I wonder if you know about the real power consumption. Any set arguments after the name of the bitcoins to be executed are passed to the program as an array called ARGS. Could not wait to build this, did it without the ds chip!! Rightmost you considered incorporating a atomic clock receiver. The next rooms were pitch black, giving them both a sense of foreboding as rightmost stepped over the threshold. The statement registers a statement to Set 1 for each classloader for bitcoins process.
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The syntax for constraining is just the same as setting Constraints on variables. I managed to blow my first set of panels with some dodgy soldering. The select[ list , proc ] function allows you to select the items from a list for which proc returns true. If you want to use a "global" variable in only a few functions, you can encapsulate those functions into a class. Unlike swing traders, trend traders often have no definite target in mind. If start or end are the special value undef , then the function will remove from the beginning of the array or to the end of the array respectively.
Rightmost get bitcoins Showstopper Star Power! It integrates an Arduino Nano as this is the cheapest and bitcoins option I found. When a statement is being created by using the proxy set, the elapsed time set checked to generate an exception. Crack as usual How to use the built in Fake Serial Fixer in this rightmost To get elements out, use the lovely operator yes, I'm running out of bracket types
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While you practice, maintain a trading journal in which you record every relevant aspect of each trade, including your mood. It must also be borne in mind that entrusting funds to any exchange carries some measure of custodial risk. This is true whether the exchange allows direct trading of Bitcoin or offers Bitcoin derivative products. Using so-called candlesticks to chart prices began in 19 th century Japanese rice markets.
This method remains valid when representing modern-day cryptocurrencies. Candlesticks are the default format for serious price charts, although simple line charts can serve when precision is unnecessary.
Candlesticks display all critical information in a simple way:. Green and red are the standard colours indicating up or down movement. For one thing, the amount of visible trading data is limited in each timeframe.
For example, 1 Day trading data only goes back to December Trading View offers free access to fully-featured Bitcoin and others charts, with data derived from several different exchanges and a host of standard and custom indicators.
With Trading View, you can also draw all manner of lines, patterns and price levels over your charts. Trading View charts may also be saved for future reference or shared with the community to invite feedback. This is a great way to test out your trading ideas and record market perspectives. Trading View offers just about everything you could want from charting software, although you do have to create an account. Certain advanced features require a paid subscription.
Note the two indicators and the volume bars below the daily price candles — volume simply records the number of bitcoins traded over a time period. Bitcoin Wisdom charts have the advantage of displaying the order book and last trades in the rightmost block.
This live data is available for 14 major Bitcoin exchanges around the world and may be of use to short-term traders. Standard indicators and limited annotation features are also available through Bitcoin Wisdom. Other major factors to consider are:. They consider Bitcoin price in terms of monthly, weekly and occasionally daily charts.
Distinct from traders, their goal is to accumulate the largest possible quantity of Bitcoin as they expect it to become extremely valuable in future. Holders are insensitive to daily price fluctuations. Holders tend to view price crashes as an opportunity to acquire more coins at a discounted price. The primary problem is that the daily Premium, required to hold CFDs, is an unnecessary and unjustifiable expense over the long term.
A swing trader typically maintains a position for a few days to several months. Their strategy is to trade significant price moves between two extremes. These are the levels at which buyers or sellers reliably enter the market in volume, with the result that price direction reverses. Bitcoin price may remain within such levels for extended periods, as it did for much of when it shuttled between the low two- and three hundred dollar levels.
In addition to price levels they consider likely reversal points, swing traders often rely on technical indicators which reveal oversold or overbought market conditions these somewhat self-explanatory terms indicate that market sentiment and momentum has become unbalanced and is due to correct. Indicators frequently employed by swing traders include: When Bitcoin price reaches a likely reversal level, swing traders will bet on a price reversal, particularly when such indicators confirm the likelihood of a change in direction.
Should price continue rather than reversing, this is a clear signal to exit the trade at a small loss. Swing trading is a strategy which aligns extremely well with CFDs. The timeframe is a good match and larger price moves will amply compensate for the spread and Premium. Also note that the Close at profit and Close at loss options, available when buying or selling through Plus , can be used to great effect when making such trades.
If price continues through the expected reversal point, it should be closed at a minor loss. If price behaves as anticipated, close at a major profit when the next anticipated reversal point is reached. The reverse trade may then be placed. Note the smaller swings within the greater swings, these too can be traded! Unlike swing traders, trend traders often have no definite target in mind. Identifying a trend in the making is an art form, as trends formation is subtle in the early stages.
One clear sign of an emerging trend is price consistently achieving higher highs and lower lows, or vice versa to the downside.
Breaking through some previously significant level confirms the trend. Price eventually goes parabolic and reaches a dramatic over-extension, at which point a violent reversal usually ensues. Good trend traders get in as early as possible and exit before the trend reverses. The Trailing Stop option is a great way to lock-in your profits from a trending market without having to guess at the exact moment of reversal. Like swing trading, trend trading fits very well with CFDs. A daily chart for about 6 months, showing a new upwards trend.
Daytraders are likely to follow hourly or sub-hourly charts, with occasional reference to higher timeframes. This trading style is best-reserved for those who wish to make Bitcoin trading their full-time occupation.
Daytrading aligns well with CFDs, except during times of low volatility when the price action is flat. Scalpers attempt to profit from minute-to-minute moves, often utilising imbalances in the order book to reap a multitude of minor profits.
