Docs: Add PyTorch .remainder() Tensor Operation documentation

content/pytorch/concepts/tensors/terms/remainder/remainder.md

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+---
+Title: '.remainder()'
+Description: 'Computes the element-wise remainder of tensor division, where the result’s sign matches the divisor.'
+Subjects:
+  - 'Computer Science'
+  - 'Data Science'
+Tags:
+  - 'AI'
+  - 'Deep Learning'
+  - 'Functions'
+CatalogContent:
+  - 'intro-to-py-torch-and-neural-networks'
+  - 'py-torch-for-classification'
+---
+
+In PyTorch, the **`.remainder()`** function computes the element-wise remainder of division between two tensors or between a tensor and a scalar. The result always has the same sign as the divisor, unlike `.fmod()`, which matches the sign of the dividend. This operation works with both integer and floating-point tensors.
+
+## Syntax
+
+```pseudo
+torch.remainder(input, other)
+```
+
+**Parameters:**
+
+- `input` (Tensor): The input tensor containing dividend values.
+- `other` (Tensor or Number): The divisor. It can be a scalar or another tensor of compatible shape.
+- `out` (Tensor, optional): The output tensor to store the result.
+
+**Return value:**
+
+Returns a tensor containing the element-wise remainder of the division.
+
+- If `other` is a scalar, the operation is applied using the same divisor for all elements.
+- If `other` is a tensor, element-wise division is performed.
+
+## Example 1: Divide a 1D Tensor by an Integer
+
+This example computes the remainder of each element in `x` when divided by 2, keeping the sign consistent with the divisor:
+
+```py
+import torch
+
+x = torch.tensor([-3, -4, -1, -6, 4, 7, 8])
+print(torch.remainder(x, 3))
+```
+
+The output of this code is:
+
+```shell
+tensor([0, 2, 2, 0, 1, 1, 2])
+```
+
+## Example 2: Divide a 2D Tensor by an Integer
+
+In this example, each negative number wraps around within the range `[0, 4)` since the remainder must match the divisor’s sign:
+
+```py
+import torch
+
+A = torch.tensor([[ 1,  2,  3],
+                  [-1, -2, -3]])
+print(torch.remainder(A, 4))
+```
+
+The output of this code is:
+
+```shell
+tensor([[1, 2, 3],
+        [3, 2, 1]])
+```
+
+## Example 3: Divide a Tensor by Another Tensor
+
+This example demonstrates element-wise remainder calculation between two tensors of the same shape:
+
+```py
+import torch
+
+num = torch.tensor([ 3, -3,  3, -3], dtype=torch.int32)
+den = torch.tensor([ 2,  2, -2, -2], dtype=torch.int32)
+print(torch.remainder(num, den))
+```
+
+The output of this code is:
+
+```shell
+tensor([ 1,  1, -1, -1])
+```
+
+> **Note:** If `input` and `other` don’t share the same shape, PyTorch tries automatic size expansion (broadcasting). Dimensions match when they’re equal or one of them is 1 (aligned from the right). If no match is possible, a size-mismatch error is raised.
+
+## Example 4: Divide a Floating-Point Tensor by a Number
+
+This example calculates remainders for floating-point values, preserving the sign of the divisor:
+
+```py
+import torch
+
+xf = torch.tensor([-7.5, 7.5, 5.0])
+print(torch.remainder(xf, 4.0))
+```
+
+The output of this code is:
+
+```shell
+tensor([0.5, 3.5, 1.0])
+```