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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: \n1- For the polynomial \\\\( x^2 + kx + 36 \\\\) to have\
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+ \ two distinct integer roots, let's denote these roots by \\\\( r_1 \\\\) and\
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+ \ \\\\( r_2 \\\\).\n\n\n2- According to Vieta's formulas, the sum of the roots\
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+ \ \\\\( r_1 + r_2 \\\\) is equal to \\\\(-k\\\\), and the product of the roots\
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+ \ \\\\( r_1 \\\\cdot r_2 \\\\) is equal to 36.\n\n\n3- To find the distinct\
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+ \ integer pairs \\\\((r_1, r_2)\\\\) whose product is 36, we need to determine\
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+ \ all pairs of integers \\\\((r_1, r_2)\\\\) such that \\\\( r_1 \\\\cdot r_2\
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+ \ = 36 \\\\) and \\\\( r_1 \\\\neq r_2 \\\\).\n\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\n\n5- Finally, since we need the\
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+ \ polynomial to have two distinct integer roots, we need to ensure that \\\\\
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+ ( r_1 \\\\) and \\\\( r_2 \\\\) are distinct.\nLet's start by finding all pairs\
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+ \ \\\\((r_1, r_2)\\\\) such that \\\\( r_1 \\\\cdot r_2 = 36 \\\\). We'll then\
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+ \ determine the values of \\\\( k \\\\) and ensure the roots are distinct.\n\
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+ ```python import itertools\n# Find all pairs (r1, r2) such that r1 * r2 = 36\
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+ \ product_36 = 36 factor_pairs = []\nfor i in range(1, product_36 + 1):\n if\
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+ \ product_36 % i == 0:\n pair = (i, product_36 // i)\n if pair[0] != pair[1]:\
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+ \ # Ensure distinct pairs\n factor_pairs.append(pair)\n \n # Calculate\
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+ \ k for each pair and ensure distinct integer roots\n valid_k_values = set()\n\
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+ \ for r1, r2 in factor_pairs:\n if r1 != r2:\n k = -(r1 + r2)\n\
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+ \ valid_k_values.add(k)\n \n print((len(valid_k_values), sorted(valid_k_values)))\n\
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+ \ ```\n \n ```output\n (4, [-37, -20, -15,-13])\n ```\n The distinct integer\
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+ \ values of \\\\( k \\\\) that make the\npolynomial \\\\( x^2 + kx + 36 \\\\\
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+ ) have two distinct integer roots are \\\\(-37, -20, -15, \\\\text{and} -13\\\
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+ \\).\nTherefore, the number of such values of \\\\( k \\\\) is:\n[ \\\\boxed{4}\
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+ \ \\\\]"
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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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+
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+ # Triangle104/NuminaMath-7B-TIR-Q5_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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+
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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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+
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+ ```bash
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+ brew install llama.cpp
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+
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+ ```
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+ Invoke the llama.cpp server or the CLI.
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+
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+ ### CLI:
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+ ```bash
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+ llama-cli --hf-repo Triangle104/NuminaMath-7B-TIR-Q5_0-GGUF --hf-file numinamath-7b-tir-q5_0.gguf -p "The meaning to life and the universe is"
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+ ```
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+
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+ ### Server:
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+ ```bash
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+ llama-server --hf-repo Triangle104/NuminaMath-7B-TIR-Q5_0-GGUF --hf-file numinamath-7b-tir-q5_0.gguf -c 2048
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+ ```
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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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+
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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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+
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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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+
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+ Step 3: Run inference through the main binary.
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+ ```
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+ ./llama-cli --hf-repo Triangle104/NuminaMath-7B-TIR-Q5_0-GGUF --hf-file numinamath-7b-tir-q5_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 Triangle104/NuminaMath-7B-TIR-Q5_0-GGUF --hf-file numinamath-7b-tir-q5_0.gguf -c 2048
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+ ```