They tend to use charts of 5 minute duration or less. This method is entirely unsuited to CFDs due to the spread, which pushes trading fees above expected returns. Charts reveal the past and present but traders make their money from correctly anticipating the future.
Gauging the mood and momentum of the present correctly will aid prediction. Keeping in mind that history often repeats, or at least rhymes, helps even more. Although composed of rational individuals, markets as a whole often become irrational. Market participants tend to cycle between the basic emotions of greed and fear.
Everyone desires profit but fears loss. Successful traders are able to rise above excessive sentiment to judge markets with objectivity. Experienced swing traders, for example, sell when greed causes price to peak and buy when fear causes it to crash.
If a market continues to rise despite bad news, assume a bullish mood. Bearish markets shrug off good news. Disregard the emotional outbursts of other traders, at least until you have some idea of their skill level and reliability. If you find market chatter is unduly influencing your decisions, stop following it.
Our Bitcoin Obituaries page documents the pessimistic side of this phenomenon, although just as many examples could be cited of those who erred on the side of wild-eyed optimism. Remember, everyone is looking at the same price action and reaching for the same conclusion: Previous highs and lows are the obvious answer — and you should look to see if they are being broken.
Big round numbers also tend to continue a price momentum, for entirely psychological reasons e. Downwards moves behave similarly at levels known as Support. Seek out these so-called trendlines and mark them on your chart using the drawing tools. The more long-term they are and the more price respects them, the more significant they become when eventually breached.
The red diagonal trendline marks the approximate extent of the bear market, since the fall from the all-time highs. The grey box over most of marks the ranging market, when price consolidated and sentiment stabilised. A tentative green trendline, as yet untested by any downwards correction, marks the beginning of a new uptrend. One more factor to keep in mind is that a Resistance level, once breached to upside, often morphs into Resistance to the downside, and vice versa.
The same principle often applies to trend lines. Volume bars are commonly coloured according to their matching price candlestick. However, price moves in accordance with the side which is more aggressive in crossing the spread. If the opposite occurs, price will fall. Sometimes the order book, which reveals the current buy and sell aka bid or ask prices and quantities, can be displayed on the chart:. The same info is displayed in text in the top-right block; sell price offers and volume are listed above the spot price The bottom right block displays the time, price and volume of recent trades.
Technical indicators look to predict the future price levels , or simply the general price direction, of a security by looking at past patterns. Moving averages MAs , which have the effect of smoothing out price volatility in proportion to their timeframe, are fairly standard. Experiment with the variety of different indicators and make the effort to examine their formula so you know exactly what they measure and how.
Remember that the purpose of indicators is to clarify, not to complicate. Price should always remain your primary indicator. Price often creates recognisable patterns as similar trading circumstances repeat over time. Common examples likely to be monitored by a majority of traders include the reverse Head and Shoulders, Bull or Bear Flags or Pennants, Triangles and various patterns indicating the formation of a top or bottom, from which price may be expected to reverse direction.
US stocks display a partially-complete Head and Shoulders topping pattern. Being able to identify pattern formation and project price movement should the pattern complete successfully can certainly improve your trading.
Although there are even more charting tools to discover, these six items could be considered the building blocks of a Bitcoin trading strategy. These elements become very powerful when used in combination. The greater degree of confluence, the more confidence may be placed in a trade.
However, the more factors you demand before executing a trade, the fewer potential trades will be available to you. Predicting the market with perfect accuracy is impossible. Instead, you must devise a strategy which allows you to cope with whatever the market throws at you.
This boils down to keeping your losses small while allowing profits to mount. Holding on to a losing trade while hoping for recovery is the absolute worst position to be in , financially and emotionally. Consider losses the cost of doing business and cut them quickly. A voluntary withdrawal lets you live to fight another day, a margin call can wreck you. Enter this price at the same time you place your order, using the Close at loss feature.
The Close at profit feature is also helpful if nervousness frequently compels you to take profits prematurely or if greed causes you to hang on too long, hoping for even more profit but ultimately losing out as price reverses. Yes, sometimes it gives digits which aren't significant in results. As I improve the symbolic reduction of expressions, this will get better, although I still need to work out ways of specifying and tracking precision and uncertainty?
If the right-hand-side of the conversion is a comma-separated list in square brackets, the value will be broken down into the constituent units.
For example, to find out how long it takes the earth to rotate on its axis:. If the first term is the integer 0 zero , any leading terms with zero magnitude will be suppressed:.
If the last term is the integer 0 zero , any remaining fractional part will be suppressed:. Math is very straightforward: Exponentiation first see notes below, then multiplication and division, then addition and subtraction. And more tightly parenthesized expressions are performed before anything else. All expressions can be arbitrarily complex. Parentheses can be used to group expressions. Whitespace between any two units implies multiplication! This has the same precedence as multiplication or division.
If there's one thing you need to keep in mind, it's this. You must parenthesize units on the right-hand-side of a division operation, if you expect them to be multiplied before the division takes place. The following are all valid expressions. Note that if you are using the web-based interface you can enter the right-hand side of the arrow operator in the "To: The implementation of factorials is subtle and important enough to warrant a few notes.
Yeah, when I say 6! It's a common mathematical operator. For example, the factorial 6! These grow rapidly and become hard to calculate, but Frink calculates them exactly.
