> ## Documentation Index
> Fetch the complete documentation index at: https://tsim.mintlify.site/llms.txt
> Use this file to discover all available pages before exploring further.

# exact_scalar

> Exact scalar arithmetic for ZX-calculus phase computations.

Implements exact arithmetic for complex numbers of the form:
(a + b*e^(i*pi/4) + c*i + d*e^(-i\*pi/4)) \* 2^power

This representation enables exact computation of phases in ZX-calculus graphs
without floating-point errors.

## class `ExactScalarArray`

```python theme={null}
ExactScalarArray(coeffs: Array, power: Array | None = None)
```

Exact scalar array for ZX-calculus phase arithmetic using dyadic representation.

Represents values of the form (c\_0 + c\_1·ω + c\_2·ω² + c\_3·ω³) × 2^power
where ω = e^(iπ/4). This enables exact computation without floating-point errors.

### `prod`

```python theme={null}
prod(axis: int = -1) -> ExactScalarArray
```

Compute product along the specified axis using associative scan.

Returns identity (1+0i with power 0) for empty reductions.

**Parameters:**

* `axis` (`int`) — The axis along which to compute the product.

**Returns:**

* `ExactScalarArray` — ExactScalarArray with the product computed along the axis.

### `sum`

```python theme={null}
sum(axis: int = -1) -> ExactScalarArray
```

Sum elements along the specified axis using normalized pairwise adds.

**Parameters:**

* `axis` (`int`) — The axis along which to sum.

**Returns:**

* `ExactScalarArray` — ExactScalarArray with the sum computed along the axis.

### `to_complex`

```python theme={null}
to_complex() -> jax.Array
```

Convert to complex number.