# class FatRat

Rational number (arbitrary-precision)

A `FatRat` is a rational number stored with arbitrary size numerator and denominator. Arithmetic operations involving a `FatRat` and optionally Int or Rat objects return a `FatRat`, avoiding loss of precision.

Since, unlike Rat, FatRat arithmetics do not fall back Num at some point, there is a risk that repeated arithmetic operations generate pathologically large numerators and denominators.

There are two common ways to generate `FatRat` objects: through the `FatRat.new(Int, Int)` constructor, which generates them from numerator and denominator, or by calling the `.FatRat` method on an Int or Rat object.

# Methods

## method raku

Returns an implementation-specific string that produces an equivalent object when given to EVAL.

# Routines supplied by role Rational

FatRat does role Rational, which provides the following routines:

## (Rational) method new

Creates a new rational object from numerator and denominator, which it normalizes to the lowest terms. The `\$denominator` can be zero, in which case the numerator is normalized to `-1`, `0`, or `1` depending on whether the original is negative, zero, or positive, respectively.

## (Rational) method Bool

Defined as:

Returns `False` if numerator is `0`, otherwise returns `True`. This applies for `<0/0>` zero-denominator Rational as well, despite `?<0/0>.Num` being `True`.

## (Rational) method Bridge

Defined as:

Returns the number, converted to `Num`.

## (Rational) method Int

Defined as:

Coerces the invocant to Int by truncating non-whole portion of the represented number, if any. If the denominator is zero, will fail with `X::Numeric::DivideByZero`.

## (Rational) method Num

Defined as:

Coerces the invocant to Num by dividing numerator by denominator. If denominator is `0`, returns `Inf`, `-Inf`, or `NaN`, based on whether numerator is a positive number, negative number, or `0`, respectively.

## (Rational) method ceiling

Defined as:

Return the smallest integer not less than the invocant. If denominator is zero, fails with `X::Numeric::DivideByZero`.

## (Rational) method floor

Defined as:

Return the largest integer not greater than the invocant. If denominator is zero, fails with `X::Numeric::DivideByZero`.

## (Rational) method isNaN

Tests whether the invocant's Num value is a NaN, an acronym for Not available Number. That is both its numerator and denominator are zero.

## (Rational) method numerator

Returns the numerator.

## (Rational) method denominator

Returns the denominator.

## (Rational) method nude

Returns a list of the numerator and denominator.

## (Rational) method norm

DEPRECATED as of 6.d. The method is no longer needed, because as of 6.d language version, it's required for `Rational` type to be normalized on creation.

Returns a normalized Rational object, i.e. with positive denominator, and numerator and denominator coprime. The denominator can also by zero, but using it in any operation or a conversion to string will result in an exception.

## (Rational) method base-repeating

Returns a list of two strings that, when concatenated, represent the number in base `\$base`. The second element is the one that repeats. For example:

19/3 is 6.333333... with the 3 repeating indefinitely.

If no repetition occurs, the second string is empty:

The precision for determining the repeating group is limited to 1000 characters, above that, the second string is `???`.

`\$base` defaults to `10`.

## (Rational) method Range

Returns a Range object that represents the range of values supported.

# Routines supplied by role Real

FatRat does role Real, which provides the following routines:

## (Real) method Bridge

Defined as:

Default implementation coerces the invocant to Num and that's the behavior of this method in core Real types. This method primarily exist to make it easy to implement custom Real types by users, with the `Bridge` method returning one of the core `Real` types (NOT necessarily a Num) that best represent the custom `Real` type. In turn, this lets all the core operators and methods obtain a usable value they can work with.

As an example, we can implement a custom `Temperature` type. It has a unit of measure and the value, which are given during instantiation. We can implement custom operators or conversion methods that work with this type. When it comes to regular mathematical operators, however, we can simply use the `.Bridge` method to convert the `Temperature` to Kelvin expressed in one of the core numeric types:

As we can see from the last two lines of the output, the type of the bridged result is not forced to be any particular core type. It is a Rat, when we instantiated `Temperature` with a `Rat` or when conversion was involved, and it is an Int when we instantiated `Temperature` with an Int.