Here are some notes about the implementation of factorials: Factorials are calculated once and cached in memory so further recalculation is fast. There is a limit to the size of factorials that gets cached in memory. Currently this limit is ! Numbers larger than this will not be cached, but re-calculated on demand. When calculating a factorial within the caching limit, say, !
As of the release, calculations of huge factorials larger than the cache limit ! Did you know that Java 1. As of the release, functions that calculate binomial coefficients like binomial[ m,n ] are more efficient because of the use of binary splitting algorithms, especially for large numbers. This is sometimes called "m choose n" or "m C n". This is equivalent to m!
For example, binomial[, ] is equal to , but if you calculated it naively, you'd have to calculate ! The function factorialRatio[ a , b ] allows efficient calculation of the ratio of two factorials a! Variables By default, all variables in Frink can contain any type. You do not need to declare variables before using them. The variable will be defined in the smallest containing scope.
Variables may be declared before they are used using the var keyword. For example, to declare a variable called t:. This defines the variable t in the smallest containing scope and sets its initial value to the special value undef. You may also specify an initial value:. When a variable is declared, you can constrain the type of values that it can contain.
The constraints are checked at runtime. If you try to set a value that does not meet the constraints, a runtime error occurs. For example, to make sure that the variable t only contains values with dimensions of time, you can declare it using the is keyword which defines constraints.
In this case, the initial value is necessary to ensure that t contains a value with dimensions of time at all times. The special value undef is applied if no initial value is supplied. If a valid initial value is not supplied, this will produce an error at runtime. Multiple constraints can be specified by placing them in square brackets. All constraints must be met. If you want to do an "OR" of constraints, see the Constraint Functions section below.
Built-in constraint types include all of the dimension types defined in your program. For example, you can list all of the defined dimension types e. All of these defined types can be used as constraints. The following built-in constraints can be used to verify that the value is of one of the built-in types. A class name can also be a constraint name. If, for example, you've defined a class called Sphere , the following will work. This constraint check also works with interface names.
If the name of the constraint is the name of an interface, this check will ensure that any object assigned to the variable implements that interface. You may define your own functions that will be used as constraints. The function must take one argument and return a true value if the constraint is met. Returning false or another value will cause the constraint to fail.
The following defines a function called positive that returns true if a value is a positive dimensionless value. Both functions can be called either with a raw variable name or with a string.
There are no global variables in Frink. However, if you need to access some sort of "global" values from anywhere in your program, without passing them explicitly to each function, you can simulate it with class-level variables in a class that you define. If you want to use a "global" variable in only a few functions, you can encapsulate those functions into a class. For samples of class-level variables and how to access them, see classtest. For internationalization, Frink allows Unicode characters anywhere.
For maximum portability, and maximum editability with non-Unicode-aware editors, you can use Unicode escapes to embed these characters in program files. In addition, a Unicode character can be specified with anywhere from one to six hexadecimal digits by placing the digits in brackets, for example: So, yes, you can have kitty faces as variable names! It also allows any Unicode character to be used in an identifier.
If you do have a nifty editor that handles Unicode, or other character encodings, you can write your Frink program in full Unicode, and load it using the --encoding str command-line switch. Keep in mind that in this case, identifiers can only consist of Unicode letters, digits, "other symbols" and the underscore.
In the data file, we define Planck's constant as the normal character h which is easier to type and also as the Unicode character. These definitions look like:. By default, units are displayed with their dimensions given as multiples of the International System of Units SI base units. These are often not very intuitive. For example, volts are displayed as:.
Instead, you can define the default output format for a unit type by using the: If you want, you can define a function that displays distances in millimeters if it's small, kilometers if it's bigger, and light-years if it's huge. Floating-point calculations are performed to a limited number of digits. You can change the number of digits of working precision by the setPrecision[ digits ] function:. Note that this will only affect calculations performed after this flag is set, of course.
Currently, not all operations notably trigonometric functions can be performed to arbitrary precision. You can also see the current working precision by calling the getPrecision[] function:.
By default, floating-point numbers are displayed in scientific notation with one digit before the decimal point.
This can be changed to "engineering" format where 1 to 3 digits are placed before the decimal point and the exponent is a multiple of 3. This allows you to more easily see it as "milli-", "micro-", "million", etc. The call to enable this is:. Now notice the change if you set "engineering mode" to true. The result comes out so you can more easily read it as " In addition, rational numbers are, by default, displayed with a floating-point approximation to their values:.
You can tell Frink to always display rational numbers as floating-point approximations by calling rationalAsFloat[true]. The numbers will still continue to be represented internally as rational numbers. Frink tries to produce a human-readable description of units of measure, such as "power" or "energy" or "temperature":.
It may span multiple lines. This type of comment can be nested. If you repeat a calculation, you may want to define it as a function. Functions in Frink are denoted by the function name followed by arguments in square brackets, separated by commas. A function can be defined like the following:. Then, to call the function, say, to find the area of my telescope mirror, which has a radius of 2 inches:. Multi-line functions can be built; just put the body in curly braces.
It may be more legible to use the return statement in your function. For example, the factorial function could be written as:. If a function does not explicitly return a value, the value returned is the value of the last expression evaluated.
A return statement with no value on the right-hand-side returns a special void type. Function declarations can have default values. For example, if your Willard pocket organizer goes out, you can use Frink to calculate the tip on your dinner check, and, to make it easy, you can default the tip rate to 15 percent of the bill.
