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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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# martintmv/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 martintmv/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 martintmv/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 martintmv/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 martintmv/NuminaMath-7B-TIR-Q8_0-GGUF --hf-file numinamath-7b-tir-q8_0.gguf -c 2048 |
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``` |
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