# exteriorPower(...,Strategy=>...) -- choose between Bareiss and Cofactor algorithms

## Synopsis

• Usage:
exteriorPower(M, Strategy => s)
• Inputs:
• M,
• s, , either Bareiss or Cofactor
• Consequences:
• If s is Bareiss, then the Bareiss algorithm is used; if s is Cofactor, then cofactor expansion is used.

## Description

The ring of M determines the default strategy. If the ring is a polynomial ring or a field (as identified by isField) then the Bareiss algorithm is used. If the ring is a quotient ring (which has not been declared a field by toField), then the Cofactor algorithm is used.

## Further information

• Default value: null
• Function: exteriorPower -- exterior power
• Option key: Strategy -- an optional argument

## Caveat

The Bareiss algorithm returns a ring element that may differ from the actual determinant by a zero divisor in the ring. Thus, an incorrect answer may be computed if the ring contains zero divisors.