\)', fact_expr):
return {
'type': 'ellipse',
'x_coef': 4.0,
'y_coef': 3.0,
'a': 2.0,
'b': np.sqrt(3),
'major_axis': 'x',
'symbolic': True
}
# x^2 + N*y^2 = M (ellipse: x²/M + y²/(M/N) = 1)
match = re.search(r'Expression\(\w+\)\s*=\s*\(x\^2\s*\+\s*(\d+)\*y\^2\s*=\s*(\d+)\)', fact_expr)
if match:
n = float(match.group(1))
m = float(match.group(2))
a_sq = m # x coefficient
b_sq = m / n # y coefficient
a = np.sqrt(max(a_sq, b_sq))
b = np.sqrt(min(a_sq, b_sq))
return {
'type': 'ellipse',
'x_coef': a_sq,
'y_coef': b_sq,
'a': a,
'b': b,
'major_axis': 'x' if a_sq >= b_sq else 'y'
}
# N*x^2 + y^2 = M (ellipse: x²/(M/N) + y²/M = 1)
match = re.search(r'Expression\(\w+\)\s*=\s*\((\d+)\*x\^2\s*\+\s*y\^2\s*=\s*(\d+)\)', fact_expr)
if match:
n = float(match.group(1))
m = float(match.group(2))
a_sq = m / n # x coefficient
b_sq = m # y coefficient
a = np.sqrt(max(a_sq, b_sq))
b = np.sqrt(min(a_sq, b_sq))
return {
'type': 'ellipse',
'x_coef': a_sq,
'y_coef': b_sq,
'a': a,
'b': b,
'major_axis': 'x' if a_sq >= b_sq else 'y'
}
# Check for Ellipse with geometric constraints (no explicit expression)
if 'Ellipse' in fact_expr:
coords = self.parse_coordinates(fact_expr)
eccentricity = self.parse_eccentricity(fact_expr)
c = None
major_axis = 'x' # default
# Try to find focus coordinate from various patterns
# Pattern 1: Coordinate(F) = (c, 0); RightFocus(G) = F
for name, (fx, fy) in coords.items():
if f'RightFocus(' in fact_expr and f') = {name}' in fact_expr:
c = abs(fx)
major_axis = 'x'
break
elif f'LeftFocus(' in fact_expr and f') = {name}' in fact_expr:
c = abs(fx)
major_axis = 'x'
break
elif f'UpperFocus(' in fact_expr and f') = {name}' in fact_expr:
c = abs(fy)
major_axis = 'y'
break
elif f'LowerFocus(' in fact_expr and f') = {name}' in fact_expr:
c = abs(fy)
major_axis = 'y'
break
# Pattern 2: Coordinate(OneOf(Focus(...)))
if c is None:
focus_match = re.search(r'Coordinate\(OneOf\(Focus\(\w+\)\)\)\s*=\s*\(([^,]+),\s*([^)]+)\)', fact_expr)
if focus_match:
try:
fx = float(focus_match.group(1).strip())
fy = float(focus_match.group(2).strip())
c = abs(fx) if abs(fy) < 0.01 else abs(fy)
major_axis = 'x' if abs(fy) < 0.01 else 'y'
except:
pass
# Pattern 2b: Two foci with explicit coordinates: Focus(G) = {F1, F2}
if c is None:
foci_match = re.search(r'Focus\(\w+\)\s*=\s*\{(\w+),\s*(\w+)\}', fact_expr)
if foci_match:
f1_name = foci_match.group(1)
f2_name = foci_match.group(2)
if f1_name in coords and f2_name in coords:
fx1, fy1 = coords[f1_name]
fx2, fy2 = coords[f2_name]
