a third through Step Generator

algebraic_steps.py

@@ -0,0 +1,197 @@
+#All Rights Reserved John Salguero
+#Steps that are generated
+
+from sympy import *
+from sympy.parsing.sympy_parser import (
+    parse_expr,
+    standard_transformations,
+    implicit_multiplication_application
+)
+transformations = standard_transformations + (implicit_multiplication_application,)
+
+def move_all_to_one_side(equation):
+    step = {}
+   
+    current = equation
+    step["before"] = current
+    left, right = current.split("=")
+    x = symbols('x')
+    
+    left_expr = parse_expr(left, transformations=transformations, evaluate=False)
+    right_expr = parse_expr(right, transformations=transformations, evaluate=False)
+    new_expr = left_expr - right_expr
+    step["after"] = f"{sstr(new_expr)} = 0"
+    
+    step["step"] = f"Subtract both sides by {sstr(right_expr)}"
+    step["rule"] = "Subtraction Property of Equality"
+    return step
+   
+def add_both_sides(equation, value):
+    step = {}
+   
+    current = equation
+    step["before"] = current
+    left, right = current.split("=")
+    x = symbols('x')
+    
+    left_expr = parse_expr(left, transformations=transformations, evaluate=False)
+    right_expr = parse_expr(right, transformations=transformations, evaluate=False)
+    
+    new_left_expr = left_expr + value
+    new_right_expr = right_expr + value
+    step["after"] = f"{sstr(new_left_expr)} = {sstr(new_right_expr)}"
+    
+    step["step"] = f"Add both sides by {sstr(value)}"
+    step["rule"] = "Addition Property of Equality"
+    return step
+   
+def subtract_both_sides(equation, value):
+    step = {}
+   
+    current = equation
+    step["before"] = current
+    left, right = current.split("=")
+    x = symbols('x')
+    
+    left_expr = parse_expr(left, transformations=transformations, evaluate=False)
+    right_expr = parse_expr(right, transformations=transformations, evaluate=False)
+    
+    new_left_expr = left_expr - value
+    new_right_expr = right_expr - value
+    step["after"] = f"{sstr(new_left_expr)} = {sstr(new_right_expr)}"
+    
+    step["step"] = f"Subtract both sides by {sstr(value)}"
+    step["rule"] = "Subtraction Property of Equality"
+    return step
+    
+def divide_both_sides(equation, value):
+    step = {}
+   
+    current = equation
+    step["before"] = current
+    left, right = current.split("=")
+    x = symbols('x')
+    
+    left_expr = parse_expr(left, transformations=transformations, evaluate=False)
+    right_expr = parse_expr(right, transformations=transformations, evaluate=False)
+    
+    new_left_expr = clean(left_expr / value)
+    new_right_expr = clean(right_expr / value)
+    step["after"] = f"{sstr(new_left_expr)} = {sstr(new_right_expr)}"
+    
+    step["step"] = f"Divide both sides by {sstr(value)}"
+    step["rule"] = "Division Property of Equality"
+    return step
+    
+def multiply_both_sides(equation, value):
+    step = {}
+   
+    current = equation
+    step["before"] = current
+    left, right = current.split("=")
+    x = symbols('x')
+    
+    left_expr = parse_expr(left, transformations=transformations, evaluate=False)
+    right_expr = parse_expr(right, transformations=transformations, evaluate=False)
+    
+    new_left_expr = left_expr * value
+    new_right_expr = right_expr * value
+    step["after"] = f"{sstr(new_left_expr)} = {sstr(new_right_expr)}"
+    
+    step["step"] = f"Multiply both sides by {sstr(value)}"
+    step["rule"] = "Multiplication Property of Equality"
+    return step
+  
+def factor_collect(equation):
+    step = {}
+   
+    current = equation
+    step["before"] = current
+    left, right = current.split("=")
+    x = symbols('x')
+    
+    left_expr = parse_expr(left, transformations=transformations, evaluate=False)
+    right_expr = parse_expr(right, transformations=transformations, evaluate=False)
+    
+    new_left_expr = factor(left_expr)
+    new_right_expr = factor(right_expr)
+    step["after"] = f"{sstr(new_left_expr)} = {sstr(new_right_expr)}"
+    
+    step["step"] = f"Collect the factors"
+    step["rule"] = "Factoring by grouping"
+    return step
+  
+def factor_form_collection(equation, factor):
+    step = {}
+   
+    current = equation
+    step["before"] = current
+    left, right = current.split("=")
+    x = symbols('x')
+    
+    left_expr = parse_expr(left, transformations=transformations, evaluate=False)
+    right_expr = parse_expr(right, transformations=transformations, evaluate=False)
+    
+    new_left_expr = collect(left_expr, factor)
+    new_right_expr = collect(right_expr, factor)
+    step["after"] = f"{sstr(new_left_expr)} = {sstr(new_right_expr)}"
+    
+    step["step"] = f"Collect the factors using factor {sstr(factor)}"
+    step["rule"] = "Factor by grouping"
+    return step
+    
+def combine_like_terms(equation):
+    step = {}
+    
+    current = equation
+    step["before"] = current
+    left, right = current.split("=")
+    x = symbols('x')
+    
+    left_expr = parse_expr(left, transformations=transformations, evaluate=False)
+    right_expr = parse_expr(right, transformations=transformations, evaluate=False)
+    
+    ## Combine Left Terms
+    left_terms = left_expr.as_ordered_terms()
+    # group by base
+    left_groups = {}
+    for t in left_terms:
+        coeff, rest = t.as_coeff_Mul()
+        left_groups.setdefault(rest, 0)
+        left_groups[rest] += coeff
+    # rebuild manually
+    new_left_terms = []
+    for base, coeff in left_groups.items():
+        if coeff != 0:
+            new_left_terms.append(coeff * base)
+    new_left_expr = sum(new_left_terms)
+    
+    ## Comnine Right Terms
+    right_terms = right_expr.as_ordered_terms()
+    # group by base
+    right_groups = {}
+    for t in right_terms:
+        coeff, rest = t.as_coeff_Mul()
+        right_groups.setdefault(rest, 0)
+        right_groups[rest] += coeff
+    # rebuild manually
+    new_right_terms = []
+    for base, coeff in right_groups.items():
+        if coeff != 0:
+            new_right_terms.append(coeff * base)
+    new_right_expr = sum(new_right_terms)
+    
+    step["after"] = f"{sstr(new_left_expr)} = {sstr(new_right_expr)}"
+    step["step"] = "Collect Like Terms"
+    step["rule"] = "Combine the like terms"
+    return step
+    
+def clean(expr):
+
+    # remove explicit 1 multipliers
+    expr = expr.replace(
+        lambda e: isinstance(e, Mul),
+        lambda e: Mul(*[arg for arg in e.args if arg != 1])
+    )
+
+    return expr

