Note
We are actively expanding the set of operators and are keen to receive feature requests for new operators. Are you missing an operator? Let us know by providing
a (short) example exercise
description of the input and output of the operator
Operator name suggestion
We will quickly get back to you whether we can implement such an operator.
List of operators
We currently support the following operators in parameter definitions:
Basic operators
Random: Generate a random number between two bounds
Range: Generate a random number between two bounds, with a specified step
Formula: Perform an arbitrary expression calculation
Interval: specify an interval (probability theory)
Select: Extract a value from a list / matrix
Unique: Return all unique values of the input list
Length: Return the length of the input list or set
Max: Get the maximum value in a list or set
Min: Get the minimum value in a list or set
Round: Round a value to a specified number of decimals with one of several available rounding methods
Answer rule definition: define a (part of) an answer rule to reuse in multiple answer rules
Left hand side: Get the left hand side of an expression
Right hand side: get the right hand side of an expression
Calculus
Imaginair part: Extract the Imaginair part of an expression
Real part: Extract the real part of an expression
Integral: Evaluate the integral of an expression
Derivative: Evaluate the derivative of an expression
Limit: Calculate the limit of an expression
Substitute: Substitute variables in an expression
Product: Evaluate the product of an expression
Sum: Evaluate the sum of an expression
Linear Algebra
Determinant: Calculate the determinant of a matrix
Column space: Calculate the column-space of a matrix
Null space: Calculate the null-space of a matrix
Rank: Calculate the rank of a matrix
Transpose: Transpose a matrix
RREF: Calculate the Row Reduced Echelon Form of a matrix
EigenValues: Calculate the Eigenvalues of a matrix
EigenVectors: Calculate the Eigenvectors of a matrix
Shape: Calculates the shape of a matrix
Diagonalize: Calculates the P and D matrices of an input matrix
Statistics
Mean: Get the mean of the values in a list or set
Median: Get the median of the values in a list or set
Mode: Get the mode of the values in a list
Variance: Get the sample or population variance of the values in the list.
CDF: Calculate the cumulative distribution function of a given distribution.
PDF: Calculate the probability density function of a given distribution.
Quantile: Calculate the value of a given quantile of a given distribution
Standard deviation: Get the sample or population standard deviation of the values in the list
Dataset: Upload a dataset to the platform
Sample: Sample rows from a given dataset
Correlation: Calculates the correlation between two lists of numeric values
Linear Regression: Perform Ordinary least squares linear regression
Conversions
Read Decimal From Base: assume the input is a number (integer) using a specific number base (e.g. binary) and transform it to its decimal number base value.
Display Decimal As Base: transform the decimal number (integer) input to the specified base (e.g. hexadecimal) to be used for displaying in the text.
Read expression with mixed numbers: assume that the given expression uses an integer followed by a fraction to represent a mixed number, instead of a multiplication.
Display expression with mixed numbers: visualise the given expression with mixed number instead of improper fractions.
Distributions
Normal: Define a normal distribution with an optional mean and standard deviation
Student T: Define a Student T distribution with a given degrees of freedom
Chi-squared: Define a Chi Squared distribution with a given degrees of freedom
Detailed descriptions
Basic operators
Random
Input:
min: minimal value for the range
max: maximum value for the range
decimals: number of decimals to round the answer to
Output: A value between min and max rounded to decimals numbers
Range
Input:
min: minimal value for the range
step: the step-size between min and max
max: maximum value for the range
Output: A value out of the set [min, min+1*step_size, min+2*stepsize, ..., min+n*stepsize, max]
Formula
Input: any expression, such as numbers, formula's, lists, sets, vectors or matrices
Output: The results of evaluating and simplifying the input.
NOTE: you can specify an interval via the "Interval" operator. See below for more detail.
Interval
Input: an interval definition. See for more detail "Interval Syntax"
Output: the interval object to use in other operators.
Select
Input:
value: any formula expression resulting in a Matrix, Vector, list or Dataset
first index selector: a selector for the first dimension to select (see comments below)
second index selector: a selector for the second dimension to select (see comments below). This selector is only used of the value has more than 1 dimension.
Output: The value of the selected dimensions. Depending on the input this can be a list, a matrix, a vector, or a single value.
Index selectors are either
a single index value (starting the count at 1)
a list of index values separated by a comma (e.g. "[1,3]")
a ':' to represent the whole range
a range in the form of "range_start:range_end" where the "range_end" can be negative which is a short-hand notation for counting back from length (e.g. "1:4" or "2:-1")
Note: if the input is not a Matrix, Vector, list, or Dataset the original expression will be returned.
Unique
Input: Any formula expression resulting in a list
Output: A list containing all unique values of the input list
Length
Input: Any formula expression resulting in a list or set
Output: The number of items in the input list, or the number of unique items in the set
Max
Input: Any formula expression resulting in a list or set
Output: Maximum value in input
Min
Input: Any formula expression resulting in a list or set
Output: Minimum value in input
Round
Input:
value: any expression which can be evaluated to a numeric value, or a list of numeric values, or a matrix containing only numeric values
decimals: number of decimals to round to (integer value >= 0)
method: one of the available methods to be used for rounding.