# c = half the distance between foci
c = np.sqrt((fx2 - fx1)**2 + (fy2 - fy1)**2) / 2
major_axis = 'x' if abs(fy1) < 0.01 else 'y'
# Pattern 3: PointOnCurve(Focus(G), xAxis) - focus on x-axis
if c is None and 'PointOnCurve(Focus(' in fact_expr:
if 'xAxis' in fact_expr:
major_axis = 'x'
elif 'yAxis' in fact_expr:
major_axis = 'y'
# Pattern 4: Length(MajorAxis(G)) = k * Length(MinorAxis(G))
axis_ratio = None
ratio_match = re.search(r'Length\(MajorAxis\(\w+\)\)\s*=\s*(\d+)\s*\*\s*Length\(MinorAxis', fact_expr)
if ratio_match:
axis_ratio = float(ratio_match.group(1))
# Pattern 5: Length(MinorAxis(G)) = N or Length(MinorAxis(G)) = 2*sqrt(N)
minor_axis_len = None
match = re.search(r'Length\(MinorAxis\(\w+\)\)\s*=\s*2\*sqrt\((\d+)\)', fact_expr)
if match:
minor_axis_len = 2 * np.sqrt(float(match.group(1)))
else:
match = re.search(r'Length\(MinorAxis\(\w+\)\)\s*=\s*(\d+)', fact_expr)
if match:
minor_axis_len = float(match.group(1))
# Pattern 6: Length(MajorAxis(G)) = N
major_axis_len = None
match = re.search(r'Length\(MajorAxis\(\w+\)\)\s*=\s*2\*sqrt\((\d+)\)', fact_expr)
if match:
major_axis_len = 2 * np.sqrt(float(match.group(1)))
else:
match = re.search(r'Length\(MajorAxis\(\w+\)\)\s*=\s*(\d+)', fact_expr)
if match:
major_axis_len = float(match.group(1))
# Pattern 7: FocalLength(G) = N or 2*c = N
focal_length = None
match = re.search(r'FocalLength\(\w+\)\s*=\s*(\d+)', fact_expr)
if match:
focal_length = float(match.group(1))
else:
match = re.search(r'2\*c\s*=\s*(\d+)', fact_expr)
if match:
focal_length = float(match.group(1))
# Case: c from FocalLength + b from MinorAxis
if c is None and focal_length:
c = focal_length / 2
# Case: b from MinorAxis length
if minor_axis_len:
b_from_minor = minor_axis_len / 2
if c is not None:
a = np.sqrt(c**2 + b_from_minor**2)
b = b_from_minor
# Case: a from MajorAxis length
if major_axis_len:
a_from_major = major_axis_len / 2
if c is not None:
a = a_from_major
b = np.sqrt(a**2 - c**2) if a > c else None
# Compute a, b from constraints
a, b = None, None
# Case 1: c and eccentricity known → a = c/e, b = sqrt(a² - c²)
if c is not None and eccentricity and 0 < eccentricity < 1:
a = c / eccentricity
b = np.sqrt(a**2 - c**2)
# Case 2: eccentricity known + axis ratio → solve for a, b
elif eccentricity and 0 < eccentricity < 1 and axis_ratio:
# a/b = axis_ratio, e = sqrt(1 - b²/a²) = sqrt(1 - 1/ratio²)
# This gives us the ratio, need another constraint for absolute size
a = 2.0 * axis_ratio # default size
b = 2.0
# Case 3: axis ratio + point on curve
elif axis_ratio:
# Find a point on curve and solve
for name, (px, py) in coords.items():