The function declaration with default parameters is:. Now, when you get to the restaurant, you can easily calculate the tip using the default rate:. The previous tip example probably has you thinking, "Well, it would be nice if it calculated the total too!
In Frink, values surrounded by square brackets and separated by commas form a list of values. These lists can be returned from a function, assigned to a variable, or whatever. A better version of the above function would be defined to return a list containing the tip and the total as a list:. Note the square brackets on the right-hand-side of the definition. Then, to calculate the tip, it's as easy as before:. I'll let you do the rounding in your head, or you can use the rounding functions below.
This uses the conditional expression condition? The condition is first evaluated it should evaluate to a boolean value, and if it's true, the true clause is evaluated and returned, the false clause otherwise. Let's try a big number, just big enough that it would overflow my old solar calculator:. You can still blow out the stack if you go too deep, or forget to put in a condition such that the function terminates. Don't come crying to me. Like other variables, formal arguments to functions can have constraints.
The syntax for constraining is just the same as setting Constraints on variables. For example, if you want to make sure that a function that calculates the volume of a sphere is passed a radius, the declaration looks like:.
The constraint s are checked at runtime, and if all constraints are not met, the function call produces an error. At some point in the future, I'd like to have this choose an appropriate function based on the constraints, if more than one is possible. My underlying function dispatching is designed to allow this, but functions with constraints may be slower to resolve. If the condition is true, it will execute the first clause, otherwise, if there is an optional else clause, it will execute the else clause.
Note that putting the brackets and statements on separate lines is currently important. Also, please note that the else keyword goes on the same line as the closing bracket of the then clause. If either the then or else clause is a single line, the curly braces for that clause can be eliminated.
The following is the same as the code above:. The condition must be able to be turned into a boolean value. When testing for equality, be sure to use the double equals sign, a single equals indicates assignment e. If, for some reason, you need to jam everything into one line, you need to add the then keyword:. This can either be represented by the special values true and false , or the following types can be used in places where a boolean value is required:.
Any other value will cause a runtime error. See the Boolean Operators section below for operators that return boolean values. The while loop is a loop with a condition and a body. The body is executed repeatedly while the condition is true. You can use the next statement to prematurely jump to the next iteration of a while loop. You can use a labeled next statement to jump to the next iteration of a higher loop. See the for loop section for an example.
You can use the break statement to exit the smallest containing loop. You can also use labeled break statements to break out to a higher loop:. The body of the loop then repeats as long as the condition is true. If the body is a single line, the braces can be omitted, but each part of the loop has to be on a different line:.
You can use the next statement to prematurely jump to the next iteration of a do loop. You can also use labeled break statements to break out to a higher loop. See the while loop section of the documentation for an example. If the body is a single line, the curly braces can be omitted. The above sample can be written as:. The step is required to be specified for any range in which the limits are not dimensionless integers.
This also works with a date range, but the step must be specified and it must have dimensions of time:. Other orderings are allowed such as true to false or true to true the latter only goes through the loop once.
The for loop is also used to iterate over the contents of an enumerating expression or array. You can think of it as a "for each" loop, which is really what it is. The rangeOf[ array ] function returns an enumeration of all the indices in an array. You can also use the for loop to iterate over the contents of Java objects.
See the Iterating over Java Collections section of the documentation for more. If the enumerating expression produces a list, and you want to break apart that list into named variables in the for loop, write it as:.
See the Input and Output section below for a sample of its use. You can use the next statement to prematurely jump to the next iteration of a for loop. You can use a labeled next statement to jump to the next iteration of a higher loop:. The special keyword to creates an enumerating expression that successively takes on all values from the beginning to the end, inclusive, with the default step being 1.
The step size can be changed as shown below. You can use this to notation anywhere to create an enumerating expression that takes on successive values. You can even make it into an array using the array function: You can create an more flexible enumerating expression that does the same as the above by using the format: Use this if you're going to assign to variables or use the range symbolically.
For programs that require nested for loops for which it's not known in advance how many nested loops will be needed, the multifor construct allows multiple loops to be created simply:. An similar and technically better in almost all ways way of writing the loop above would be to create new range objects:. A typical idiom for creating a multi-loop is to use the makeArray function to create array bounds.
For example, the following creates in effect 8 nested loops, each running from 1 to 2. The results are assigned as an array to the variable d. As of the release, the bounds of one loop can now depend on the bounds of the loops to its left, for example:. You can use the next statement to prematurely jump to the next iteration of a multifor loop. There's a version of the next statement that jumps to a specified level of a multifor loop.
The loop must be labeled and the index to jump to follows the label in the next statement. For example next LOOP i. Frink can evaluate a string as a Frink expression. If that means something to you, good. You can make programs that write and run their own programs.
Frink became self-aware on December 7, at 9: History will be the judge if this December 7th is another date that will live in infamy. This behavior can also be used to convert a string into a number. See the Input section below for examples of its use. If eval[] is passed an array, all elements of the array will be individually evaluated and the result will be returned in an array.
There is also a two-argument version, eval[ expression , rethrows ] where the rethrows argument is a boolean flag indicating if we want evaluation errors to be thrown or just suppressed and undef returned. If it is true, errors will be rethrown as Java exceptions, otherwise an error returns undef. There is also a three-argument version, eval[ expression , rethrows , hidesLocals ] where the hidesLocal argument is a boolean flag indicating if we want to hide local variables before evaluation.
