Arithmetic Operations

Basic arithmetic operations on tensors.

Supported Operations

Nicole tensors support standard arithmetic operations:

Addition and Subtraction

C = A + B  # Element-wise addition
D = A - B  # Element-wise subtraction
E = A + scalar  # Add scalar to all blocks

Requirements: Tensors must have identical index structure (same indices, same tags).

Scalar Multiplication

F = 2.0 * A  # Multiply by scalar
G = A * 3.0  # Multiply by scalar
H = A / 2.0  # Divide by scalar

Negation

I = -A  # Negate all elements

Description

Arithmetic operations are performed block-wise. Each operation processes only the blocks that exist in both tensors (for binary operations) or in the single tensor (for unary operations).

See Also

• oplus: Direct sum operation
• Tensor: Main tensor class
• Examples: Arithmetic

Notes

• Operations preserve block structure
• Results have same dtype unless promotion occurs
• Blocks must have matching shapes for addition/subtraction
• For non-Abelian groups, linearly dependent components introduced by the operation are automatically compressed away