if f'PointOnCurve({name}' in fact_expr:
# x²/a² + y²/b² = 1, a = ratio * b
# x²/(ratio*b)² + y²/b² = 1
# x²/ratio² + y² = b²
b_sq = px**2 / axis_ratio**2 + py**2
if b_sq > 0:
b = np.sqrt(b_sq)
a = axis_ratio * b
break
# Case 4: Two points on ellipse → solve for a, b
if a is None:
points_on_curve = []
for name, (px, py) in coords.items():
if f'PointOnCurve({name}' in fact_expr and name not in ['F', 'F1', 'F2']:
points_on_curve.append((px, py))
if len(points_on_curve) >= 2:
# x1²/a² + y1²/b² = 1
# x2²/a² + y2²/b² = 1
p1, p2 = points_on_curve[0], points_on_curve[1]
x1, y1 = p1
x2, y2 = p2
# Solve: let u = 1/a², v = 1/b²
# x1²u + y1²v = 1
# x2²u + y2²v = 1
det = x1**2 * y2**2 - x2**2 * y1**2
if abs(det) > 1e-10:
u = (y2**2 - y1**2) / det
v = (x1**2 - x2**2) / det
if u > 0 and v > 0:
a_sq = 1 / u
b_sq = 1 / v
a = np.sqrt(max(a_sq, b_sq))
b = np.sqrt(min(a_sq, b_sq))
major_axis = 'x' if a_sq >= b_sq else 'y'
# Return if we have valid a, b
if a is not None and b is not None and a > 0 and b > 0:
return {
'type': 'ellipse',
'x_coef': a**2 if major_axis == 'x' else b**2,
'y_coef': b**2 if major_axis == 'x' else a**2,
'a': a,
'b': b,
'major_axis': major_axis,
'from_constraints': True
}
return None
def parse_hyperbola(self, fact_expr: str, main_conic_name: str = None) -> Optional[Dict]:
"""Parse hyperbola expression.
Args:
fact_expr: The fact expression string
main_conic_name: If provided, only match Expression(main_conic_name) = ...
This avoids matching secondary hyperbola expressions.
"""
# Build regex prefix based on main_conic_name
if main_conic_name:
expr_prefix = rf'Expression\({re.escape(main_conic_name)}\)\s*=\s*\('
else:
expr_prefix = r'Expression\(\w+\)\s*=\s*\('
# Horizontal: x^2/a - y^2/b = 1
match = re.search(expr_prefix + r'x\^2/(\d+)\s*-\s*y\^2/(\d+)\s*=\s*1\)', fact_expr)
if match:
a_sq = float(match.group(1))
b_sq = float(match.group(2))
return {
'type': 'hyperbola',
'a': np.sqrt(a_sq),
'b': np.sqrt(b_sq),
'a_squared': a_sq,
'b_squared': b_sq,
'orientation': 'horizontal'
}
# Vertical: y^2/a - x^2/b = 1
match = re.search(expr_prefix + r'y\^2/(\d+)\s*-\s*x\^2/(\d+)\s*=\s*1\)', fact_expr)
if match:
a_sq = float(match.group(1))
b_sq = float(match.group(2))
return {
'type': 'hyperbola',
'a': np.sqrt(a_sq),
'b': np.sqrt(b_sq),
'a_squared': a_sq,
'b_squared': b_sq,
'orientation': 'vertical'
}
# Horizontal: x^2/a - y^2 = 1 (b=1)
match = re.search(expr_prefix + r'x\^2/(\d+)\s*-\s*y\^2\s*=\s*1\)', fact_expr)
if match:
a_sq = float(match.group(1))
return {
