# Vocabulary/gtco

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`>: y`Increment

Rank 0 *-- operates on individual atoms of y, producing a result of the same shape --*
WHY IS THIS IMPORTANT?

Equivalent to `y+1`.

>: _5 1 0 5 _4 2 1 6

### Common uses

1. Simplify a phrase which increments a given value

y=. >:y NB. increment y z=: '[a,b]' (>: z i. ',') { z NB. pick the letter AFTER the comma b

2. Simplify an unwieldy phrase

z=: 10 (100-z)+1 91 >: 100-z 91

3. Compile a simpler tacit definition from a given explicit (verb) definition

the verb below computes the common mathematical expression: *(1+y)/y*

13 : '(1+y)%y' ] %~ 1 + ] 13 : '(>:y)%y' >: % ]

### Related Primitives

Decrement (`<:`)

### Use These Combinations

Combinations using ` >:y` that have exceptionally good performance include:

**What it does****Type;**

**Precisions;**

Ranks**Syntax****Variants;**

**Restrictions****Benefits;**

**Bug Warnings**Create list of integers from `1`to`# y`, or the reverse`#\ y`also `#\.`which is the reversefaster than `>:@i.@# y`

`x >: y`Larger Or Equal

Rank 0 0 *-- operates on individual atoms of x and y, producing a result of the same shape --*
WHY IS THIS IMPORTANT?

Compares `x` and `y` atom-by-atom. See Equal (`=`) for the details.

Wherever `x` is greater than, or equal to, `y`, returns 1 in that position, else 0.

z=: 7 8 9 z >: 8 0 1 1

`x` and `y` must both be numeric, else you get a `domain error`

'a' >: 9 |domain error | 'a' >:9

This differs from what happens with Equal (`=`)

'a' = 9 0

**Larger Or Equal** (`>:`) uses tolerant comparison
in the same way as Equal (`=`).

To require exact comparison, use (` >:!.0 `) in place of (`>:`) to temporarily set the comparison tolerance to zero

1.99999999999999 >: 2 1 1.99999999999999 (>:!.0) 2 0

### Common uses

1. Make a conditional phrase in a verb definition (explicit definition)

if. x>:y do. 'x y'=. y;x end.

2. Make a mask of the same shape as `array`, to process `array` in some chosen way

array=: 3 1 4 1 5 9 2 6 mask=: array >: 5 array ,: mask 3 1 4 1 5 9 2 6 0 0 0 0 1 1 0 1 mask # array NB. keep only the atoms that are >: 5 5 9 6

**NOTE:**
The boolean atoms of `mask` are not only truth values but also valid numbers, 0 or 1.
Therefore you can use `mask` directly to process `array` like this:

array + 3 * mask NB. add 3 to the atoms that are >: 5 3 1 4 1 8 12 2 9

### Related Primitives

Less Than (`x < y`),
Equal (`x = y`),
Not-Equal (`x ~: y`),
Less Or Equal (`x <: y`),
Larger Than (`x > y`)

### More Information

1. If an argument to ` x >: y ` is complex, its imaginary part must be tolerantly equal to 0, using the default tolerance of `2^_44` even if the comparison ` x >: y ` itself uses a different tolerance.

### Use These Combinations

Combinations using `x >: y` that have exceptionally good performance include those shown in Searching and Matching Items: Fast List Operations (FLOs), as well as the following:

**What it does****Type;**

**Precisions;**

Ranks**Syntax****Variants;**

**Restrictions****Benefits;**

**Bug Warnings**Boolean reductions along diagonals Boolean `+.//. y``*. = ~: < <: > >:`in place of`+.`avoids building argument cells