## (Real) method Complex

Converts the number to a `Complex` with the number converted to a `Num` as its real part and 0e0 as the imaginary part.

## (Real) method Int

Calls the `Bridge` method on the invocant and then the `Int` method on its return value.

## (Real) method Rat

Calls the `Bridge` method on the invocant and then the `Rat` method on its return value with the `\$epsilon` argument.

## (Real) method Real

Defined as:

The `:D` variant simply returns the invocant. The `:U` variant issues a warning about using an uninitialized value in numeric context and then returns `self.new`.

## (Real) method Str

Calls the `Bridge` method on the invocant and then the `Str` method on its return value.

## (Real) method Num

Calls the `Bridge` method on the invocant and then the `Num` method on its return value.

## (Real) routine rand

Returns a pseudo-random number between zero (inclusive) and the number (non-inclusive). The `Bridge` method is used to coerce the `Real` to a numeric that supports rand method.

The term form returns a pseudo-random `Num` between 0e0 (inclusive) and 1e0 (non-inclusive.)

## (Real) method sign

Returns `-1` if the number is negative, `0` if it is zero and `1` otherwise.

## (Real) method round

Rounds the number to scale `\$scale`. If `\$scale` is 1, rounds to an integer. If scale is `0.1`, rounds to one digit after the radix point (period or comma), etc.

## (Real) method floor

Return the largest integer not greater than the number.

## (Real) method ceiling

Returns the smallest integer not less than the number.

## (Real) method truncate

Rounds the number towards zero.

## (Real) method polymod

Returns the remainders after applying sequentially all divisors in the `@mods` argument; the last element of the array will be the last remainder.

`10 xx 8` is simply an array with eight number 10s; the first division by 10 will return `1` as a remainder, while the rest, up to the last, will return 0. With 8 divisors, as above, the result will have one more elements, in this case for the last remainder.

## (Real) method base

Converts the number to a string, using `\$base` as base. For `\$base` larger than ten, capital Latin letters are used.

The optional `\$digits` argument asks for that many digits of fraction (which may not be negative). If omitted, a reasonable default is chosen based on type. For Int this default is 0. For Num, the default is 8. For Rational, the number of places is scaled to the size of the denominator, with a minimum of 6.

A special value of `Whatever` (`*`) can be given as `\$digits`, which functions the same as when `\$digits` is not specified for all `Real` types except the `Rationals`. For `Rationals`, the `Whatever` indicates that you wish all of the possible digits of the fractional part, but use caution: since there's no detection of repeating fractional parts (the algorithm will eventually stop after generating 2**63 digits).

The final digit produced is always rounded.

For reverse operation, see `parse-base`

# Routines supplied by role Numeric

FatRat does role Numeric, which provides the following routines:

## (Numeric) method Numeric

Defined as:

The `:D` variant simply returns the invocant. The `:U` variant issues a warning about using an uninitialized value in numeric context and then returns `self.new`.

## (Numeric) method narrow

Returns the number converted to the narrowest type that can hold it without loss of precision.

## (Numeric) method ACCEPTS

Returns `True` if `\$other` can be coerced to Numeric and is numerically equal to the invocant (or both evaluate to `NaN`).

## (Numeric) routine log

Calculates the logarithm to base `\$base`. Defaults to the natural logarithm. Returns `NaN` if `\$base` is negative. Throws an exception if `\$base` is `1`.

## (Numeric) routine log10

Calculates the logarithm to base 10. Returns `NaN` for negative arguments and `-Inf` for `0`.

## (Numeric) routine log2

Calculates the logarithm to base 2. Returns `NaN` for negative arguments and `-Inf` for `0`.

## (Numeric) routine exp

Returns `\$base` to the power of the number, or `e` to the power of the number if called without a second argument.

## (Numeric) method roots

Returns a list of the `\$n` complex roots, which evaluate to the original number when raised to the `\$n`th power.

## (Numeric) routine abs

Returns the absolute value of the number.

## (Numeric) routine sqrt

Returns a square root of the number. For real numbers the positive square root is returned.

On negative real numbers, `sqrt` returns `NaN` rather than a complex number, in order to not confuse people who are not familiar with complex arithmetic. If you want to calculate complex square roots, coerce to `Complex` first, or use the `roots` method.

