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