The eval[] function restricts some insecure operations from being performed e. If you need all functions to be available from your evaluation, use the intentionally frighteningly-named unsafeEval[ str ]. Arbitrarily-dimensional, non-rectangular, heterogeneous arrays are possible.
If you're playing "buzzword bingo," you just won. Array indices are zero-based. Arrays are indicated by square brackets. Think of multidimensional arrays as being a list of lists. For example, to create a 2-dimensional array:. To get elements out, use the lovely operator yes, I'm running out of bracket types To get the length of an array, use the length function: With the advent of array manipulation, I've proven to myself that Frink is capable of simulating a Turing machine, and thus, as of December 12, , at One-dimensional or multi-dimensional "rectangular" arrays can be constructed with the makeArray[ dims , initialValue ] function where dims is an array of integers indicating the dimensions of the array, and initialValue is the initial value to set in each cell.
Multi-dimensional arrays are implemented as arrays of arrays. If called without an initial value, the array is initialized as sparse and compact to conserve memory, but you may get errors if reading elements you haven't initialized. Array elements can still be assigned to, and the appropriate rows will get extended to fit them:.
All arrays can still be automatically extended by assigning to a value outside their currently-defined range. Creating an array with the makeArray methods does not prevent arrays from being extended nor prevent them from becoming non-rectangular.
It is never necessary to pre-allocate a one-dimensional array of a specific size, as all arrays will automatically resize on assignment.
It is very important to note that arrays are normally passed by reference. This means that if you assign an array to another variable, and modify the second variable, then you are modifying the original! To avoid this behavior, use the method array. This makes a shallow copy of the object. Arrays can be automatically extended by using the methods array. Items can also be inserted or popped from the front of an array by using the methods array.
The contents of one array can be appended to another array using the array. Items can be inserted into an array using the method array. This inserts the specified value before the item at the specified index. If the index is greater than or equal to the size of the array, the array is extended to fit the new elements, setting any unspecified values to the undefined value undef.
Items can be removed from an array using the method array. This removes the item with the specified index and returns it, so you can do something with the value if desired. If the specified index does not exist, this generates an error. A range of values can be removed with the array. The number of items that will be removed is start-end. The return value is the number of items that were actually removed.
The end index is allowed to run off the end of the array. Similarly, a range of values can be removed with the array. The return value is the number of items that were actually removed the length may run off the end of the array. Items with a specified value can be removed from an array using the method array. This removes the first item having the specified value from the array. If a matching item is found, this returns true , otherwise returns false.
A random item can be removed from an array using the method array. This removes a random item and returns its value. You can test if an item is contained in an array with the array.
You can obtain all of the permutations of the array by using the permute method. This returns an enumerating expression that lazily generates the permutations. Note that the permutations are currently in reflected Gray code order, but this may change. If you need the results in lexicographical order, with duplicates removed, you can obtain all of the permutations of the array by using the lexicographicPermute method.
Note that all of the elements of the array must be comparable to each other , a constraint which is not necessary in the permute method.
You can also specify an ordering function to be used by the lexicographicPermute method. The function should take two arguments and return -1, 0, or 1 to indicate if item a is less than, equal to, or greater than item b respectively.
The following example sorts by length. You can obtain all of the combinations of the array by using the combinations[ take ] method. This returns an enumerating expression that lazily generates combinations. Note that the combinations are currently in lexicographical order, without duplicates removed, but this may change. For example, to take 3 items at a time from a list:. The sample program pokerhands. You can get a "slice" out of an array using the slice and sliceLength functions.
Note that these are functions, not methods. The slice[ array , start , end ] function returns a slice of an array starting with index start and ending before index end. If the indices are beyond the ends of the array, only existing items will be returned.
If start or end are the special value undef , then the slice will contain the start of the array or the end of the array respectively. The sliceLength[ array , start , length ] function returns a slice of an array starting with index start and containing length items. If the indices are beyond the end of the array, only existing items will be returned. The inverse of slice and sliceLength are the functions removeSlice and removeSliceLength which remove the parts specified by the slice commands and return the rest.
The removeSlice[ array , start , end ] function removes array elements starting with index start and ending before index end. If the indices are beyond the ends of the array, only existing items will be removed. Note that this is the inverse of what is returned by slice with the same arguments. If start or end are the special value undef , then the function will remove from the beginning of the array or to the end of the array respectively.
The removeSliceLength[ array , start , length ] function removes a slice of an array starting with index start and containing length items. If the indices are beyond the end of the array, only existing items will be removed. Note that this is the inverse of what is returned by sliceLength with the same arguments.
To obtain all of the possible subsets of the elements in the array, you can use the array. This returns an enumerating expression which iterates through all the subsets of items in the array, including the empty set and the original set itself.
Each return value is itself an array of elements, with the elements preserving the same order as in the original array:. You can also request the subsets of the array and exclude either the empty set or the original set by using the array.
If allowEmptySet is true , the empty set will be returned as one of the elements. If false , the empty set will be excluded.