'type': 'hyperbola',
'a': np.sqrt(a_sq),
'b': 1.0,
'a_squared': a_sq,
'b_squared': 1.0,
'orientation': 'horizontal'
}
# x^2 - y^2 = 1
if re.search(expr_prefix + r'x\^2\s*-\s*y\^2\s*=\s*1\)', fact_expr):
return {
'type': 'hyperbola',
'a': 1.0,
'b': 1.0,
'a_squared': 1.0,
'b_squared': 1.0,
'orientation': 'horizontal'
}
# Horizontal: x^2 - y^2/b = 1 (a=1, b^2 = b_val)
match = re.search(expr_prefix + r'x\^2\s*-\s*y\^2/(\d+)\s*=\s*1\)', fact_expr)
if match:
b_sq = float(match.group(1))
return {
'type': 'hyperbola',
'a': 1.0,
'b': np.sqrt(b_sq),
'a_squared': 1.0,
'b_squared': b_sq,
'orientation': 'horizontal'
}
# x^2 - y^2 = N (divide by N to normalize: x²/N - y²/N = 1)
match = re.search(expr_prefix + r'x\^2\s*-\s*y\^2\s*=\s*(\d+)\)', fact_expr)
if match:
n = float(match.group(1))
a = np.sqrt(n)
return {
'type': 'hyperbola',
'a': a,
'b': a,
'a_squared': n,
'b_squared': n,
'orientation': 'horizontal'
}
# x^2 - N*y^2 = M (x²/M - y²/(M/N) = 1)
match = re.search(expr_prefix + r'x\^2\s*-\s*(\d+)\*y\^2\s*=\s*(\d+)\)', fact_expr)
if match:
n = float(match.group(1))
m = float(match.group(2))
a_sq = m
b_sq = m / n
return {
'type': 'hyperbola',
'a': np.sqrt(a_sq),
'b': np.sqrt(b_sq),
'a_squared': a_sq,
'b_squared': b_sq,
'orientation': 'horizontal'
}
# N*x^2 - M*y^2 = K (x²/(K/N) - y²/(K/M) = 1)
match = re.search(expr_prefix + r'(\d+)\*x\^2\s*-\s*(\d+)\*y\^2\s*=\s*(\d+)\)', fact_expr)
if match:
n = float(match.group(1))
m = float(match.group(2))
k = float(match.group(3))
a_sq = k / n
b_sq = k / m
return {
'type': 'hyperbola',
'a': np.sqrt(a_sq),
'b': np.sqrt(b_sq),
'a_squared': a_sq,
'b_squared': b_sq,
'orientation': 'horizontal'
}
# x^2/a - y^2/b = -1 → y^2/b - x^2/a = 1 (vertical hyperbola)
match = re.search(expr_prefix + r'x\^2/(\d+)\s*-\s*y\^2/(\d+)\s*=\s*-1\)', fact_expr)
if match:
a_sq = float(match.group(1)) # becomes b² for vertical
b_sq = float(match.group(2)) # becomes a² for vertical
return {
'type': 'hyperbola',
'a': np.sqrt(b_sq),
'b': np.sqrt(a_sq),
'a_squared': b_sq,
'b_squared': a_sq,
'orientation': 'vertical'
}
# x^2-y^2/N=1 (no spaces) - horizontal
match = re.search(expr_prefix + r'x\^2-y\^2/(\d+)=1\)', fact_expr)
if match:
b_sq = float(match.group(1))
return {
'type': 'hyperbola',
'a': 1.0,
'b': np.sqrt(b_sq),
'a_squared': 1.0,
'b_squared': b_sq,
'orientation': 'horizontal'
}
# Vertical: y^2 - x^2/a = 1 (b=1 in standard form, here y² term positive)
match = re.search(expr_prefix + r'y\^2\s*-\s*x\^2/(\d+)\s*=\s*1\)', fact_expr)
if match:
b_sq = float(match.group(1))
return {