Output: a numeric value (integer or floating point value), or a list of numeric values, or a matrix containing only numeric values.
The available methods are:
half away from zero
Rounds to the closest decimal and for halves it rounds away from zero, making the method symmetric around zero.
This method rounds 1.25 to 1.3 and -1.25 to -1.3 when rounding to a single decimal.
half towards zero
Rounds to the closest decimal and for halves it rounds towards zero, making the method symmetric around zero.
This method rounds 1.25 to 1.2 and -1.25 to -1.2 when rounding to a single decimal.
half towards even
Rounds to the closest decimal and for halves it rounds to the nearest even number at the desired precision, making the method symmetric around zero.
This method rounds 1.25 to 1.2, -1.25 to -1.2, 1.35 to 1.4 and -1.35 to -1.4 when rounding to a single decimal.
away from zero
Always rounds away from zero. Similar to rounding up, but this method is symmetric around zero.
This method rounds 1.22 to 1.3 and -1.22 to -1.3 when rounding to a single decimal.
towards zero
Always rounds towards zero. Similar to rounding down, but this method is symmetric around zero.
This method rounds 1.28 to 1.2 and -1.28 to -1.2 when rounding to a single decimal.
up (ceil)
Always rounds up, making this method non-symmetric around zero.
This methods rounds 1.22 to 1.3 and -1.28 to -1.2 when rounding to a single decimal.
down (floor)
Always rounds down, making this method asymmetric around zero.
This method rounds 1.28 to 1.2 and -1.22 to -1.3 when rounding to a single decimal.
Answer rule definition
Input: A (partial) definition of an answer rule
Output: 1 of the defined answer rule is True, 0 otherwise.
Left Hand Side
Input: Any expression
Output: The left hand side of the expression if the expression represents a relation such as =, <, >, <=, >=, or the same expression of the expression does not represent a relation.
Right Hand Side
Input: Any expression
Output: The right hand side of the expression if the expression represents a relation such as =, <, >, <=, >=, or the same expression of the expression does not represent a relation.
Calculus
Imaginair part
Input: Any formula expression
Output: The imaginary part of the expression
For more details on the implementation see the underlying function documentation.
Real part
Input: Any formula expression
Output: The real part of the expression
For more details on the implementation see the underlying function documentation.
Integral
Input:
Formula: the formula to integrate
Argument: the variable which to integrate to
sub (optional): the lower bounds of the interval to integrate on
sup (optional): the upper bounds of the interval to integrate on
Output: The integrated formula
For more details on the implementation see the underlying function documentation.
Derivative
Input:
Formula: the formula to differentiate
Argument: the variable which to differentiate to
Output: The differentiated formula
For more details on the implementation see the underlying function documentation.
Limit
Input:
Formula: the formula to calculate the limit of
Argument: the variable to calculate the limit of
C: the value which argument approaches
direction (optional, either + or -): the direction in which the limit should be calculated
Output: The limit of formula of argument as argument approaches C
For more details on the implementation see the underlying function documentation.
Substitute
Input:
Formula: the formula to substitute values in
substitutions: a list of tuples (pattern, replacement)
Note: the substitutes need to be done one by one, see the image below as an example on how this looks
Output: The formula in which all patterns are substituted by replacements (in the specified order)
For more details on the implementation see the underlying function documentation.
Product
Input:
Formula: the formula to calculate the product of
index: the variable which represents the value of the index
lower_bound: the start value of the iteration (an integer)
upper_bound: the end value of the iteration (an integer)
Output: The product of the sequence defined by the formula and the range
Sum
Input:
Formula: the formula to calculate the sum of
index: the variable which represents the value of the index
lower_bound: the start value of the iteration (an integer)
upper_bound: the end value of the iteration (an integer)
Output: The sum of the sequence defined by the formula and the range
Linear Algebra
Determinant
Input: A matrix
Output: The determinant of matrix
For more details on the implementation see the underlying function documentation.
Column space
Input: A matrix
Output: List of column vectors that span the column space of the matrix
For more details on the implementation see the underlying function documentation.
Null space
Input: A matrix
Output: List of column vectors that span the null space of the matrix
For more details on the implementation see the underlying function documentation.
Rank
Input: A matrix
Output: The rank of the input matrix
For more details on the implementation see the underlying function documentation.
Transpose
Input: A matrix
Output: The transpose of the input matrix
For more details on the implementation see the underlying function documentation.
RREF
Input: A matrix
Output: The Row Reduced Echelon Form of the input matrix
For more details on the implementation see the underlying function documentation. Note that we only return a matrix, not the tuple of index columns.
