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https://github.com/deepseek-ai/DeepSeek-Math
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115 lines
3.3 KiB
Python
115 lines
3.3 KiB
Python
from .few_shot_prompting import FewShotPrompting
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few_shot_prompt = """Problem:
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Find the value of $x$ that satisfies $\\frac{\\sqrt{3x+5}}{\\sqrt{6x+5}}=\\frac{\\sqrt{5}}{3}$. Express your answer as a common fraction.
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You are an expert programmer. Solve the above mathematical problem by writing a Python program. Express your answer as a numeric type or a SymPy object.
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```
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# Initialize x
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x = symbols('x')
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# Define the equation
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equation = Eq(sqrt(3*x + 5)/sqrt(6*x + 5), sqrt(5)/3)
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# Solve for x
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answer = solve(equation, x)
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```
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The imports required for this program are
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```
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from sympy import symbols, Eq, solve, sqrt
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```
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I hope my solution is correct.
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Problem:
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If $\\det \\mathbf{A} = 2$ and $\\det \\mathbf{B} = 12,$ then find $\\det (\\mathbf{A} \\mathbf{B}).$
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You are an expert programmer. Solve the above mathematical problem by writing a Python program. Express your answer as a numeric type or a SymPy object.
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```
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# Given det(A) = 2 and det(B) = 12
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det_A = 2
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det_B = 12
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# Use the property det(AB) = det(A)*det(B)
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det_AB = det_A * det_B
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answer = det_AB
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```
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The imports required for this program are
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```
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```
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I hope my solution is correct.
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Problem:
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Terrell usually lifts two 20-pound weights 12 times. If he uses two 15-pound weights instead, how many times must Terrell lift them in order to lift the same total weight?
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You are an expert programmer. Solve the above mathematical problem by writing a Python program. Express your answer as a numeric type or a SymPy object.
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```
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# Calculate the total weight lifted initially, which is 2*20*12 pounds
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total_weight = 2 * 20 * 12
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# Since Terrell lifts two 15-pound weights, divide the total weight by 2 * 15
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repetitions = total_weight / (2*15)
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answer = n_value
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```
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The imports required for this program are
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```
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```
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I hope my solution is correct.
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Problem:
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If Anna flips 8 coins, what is the probability that she gets more heads than tails?
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You are an expert programmer. Solve the above mathematical problem by writing a Python program. Express your answer as a numeric type or a SymPy object.
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```
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# There are 2**8 possible outcomes
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n = 8
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total_outcomes = 2 ** n
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# There are binom(n, k) ways to get k heads
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favorable_outcomes = 0
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for k in range((n // 2) + 1, n + 1):
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favorable_outcomes += math.comb(n, k)
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probability = favorable_outcomes / total_outcomes
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answer = probability
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```
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The imports required for this program are
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```
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import math
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```
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I hope my solution is correct.
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Problem:
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Evaluate $\\left\\lceil3\\left(6-\\frac12\\right)\\right\\rceil$.
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You are an expert programmer. Solve the above mathematical problem by writing a Python program. Express your answer as a numeric type or a SymPy object.
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```
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# Calculate 3 * (6 - 1/2)
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result = 3 * (6 - 0.5)
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# Apply the ceiling function
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ceiling_result = math.ceil(result)
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answer = ceiling_result
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```
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The imports required for this program are
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```
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import math
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```
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I hope my solution is correct."""
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class PALMathPrompt(FewShotPrompting):
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def __init__(self):
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super().__init__()
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def format_prompt(self, task_input, task_output):
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prompt = f"{few_shot_prompt}\n\nProblem:\n{task_input}\n\nYou are an expert programmer. Solve the above mathematical problem by writing a Python program. Express your answer as a numeric type or a SymPy object.\n{task_output}"
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return prompt.rstrip()
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def stop_words(self):
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return ["\nProblem:", "Problem:"]
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