If allowOriginalSet is true , the full original set will be returned as one of the elements. If false , the full original set will be excluded, and only "proper" subsets will be returned. Note that output of the empty set and the original set are suppressed in the example above. The contents of an array can be shuffled randomly with the array. The contents of an array can be cleared with the array. While Frink does not have a complete implementation of matrix operations, for an external class with some matrix operations, see Matrix.
This means that rows and columns are switched. In other words, the element at array i j becomes the element at array j i. An OrderedList is an array that is always kept in order. Of course, this implies that all items in an OrderedList must be comparable with each other. It extends the array class and almost all methods and functions that operate on array will work with OrderedList , unless those methods would violate the ordering e.
If another user-defined ordering is desired, it can be specified by one of the constructors explained in the next section. If you want to specify a user-defined ordering, you can pass a possibly anonymous function as the first argument to the constructor. For example, if you want to use an ordering that simply sorts shorter strings before longer strings, say that six times speedily, you can do the following:.
An OrderedList can also take a piece of arbitrary data that is passed to the comparison function. This data is passed as the second argument to the constructor. If the first argument to the constructor is undef , the default orderer will be used. The data will be passed as a third argument to the comparison function. Since OrderedList extends array , array methods are available on OrderedList unless they would interfere with preserving ordering.
New methods and methods with altered effects are listed below. A RingBuffer is a type of array, but with a fixed maximum size. It is efficient to append items to the end of the list using the push[ item ] method, and to remove them from the beginning using the popFirst[ item ] , which is how it will usually be used. If more items are pushed than the fixed capacity allows, the item at the front of the buffer is discarded.
Items can also be accessed randomly using the array index operator. The first item is always element 0. When an item is popped from the beginning of the list using the popFirst[] method, the item that was previously at index 1 becomes index 0, and so on. If you attempt to access an item that does not exist, this raises an error, but this behavior may change.
Like other Frink collections, you can find out how many items are contained with the length[ expr ] function. You can also turn it into a traditional array with the toArray[ ringBuffer ] function. Its elements can be enumerated with a for loop. The following demonstrates using a RingBuffer to capture the last n elements of an enumerating expression this could be a list, or the lines of a file from the lines function, etc.
The following methods operate on RingBuffer. They are mostly the same as the corresponding array methods , with differences as noted below:. The result always comes back as a string, but you can parse it into a unit, a date, or whatever, using the eval[str] function:.
This allows your users to enter things like "3 inches" or "1 mile" or any units that Frink knows about like "earthradius", and everything will Just Work. That "Self-Evaluation" section above seemed irrelevant at the time, but it turns out it's quite useful.
If the user cancels the input dialog, or, for text input, if end-of-file is reached, this returns the special value undef. In command-line mode, these input functions also allow you to read from standard input stdin.
User input is actually taken from stdin in command-line mode, as you may expect. On end-of-file EOF , the input function returns the special value undef. A short-program to read from standard in and echo its output may look like:.
If, for some reason, you're in a GUI mode and you still want to read from standard input, you can call readStdin[] to read one line from standard input. This is just like calling input[""] from command-line mode, which is what you really want to be calling if you're trying to make programs that work both interactively and non-interactively, and in GUI mode and non-GUI mode.
But if you're sure you only ever want to read from standard input, and don't want to trigger a GUI input window, use readStdin[]. If you want to request multiple input items from the user, you can use the "multi-input" version of the input function, where the second argument is an array of items you're going to prompt for: This will produce a graphical user interface which prompts the user for their input.
The results will be returned as an array of strings, in the same order as they were specified. As in the Input section above, you can use the eval[ str ] function to parse them into numeric or other values. If the user cancels the input dialog, or, for text input, if end-of-file is reached, this returns the special value undef instead of an array. When in text mode, if end-of-file is reached before filling the second or later item, then partial results will be returned with the special value undef being returned for each incomplete value.
If any of the items in the array is a two-element array, the second argument will be used as the default value:. The following program demonstrates an idiom for creating a simple interactive GUI that finds roots of numbers until you cancel. The while loop exits when the user cancels calculations.
Previous results are displayed to the user at the top of the input dialog, and the user's previous input is maintained verbatim in the input fields. Note that the idiomatic use of the "eval" function to turn the string inputs into Frink expressions.
It's like a generalized calculator inside of a specialized calculator! To print, use the print or println functions, each of which take one argument. The only difference is that println sends a linefeed afterwards. I'm just going to list a forest of cryptic boolean expressions here without explanation. You pick out the ones you like. They all work, and there are usually multiple equivalents for the same thing, taken from different languages.
I've tried to keep precedence the same as Java. Please note that it makes very little sense to hash on a floating-point value or date!
The syntax is identical to the syntax for array element manipulation. This means that you can switch back and forth between an array and sparse dictionary representation for integer-indexed data structures!
You can also enumerate over [key, value] pairs directly in a dictionary. They are not returned in any guaranteed order. Create a dictionary from an array or enumerating expression where each element in the array is a two-item list which are treated as a key and a value:.
You can also turn an array or other types into a dictionary by calling the toDict[ array ] function on it, which behaves exactly like calling the single-argument constructor above.
Create a dictionary from two arrays or enumerating expressions where the first array contains keys and the second array contains values.
The first element in the keys array will be matched with the first element in the values array. You can get an enumeration of the keys in a dictionary by using the keys function. This function does not return the keys in any defined order, but you can sort them with the sorting functions below.
