# kalker

### A scientific calculator that supports math-like syntax with user-defined variables, functions, derivation, integration, and complex numbers.

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- Operators: +, -, *, /, !, %
- Groups: (), [], ⌈ceil⌉, ⌊floor⌋
- Vectors: (x, y, z, ...)
- Matrices: [x, y, z; a, b, c; ...]
- Pre-defined functions and constants
- User-defined functions and variables
- 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 quotinent (and derivatives of higher order can be a bit inaccurate as of now) - Complex numbers
- Understands fairly ambiguous syntax (eg. 2sinx + 2xy)
- Syntax highlighting
- 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 - 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

`+`

,`-`

,`*`

,`/`

`!`

Factorial, eg.`5!`

gives`120`

`%`

Percent, eg.`5%`

gives`0.05`

,`10 + 50%`

gives`15`

`%`

,`mod`

Modulus (remainder), eg.`23 % 3`

gives`2`

`true`

,`false`

Boolean literals`and`

,`or`

,`not`

You can type special symbols (such as √) by typing the normal function or constant name and pressing tab.

`*`

becomes`×`

`/`

becomes`÷`

`and`

becomes`∧`

`or`

becomes`¬`

`not`

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 are defined with the following syntax: `name = value`

`x = 3/4`

Functions are defined with the following syntax: `name(param1, param2, etc.) = value`

`f(x) = 2x+3`

`A(x, y) = (xy)/2`

They are used like this: `name(arg1, arg2, etc.)`

`f(3) + 3`

`A(2, 3)`

Derivation can be done like this: `name'(arg1)`

`f'(3) + 3`

`sin'(pi)`

`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 log_{10}(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)`

is the same as`sum`

- eg.`sum(n=1, 4, 2n)`

is the same as

`pi`

or `π`

= `3.14159265`

`e`

= `2.71828182`

`tau`

or `τ`

= `6.2831853`

`phi`

or `ϕ`

= `1.61803398`

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.
`vector[[index]]`

. Indexes start at 1.
`[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 `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]`

.
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 tranpose of a matrix with the
syntax `A^T`

, where `A`

is a matrix and `T`

is
a literal `matrix[[rowIndex, columnIndex]]`

. Indexes start at 1.
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/`

`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.