mirror of
https://github.com/PaddiM8/kalker.git
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170 lines
7.1 KiB
Plaintext
170 lines
7.1 KiB
Plaintext
Overview of features
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Operators: +, -, *, /, !, %
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Groups: (), ⌈⌉, ⌊⌋, []
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Vectors: (x, y, z, ...)
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Matrices: [x, y, z; a, b, c; ...]
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Pre-defined functions and constants
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User-defined functions and variables
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Understands fairly ambiguous syntax. Eg. 2sinx + 2xy
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Complex numbers
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Piecewise functions: f(x) = { f(x + 1) if x <= 1; x otherwise },
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pressing enter before typing the final "}" will make a new line without
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submitting. Semicolons are only needed when writing everything on the
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same line.
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Different number bases: Either with a format like 0b1101, 0o5.3, 0xff
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or a format like 1101_2. The latter does not support letters, as they
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would be interpreted as variables. The "base" command can be used to
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tell the REPL to also show output in another number base. For example,
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"base 16" would make it show results in hexadecimal as well as decimal.
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Root finding using Newton's method (eg. x^2 = 64). Note: estimation and
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limited to one root.
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Derivation (prime notation) and integration (eg. integral(a, b, x dx)
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The value of an integral is estimated using Simpson's 3/8 rule,
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while derivatives are estimated using the symmetric difference
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quotient (and derivatives of higher order can be a bit inaccurate as of now)
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Syntax highlighting
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Completion for special symbols on tab
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Sum/prod functions
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Load files that can contain predefined variable and function declarations.
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(you can also have automatically loaded files)
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Operators
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+, -, *, /
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! Factorial, eg. 5! gives 120
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% Percent, eg. 5% gives 0.05, 10 + 50% gives 15
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% Modulus (remainder), eg. 23 % 3 gives 2
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and, or, not
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Completion for special symbols
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You can type special symbols (such as √) by typing the normal function or constant name and pressing tab.
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* becomes ×
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/ becomes ÷
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and becomes ∧
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not becomes ¬
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or becomes ∨
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[[ becomes ⟦⟧
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_123 becomes ₁₂₃
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asin, acos, etc. become sin⁻¹(), cos⁻¹(), etc
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sqrt becomes √
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deg becomes °
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pi becomes π
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sum becomes Σ()
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prod becomes ∏()
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integrate becomes ∫()
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tau becomes τ
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phi becomes ϕ
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floor becomes ⌊⌋
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ceil becomes ⌈⌉
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gamma becomes Γ
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( becomes ()
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Variables
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Variables are defined with the following syntax: name = value
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Example: x = 3/4
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Predefined variables
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ans - receives the value computed of the most recent expression
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Functions
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Functions are defined with the following syntax: name(param1, param2, etc.) = value
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Examples: f(x) = 2x+3; A(x, y) = (xy)/2
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They are used like this: name(arg1, arg2, etc.)
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Example: f(3) + 3A(2, 3)
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Predefined functions
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sin, cos, tan, cot, cosec, sec
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sinh, cosh, tanh, coth, cosech, sech
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asin, acos, atan, acot, acosec, asec
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asinh, acosh, atanh, acoth, acosech, asech
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abs, ceil or ⌈⌉, floor or ⌊⌋, frac, round, trunc
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sqrt or √, cbrt, exp, log, ln, arg, Re, Im
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gamma or Γ
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asinh, acosh, atanh, acoth, acosech, asech
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bitcmp, bitand, bitor, bitxor, bitshift
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comb or nCr, perm or nPr
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gcd, lcm
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min, max, hypot
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log - eg. log(1000, 10) is the same as log10(1000)
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root - eg. root(16, 3) is the same as 3√16
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average, perms, sort
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transpose
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matrix - takes a vector of vectors and returns a matrix
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integrate - eg. integrate(0, pi, sin(x) dx)
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sum Eg. sum(n=1, 4, 2n), example below
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Sum function
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The sum function lets you sum an expression with an incrementing variable.
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It takes three arguments: start value, end value, and expression.
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If you press tab after typing out "sum", it will be replaced with a sigma symbol.
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The expression is what will be summed, and will be able to use the variable defined
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in first argument (eg. n=1). The value of the variable increments by one.
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Example: sum(n=1, 4, 2n) will be the same as 2*1 + 2*2 + 2*3 + 2*4 = 20
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This can for example be used to calculate e: Σ(n=0, 10000, 1/n!) = 2.7182818284590455
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More precision can be gotten by changing the "--precision" flag. Run `kalker --help` for more info.
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The sum function can also be used to sum vectors, eg. sum(1, 2, 3) or sum(v) or sum[1, 2, 3].
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Prod function
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The prod function works the same way as the sum function but performs
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multiplication instead of addition.
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Constants
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pi or π = 3.14159265
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e = 2.71828182
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tau or τ = 6.2831853
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phi or ϕ = 1.61803398
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Vectors
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A vector in kalker is an immutable list of values, defined with the syntax (x, y, z)
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which may contain an arbitrary amount of items. Generally, when an operation is
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performed on a vector, it is done on each individual item. This means that (2, 4, 8) / 2
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gives the result (1, 2, 4). An exception to this is multiplication with two vectors,
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for which the result is the dot product of the vectors. When a vector is given to a
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regular function, the function is applied to all of the items in the vector.
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Indexing
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A specific item can be retrieved from a vector using an indexer, with the
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syntax vector[[index]]. Indexes start at 1.
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Vector comprehensions (experimental)
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Vectors can be created dynamically using vector comprehension notation, which is
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similar to set-builder notation. The following example creates a vector containing
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the square of every number between one and nine except five: [n^2 : 0 < n < 10 and n != 5].
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A comprehension consists of two parts. The first part defines what should be done to each
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number, while the second part defines the numbers which should be handled in the first
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part. At the moment, it is mandatory to begin the second part with a range of the
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format a < n < b where n defines the variable which should be used in the comprehension.
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Several of these variables can be created by separating the conditions by a comma,
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for example [ab : 0 < a < 5, 0 < b < 5].
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Matrices
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A matrix is an immutable two-dimensional list of values, defined with the syntax [x, y, z; a, b, c]
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where semicolons are used to separate rows and commas are used to separate items. It is also
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possible to press the enter key to create a new row, instead of writing a semicolon. Pressing
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enter will not submit if there is no closing square bracket. Operations on matrices work the
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same way as with vectors, except that two matrices multiplied result in matrix multiplication.
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It is also possible to obtain the transpose of a matrix with the syntax A^T, where A is a matrix
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and T is a literal T.
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Indexing
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A specific item can be retrieved from a matrix using an indexer, with the
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syntax matrix[[rowIndex, columnIndex]]. Indexes start at 1.
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Files
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Kalker looks for kalker files in the system config directory.
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Linux: ~/.config/kalker/
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macOS: ~/Library/Application Support/kalker/ or ~/Library/Preferences/kalker
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Windows: %appdata%/kalker/
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If a file with the name default.kalker is found, it will be loaded automatically every time
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kalker starts. Any other files in this directory with the .kalker extension can be loaded
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at any time by doing load filename in kalker. Note that the extension should not be included here.
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