GAP (Modules) - Chapter 11: Symmetric Algebra and Koszul Complex

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11 Symmetric Algebra and Koszul Complex
11.1 Symmetric Algebra: Constructor
11.1-1 SymmetricPower
11.2 Symmetric Algebra: Properties and Attributes
11.2-1 IsSymmetricPower
11.2-2 SymmetricPowerExponent
11.2-3 SymmetricPowerBaseModule

### 11 Symmetric Algebra and Koszul Complex

#### 11.1 Symmetric Algebra: Constructor

##### 11.1-1 SymmetricPower

`‣ SymmetricPower`( k, M ) | ( operation )

Returns: a homalg module

Construct the k-th exterior power of module M.

#### 11.2 Symmetric Algebra: Properties and Attributes

##### 11.2-1 IsSymmetricPower

`‣ IsSymmetricPower`( M ) | ( property )

Returns: `true` or `false`

Marks a module as an symmetric power of another module.

##### 11.2-2 SymmetricPowerExponent

`‣ SymmetricPowerExponent`( M ) | ( attribute )

Returns: an integer

The exponent of the symmetric power.

##### 11.2-3 SymmetricPowerBaseModule

`‣ SymmetricPowerBaseModule`( M ) | ( attribute )

Returns: a homalg module

The module that M is an symmetric power of.

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