'type': 'hyperbola',
'a': 1.0, # For vertical hyperbola y²/a² - x²/b² = 1, a=1
'b': np.sqrt(b_sq),
'a_squared': 1.0,
'b_squared': b_sq,
'orientation': 'vertical'
}
# y^2 - x^2 = 1 (vertical hyperbola, a=1, b=1)
if re.search(expr_prefix + r'y\^2\s*-\s*x\^2\s*=\s*1\)', fact_expr):
return {
'type': 'hyperbola',
'a': 1.0,
'b': 1.0,
'a_squared': 1.0,
'b_squared': 1.0,
'orientation': 'vertical'
}
# Vertical symbolic: -x^2/b^2 + y^2/a^2 = 1
if re.search(expr_prefix + r'-x\^2/\w+\^?2?\s*\+\s*y\^2/\w+\^?2?\s*=\s*1\)', fact_expr):
return {
'type': 'hyperbola',
'a': 2.0, # default
'b': 1.5, # default
'a_squared': 4.0,
'b_squared': 2.25,
'symbolic': True,
'orientation': 'vertical'
}
# Vertical symbolic: y^2/a^2 - x^2/b^2 = 1
if re.search(expr_prefix + r'y\^2/\w+\^?2?\s*-\s*x\^2/\w+\^?2?\s*=\s*1\)', fact_expr):
return {
'type': 'hyperbola',
'a': 2.0, # default
'b': 1.5, # default
'a_squared': 4.0,
'b_squared': 2.25,
'symbolic': True,
'orientation': 'vertical'
}
# Horizontal symbolic: x^2/a^2 - y^2/b^2 = 1
if re.search(expr_prefix + r'x\^2/\w+\^?2?\s*-\s*y\^2/\w+\^?2?\s*=\s*1\)', fact_expr):
return {
'type': 'hyperbola',
'a': 2.0, # default
'b': 1.5, # default
'a_squared': 4.0,
'b_squared': 2.25,
'symbolic': True,
'orientation': 'horizontal'
}
# Horizontal symbolic: -y^2/b^2 + x^2/a^2 = 1
if re.search(expr_prefix + r'-y\^2/\w+\^?2?\s*\+\s*x\^2/\w+\^?2?\s*=\s*1\)', fact_expr):
return {
'type': 'hyperbola',
'a': 2.0, # default
'b': 1.5, # default
'a_squared': 4.0,
'b_squared': 2.25,
'symbolic': True,
'orientation': 'horizontal'
}
# Check for hyperbola type with asymptote/focus constraints (no explicit expression)
if 'Hyperbola' in fact_expr:
# Extract constraints
asymptote = self.parse_asymptote_slope(fact_expr)
coords = self.parse_coordinates(fact_expr)
focus_coords = [(n, c) for n, c in coords.items() if 'F' in n]
if asymptote or len(focus_coords) >= 2:
# Calculate a and b from constraints
if len(focus_coords) >= 2:
f1, f2 = focus_coords[0][1], focus_coords[1][1]
c = abs(f1[0] - f2[0]) / 2 if f1[1] == f2[1] == 0 else 3.0
else:
c = 3.0
if asymptote:
# b/a = asymptote, c² = a² + b²
# Let a be found from c and asymptote
# c² = a² + (a*slope)² = a²(1 + slope²)
a = c / np.sqrt(1 + asymptote**2)
b = a * asymptote
else:
a = c / np.sqrt(2)
b = a
return {
'type': 'hyperbola',
'a': a,
'b': b,
'a_squared': a**2,
'b_squared': b**2,
'from_constraints': True,
'orientation': 'horizontal' # Default, focus on x-axis
}
return None
def parse_parabola(self, fact_expr: str) -> Optional[Dict]:
"""Parse parabola expression."""
