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lucataco /numinamath-7b-tir:3749451b
Input
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npx create-replicate --model=lucataco/numinamath-7b-tir
or set up a project from scratch
Install Replicate’s Node.js client library:
npm install replicateSet the
REPLICATE_API_TOKEN environment variable:export REPLICATE_API_TOKEN=<paste-your-token-here>Find your API token in your account settings.
Import and set up the client:
import Replicate from "replicate";
const replicate = new Replicate({
auth: process.env.REPLICATE_API_TOKEN,
});Run lucataco/numinamath-7b-tir using Replicate’s API. Check out the model's schema for an overview of inputs and outputs.
const output = await replicate.run(
"lucataco/numinamath-7b-tir:3749451b2f11e1cd14cc3adc1b66a17356c0f3529780382f3245f486908bd215",
{
input: {
top_k: 50,
top_p: 0.9,
prompt: "For how many values of the constant $k$ will the polynomial $x^{2}+kx+36$ have two distinct integer roots?",
max_tokens: 512,
min_tokens: 0,
temperature: 0.6,
system_prompt: "You are a helpful assistant.",
presence_penalty: 0,
frequency_penalty: 0
}
}
);
console.log(output);To learn more, take a look at the guide on getting started with Node.js.
Install Replicate’s Python client library:
pip install replicateSet the
REPLICATE_API_TOKEN environment variable:export REPLICATE_API_TOKEN=<paste-your-token-here>Find your API token in your account settings.
Import the client:
import replicateRun lucataco/numinamath-7b-tir using Replicate’s API. Check out the model's schema for an overview of inputs and outputs.
output = replicate.run(
"lucataco/numinamath-7b-tir:3749451b2f11e1cd14cc3adc1b66a17356c0f3529780382f3245f486908bd215",
input={
"top_k": 50,
"top_p": 0.9,
"prompt": "For how many values of the constant $k$ will the polynomial $x^{2}+kx+36$ have two distinct integer roots?",
"max_tokens": 512,
"min_tokens": 0,
"temperature": 0.6,
"system_prompt": "You are a helpful assistant.",
"presence_penalty": 0,
"frequency_penalty": 0
}
)
# The lucataco/numinamath-7b-tir model can stream output as it's running.
# The predict method returns an iterator, and you can iterate over that output.
for item in output:
# https://replicate.com/lucataco/numinamath-7b-tir/api#output-schema
print(item, end="")To learn more, take a look at the guide on getting started with Python.
Set the
REPLICATE_API_TOKEN environment variable:export REPLICATE_API_TOKEN=<paste-your-token-here>Find your API token in your account settings.
Run lucataco/numinamath-7b-tir using Replicate’s API. Check out the model's schema for an overview of inputs and outputs.
curl -s -X POST \
-H "Authorization: Bearer $REPLICATE_API_TOKEN" \
-H "Content-Type: application/json" \
-H "Prefer: wait" \
-d $'{
"version": "lucataco/numinamath-7b-tir:3749451b2f11e1cd14cc3adc1b66a17356c0f3529780382f3245f486908bd215",
"input": {
"top_k": 50,
"top_p": 0.9,
"prompt": "For how many values of the constant $k$ will the polynomial $x^{2}+kx+36$ have two distinct integer roots?",
"max_tokens": 512,
"min_tokens": 0,
"temperature": 0.6,
"system_prompt": "You are a helpful assistant.",
"presence_penalty": 0,
"frequency_penalty": 0
}
}' \
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Output
1. **Understand the Polynomial and its Roots**:
The polynomial given is \(x^2 + kx + 36\).
Let the roots of the polynomial be \(r_1\) and \(r_2\).
2. **Relationships Between Roots and Coefficients**:
For a polynomial \(x^2 + bx + c = 0\), the sum of the roots \(r_1 + r_2 = -b\) and the product of the roots \(r_1 \cdot r_2 = c\).
In our case, \(r_1 + r_2 = -k\) and \(r_1 \cdot r_2 = 36\).
3. **Conditions for Distinct Integer Roots**:
We need to find pairs of distinct integers \((r_1, r_2)\) such that their product is 36. Then, for each pair, we will determine the corresponding value of \(k\).
4. **Check for Distinct Pairs**:
Ensure \(r_1 \neq r_2\).
5. **Calculate the Values of \(k\)**:
For each valid pair \((r_1, r_2)\), compute \(k = -(r_1 + r_2)\) and count the distinct values.
Let's implement this in Python to find the number of distinct values of \(k\).
