Funktionierender Generator für Addieren / Subtrahieren ungleichnamiger Brüche
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@ -15,13 +15,15 @@ ops = {
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# Konstanten
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# Anzahl der zu generierenden Fragen.
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NUM_QUESTIONS = 1
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NUM_QUESTIONS = 5
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# Algebraische Struktur der Aufgaben
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STRUCTURE = "-(+)-"
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STRUCTURE = "(-)-(+(-))"
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# Gleiche Nenner erlauben
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# TODO
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# Größter Zähler
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MAX_NUMERATOR = 20
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MAX_NUMERATOR = 10
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# Größter Nenner
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MAX_DENOMINATOR = 20
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MAX_DENOMINATOR = 8
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# Größter erlaubter gemeinsamer Nenner
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MAX_COMMON_DENOMINATOR = 100
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# Dateiname für Ausgabe
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@ -36,18 +38,18 @@ def parse_expression(expression):
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max_depth = 0
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for i, char in enumerate(expression):
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if char == '(':
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paren_count += 1
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elif char == ')':
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paren_count -= 1
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# Update max depth when a closed parenthesis is encountered
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max_depth = max(max_depth, paren_count)
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# if char == '(':
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# paren_count += 1
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# elif char == ')':
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# paren_count -= 1
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#
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# # Update max depth when a closed parenthesis is encountered
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# max_depth = max(max_depth, paren_count)
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if char in ops.keys():
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op_count += 1
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return max_depth + op_count
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return max_depth + op_count + 1
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# Anzahl der benötigten Brüche
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NUM_FRACTIONS = parse_expression(STRUCTURE)
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@ -87,7 +89,7 @@ def add_placeholders(expression):
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need_placeholder = False # Nach einem Platzhalter sollten wir keinen weiteren setzen
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# Platzhalter am Beginn hinzufügen
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if output and output[0] != f'n{0}':
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if output and not (output[0] == f'n{0}' or output[0] == '('):
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result = [placeholder_generator()] + output
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else:
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result = output
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@ -99,6 +101,7 @@ def add_placeholders(expression):
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# Zusammensetzen des finalen Ausdrucks
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final_expression = ''.join(result).strip()
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print(final_expression)
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return final_expression
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@ -119,6 +122,54 @@ def calculate(expression, numbers):
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# Evaluate the result
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return eval(expression)
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def gen_calculate_string(expression :str, liststring :str):
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# Replace placeholders with actual number values
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for i in range(NUM_FRACTIONS):
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placeholder = f'n{i}'
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expression = re.sub(rf'\{placeholder}\s*([+-/*])', rf'{liststring}[{i}] \1', expression)
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expression = re.sub(rf'({placeholder})\s*', rf'{liststring}[{i}]', expression)
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print(expression)
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# Return the changed expression
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return expression
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def gen_latex_calculate_string(expression :str, liststring: str):
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# Replace placeholders with actual number values
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for i in range(NUM_FRACTIONS):
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placeholder = f'n{i}'
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replacement = liststring[i]
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print(replacement)
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expression = re.sub(rf'\{placeholder}\s*([+-/*])', replacement, expression)
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expression = re.sub(rf'({placeholder})\s*', replacement, expression)
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# Klammern anpassen
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expression = re.sub(rf'\(', u'\\\\left(', expression)
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expression = re.sub(rf'\)', u'\\\\right)', expression)
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# print(expression)
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# Return the changed expression
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return expression
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def create_html_table_for_fracture_input(rows: list):
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table_rows = []
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# Tabellenzeilen festlegen
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for i, row in enumerate(rows):
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if (i % 2) == 0:
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table_row = "<tr style='border-bottom: 1px solid black;'>"
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else:
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table_row = "<tr>"
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for cell in row:
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table_row += f"<td style='padding: 5px;'>{cell}</td>"
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table_row += "</tr>"
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table_rows.append(table_row)
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# Tabelle zusammenbauen
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table_html = f"<table style='border-collapse: collapse; display: inline-table;'>\n" + "\n".join(table_rows) + "</table>"
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return table_html
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def create_formula_question(ex_number: int):
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numerators = []
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denominators = []
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@ -132,7 +183,12 @@ def create_formula_question(ex_number: int):
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same_denominators = [k for k,v in Counter(denominators).items() if v>1]