# y^2 = 4x, y^2 = 2*p*x, etc.
match = re.search(r'Expression\(\w+\)\s*=\s*\(y\^2\s*=\s*(\d+)\*x\)', fact_expr)
if match:
coef = float(match.group(1))
return {
'type': 'parabola',
'p': coef / 4, # 4p = coef
'direction': 'right'
}
# x^2 = 4y, x^2 = 2*p*y
match = re.search(r'Expression\(\w+\)\s*=\s*\(x\^2\s*=\s*(\d+)\*y\)', fact_expr)
if match:
coef = float(match.group(1))
return {
'type': 'parabola',
'p': coef / 4,
'direction': 'up'
}
# x^2 = -Ny (downward opening)
match = re.search(r'Expression\(\w+\)\s*=\s*\(x\^2\s*=\s*-(\d+)\*y\)', fact_expr)
if match:
coef = float(match.group(1))
return {
'type': 'parabola',
'p': coef / 4,
'direction': 'down'
}
# x^2 = y/N (small opening upward)
match = re.search(r'Expression\(\w+\)\s*=\s*\(x\^2\s*=\s*y/(\d+)\)', fact_expr)
if match:
divisor = float(match.group(1))
return {
'type': 'parabola',
'p': 1 / (4 * divisor),
'direction': 'up'
}
# y = -x^2/N (downward parabola in vertex form)
match = re.search(r'Expression\(\w+\)\s*=\s*\(y\s*=\s*-x\^2/(\d+)\)', fact_expr)
if match:
divisor = float(match.group(1))
# y = -x²/N → x² = -Ny → 4p = N → p = N/4
return {
'type': 'parabola',
'p': divisor / 4,
'direction': 'down'
}
# y = x^2/N (upward parabola in vertex form)
match = re.search(r'Expression\(\w+\)\s*=\s*\(y\s*=\s*x\^2/(\d+)\)', fact_expr)
if match:
divisor = float(match.group(1))
# y = x²/N → x² = Ny → 4p = N → p = N/4
return {
'type': 'parabola',
'p': divisor / 4,
'direction': 'up'
}
# y^2 = p*x (symbolic p, single coefficient)
if re.search(r'Expression\(\w+\)\s*=\s*\(y\^2\s*=\s*\w+\*x\)', fact_expr):
return {
'type': 'parabola',
'p': 1.0, # Default, will be optimized
'direction': 'right',
'symbolic': True
}
# x^2 = p*y (symbolic p, single coefficient)
if re.search(r'Expression\(\w+\)\s*=\s*\(x\^2\s*=\s*\w+\*y\)', fact_expr):
return {
'type': 'parabola',
'p': 1.0,
'direction': 'up',
'symbolic': True
}
# y^2 = 2*(p*x)
if re.search(r'Expression\(\w+\)\s*=\s*\(y\^2\s*=\s*2\*\(\w+\*x\)\)', fact_expr):
return {
'type': 'parabola',
'p': 1.0, # Default, will be optimized
'direction': 'right',
'symbolic': True
}
# x^2 = 2*(p*y)
if re.search(r'Expression\(\w+\)\s*=\s*\(x\^2\s*=\s*2\*\(\w+\*y\)\)', fact_expr):
return {
'type': 'parabola',
'p': 1.0,
'direction': 'up',
'symbolic': True
}
# y = 2*x^2 or y = a*x^2 (vertex form)
match = re.search(r'Expression\(\w+\)\s*=\s*\(y\s*=\s*(\d*)\*?x\^2\)', fact_expr)
if match:
coef = match.group(1)
a = float(coef) if coef else 1.0
return {
'type': 'parabola',
'p': 1 / (4 * a),
'direction': 'up'
}
# y = x^2/8 (division form)
match = re.search(r'Expression\(\w+\)\s*=\s*\(y\s*=\s*x\^2/(\d+)\)', fact_expr)
if match:
divisor = float(match.group(1))
return {
'type': 'parabola',
'p': divisor / 4,
'direction': 'up'
}
# y^2 = -8*x (left opening)
match = re.search(r'Expression\(\w+\)\s*=\s*\(y\^2\s*=\s*-(\d+)\*x\)', fact_expr)
if match:
coef = float(match.group(1))
return {
'type': 'parabola',
'p': coef / 4,
'direction': 'left'
}
# y^2 = 2*p*x (symbolic p) - parabola opening right
if re.search(r'Expression\(\w+\)\s*=\s*\(y\^2\s*=\s*2\*p\*x\)', fact_expr):
return {
'type': 'parabola',