```python
import sympy as sp
# Define the product of the roots
product = 36
# Find all pairs of integers (r1, r2) such that r1 * r2 = product
integer_pairs = []
for i in range(1, product + 1):
if product % i == 0:
j = product // i
integer_pairs.append((i, j))
integer_pairs.append((j, i)) # Include both (i, j) and (j, i)
# Filter pairs to ensure they are distinct and r1 != r2
distinct_pairs = [(r1, r2) for r1, r2 in integer_pairs if r1 != r2]
# Calculate the corresponding values of k
k_values = set(-(r1 + r2) for r1, r2 in distinct_pairs)
# Output the number of
{
"completed_at": "2024-07-12T13:42:40.836981Z",
"created_at": "2024-07-12T13:39:35.094000Z",
"data_removed": false,
"error": null,
"id": "5484t65a6srgm0cgmwns1qkfg0",
"input": {
"top_k": 50,
"top_p": 0.9,
"prompt": "For how many values of the constant $k$ will the polynomial $x^{2}+kx+36$ have two distinct integer roots?",
"max_tokens": 512,
"min_tokens": 0,
"temperature": 0.6,
"system_prompt": "You are a helpful assistant.",
"presence_penalty": 0,
"frequency_penalty": 0
},
"logs": "INFO 07-12 13:42:28 async_llm_engine.py:646] Received request ed4c5fab43324c8b8e97700a86a10dea: prompt: '### Problem: For how many values of the constant $k$ will the polynomial $x^{2}+kx+36$ have two distinct integer roots?\\n### Solution: ', params: SamplingParams(n=1, best_of=1, presence_penalty=0.0, frequency_penalty=0.0, repetition_penalty=1.0, temperature=0.6, top_p=0.9, top_k=50, min_p=0.0, seed=None, use_beam_search=False, length_penalty=1.0, early_stopping=False, stop=[], stop_token_ids=[100001], include_stop_str_in_output=False, ignore_eos=False, max_tokens=512, min_tokens=0, logprobs=None, prompt_logprobs=None, skip_special_tokens=True, spaces_between_special_tokens=True, truncate_prompt_tokens=None), prompt_token_ids: None, lora_request: None.\n stdoutINFO 07-12 13:42:32 metrics.py:295] Avg prompt throughput: 7.6 tokens/s, Avg generation throughput: 26.5 tokens/s, Running: 1 reqs, Swapped: 0 reqs, Pending: 0 reqs, GPU KV cache usage: 0.3%, CPU KV cache usage: 0.0%.\n stdoutINFO 07-12 13:42:37 metrics.py:295] Avg prompt throughput: 0.0 tokens/s, Avg generation throughput: 43.4 tokens/s, Running: 1 reqs, Swapped: 0 reqs, Pending: 0 reqs, GPU KV cache usage: 0.6%, CPU KV cache usage: 0.0%.\n stdoutGeneration took 1720790260.82sFormatted prompt: ### Problem: For how many values of the constant $k$ will the polynomial $x^{2}+kx+36$ have two distinct integer roots?\n### Solution: INFO 07-12 13:42:40 async_llm_engine.py:134] Finished request ed4c5fab43324c8b8e97700a86a10dea.\n stdout",
"metrics": {
"predict_time": 11.85670725,
"total_time": 185.742981
},
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"started_at": "2024-07-12T13:42:28.980274Z",
"status": "succeeded",
"urls": {
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"get": "https://api.replicate.com/v1/predictions/5484t65a6srgm0cgmwns1qkfg0",
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"version": "3749451b2f11e1cd14cc3adc1b66a17356c0f3529780382f3245f486908bd215"
}Generated in
INFO 07-12 13:42:28 async_llm_engine.py:646] Received request ed4c5fab43324c8b8e97700a86a10dea: prompt: '### Problem: For how many values of the constant $k$ will the polynomial $x^{2}+kx+36$ have two distinct integer roots?\n### Solution: ', params: SamplingParams(n=1, best_of=1, presence_penalty=0.0, frequency_penalty=0.0, repetition_penalty=1.0, temperature=0.6, top_p=0.9, top_k=50, min_p=0.0, seed=None, use_beam_search=False, length_penalty=1.0, early_stopping=False, stop=[], stop_token_ids=[100001], include_stop_str_in_output=False, ignore_eos=False, max_tokens=512, min_tokens=0, logprobs=None, prompt_logprobs=None, skip_special_tokens=True, spaces_between_special_tokens=True, truncate_prompt_tokens=None), prompt_token_ids: None, lora_request: None.
stdoutINFO 07-12 13:42:32 metrics.py:295] Avg prompt throughput: 7.6 tokens/s, Avg generation throughput: 26.5 tokens/s, Running: 1 reqs, Swapped: 0 reqs, Pending: 0 reqs, GPU KV cache usage: 0.3%, CPU KV cache usage: 0.0%.
stdoutINFO 07-12 13:42:37 metrics.py:295] Avg prompt throughput: 0.0 tokens/s, Avg generation throughput: 43.4 tokens/s, Running: 1 reqs, Swapped: 0 reqs, Pending: 0 reqs, GPU KV cache usage: 0.6%, CPU KV cache usage: 0.0%.
stdoutGeneration took 1720790260.82sFormatted prompt: ### Problem: For how many values of the constant $k$ will the polynomial $x^{2}+kx+36$ have two distinct integer roots?
### Solution: INFO 07-12 13:42:40 async_llm_engine.py:134] Finished request ed4c5fab43324c8b8e97700a86a10dea.
stdout