main.py

@@ -1,44 +1,19 @@
 #All Rights Reserved John Salguero
 #Starts the backend to my Youtube stream
 
-from problem_generator import generate_problem, normalize
+from problem_generator import generate_problem
-from mathhook import parse, solve
+from steps_generator import generate_steps
-from sympy import sympify
 
 #define the entry point to the programs
 def main():
     problem = generate_problem()
-    
+    steps = generate_steps(problem);
 
     print("Generated Problem:")
     print(problem)
-    print("Solve:")
-    equation = apply_strategy(problem)
     
-    expr = parse(equation)
+    print("Steps:")
-    result = solve(expr, "x")
+    print(steps)
-    print(result)
-
-def square_both_sides(problem):
-    lhs, rhs = problem["problem"].split("=")
-
-    lhs = sympify(lhs.strip())
-    rhs = sympify(rhs.strip())
-    
-    lhs = lhs ** 2
-    rhs = rhs ** 2
-    
-    return f"{normalize(lhs)} = {normalize(rhs)}"
-
-def factor_or_formula(problem) :
-    return problem["problem"]
-
-def apply_strategy(problem):
-    if problem["type"] == "radical":
-        return square_both_sides(problem)
-    if problem["type"] == "quadratics":
-        return factor_or_formula(problem)
-    return problem["problem"]
 