## (Numeric) method conj

Returns the complex conjugate of the number. Returns the number itself for real numbers.

## (Numeric) method Bool

Returns `False` if the number is equivalent to zero, and `True` otherwise.

## (Numeric) method succ

Returns the number incremented by one (successor).

## (Numeric) method pred

Returns the number decremented by one (predecessor).

# Routines supplied by class Cool

FatRat inherits from class Cool, which provides the following routines:

## (Cool) routine abs

Defined as:

Coerces the invocant (or in the sub form, the argument) to Numeric and returns the absolute value (that is, a non-negative number).

## (Cool) method conj

Defined as:

Coerces the invocant to Numeric and returns the complex conjugate (that is, the number with the sign of the imaginary part negated).

## (Cool) method EVAL

Defined as:

It calls the subroutine form with the invocant as the first argument, `\$code`, passing along named args, if any.

## (Cool) routine sqrt

Defined as:

Coerces the invocant to Numeric (or in the sub form, the argument) and returns the square root, that is, a non-negative number that, when multiplied with itself, produces the original number.

## (Cool) method sign

Defined as:

Coerces the invocant to Numeric and returns its sign, that is, 0 if the number is 0, 1 for positive and -1 for negative values.

## (Cool) method rand

Defined as:

Coerces the invocant to Num and returns a pseudo-random value between zero and the number.

## (Cool) routine sin

Defined as:

Coerces the invocant (or in the sub form, the argument) to Numeric, interprets it as radians, returns its sine.

Note that Raku is no computer algebra system, so `sin(pi)` typically does not produce an exact 0, but rather a very small floating-point number.

## (Cool) routine asin

Defined as:

Coerces the invocant (or in the sub form, the argument) to Numeric, and returns its arc-sine in radians.

## (Cool) routine cos

Defined as:

Coerces the invocant (or in sub form, the argument) to Numeric, interprets it as radians, returns its cosine.

## (Cool) routine acos

Defined as:

Coerces the invocant (or in sub form, the argument) to Numeric, and returns its arc-cosine in radians.

## (Cool) routine tan

Defined as:

Coerces the invocant (or in sub form, the argument) to Numeric, interprets it as radians, returns its tangent.

## (Cool) routine atan

Defined as:

Coerces the invocant (or in sub form, the argument) to Numeric, and returns its arc-tangent in radians.

## (Cool) routine atan2

Defined as:

The sub should usually be written with two arguments for clarity as it is seen in other languages and in mathematical texts, but the single-argument form is available; its result will always match that of atan.

The method coerces self and its single argument to Numeric, using them to compute the two-argument arc-tangent in radians.

The \$x argument in either the method or the sub defaults to 1 so, in both single-argument cases, the function will return the angle θ in radians between the x-axis and a vector that goes from the origin to the point (3, 1).

## (Cool) routine sec

Defined as:

Coerces the invocant (or in sub form, its argument) to Numeric, interprets it as radians, returns its secant, that is, the reciprocal of its cosine.

## (Cool) routine asec

Defined as:

Coerces the invocant (or in sub form, its argument) to Numeric, and returns its arc-secant in radians.

## (Cool) routine cosec

Defined as:

Coerces the invocant (or in sub form, its argument) to Numeric, interprets it as radians, returns its cosecant, that is, the reciprocal of its sine.

## (Cool) routine acosec

Defined as:

Coerces the invocant (or in sub form, its argument) to Numeric, and returns its arc-cosecant in radians.

## (Cool) routine cotan

Defined as:

Coerces the invocant (or in sub form, its argument) to Numeric, interprets it as radians, returns its cotangent, that is, the reciprocal of its tangent.

## (Cool) routine acotan

Defined as:

Coerces the invocant (or in sub form, its argument) to Numeric, and returns its arc-cotangent in radians.

## (Cool) routine sinh

Defined as:

Coerces the invocant (or in method form, its argument) to Numeric, and returns its Sine hyperbolicus.

## (Cool) routine asinh

Defined as:

Coerces the invocant (or in sub form, its argument) to Numeric, and returns its Inverse Sine hyperbolicus.