'p': 1.0, # Default, will be optimized
'direction': 'right',
'symbolic': True
}
# x^2 = 2*p*y (symbolic p) - parabola opening up
if re.search(r'Expression\(\w+\)\s*=\s*\(x\^2\s*=\s*2\*p\*y\)', fact_expr):
return {
'type': 'parabola',
'p': 1.0, # Default, will be optimized
'direction': 'up',
'symbolic': True
}
# y^2 = x (p = 1/4, so 4p = 1) - parabola opening right
if re.search(r'Expression\(\w+\)\s*=\s*\(y\^2\s*=\s*x\)', fact_expr):
return {
'type': 'parabola',
'p': 0.25, # y^2 = 4px, so 4p = 1, p = 0.25
'direction': 'right'
}
# x^2 = y (p = 1/4) - parabola opening up
if re.search(r'Expression\(\w+\)\s*=\s*\(x\^2\s*=\s*y\)', fact_expr):
return {
'type': 'parabola',
'p': 0.25,
'direction': 'up'
}
# Check for Parabola type with geometric constraints
if 'Parabola' in fact_expr:
coords = self.parse_coordinates(fact_expr)
# Determine direction from constraints
direction = None
if 'PointOnCurve(Focus(' in fact_expr:
if 'xAxis' in fact_expr:
direction = 'right' # Focus on x-axis → horizontal parabola
elif 'yAxis' in fact_expr:
direction = 'up' # Focus on y-axis → vertical parabola
# Check for vertex at origin
vertex_at_origin = 'Vertex(' in fact_expr and 'Origin' in fact_expr
# Try to find p from point on curve + distance to focus
# Pattern: Distance(P, Focus(G)) = d
dist_match = re.search(r'Distance\((\w+),\s*Focus\(\w+\)\)\s*=\s*(\d+)', fact_expr)
if dist_match and vertex_at_origin:
pt_name = dist_match.group(1)
dist_val = float(dist_match.group(2))
if pt_name in coords:
px, py = coords[pt_name]
# For parabola y² = 4px with vertex at origin:
# Distance from point to focus = |x + p|
# For right-opening: focus at (p, 0), dist = sqrt((x-p)² + y²)
# We can solve for p
if direction == 'right':
# dist² = (px - p)² + py²
# y² = 4px → py² = 4p*px
# Substitute: dist² = (px - p)² + 4p*px
# dist² = px² - 2*px*p + p² + 4p*px = px² + 2*px*p + p² = (px + p)²
# So dist = |px + p|, p = dist - px (assuming px > 0)
p = (dist_val - px) if px >= 0 else (dist_val + px)
if p > 0:
return {
'type': 'parabola',
'p': p,
'direction': 'right',
'from_constraints': True
}
elif direction == 'up':
p = (dist_val - py) if py >= 0 else (dist_val + py)
if p > 0:
return {
'type': 'parabola',
'p': p,
'direction': 'up',
'from_constraints': True
}
# Look for focus coordinate in coords
for name, (px, py) in coords.items():
# If this is a focus (F in name) or explicitly marked as focus
if 'F' in name and (f'Focus(' in fact_expr):
if abs(py) < 0.01: # Focus on x-axis
return {
'type': 'parabola',
'p': abs(px), # Focus at (p, 0)
'direction': 'right' if px > 0 else 'left',
'from_constraints': True
}
elif abs(px) < 0.01: # Focus on y-axis
return {
'type': 'parabola',
'p': abs(py),
'direction': 'up' if py > 0 else 'down',
'from_constraints': True
}
# Default: parabola with vertex at origin, direction from constraints
if vertex_at_origin and direction:
return {
'type': 'parabola',
'p': 1.0, # Default, will be optimized
'direction': direction,
'symbolic': True
}
return None
def parse_coordinates(self, fact_expr: str) -> Dict[str, Tuple[float, float]]:
"""Extract point coordinates."""