 #Starts the program
 if __name__ == "__main__":

problem_generator.py

@@ -4,17 +4,26 @@
 import random
 from sympy import *
 
+TEMPLATES = {}
+
+def register_problem_generator(problem_type):
+    def decorator(func):
+        TEMPLATES[problem_type] = func
+        return func
+    return decorator
+
+@register_problem_generator("linear")
 def generate_linear():
     #ax + b = c
     a = random.choice([i for i in range(-10, 16) if i != 0])
     ans = random.choice([i for i in range(-10, 11)])
-    b = random.choice([i for i in range(-10, 11)])
+    b = random.choice([i for i in range(-10, 11) if a != 1 or i != 0])
 
     c = a * ans + b
     x = symbols('x')
     expr = a * x + b
     # expanded = n
-    s = normalize(expr)
+    s = sstr(expr)
 
     return {
         "type": "linear",
@@ -22,20 +31,21 @@ def generate_linear():
         "solution": ans
     }
     
+@register_problem_generator("hidden_factor")
 def generate_hidden_factor():
     #a(x + b) + c(x + b) = d 
     ans = random.choice([i for i in range(-10, 16)])
     b = random.choice([i for i in range(-5, 6) if i != 0])
 
     a = random.choice([i for i in range(-5, 6) if i != 0])
-    c = random.choice([i for i in range(-5, 6) if i != 0])
+    c = random.choice([i for i in range(-5, 6) if i != 0 and i != -a])
 
     x = symbols('x')
     inner_expr = x + b
     inner_value = ans + b
     right_side = a * inner_value + c * inner_value
 
-    problem = f"{a}({normalize(inner_expr)}) + {c}({normalize(inner_expr)}) = {right_side}"
+    problem = f"{a}({sstr(inner_expr)}) + {c}({sstr(inner_expr)}) = {right_side}"
 
     return {
         "type": "hidden_factor",
@@ -43,6 +53,7 @@ def generate_hidden_factor():
         "solution": ans
     }
 
+@register_problem_generator("distribution")
 def generate_distribution ():
     #a(x + b) = c
     ans = random.choice([i for i in range(-10, 16)])
@@ -55,10 +66,11 @@ def generate_distribution ():
 
     return {
         "type": "distribution",
-        "problem": f"{a}({normalize(inner_expr)}) = {c}",
+        "problem": f"{a}({sstr(inner_expr)}) = {c}",
         "solution": ans
     }
     
+@register_problem_generator("two_sides")
 def generate_two_sides ():
     #ax + b = dx + e : a != d
     ans = random.choice([i for i in range(-10, 16)])
@@ -73,10 +85,11 @@ def generate_two_sides ():
 
     return {
         "type": "two_sides",
-        "problem": f"{normalize(left_exp)} = {normalize(right_exp)}",
+        "problem": f"{sstr(left_exp)} = {sstr(right_exp)}",
         "solution": ans
     }
     
+@register_problem_generator("like_terms")
 def generate_like_terms ():
     #ax + bx + c = d
     ans = random.choice([i for i in range(-10, 16)])
@@ -90,10 +103,11 @@ def generate_like_terms ():
 
     return {
         "type": "like_terms",
-        "problem": f"{normalize(expr)} = {d}",
+        "problem": f"{sstr(expr)} = {d}",
         "solution": ans
     }
     
+@register_problem_generator("quadratic")
 def generate_quadratic ():
     #ax² + bx + c = 0
     r1 = random.choice([i for i in range(-10, 16)])
@@ -103,7 +117,7 @@ def generate_quadratic ():
 
     x = symbols('x')
     expr = n *(x - r1) * (x - r2)
-    expr = simplify(expr)
+    expr = expand(expr)
     if r1 == r2:
         solution = r1
     else:
@@ -111,10 +125,11 @@ def generate_quadratic ():
 
     return {
         "type": "quadratic",
-        "problem": f"{normalize(expr)} = 0",
+        "problem": f"{sstr(expr)} = 0",
         "solution": solution
     }
     
