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--- |
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base_model: AI-MO/NuminaMath-7B-TIR |
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license: apache-2.0 |
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pipeline_tag: text-generation |
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tags: |
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- alignment-handbook |
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- generated_from_trainer |
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- llama-cpp |
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- gguf-my-repo |
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widget: |
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- example_title: Math problem |
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messages: |
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- role: user |
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content: For how many values of the constant $k$ will the polynomial $x^{2}+kx+36$ |
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have two distinct integer roots? |
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output: |
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text: '### Solution: 1. For the polynomial \\( x^2 + kx + 36 \\) to have two distinct |
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integer roots, let''s denote these roots by \\( r_1 \\) and \\( r_2 \\).\n\n2. |
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According to Vieta''s formulas, the sum of the roots \\( r_1 + r_2 \\) is equal |
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to \\(-k\\), and the product of the roots \\( r_1 \\cdot r_2 \\) is equal to |
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36.\n\n3. To find the distinct integer pairs \\((r_1, r_2)\\) whose product |
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is 36, we need to determine all pairs of integers \\((r_1, r_2)\\) such that |
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\\( r_1 \\cdot r_2 = 36 \\) and \\( r_1 \\neq r_2 \\).\n\n4. From the equation |
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\\( r_1 + r_2 = -k \\), for each valid pair \\((r_1, r_2)\\), we can compute |
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the corresponding value of \\( k \\).\n\n5. Finally, since we need the polynomial |
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to have two distinct integer roots, we need to ensure that \\( r_1 \\) and \\( |
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r_2 \\) are distinct.\n\nLet''s start by finding all pairs \\((r_1, r_2)\\) |
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such that \\( r_1 \\cdot r_2 = 36 \\). We''ll then determine the values of \\( |
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k \\) and ensure the roots are distinct.\n```python\nimport itertools\n\n# Find |
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all pairs (r1, r2) such that r1 * r2 = 36\nproduct_36 = 36\nfactor_pairs = []\n\nfor |
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i in range(1, product_36 + 1):\n if product_36 % i == 0:\n pair = (i, product_36 |
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// i)\n if pair[0] != pair[1]: # Ensure distinct pairs\n factor_pairs.append(pair)\n\n# |
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Calculate k for each pair and ensure distinct integer roots\nvalid_k_values |
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= set()\nfor r1, r2 in factor_pairs:\n if r1 != r2:\n k = -(r1 + r2)\n valid_k_values.add(k)\n\nprint((len(valid_k_values), |
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sorted(valid_k_values)))\n```\n```output\n(4, [-37, -20, -15, -13])\n```\nThe |
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distinct integer values of \\( k \\) that make the polynomial \\( x^2 + kx + |
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36 \\) have two distinct integer roots are \\(-37, -20, -15, \\text{and} -13\\).\n\nTherefore, |
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the number of such values of \\( k \\) is:\n\n\\[\n\\boxed{4}\n\\]\n' |
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model-index: |
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- name: NuminaMath-7B-TIR |
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results: [] |
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--- |
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# NikolayKozloff/NuminaMath-7B-TIR-Q8_0-GGUF |
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This model was converted to GGUF format from [`AI-MO/NuminaMath-7B-TIR`](https://huggingface.co/AI-MO/NuminaMath-7B-TIR) using llama.cpp via the ggml.ai's [GGUF-my-repo](https://huggingface.co/spaces/ggml-org/gguf-my-repo) space. |
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Refer to the [original model card](https://huggingface.co/AI-MO/NuminaMath-7B-TIR) for more details on the model. |
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## Use with llama.cpp |
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Install llama.cpp through brew (works on Mac and Linux) |
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```bash |
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brew install llama.cpp |
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``` |
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Invoke the llama.cpp server or the CLI. |
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### CLI: |
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```bash |
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llama-cli --hf-repo NikolayKozloff/NuminaMath-7B-TIR-Q8_0-GGUF --hf-file numinamath-7b-tir-q8_0.gguf -p "The meaning to life and the universe is" |
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``` |
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### Server: |
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```bash |
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llama-server --hf-repo NikolayKozloff/NuminaMath-7B-TIR-Q8_0-GGUF --hf-file numinamath-7b-tir-q8_0.gguf -c 2048 |
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``` |
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Note: You can also use this checkpoint directly through the [usage steps](https://github.com/ggerganov/llama.cpp?tab=readme-ov-file#usage) listed in the Llama.cpp repo as well. |
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Step 1: Clone llama.cpp from GitHub. |
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``` |
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git clone https://github.com/ggerganov/llama.cpp |
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``` |
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Step 2: Move into the llama.cpp folder and build it with `LLAMA_CURL=1` flag along with other hardware-specific flags (for ex: LLAMA_CUDA=1 for Nvidia GPUs on Linux). |
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``` |
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cd llama.cpp && LLAMA_CURL=1 make |
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``` |
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Step 3: Run inference through the main binary. |
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``` |
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./llama-cli --hf-repo NikolayKozloff/NuminaMath-7B-TIR-Q8_0-GGUF --hf-file numinamath-7b-tir-q8_0.gguf -p "The meaning to life and the universe is" |
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``` |
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or |
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``` |
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./llama-server --hf-repo NikolayKozloff/NuminaMath-7B-TIR-Q8_0-GGUF --hf-file numinamath-7b-tir-q8_0.gguf -c 2048 |
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``` |
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