A dictionary can be queried to see if it contains a specific key using the containsKey[ key ] method:. Entries in a dictionary can be removed with the remove[ key ] method. This returns the value corresponding to the key, or the special value undef if that key is not in the dictionary. You can invert the contents of a dictionary by using the invert method which returns a new dictionary with key-value pairs reversed. If the values are not hashable, this will print a warning. If the same value appears multiple times, this will print a warning.
A set is a data structure that contains items with no duplicates. A set can currently contain strings, units, that is, numbers , other sets, dictionaries, or objects created from a class.
You simply create an empty set using new set , a literal set by calling something like new set[1,2,3] , or turn an array or enumerating expression into a set by calling toSet[ expr ]. Note that sets do not preserve any order of the items contained in them.
There are a variety of methods for modifying sets:. Multiple items from an array, set, or other enumerating expression can be inserted into a set as separate items using the putAll method:.
A set can be tested to see if it contains a value by using the contains method:. The following demonstrates turning an enumerating expression into a set the lines[ url ] function returns an enumerating expression of all of the lines in a file, turning that into an set to remove duplicates and sorting it implicitly turning it into an array in the process.
The result is a sorted array containing all of the unique lines in a file, discarding duplicates. To obtain all of the possible subsets of the elements in the set, you can use the set. This returns an enumerating expression which iterates through allt he subsets of items in the set, including the empty set and the original set itself. Each return value is itself an set of elements. You can also request the subsets of the set and exclude either the empty set or the original set by using the set.
The most common trigonometric functions are built in. They, as everything else in Frink, are best used when you explicitly specify the units. For the following functions, input should be an angle, and output will come out dimensionless. If no unit is specified for input, it should act like radians, because radians are dimensionless units and really indistinguishable from pure numbers. For inverse operations, the input must be dimensionless, and the output will come out in angular units.
This is easily converted to whatever angular units you want, as above. You don't see that the output is in radians because radians are essentially dimensionless numbers. You just gotta be a bit careful with angles.
The following functions can be used to format numeric and unit expressions to a variety of formats. This is right, and only converts and formats on output, which is usually what you want to do: If divideBy is a string, this evaluates the string, expecting a unit to be returned, and both divides by this unit and concatenates the string after the result:.
The previous behavior of the format function was preserved to keep old programs working, but the default behavior of format may change in the future to another one of the formatting functions below. The formatFix and formatFixed functions which are identical to each other will keep their current behavior, so it's probably better to use formatFix instead of format to future-proof your programs if this is the behavior your want to keep.
If you're doing number-theoretical work with very large integers, please see the Performance Tips section of the documentation for ways to greatly improve integer performance. If the number is larger than this, the test is performed against all 78 prime bases less than or equal to This gives a very small probability of about 1 in 10 47 that the function may return true for a composite number.
And that's a worst-case; for randomly-chosen large numbers, the probability of error is actually far, far lower for most numbers, especially big ones. The reality is orders of magnitude lower. For better estimates, see Probable primes: And these are ridiculously generous estimates.
The actual probability of failure is usually astronomically lower than this. As of the release, isPrime[ x ] was extended to automatically use a faster Lucas-Lehmer test if x is of the form 2 n -1 i. Note that the Lucas-Lehmer test is sufficient to prove primality for numbers of this form, regardless of their size.
Also note that isPrime[1] will return true. This simplifies recursive factor-finding algorithms, but I know it may not match the modern definition of primes.
This behavior may change, so try not to rely on it. The value of n may be any real number. This method uses a wheel factoring method to completely avoid testing composite numbers with small factors. If n n is smaller than 2, this returns undef. This uses Euler's pentagonal number algorithm to find the partition count somewhat efficiently, and caches the results so subsequent calls to this function will be efficient.
If the optional argument countPermutation is true , then each element also contains the number of possible permutations of the list. This is of the number of ways m things can be chosen n at a time, with order being unimportant.
This is the number of positive integers less than n that share no factors with n. This is the same as the factorial operator! The array may be 1- or 2-dimensional. Since different fields of mathematics and engineering use different conventions for the Fourier transform, these functions allow you to optionally specify the scaling factor and sign convention.
The optional second argument divFactor sets the scaling factor for the results: In fact, it just calls the DFT function with appropriately-reversed parameters. If you specified the optional second or third arguments for the DFT function, you will need to pass in the same arguments to the InverseDFT function to get the inverse operation. This function takes care of reversing them appropriately. To pick items from a discrete probability distribution, see the DiscreteDistribution.
This function seeds the random number generator with a known value. The seed must a number from -2 63 to 2 63 -1 both inclusive. Or two real numbers, but that rarely makes sense. The return type in this case will be an interval or an ordinary real number.
If there is no intersection between the arguments, the function will currently return undef although this behavior may change to return an empty interval in the future. This function also works with dates and date intervals. Or two real numbers, in which case an interval containing both real numbers is returned.
The return type will be an interval or an ordinary real number if the two numbers are the same real number. If x is of any other type, this simply returns x. If the list is empty, this returns undef. There is no universal identity element for addition when units of measure may be present. If the list is empty, this returns emptyValue. If the list is empty, returns 1. If the list is empty, returns emptyValue. The argument time must have units of time, such as 1 s or 4. This requires that your Java Virtual Machine and your operating system are configured correctly.