## (Cool) routine cosh

Defined as:

Coerces the invocant (or in sub form, its argument) to Numeric, and returns its Cosine hyperbolicus.

## (Cool) routine acosh

Defined as:

Coerces the invocant (or in sub form, its argument) to Numeric, and returns its Inverse Cosine hyperbolicus.

## (Cool) routine tanh

Defined as:

Coerces the invocant (or in sub form, its argument) to Numeric, interprets it as radians and returns its Tangent hyperbolicus.

## (Cool) routine atanh

Defined as:

Coerces the invocant (or in sub form, its argument) to Numeric, and returns its Inverse tangent hyperbolicus.

## (Cool) routine sech

Defined as:

Coerces the invocant (or in sub form, its argument) to Numeric, and returns its Secant hyperbolicus.

## (Cool) routine asech

Defined as:

Coerces the invocant (or in sub form, its argument) to Numeric, and returns its Inverse hyperbolic secant.

## (Cool) routine cosech

Defined as:

Coerces the invocant (or in sub form, its argument) to Numeric, and returns its Hyperbolic cosecant.

## (Cool) routine acosech

Defined as:

Coerces the invocant (or in sub form, its argument) to Numeric, and returns its Inverse hyperbolic cosecant.

## (Cool) routine cotanh

Defined as:

Coerces the invocant (or in sub form, its argument) to Numeric, and returns its Hyperbolic cotangent.

## (Cool) routine acotanh

Defined as:

Coerces the invocant (or in sub form, its argument) to Numeric, and returns its Inverse hyperbolic cotangent.

## (Cool) routine cis

Defined as:

Coerces the invocant (or in sub form, its argument) to Numeric, and returns cos(argument) + i*sin(argument).

## (Cool) routine log

Defined as:

Coerces the arguments (including the invocant in the method form) to Numeric, and returns its Logarithm to base `\$base`, or to base `e` (Euler's Number) if no base was supplied (Natural logarithm). Returns `NaN` if `\$base` is negative. Throws an exception if `\$base` is `1`.

## (Cool) routine log10

Defined as:

Coerces the invocant (or in the sub form, the argument) to Numeric (or uses it directly if it's already in that form), and returns its Logarithm in base 10, that is, a number that approximately produces the original number when 10 is raised to its power. Returns `NaN` for negative arguments and `-Inf` for `0`.

## (Cool) routine log2

Defined as:

Coerces the invocant to Numeric, and returns its Logarithm in base 2, that is, a number that approximately (due to computer precision limitations) produces the original number when 2 is raised to its power. Returns `NaN` for negative arguments and `-Inf` for `0`.

## (Cool) routine exp

Defined as:

Coerces the arguments (including the invocant in the method from) to Numeric, and returns `\$base` raised to the power of the first number. If no `\$base` is supplied, `e` (Euler's Number) is used.

## (Cool) method unpolar

Defined as:

Coerces the arguments (including the invocant in the method form) to Numeric, and returns a complex number from the given polar coordinates. The invocant (or the first argument in sub form) is the magnitude while the argument (i.e. the second argument in sub form) is the angle. The angle is assumed to be in radians.

## (Cool) routine round

Defined as:

Coerces the invocant (or in sub form, its argument) to Numeric, and rounds it to the unit of `\$scale`. If `\$scale` is 1, rounds to the nearest integer; an arbitrary scale will result in the closest multiple of that number.

Always rounds up if the number is at mid-point:

Pay attention to types when using this method, as ending up with the wrong type may affect the precision you seek to achieve. For Real types, the type of the result is the type of the argument (Complex argument gets coerced to Real, ending up a Num). If rounding a Complex, the result is Complex as well, regardless of the type of the argument.

## (Cool) routine floor

Defined as:

Coerces the invocant (or in sub form, its argument) to Numeric, and rounds it downwards to the nearest integer.

## (Cool) method fmt

Defined as:

Uses `\$format` to return a formatted representation of the invocant; equivalent to calling sprintf with `\$format` as format and the invocant as the second argument. The `\$format` will be coerced to Stringy and defaults to `'%s'`.