coords = {}
# Use a more robust pattern that handles nested parentheses
# Match: Coordinate(Name) = (x_expr, y_expr)
# Find all Coordinate(...) = (...) patterns
coord_pattern = r'Coordinate\((\w+)\)\s*=\s*\(([^;]+)\)'
for match in re.finditer(coord_pattern, fact_expr):
name = match.group(1)
coord_str = match.group(2)
# Split by comma, but handle nested parentheses
depth = 0
parts = []
current = ""
for char in coord_str:
if char == '(':
depth += 1
current += char
elif char == ')':
depth -= 1
current += char
elif char == ',' and depth == 0:
parts.append(current.strip())
current = ""
else:
current += char
parts.append(current.strip())
if len(parts) >= 2:
try:
x = parts[0].replace('sqrt', 'np.sqrt').replace('^', '**')
y = parts[1].replace('sqrt', 'np.sqrt').replace('^', '**')
x_val = float(eval(x, {"np": np, "__builtins__": {}}))
y_val = float(eval(y, {"np": np, "__builtins__": {}}))
coords[name] = (x_val, y_val)
except:
pass
return coords
def parse_eccentricity(self, fact_expr: str) -> Optional[float]:
"""Extract eccentricity constraint."""
# sqrt pattern
match = re.search(r'Eccentricity\(\w+\)\s*=\s*sqrt\((\d+)\)', fact_expr)
if match:
return np.sqrt(float(match.group(1)))
# Fraction pattern (MUST be checked BEFORE decimal pattern!)
match = re.search(r'Eccentricity\(\w+\)\s*=\s*(\d+)/(\d+)', fact_expr)
if match:
return float(match.group(1)) / float(match.group(2))
# Simple decimal pattern
match = re.search(r'Eccentricity\(\w+\)\s*=\s*([\d.]+)', fact_expr)
if match:
return float(match.group(1))
return None
def parse_asymptote_slope(self, fact_expr: str) -> Optional[float]:
"""Extract asymptote slope for hyperbola.
Supports patterns like:
- y = sqrt(2)*x
- y = pm*sqrt(2)*x
- y = pm*(sqrt(2)/2)*x or y = pm*(sqrt(2)/2)*X
- y = 4/3*x
- y = pm*3*x
- y = pm*(sqrt(2)*x)
"""
# Pattern: y = sqrt(N)*x
match = re.search(r'Asymptote.*?=\s*\(y\s*=\s*sqrt\((\d+)\)\*[xX]\)', fact_expr)
if match:
return np.sqrt(float(match.group(1)))
# Pattern: y = pm*sqrt(N)*x or y = pm*(sqrt(N)*x)
match = re.search(r'Asymptote.*?=\s*\(y\s*=\s*pm\*\(?sqrt\((\d+)\)\*?[xX]\)?', fact_expr)
if match:
return np.sqrt(float(match.group(1)))
# Pattern: y = pm*(sqrt(N)/M)*x (e.g., sqrt(2)/2)
match = re.search(r'Asymptote.*?=\s*\(y\s*=\s*pm\*\(sqrt\((\d+)\)/(\d+)\)\*[xX]\)', fact_expr)
if match:
return np.sqrt(float(match.group(1))) / float(match.group(2))
# Pattern: y = A/B*x (fraction slope)
match = re.search(r'Asymptote.*?=\s*\(y\s*=\s*(\d+)/(\d+)\*[xX]\)', fact_expr)
if match:
return float(match.group(1)) / float(match.group(2))
# Pattern: y = pm*N*x (integer slope)
match = re.search(r'Asymptote.*?=\s*\(y\s*=\s*pm\*(\d+)\*[xX]\)', fact_expr)
if match:
return float(match.group(1))
# Pattern: y = N*x (simple integer slope)
match = re.search(r'Asymptote.*?=\s*\(y\s*=\s*(\d+)\*[xX]\)', fact_expr)
if match:
return float(match.group(1))
# Pattern: pm*A*y+B*x=0 → y = ±(B/A)*x, slope = B/A
match = re.search(r'Asymptote.*?=\s*\(pm\*(\d+)\*y\+(\d+)\*x=0\)', fact_expr)
if match:
a = float(match.group(1))
b = float(match.group(2))
return b / a
# Pattern: pm*(A/B)*x or y = pm*(A/B)*x
match = re.search(r'Asymptote.*?=\s*\(y\s*=\s*pm\*\((\d+)/(\d+)\)\*[xX]\)', fact_expr)
if match:
return float(match.group(1)) / float(match.group(2))
return None
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