+@register_problem_generator("difference_squares")
 def generate_difference_squares ():
     #x² - a² = 0
     ans = random.choice([i for i in range(0, 13)])
@@ -130,10 +145,11 @@ def generate_difference_squares ():
 
     return {
         "type": "difference_squares",
-        "problem": f"{normalize(expr)} = 0",
+        "problem": f"{sstr(expr)} = 0",
         "solution": solution
     }
     
+@register_problem_generator("zero_product")
 def generate_zero_product ():
     #(x + a)(x + b) = 0
     a = random.choice([i for i in range(-5, 6)])
@@ -144,10 +160,11 @@ def generate_zero_product ():
 
     return {
         "type": "zero_product",
-        "problem": f"{normalize(expr)} = 0",
+        "problem": f"{sstr(expr)} = 0",
         "solution": [-a, -b]
     }
     
+@register_problem_generator("radical")
 def generate_radical ():
     #√(x + a) = b
     a = random.choice([i for i in range(-10, 16)])
@@ -159,10 +176,11 @@ def generate_radical ():
 
     return {
         "type": "radical",
-        "problem": f"{normalize(expr)} = {b}",
+        "problem": f"{sstr(expr)} = {b}",
         "solution": ans
     }
     
+@register_problem_generator("fraction")
 def generate_fraction ():
     #(x/a) + b = c
     a = random.choice([i for i in range(-7, 8) if i != 0 and i != 1])
@@ -175,10 +193,11 @@ def generate_fraction ():
 
     return {
         "type": "fraction",
-        "problem": f"{normalize(expr)} = {c}",
+        "problem": f"{sstr(expr)} = {c}",
         "solution": ans
     }
     
+@register_problem_generator("binomial")
 def generate_binomial ():
     #a(x + b) + c(x + d) = e
     ans = random.choice([i for i in range(-15, 16)])
@@ -197,12 +216,13 @@ def generate_binomial ():
 
     return {
         "type": "binomial",
-        "problem": f"{normalize(expr)} = {e}",
+        "problem": f"{sstr(expr)} = {e}",
         "solution": ans
     }
     
+@register_problem_generator("tricky")
 def generate_tricky ():
-    #generate random numbers
+    #(x² - x - a) / (x + b) = c
     n = random.choice([i for i in range(-5, 6) if i != 0])
     r1 = random.choice([i for i in range(-10, 16)])
     r2 = random.choice([i for i in range(-10, 16) if i != r1])
@@ -214,7 +234,7 @@ def generate_tricky ():
     expanded = expanded - expr
     expanded = expanded / (x - r1)
     # expanded = n
-    s = normalize(expanded)
+    s = sstr(expanded)
 
     return {
         "type": "tricky",
@@ -222,24 +242,15 @@ def generate_tricky ():
         "solution": r2
     }
     
-def normalize(expr):
-    return sstr(expr).replace("**", "^")
     
 def generate_problem():
-    template = random.choice(TEMPLATES)
+    types = list(TEMPLATES.keys())
-    return template()
+    #print(types)
+    #         ['linear', 'hidden_factor', 'distribution', 'two_sides', 'like_terms', 'quadratic', 'difference_squares', 'zero_product', 'radical', 'fraction', 'binomial', 'tricky']
+    weights = [0.80    , 0.90           , 0.70          , 1.00       , 0.9         , 1.0        , 0.80                , 0.70          , 0.70     , 1.00      , 1.00       , 0.65]
     