## (Cool) routine ceiling

Defined as:

Coerces the invocant (or in sub form, its argument) to Numeric, and rounds it upwards to the nearest integer.

## (Cool) routine truncate

Defined as:

Coerces the invocant (or in sub form, its argument) to Numeric, and rounds it towards zero.

## (Cool) routine ord

Defined as:

Coerces the invocant (or in sub form, its argument) to Str, and returns the Unicode code point number of the first code point.

The inverse operation is chr.

Mnemonic: returns an ordinal number

## (Cool) method path

Defined as:

DEPRECATED. It's been deprecated as of the 6.d version. Will be removed in the next ones.

Stringifies the invocant and converts it to IO::Path object. Use the `.IO method` instead.

## (Cool) routine chr

Defined as:

Coerces the invocant (or in sub form, its argument) to Int, interprets it as a Unicode code points, and returns a string made of that code point.

The inverse operation is ord.

Mnemonic: turns an integer into a character.

## (Cool) routine chars

Defined as:

Coerces the invocant (or in sub form, its argument) to Str, and returns the number of characters in the string. Please note that on the JVM, you currently get codepoints instead of graphemes.

If the string is native, the number of chars will be also returned as a native `int`.

Graphemes are user visible characters. That is, this is what the user thinks of as a “character”.

Graphemes can contain more than one codepoint. Typically the number of graphemes and codepoints differs when `Prepend` or `Extend` characters are involved (also known as Combining characters), but there are many other cases when this may happen. Another example is `\c[ZWJ]` (Zero-width joiner).

You can check `Grapheme_Cluster_Break` property of a character in order to see how it is going to behave:

You can read more about graphemes in the Unicode Standard, which Raku tightly follows, using a method called NFG, normal form graphemes for efficiently representing them.

## (Cool) routine codes

Defined as:

Coerces the invocant (or in sub form, its argument) to Str, and returns the number of Unicode code points.

The same result will be obtained with

ords first obtains the actual codepoints, so there might be a difference in speed.

## (Cool) routine flip

Defined as:

Coerces the invocant (or in sub form, its argument) to Str, and returns a reversed version.

## (Cool) routine trim

Defined as:

Coerces the invocant (or in sub form, its argument) to Str, and returns the string with both leading and trailing whitespace stripped.

Defined as:

Coerces the invocant (or in sub form, its argument) to Str, and returns the string with leading whitespace stripped.

## (Cool) routine trim-trailing

Defined as:

Coerces the invocant (or in sub form, its argument) to Str, and returns the string with trailing whitespace stripped.

## (Cool) routine lc

Defined as:

Coerces the invocant (or in sub form, its argument) to Str, and returns it case-folded to lower case.

## (Cool) routine uc

Defined as:

Coerces the invocant (or in sub form, its argument) to Str, and returns it case-folded to upper case (capital letters).

## (Cool) routine fc

Defined as:

Coerces the invocant (or in sub form, its argument) to Str, and returns the result a Unicode "case fold" operation suitable for doing caseless string comparisons. (In general, the returned string is unlikely to be useful for any purpose other than comparison.)

## (Cool) routine tc

Defined as:

Coerces the invocant (or in sub form, its argument) to Str, and returns it with the first letter case-folded to title case (or where not available, upper case).

## (Cool) routine tclc

Defined as:

Coerces the invocant (or in sub form, its argument) to Str, and returns it with the first letter case-folded to title case (or where not available, upper case), and the rest of the string case-folded to lower case.

## (Cool) routine wordcase

Defined as:

Coerces the invocant (or in sub form, the first argument) to Str, and filters each word that smartmatches against `\$where` through the `&filter`. With the default filter (first character to upper case, rest to lower) and matcher (which accepts everything), this title-cases each word:

With a matcher:

With a customer filter too:

## (Cool) routine samecase

Defined as:

Coerces the invocant (or in sub form, the first argument) to Str, and calls `Str.samecase` on it.

## (Cool) routine uniprop

Defined as:

Returns the unicode property of the first character. If no property is specified returns the General Category. Returns a Bool for Boolean properties. A uniprops routine can be used to get the property for every character in a string.

