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# ^ -- a binary operator, usually used for powers

- Usage:
    `x ^ y`

## Description

This operator is used for exponentiation, making free modules and sheaves, for shifting complexes left or right, for projection maps involving direct sums, and for making nets.

## Ways to use symbol ^:

- Ideal ^ Array -- bracket power of an ideal
- `MonomialIdeal ^ Array` -- see Ideal ^ Array -- bracket power of an ideal
- Ideal ^ ZZ -- power of an ideal
- `MonomialIdeal ^ ZZ` -- see Ideal ^ ZZ -- power of an ideal
- `Number ^ Ring` -- see lift -- lift to another ring
- `Number ^ RingFamily` -- see lift -- lift to another ring
- List ^ List (missing documentation)
- Matrix ^ Array -- component of map corresponding to summand of target
- Matrix ^ List -- select rows
- `MutableMatrix ^ List` -- see Matrix ^ List -- select rows
- `Vector ^ List` -- see Matrix ^ List -- select rows
- Matrix ^ ZZ -- power
- `MutableMatrix ^ ZZ` -- see Matrix ^ ZZ -- power
- Module ^ Array -- projection onto summand
- Module ^ List -- projection onto summand
- Module ^ ZZ -- direct sum
- Net ^ ZZ -- raise a net or string
- `String ^ ZZ` -- see Net ^ ZZ -- raise a net or string
- Ring ^ BettiTally
- Ring ^ List -- make a free module
- `RingFamily ^ List` -- see Ring ^ List -- make a free module
- Ring ^ ZZ -- make a free module
- `RingFamily ^ ZZ` -- see Ring ^ ZZ -- make a free module
- `MonoidElement ^ ZZ` -- see RingElement ^ ZZ -- power
- RingElement ^ ZZ -- power
- RingMap ^ ZZ -- power
- `ScriptedFunctor ^ Thing` -- see ScriptedFunctor -- the class of all scripted functors
- String ^ Sequence -- vertically stacked copies of a string

## For the programmer

The object ^ is a keyword.

This operator may be used as a binary operator in an expression like x^y. The user may install binary methods for handling such expressions with code such as

             X ^ Y := (x,y) -> ...

where X is the class of x and Y is the class of y.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Macaulay2Doc/operators/caret.m2:38:0.