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