-TEMPLATES = [
+    problem_type = random.choices(types, weights=weights)[0]
-    generate_linear,
+    template = TEMPLATES[problem_type]
-    generate_hidden_factor,
+    return generate_like_terms()
-    generate_distribution,
+    #return template()
-    generate_two_sides,
+    
-    generate_like_terms,
-    generate_quadratic,
-    generate_difference_squares,
-    generate_zero_product,
-    generate_radical,
-    generate_fraction,
-    generate_binomial,
-    generate_tricky
-    ]

requirements.txt

@@ -1,2 +1 @@
-sympy
+sympy
-mathhook

steps_generator.py

@@ -0,0 +1,244 @@
+#All Rights Reserved John Salguero
+#Generates steps depending on the problem
+
+import algebraic_steps
+from sympy import *
+from sympy.parsing.sympy_parser import (
+    parse_expr,
+    standard_transformations,
+    implicit_multiplication_application
+)
+transformations = standard_transformations + (implicit_multiplication_application,)
+
+STEP_GENERATORS = {}
+
+def register_steps_generator(problem_type):
+    def decorator(func):
+        STEP_GENERATORS[problem_type] = func
+        return func
+    return decorator
+    
+@register_steps_generator("linear")
+def generate_linear_steps(problem):
+    #ax + b = c
+    steps = []
+    
+    x = symbols('x')
+    current = problem["problem"]
+    left, right = current.split("=")
+    expr = parse_expr(left)
+    a = expr.coeff(x)
+    b = expr.subs(x, 0)
+    
+    ## First Step
+    if b.is_zero == False:
+        if b.is_negative:
+            steps.append(algebraic_steps.add_both_sides(current, -b))
+        elif b.is_positive:
+            steps.append(algebraic_steps.subtract_both_sides(current, b))
+        current = steps[-1]["after"]
+    ## Second Step
+    if a != 1:
+        steps.append(algebraic_steps.divide_both_sides(current, a))
+    
+    return steps
+    
+@register_steps_generator("hidden_factor")
+def generate_hidden_factor_steps(problem):
+    #a(x + b) + c(x + b) = d 
+    steps = []
+    
+    x = symbols('x')
+    current = problem["problem"]
+    left, right = current.split("=")
+    left_expr = parse_expr(left, transformations=transformations, evaluate=False)
+    right_expr = parse_expr(right)
+    terms = left_expr.as_ordered_terms()
+    #factors = [term.as_ordered_factors() for term in terms]
+    #common = set(factors[0]) & set(factors[1])
+    #base = list(common)[0]
+    base = terms[0].args[1]
+    
+    ## First Step
+    steps.append(algebraic_steps.factor_collect(current))
+    current = steps[-1]["after"]
+    
+    ## Second Step
+    div = simplify(left_expr / base)
+    steps.append(algebraic_steps.divide_both_sides(current, div))
+    current = steps[-1]["after"]
+    
+    ## Third Step
+    b = base.subs(x, 0)
+    if b.is_negative:
+        steps.append(algebraic_steps.add_both_sides(current, -b))
+    elif b.is_positive:
+        steps.append(algebraic_steps.subtract_both_sides(current, b))
+    
+    current = steps[-1]["after"]
+    left, right = current.split("=")
+    left_expr = parse_expr(left, transformations=transformations)
+    right_expr = parse_expr(right)
+    steps[-1]["after"] = f"{sstr(left_expr)} = {sstr(right_expr)}"
+    
+    return steps
+    
+
+@register_steps_generator("distribution")
+def generate_distribution_steps (problem):
+    #a(x + b) = c
+    steps = []
+    
+    x = symbols('x')
+    current = problem["problem"]
+    left, right = current.split("=")
+    left_expr = parse_expr(left, transformations=transformations, evaluate=False)
+    right_expr = parse_expr(right)
+    terms = left_expr.as_ordered_terms()
+    base = terms[0].args[1]
+    div = simplify(left_expr / base)
+    
+    ## First Step
+    steps.append(algebraic_steps.divide_both_sides(current, div))
+    current = steps[-1]["after"]
+    
+    ## Second Step
+    b = base.subs(x, 0)
+    if b.is_negative:
+        steps.append(algebraic_steps.add_both_sides(current, -b))
+    elif b.is_positive:
+        steps.append(algebraic_steps.subtract_both_sides(current, b))
+    
+    current = steps[-1]["after"]
+    left, right = current.split("=")
+    left_expr = parse_expr(left, transformations=transformations)
+    right_expr = parse_expr(right)
+    steps[-1]["after"] = f"{sstr(left_expr)} = {sstr(right_expr)}"
+    
+    return steps
+    
+@register_steps_generator("two_sides")
+def generate_two_sides_steps (problem):
+    #ax + b = dx + e : a != d
+    steps = []
+    
+    x = symbols('x')
+    current = problem["problem"]
+    left, right = current.split("=")
+    left_expr = parse_expr(left)
+    right_expr = parse_expr(right)
+    a = left_expr.coeff(x)
+    b = left_expr.subs(x, 0)
+    d = right_expr.coeff(x)
+    e = right_expr.subs(x, 0)
+    
+    ## First Step
+    if d.is_negative:
+        steps.append(algebraic_steps.add_both_sides(current, -d*x))
+    elif d.is_positive:
+        steps.append(algebraic_steps.subtract_both_sides(current, d*x))
+    current = steps[-1]["after"]
+    left, right = current.split("=")
+    left_expr = parse_expr(left)
+    right_expr = parse_expr(right)
+    steps[-1]["after"] = f"{sstr(left_expr)} = {sstr(right_expr)}"
+    current = steps[-1]["after"]
+    
+    ## Second Step
+    if b.is_negative:
+        steps.append(algebraic_steps.add_both_sides(current, -b))
+    elif b.is_positive:
+        steps.append(algebraic_steps.subtract_both_sides(current, b))
+    current = steps[-1]["after"]
+    left, right = current.split("=")
+    left_expr = parse_expr(left, transformations=transformations)
+    right_expr = parse_expr(right)
+    steps[-1]["after"] = f"{sstr(left_expr)} = {sstr(right_expr)}"
+    current = steps[-1]["after"]
+    
+    ## Third Step
+    new_left, new_right = current.split("=")
+    new_left_expr = parse_expr(left, transformations=transformations, evaluate=False)
+    new_right_expr = parse_expr(right, transformations=transformations, evaluate=False)
+    div = left_expr.coeff(x)
+    if div != 1 and div != -1:
+        steps.append(algebraic_steps.divide_both_sides(current, div))
+    elif div == -1:
+        steps.append(algebraic_steps.multiply_both_sides(current, div))
+    
+    return steps
+    
+@register_steps_generator("like_terms")
+def generate_like_terms_steps (problem):
+    #ax + bx + c = d
+    steps = []
+    
+    current = problem["problem"]
+    
+    ## First Step
+    steps.append(algebraic_steps.combine_like_terms(current))
+    current = steps[-1]["after"]
+    
+    ## Second Step
+    left, right = current.split("=")
+    left_expr = parse_expr(left)
+    b = left_expr.subs(x, 0)
+    
+    return steps
+    
+@register_steps_generator("quadratic")
+def generate_quadratic_steps (problem):
+    #ax² + bx + c = 0
+    steps = []
+    
+    return steps
+    
+@register_steps_generator("difference_squares")
+def generate_difference_squares_steps (problem):
+    #x² - a² = 0
+    steps = []
+    
+    return steps
+    
+@register_steps_generator("zero_product")
+def generate_zero_product_steps (problem):
+    #(x + a)(x + b) = 0
+    steps = []
+    
+    return steps
+    
+@register_steps_generator("radical")
+def generate_radical_steps (problem):
+    #√(x + a) = b
+    steps = []
+    
+    return steps
+    
+@register_steps_generator("fraction")
+def generate_fraction_steps (problem):
+    #(x/a) + b = c
+    steps = []
+    
+    return steps
+    
+@register_steps_generator("binomial")
+def generate_binomial_steps (problem):
+    #a(x + b) + c(x + d) = e
+    steps = []
+    
+    return steps
+    
+@register_steps_generator("tricky")
+def generate_tricky_steps (problem):
+    #(x² - x - a) / (x + b) = c
+    steps = []
+    
+    return steps
+    
+def generate_steps(problem):
+    problem_type = problem["type"]
+    
+    if problem_type not in STEP_GENERATORS:
+        raise ValueError(f"No step generator for type: {problem_type}")
+    
+    return STEP_GENERATORS[problem["type"]](problem)