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while len(same_denominators) > 1:
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new_denom = random.randint(2, MAX_DENOMINATOR)
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denominators.replace(same_denominators[0], new_denom)
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try:
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index = denominators.index(same_denominators[0])
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denominators[index] = new_denom
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except ValueError:
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pass
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# denominators.replace(same_denominators[0], new_denom)
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same_denominators = [k for k,v in Counter(denominators).items() if v>1]
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# [DEBUG]
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print(numerators)
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@ -165,11 +221,12 @@ def create_formula_question(ex_number: int):
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result_numerator = calculate(STRUCTURE_PH, expanded_numerators)
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# [DEBUG]
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print(result_numerator)
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print(cd)
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# [DEBUG]
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gcd_result = gcd(result_numerator, cd)
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if gcd_result > 1:
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# print("kürzbar")
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print("kürzbar")
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shortable = True
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shortened_numerator = result_numerator // gcd_result
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shortened_denominator = common_denominator // gcd_result
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@ -186,16 +243,16 @@ def create_formula_question(ex_number: int):
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has_div = '/' in STRUCTURE
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if has_plus and has_minus:
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expression_type = "Addition/Subtraktion"
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expression_type = "Addition/Subtraktion" + f" ({STRUCTURE})"
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exercise_text = "Berechne den Term"
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elif has_plus:
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expression_type = "Addition"
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expression_type = "Addition" + f" ({STRUCTURE})"
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exercise_text = "Addiere die Brüche"
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elif has_minus:
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expression_type = "Subtraktion"
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expression_type = "Subtraktion" + f" ({STRUCTURE})"
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exercise_text = "Subtrahiere die Brüche"
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else:
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expression_type = "Rechnung"
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expression_type = "Rechnung" + f" ({STRUCTURE})"
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exercise_text = "Berechne den Term"
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name_elem = ET.SubElement(question, 'name')
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text_elem = ET.SubElement(name_elem, 'text')
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@ -272,16 +329,160 @@ def create_formula_question(ex_number: int):
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ET.SubElement(answertype_elem, 'text').text = '0'
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numbox_elem = ET.SubElement(answers_elem, 'numbox')
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ET.SubElement(numbox_elem, 'text').text = '2'
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return question
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# Berechnungsvariablen
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# common divisor
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cdtext = ""
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for i in range(NUM_FRACTIONS):
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if i == 0:
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pass
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elif i == 1:
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cdtext += f"cd{i} = lcm(d[{i}],d[{i-1}]);"
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else:
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cdtext += f"cd{i} = lcm(cd{i-1}, d[{i}]);"
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cdtext += f"cd = cd{NUM_FRACTIONS-1};"
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# expansions
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extext = "e = ["
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for i in range(NUM_FRACTIONS):
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extext += f"cd / d[{i}],"
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extext = extext[:-1]
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extext += "];"
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# expanded_numerators
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entext = "ens = ["
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for i in range(NUM_FRACTIONS):
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entext += f"n[{i}]*e[{i}],"
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entext = entext[:-1]
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entext += "];"
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# result numerator
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resnum = "resnum = " + gen_calculate_string(STRUCTURE_PH, "ens") + ";"
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# gcd of result numerator and result (common) denominator
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resgcd = "resgcd = gcd(resnum, cd);"
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# shortened result numerator
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sresnum = "sresnum = resnum / resgcd;"
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# shortened result denominator
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sresden = "sresden = cd / resgcd;"
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vars1_elem = ET.SubElement(answers_elem, 'vars1')
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if shortable:
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vars1_elem_text = "<![CDATA[ g = gcd(d[0],d[1]);\n cd = abs(d[0] * d[1]) / g;\n e = [cd / d[0], cd / d[1]];\n nums = [n[0]*e[0], n[1]*e[1]];\n thesumnum = nums[0] - nums[1];\n gcdres = gcd(thesumnum,cd);\n snum = thesumnum / gcdres;\n sdenom = cd / gcdres;]]>"
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vars1_elem_text = f"<![CDATA[{cdtext}\n {extext}\n {entext}\n {resnum}\n {resgcd}\n {sresnum}\n {sresden}]]>"
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else:
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vars1_elem_text = "<![CDATA[ g = gcd(d[0],d[1]);\ncd = abs(d[0] * d[1]) / g;\ne = [cd / d[0], cd / d[1]];\nnums = [n[0]*e[0], n[1]*e[1]];\nthesumnum = nums[0] - nums[1];]]>"
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vars1_elem_text = f"<![CDATA[{cdtext}\n {extext}\n {entext}\n {resnum}]]>"
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ET.SubElement(vars1_elem, 'text').text = vars1_elem_text
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# Antwort
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answer_elem = ET.SubElement(answers_elem, 'answer')
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if shortable:
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answer_text = '[resnum, cd, sresnum, sresden]'
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else:
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answer_text = '[resnum, cd]'
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ET.SubElement(answer_elem, 'text').text = answer_text
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answernotunique_elem = ET.SubElement(answers_elem, 'answernotunique')