## (Cool) sub uniprops

Defined as:

Interprets the invocant as a Str, and returns the unicode property for each character as a Seq. If no property is specified returns the General Category. Returns a Bool for Boolean properties. Similar to uniprop, but for each character in the passed string.

## (Cool) routine uniname

Defined as:

Interprets the invocant or first argument as a Str, and returns the Unicode codepoint name of the first codepoint of the first character. See uninames for a routine that works with multiple codepoints, and uniparse for the opposite direction.

## (Cool) routine uninames

Defined as:

Returns of a Seq of Unicode names for the all the codepoints in the Str provided.

Note this example, which gets a Seq where each element is a Seq of all the codepoints in that character.

See uniparse for the opposite direction.

## (Cool) routine unimatch

Defined as:

Checks if the given integer codepoint or the first letter of the given string has a unicode property equal to the value you give. If you supply the Unicode property to be checked it will only return True if that property matches the given value.

The last property corresponds to "lowercase letter", which explains why it returns false.

## (Cool) routine chop

Defined as:

Coerces the invocant (or in sub form, its argument) to Str, and returns it with the last character removed.

## (Cool) routine chomp

Defined as:

Coerces the invocant (or in sub form, its argument) to Str, and returns it with the last character removed, if it is a logical newline.

## (Cool) routine substr

Defined as:

Coerces the invocant (or in the sub form, the first argument) to Str, and calls Str.substr with the arguments.

## (Cool) routine substr-rw

Defined as:

Coerces the invocant (or in the sub form, the first argument) to Str, and calls Str.substr-rw with the arguments.

## (Cool) routine ords

Defined as:

Coerces the invocant (or in the sub form, the first argument) to Str, and returns a list of Unicode codepoints for each character.

This is the list-returning version of ord. The inverse operation in chrs. If you are only interested in the number of codepoints, codes is a possibly faster option.

## (Cool) routine chrs

Defined as:

Coerces the invocant (or in the sub form, the argument list) to a list of integers, and returns the string created by interpreting each integer as a Unicode codepoint, and joining the characters.

This is the list-input version of chr. The inverse operation is ords.

## (Cool) routine split

Defined as:

[1]

Coerces the invocant (or in the sub form, the second argument) to Str, splits it into pieces based on delimiters found in the string and returns the result as a `Seq`.

If `\$delimiter` is a string, it is searched for literally and not treated as a regex. You can also provide multiple delimiters by specifying them as a list, which can mix `Cool` and `Regex` objects.

By default, `split` omits the matches, and returns a list of only those parts of the string that did not match. Specifying one of the `:k, :v, :kv, :p` adverbs changes that. Think of the matches as a list that is interleaved with the non-matching parts.

The `:v` interleaves the values of that list, which will be either Match objects, if a Regex was used as a matcher in the split, or Str objects, if a Cool was used as matcher. If multiple delimiters are specified, Match objects will be generated for all of them, unless all of the delimiters are Cool.

`:k` interleaves the keys, that is, the indexes:

`:kv` adds both indexes and matches:

and `:p` adds them as Pairs, using the same types for values as `:v` does:

You can only use one of the `:k, :v, :kv, :p` adverbs in a single call to `split`.

Note that empty chunks are not removed from the result list. For that behavior, use the `:skip-empty` named argument:

## (Cool) routine lines

Defined as:

Coerces the invocant (and in sub form, the argument) to Str, decomposes it into lines (with the newline characters stripped), and returns the list of lines.

This method can be used as part of an `IO::Path` to process a file line-by-line, since `IO::Path` objects inherit from `Cool`, e.g.:

Without any arguments, sub `lines` operates on `\$*ARGFILES`.

To modify values in place use `is copy` to force a writable container.

## (Cool) method words

Defined as:

Coerces the invocant (or first argument, if it is called as a subroutine) to Str, and returns a list of words that make up the string. Check `Str.words` for additional arguments and its meaning.

`Cool` is the base class for many other classes, and some of them, like Match, can be converted to a string. This is what happens in this case:

The example above illustrates two of the ways `words` can be invoked, with the first argument turned into invocant by its signature. Of course, `Inf` is the default value of the second argument, so in both cases (and forms) it can be simply omitted.