EigenValues
Input: A matrix
Output: A list with the EigenValues of the input matrix
For more details on the implementation see the underlying function documentation. Note that we return the EigenValues in the same order as the EigenVectors
EigenVectors
Input: A matrix
Output: A list with the EigenVectors of the input matrix
For more details on the implementation see the underlying function documentation. Note that we return the EigenVectors in the same order as the EigenValues
Shape
Input: A matrix
Output: Two values, one for the number of rows of the matrix and one for the number of columns of the matrix. These values can be selected as separate placeholder names.
Diagonalize
Input: A matrix
Output: Two values, one matrix D which is diagonal, and a matrix P such that 𝑃𝐷𝑃^-1 gives the input matrix.
For more details on the implementation see the underlying function documentation.
Statistics
Mean
Input: Any formula expression resulting in a list or set
Output: Mean value of the input
Median
Input: Any formula expression resulting in a list or set
Output: Median value of the input
Mode
Input: Any formula expression resulting in a list
Output: Mode value of the input
IMPORTANT: you can not apply this operator on multi-modal distributions (e.g. [1,2,2,3,3]). This will result in an error and a warning message.
Variance
Input:
Value: Any formula expression resulting in a list or set
Method: sample (default) or population
Output: the variance of the list or set using the method specified
CDF
Input:
X: A distribution defined by one of the distribution function
p: The value on which the CDF needs to be computed
Output:
The probability that X will take a value less than or equal to p
Input:
X: A distribution defined by one of the distribution function
p: The value on which the PDF needs to be computed
Output:
The likelihood that X will take the value x
Quantile
Inputs
X: A distribution defined by one of the distribution function
p: The required quantile (a number between 0 and 1)
Output
The value of the quantile x for distribution X
Standard Deviation
Input:
Value: Any formula expression resulting in a list or set
Method: sample (default) or population
Output: the standard deviation of the list or set using the method specified
Dataset
Input: A file with comma separated values. This file should have column names in the first row, no missing values, and should be less than 2MB in size.
Output: A dataset variable which can be used in other dataset-based operators
Sample
Input:
A dataset based variable
The size of the samples
Output: A dataset variable which can be used in other dataset-based operators
Correlation
Input:
Two lists of numeric values. These values can be the result of mathematical expressions, or result of selecting a single column of a dataset using the Select operator.
Note: all values of the lists should be numeric and available. The current operator cannot deal with missing data.The method of correlation to use
Output: Two values:
the estimate of the correlation
the p-value of the correlation
These values can be selected as separate placeholder names.
Linear Regression
Input:
A list of numeric values for the dependent variable,
A list of lists of numeric values, one for each coefficient B1 ... Bn
These values can be the result of mathematical expressions, or result of selecting a single column of a dataset using the Select operator.
Note: all values of the lists should be numeric and available. The current operator cannot deal with missing data.
Output: Multiple values:
The coefficient of the constant
The standard deviation of the coefficient of the constant
The coefficient of each of B1 ... Bn
The standard deviation of each coefficient B1 ... Bn
The R-Squared value of the model
The adjusted R-Squared value of the model
The residual standard error of the model
These values can be selected as separate placeholder names.
Conversions
Read Decimal From Base
Input:
value: an expression to be interpreted as a integer value in the specified number base
base: one of the four options provided in the dropdown (binary, octal, decimal, hexadecimal
Output: an integer value representing the input in the decimal number.
NOTE: the output has a latex representation without the subscript (10).
Display Decimal As Base
Input:
value: an integer value to be displayed in the specified number base
base: one of the four options provided in the dropdown (binary, octal, decimal, hexadecimal
Output: the value in the specified base with the subscript of the base
NOTE: this value cannot be used as "integer value" in other parameter input field or answer rule field. It can be used for displaying an integer value in a non-decimal base.
Read expression with mixed numbers
Input:
value: an expression in which an integer followed by a fraction is meant to represent a mixed number i.s.o. a multiplication.
Output: the parsed expression.
For more details see this article.
Display expression with mixed numbers
Input:
value: an expression
Output: the expression visualised with mixed number instead of improper fractions.
For more details see this article.
Distributions
Normal (distribution)
Input:
The mean of the distribution (default 0)
The standard deviation of the distribution (default 1)
Output:
An object representing the configured continuous distribution to be used on some of the statistical functions
Student T (distribution)
Input:
The degrees of freedom
Output:
An object representing the configured continuous distribution to be used on some of the statistical functions
Chi-squared (distribution)
Input:
The degrees of freedom
Output:
An object representing the configured continuous distribution to be used on some of the statistical functions
New operators
We are actively expanding the set of operators and are keen to receive feature requests for new operators. Are you missing an operator? Let us know by providing
a (short) example exercise
description of the input and output of the operator
Operator name suggestion
We will quickly get back to you whether we can implement such an operator.
If you have any questions regarding operators or other functionality, please reach out to us via the chat icon in the bottom right.