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ET.SubElement(answernotunique_elem, 'text').text = '0'
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vars2_elem = ET.SubElement(answers_elem, 'vars2')
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if shortable:
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vars2_elem_text = "<![CDATA[ ga = _0 == resnum && _1 == cd;\n gb = (_0 / _1) == (resnum / cd);\n gsa = _2 == sresnum && _3 == sresden;\n gsb = (_2 / _3) == (sresnum / sresden); ]]>"
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else:
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vars2_elem_text = "<![CDATA[ ga = _0 == resnum && _1 == cd; gb = (_0 / _1) == (resnum / cd); ]]>"
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ET.SubElement(vars2_elem, 'text').text = vars2_elem_text
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correctness_elem = ET.SubElement(answers_elem, 'correctness')
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if shortable:
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ET.SubElement(correctness_elem, 'text').text = '0.25*ga + 0.25*gb + 0.25*gsa + 0.25*gsb'
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else:
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ET.SubElement(correctness_elem, 'text').text = '0.5*ga + 0.5*gb'
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unitpenalty_elem = ET.SubElement(answers_elem, 'unitpenalty')
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ET.SubElement(unitpenalty_elem, 'text').text = '1'
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postunit_elem = ET.SubElement(answers_elem, 'postunit')
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ET.SubElement(postunit_elem, 'text').text = ' '
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ruleid_elem = ET.SubElement(answers_elem, 'ruleid')
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ET.SubElement(ruleid_elem, 'text').text = '1'
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otherrule_elem = ET.SubElement(answers_elem, 'otherrule')
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ET.SubElement(otherrule_elem, 'text').text = ' '
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# Unterfragen-Text
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subqtext_elem = ET.SubElement(answers_elem, 'subqtext', attrib={'format': 'html'})
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fractions_latex_strings = []
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for i in range(NUM_FRACTIONS):
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l_str = "\\\\frac{{"+ f"n[{i}]" +"}}{{"+ f"d[{i}]" +"}}"
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fractions_latex_strings.append(l_str)
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latex_calculation = gen_latex_calculate_string(STRUCTURE_PH, fractions_latex_strings)
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sub_q_t_begin = "<![CDATA[ <p>Berechne:</p>"
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sub_q_t_math = "<p>\\(\\Large \\displaystyle " + f"{latex_calculation}" + "=\\)</p>"
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rows_list = [
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["Zähler:", "{_0}"],
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["Nenner:", "{_1}"]
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]
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sub_q_t_input = '<div style="display: inline-table"> ='
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if shortable:
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sub_q_t_input += create_html_table_for_fracture_input(rows_list)
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rows_list_s = [["Gekürzter Zähler:", "{_2}"],
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["Gekürzter Nenner:", "{_3}"]]
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sub_q_t_input += " = "
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sub_q_t_input += create_html_table_for_fracture_input(rows_list_s)
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else:
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sub_q_t_input += create_html_table_for_fracture_input(rows_list)
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sub_q_t_input += '</div>'
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sub_q_t_end = "]]>"
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sub_question_text = sub_q_t_begin + sub_q_t_math + sub_q_t_input + sub_q_t_end
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ET.SubElement(subqtext_elem, 'text').text = sub_question_text
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expanded_fractions_latex_strings = []
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for i in range(NUM_FRACTIONS):
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l_str = "\\\\frac{{"+ f"ens[{i}]" +"}}{{"+ f"cd" +"}}"
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expanded_fractions_latex_strings.append(l_str)
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expanded_latex_calculation = gen_latex_calculate_string(STRUCTURE_PH, expanded_fractions_latex_strings)
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# Lösungshinweis
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feedback_elem = ET.SubElement(answers_elem, 'feedback', attrib={'format': 'html'})
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if shortable:
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feedback_text = '''<![CDATA[ <h4>Lösungshinweis</h4>
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<p>Die korrekte Lösung ist:</p>
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<p>\\(\\displaystyle''' + f"{latex_calculation}" +" = " + f"{expanded_latex_calculation}" + ''' = \\frac{{resnum}}{{cd}} = \\frac{{sresnum}}{{sresden}} \\) </p> ]]>'''
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else:
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feedback_text = '''<![CDATA[ <h4>Lösungshinweis</h4>
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<p>Die korrekte Lösung ist:</p>
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<p>\\( \\displaystyle ''' + f"{latex_calculation}" +" = " + f"{expanded_latex_calculation}" + ''' = \\frac{{resnum}}{{cd}} \\) </p> ]]>'''
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ET.SubElement(feedback_elem, 'text').text = feedback_text
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# correctfeedback
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correctfeedback_elem = ET.SubElement(answers_elem, 'correctfeedback', attrib={'format': 'html'})
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correctfeedback_text = '''<![CDATA[ <p>Richtig!</p>]]>'''
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ET.SubElement(correctfeedback_elem, 'text').text = correctfeedback_text
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# partially correct feedback
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pcorrectfeedback_elem = ET.SubElement(answers_elem, 'partiallycorrectfeedback', attrib={'format': 'html'})
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pcorrectfeedback_text = '''<![CDATA[ <p>Teilweise richtig.</p>]]>'''
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ET.SubElement(pcorrectfeedback_elem, 'text').text = pcorrectfeedback_text
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# incorrect feedback
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incorrectfeedback_elem = ET.SubElement(answers_elem, 'incorrectfeedback', attrib={'format': 'html'})
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incorrectfeedback_text = '''<![CDATA[ <p>Leider nicht richtig.</p>]]>'''
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ET.SubElement(incorrectfeedback_elem, 'text').text = incorrectfeedback_text
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return question
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def generate_questions(num_questions):
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@ -328,6 +529,7 @@ def save_to_file(xml_element, filename):
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None
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"""
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tree = ET.ElementTree(xml_element)
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ET.indent(tree, space="\t", level=0)
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with open(filename, 'wb') as f:
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tree.write(f, encoding='utf_8', xml_declaration=True)
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