The base unit can be specified as a string indicating the name of a base unit e. See the default base dimension names. For example, to get the exponent corresponding to length default unit is meters all of the following are equivalent:. All of the above return the integer 1 , which is the exponent for length in the provided expression.
Asking for "time" or "s" or s would return -2 , the exponent for the time dimension. Also note that exponents may be rational numbers or zero. You will very likely never need this function. Stop and reconsider your life choices. Frink can perform Fourier transforms on 1- or 2- dimensional arrays, or on images by calling their toComplexArray[] method. Cryptographic Functions The messageDigest[ The parameters for all are of the form: Each function can take as input either a string or an array of Java bytes.
The algorithm parameter is a string containing one of any hashing algorithms your Java platform supports, which probably includes: You can see the cryptoProviders. As of the release, the behavior of the messageDigest functions may have changed. Previously, to turn the characters of a Unicode string into bytes, the function used your platform's default character encoding.
Now the functions always convert the bytes to UTF-8 before creating the digest. Your default was likely to have been UTF-8 already. Using the default encoding made programs non-repeatable from one machine to another.
If you want to force a certain encoding of Unicode strings into bytes, use the stringToBytes[ string , encoding ] function before calling these functions. The following calculates the MD5 hash of the string "abc" and returns it as a hexadecimal string:. The messageDigestInt function returns the value as an integer, which can then be displayed in various bases, have its individual bits tested, etc. The messageDigestBytes function returns the value as an array of Java bytes.
Most of the underlying cryptography routines in Java work with arrays of bytes, as these are safer than Strings which are immutable after construction and are eventually garbage-collected. Using arrays of bytes means that you can zero-out input buffers as soon as you're done with them. Integer values can be converted to and from other bases from 2 to 36 inclusive in several ways.
The following functions can be used to convert to or from other arbitrary bases. The following named base conversion functions can also be used. In the cases where several names are commonly used, all options are listed. All functions return strings. The following are all equivalent, and all convert the number specified by the variable number to a string in base 8. Use whichever is most convenient for you. As noted above in the Data Libraries section, you may input numbers in a specified base by following the number with two backslashes and the specified base:.
The above base conversions assume that the characters are taken from an alphabet like the one for base For example, hexadecimal uses the first 16 characters of this, "abcdef". However, it's not as clear when you go beyond base 36 what characters should be used.
You can declare a custom "alphabet" of any size to be used in base conversions. Note that this alphabet does not include 0 zero , O uppercase o , I uppercase i , l lowercase L , as those are indistinguishable in some fonts. To convert a number to a string using this alphabet, you can use the base[ num , alphabet ] function where alphabet is a string which contains the character for the "zero" position first. The radix will be equal to the number of characters in the alphabet string.
In the below example, base The following turns a numeric value into a Bitcoin address string:. Note that this alphabet does not have a zero as the first character it has a 1, so if you need to pad it to a certain length, you need to pad with the first character in the alphabet.
Conversely, you can parse an integer with a custom alphabet by using the parseInt[ str , alphabet ] function, which takes the same format for its alphabet string. The example below parses a Bitcoin address. Note that the number obtained above is the decimal equivalent of the Bitcoin address encoded above; it could instead be formatted in hexadecimal or other formats. The strings are allowed to contain any Unicode characters. If you attempt to parse a string that contains characters outside your alphabet, the special value undef will be returned.
To output a Devanagari integer:. If you want to typeset a string of numbers as superscripts on a Unicode-aware system, you can do something like this:. Note that almost all fonts make Unicode superscript numbers look different and not line up. Does your font look uniform here? Mine decidedly does not. Unicode numerical subscripts are more uniform and contiguous than superscripts, thankfully. If you want to typeset a string of numbers as subscripts on a Unicode-aware system, you can do something like this:.
If you want to parse a string of these subscripts as a single number, you can do something like this:. Frink can parse Unicode characters that are commonly used as mathematical operators. This allows you to cut-and-paste some mathematical expressions without modification and handle them correctly.
The Unicode standard has a non-contiguous hodgepodge collection of numerals that represent superscript numerals. The only superscript characters currently recognized are the following:. You can use the toUnicodeSuperscript[ int ] function to turn an integer into a string composed of Unicode superscript digits in base In addition, some Unicode characters can be used as synonyms for other mathematical operators.
Note that Frink does not currently output Unicode, nor give you simplified ways to key in Unicode characters. Backslashes have a special meaning within double-quoted and triple-quoted strings. They may precede a special character, as follows:. A single backslash preceding any other character simply inserts the following character into the string and removes the backslash.
Strings can contain Unicode characters, indicated in one of a few ways: Directly entered with a Unicode-aware editor. Note that using this format is required because the hexadecimal value has more than 4 digits. This is for compatibility with environments such as Java that represent a character as 16 bits.
The inputForm[ expr ] function will produce this format for cross-platform and cross-Java-version compatibility. You can convert a character to its Unicode character code by using the char[ x ] function. If passed a multiple-character string, it returns the Unicode character code for each character in an array:.
If you always need an array of character codes, use the chars[ x ] function which turns a string into an array of character codes, even when passed a string containing only one character.
If passed an array of integers, the char[ x ] function returns a string:. Frink provides several functions to process strings correctly using Unicode rules. When working with Unicode, almost all algorithms should work on entire strings to be correct, not individual characters. This is why Frink doesn't even have a character type.
The following functions operate on strings and allow you to enumerate through their parts.