Commands Reference

This is a complete overview of the math commands available for scripting in Algebrakit. Click a command for more information.

Constructs

Command Description
For For executes a script block once for each element of a list.
If If checks a condition and executes a script block based on the result.
While While executes a script block repeatedly, as long as a condition holds.

List Commands

Command Description
CartesianProduct CartesianProduct returns all pairs of an element of the first list and an element of the second list.
Concat Concat joins lists and expressions into a single list.
ConstantArray ConstantArray creates a list containing n copies of a given value.
Difference Difference returns a copy of the first list, with the elements of the other lists removed.
DifferenceI DifferenceI returns the indices of the elements of the first list that remain when the elements of the second list are removed.
Elm ([[ ]]) Elm returns the element at a given position of a list or expression, as in L[[2]].
FindI FindI returns the position of the first occurrence of an expression in a list.
Flatten Flatten removes nested lists, putting all elements in one list.
ImplicitList ImplicitList displays expressions as a comma-separated list, without curly braces.
Intersect Intersect returns the elements of the first list that also occur in all other lists.
IntersectI IntersectI returns the indices of the elements of the first list that also occur in all other lists.
Length Length returns the number of elements in a list.
Map Map applies a given function or mapping to each element of a given list.
Max Max returns the largest value in a list.
MaxI MaxI returns the index of the largest value in a list.
Min Min returns the smallest value in a list.
MinI MinI returns the index of the smallest value in a list.
Range Range creates a list of evenly spaced numbers.
RemoveAllFromList RemoveAllFromList returns a copy of a list with all occurrences of the given elements removed.
RemoveI RemoveI returns a copy of a list with the elements at the given positions removed.
Replace Replace replaces the elements at the given positions of a list.
Select Select returns all parts of an expression that satisfy a condition.
SelectI SelectI returns the positions of the elements of a list that satisfy a condition.
SelectStrictI SelectStrictI returns the positions of the elements of a list that certainly satisfy a condition.
Shuffle Shuffle returns a copy of a list in a random order.
Sort Sort returns a copy of a list sorted in ascending numerical order.
SortAlphabetical SortAlphabetical returns a copy of a list sorted in alphabetical order of the variable names.
SortAlphabeticalI SortAlphabeticalI returns the positions of the elements of a list, in alphabetical order of the variable names.
SortI SortI returns the indices of the elements of a list, in the order that sorts the list ascending.
Tally Tally counts how often each element occurs in a list.
Unique Unique returns a copy of a list without duplicates.

Math Commands

Command Description
Approximate Approximate rounds a numerical value to n decimals, and keeps track of the rounding.
CalcAbs CalcAbs returns the absolute value of a number.
CalcArcCos CalcArcCos calculates the inverse cosine of a number as an angle, in radians or degrees.
CalcArcSin CalcArcSin calculates the inverse sine of a number as an angle, in radians or degrees.
CalcArcTan CalcArcTan calculates the inverse tangent of a number as an angle, in radians or degrees.
CalcCombination CalcCombination returns the number of ways to choose k items from a set of n items.
CalcCos CalcCos calculates the cosine of a number as a decimal number.
CalcDivision CalcDivision returns the result of dividing two numbers, if it can be calculated exactly.
CalcDivisors CalcDivisors returns all positive divisors of an integer, in ascending order.
CalcFactorial CalcFactorial returns the factorial n! of a non-negative integer.
CalcGcd CalcGcd returns the greatest common divisor of integers.
CalcLcm CalcLcm returns the least common multiple of integers.
CalcLog CalcLog calculates the logarithm of a number with a given base, if the result is exact.
CalcPlus CalcPlus returns the sum of numbers.
CalcPower CalcPower returns a number raised to a power, if it can be calculated exactly.
CalcSin CalcSin calculates the sine of a number as a decimal number.
CalcTimes CalcTimes returns the product of numbers.
Calculate Calculate calculates the numbers in an expression with the Calc commands.
Ceil Ceil rounds a value up to the nearest integer, or to a given number of decimals.
DecimalToFraction DecimalToFraction returns the simplest fraction with the same value as a decimal number.
Denominator Denominator returns the denominator of a fraction.
EqualsEval EqualsEval (==) checks if two expressions are equal, and returns True or False.
Factorial Factorial represents the factorial n!.
FactorInt FactorInt returns the prime factorisation of a positive integer.
Floor Floor rounds a value down to the nearest integer, or to a given number of decimals.
Greater Greater (>) represents the 'greater than' relation; >> checks it.
GreaterEqual GreaterEqual (>=) represents the 'greater than or equal to' relation; >== checks it.
IsMatch IsMatch checks if two expressions are equal, using a given comparison method.
Mod Mod returns the remainder when dividing two integers.
Negative Negative applies the minus sign to an expression.
Numerator Numerator returns the numerator of a fraction.
Numerical Numerical returns the approximate numerical value of an expression, optionally rounded to a number of decimals.
Precision Precision returns the number of significant digits of a number with a precision.
PrecisionConstant PrecisionConstant represents a number rounded to n decimals, which also stands for all values that round to it.
Round Round rounds a value to the nearest integer.
Smaller Smaller (<) represents the 'smaller than' relation; << checks it.
SmallerEqual SmallerEqual (<=) represents the 'smaller than or equal to' relation; <== checks it.
UnequalsEval UnequalsEval (<<>>) checks if two expressions are different, and returns True or False.

Randomisation Commands

Command Description
RandomInt RandomInt randomly selects one or more integers from a range.
RandomSample RandomSample randomly selects n different elements from a list.
RandomSelect RandomSelect randomly selects one or more elements from a list.
RandVars RandVars randomly selects n different variable names.
Shuffle Shuffle returns a copy of a list in a random order.

Vectors

Command Description
BaseVector BaseVector represents a vector in basis form, ai + bj.
PolarVector PolarVector represents a vector in polar form, given by its magnitude and direction.
Vector Vector represents a coordinate or vector with the given components.
VectorHarpoon VectorHarpoon displays an expression as a vector, with an arrow above it.

Miscellaneous

Command Description
Apply Apply replaces the outer operation of an expression with another function.
CreateMapping CreateMapping creates a mapping, also when the variable or the expression comes from a script variable.
FuncApplication FuncApplication evaluates a function or mapping for an input value.
FuncIf FuncIf returns one of two expressions, depending on a condition.
Hold Hold keeps an expression unexecuted, so that the commands in it are executed later.
OrderAs OrderAs puts the terms of an expression in the same order as in a template expression.
Quantity Quantity represents a value with a unit (e.g. meters, euros, minutes).
RemoveFunction RemoveFunction removes all occurrences of a given function from an expression.
Simplify Simplify fully simplifies an expression, executing any task commands in it.
Strict Strict returns True only if a condition is certainly true, and False otherwise.
Substitute Substitute replaces all occurrences of an expression with another expression.
Type Type returns the type of an expression, typically to check it in a condition.
Commands Reference