Only whitespace (including no-break space) counts as word boundaries

In this case, "Boeing 747" includes a (visible only in the source) no-break space; `words` still splits the (resulting) `Str` on it, even if the original array only had 4 elements:

Please see `Str.words` for more examples and ways to invoke it.

## (Cool) routine comb

Defined as:

Returns a Seq of all (or if supplied, at most `\$limit`) matches of the invocant (method form) or the second argument (sub form) against the Regex, string or defined number.

The second statement exemplifies the first form of `comb`, with a `Regex` that excludes multiples of ten, and a `Range` (which is `Cool`) as `\$input`. `comb` stringifies the `Range` before applying `.comb` on the resulting string. Check `Str.comb` for its effect on different kind of input strings. When the first argument is an integer, it indicates the (maximum) size of the chunks the input is going to be divided in

In this case the input is a list, which after transformation to `Str` (which includes the spaces) is divided in chunks of size 3.

## (Cool) method contains

Defined as:

Coerces the invocant to a `Str`, and calls `Str.contains` on it. Please refer to that version of the method for arguments and general syntax.

Since Int is a subclass of `Cool`, `123` is coerced to a `Str` and then `contains` is called on it.

Seqs are also subclasses of `Cool`, and they are stringified to a comma-separated form. In this case we are also using an `Int`, which is going to be stringified also; `"233"` is included in that sequence, so it returns `True`. Please note that this sequence is not lazy; the stringification of lazy sequences does not include each and every one of their components for obvious reasons.

## (Cool) routine index

Defined as:

Coerces the first two arguments (in method form, also counting the invocant) to a Str, and searches for `\$needle` in the string `\$s` starting from `\$pos`. It returns the offset into the string where `\$needle` was found, and `Nil` if it was not found.

See the documentation in type Str for examples.

## (Cool) routine rindex

Defined as:

Coerces the first two arguments (including the invocant in method form) to Str and `\$pos` to Int, and returns the last position of `\$needle` in the string not after `\$pos`. Returns `Nil` if `\$needle` wasn't found.

See the documentation in type Str for examples.

## (Cool) method match

Defined as:

Coerces the invocant to Stringy and calls the method match on it.

## (Cool) routine roots

Defined as:

Coerces the first argument (and in method form, the invocant) to Numeric and the second (`\$n`) to Int, and produces a list of `\$n` Complex `\$n`-roots, which means numbers that, raised to the `\$n`th power, approximately produce the original number.

For example

## (Cool) method subst

Defined as:

Coerces the invocant to Stringy and calls Str.subst.

## (Cool) method trans

Defined as:

Coerces the invocant to Str and calls Str.trans

## (Cool) method IO

Defined as:

Coerces the invocant to IO::Path.

## (Cool) method sprintf

Defined as:

Returns a string according to a series format directives that are common in many languages; the object will be the format string, while the supplied arguments will be what's going to be formatted according to it.

## (Cool) method printf

Defined as:

Uses the object, as long as it is a format string, to format and print the arguments

## (Cool) method Complex

Defined as:

Coerces the invocant to a `Numeric` and calls its `.Complex` method. Fails if the coercion to a `Numeric` cannot be done.

## (Cool) method FatRat

Defined as:

Coerces the invocant to a `Numeric` and calls its `.FatRat` method. Fails if the coercion to a `Numeric` cannot be done.

## (Cool) method Int

Defined as:

Coerces the invocant to a `Numeric` and calls its `.Int` method. Fails if the coercion to a `Numeric` cannot be done.

## (Cool) method Num

Defined as:

Coerces the invocant to a `Numeric` and calls its `.Num` method. Fails if the coercion to a `Numeric` cannot be done.

## (Cool) method Rat

Defined as:

Coerces the invocant to a `Numeric` and calls its `.Rat` method. Fails if the coercion to a `Numeric` cannot be done.

## (Cool) method Real

Defined as:

Coerces the invocant to a `Numeric` and calls its `.Real` method. Fails if the coercion to a `Numeric` cannot be done.

## (Cool) method UInt

Defined as:

Coerces the invocant to an `Int`. Fails if the coercion to an `Int` cannot be done or if the `Int` the invocant had been coerced to is negative.