Note
We are actively expanding the set of check-methods and are keen to receive feature requests for new ones. Are you missing a check-method? Let us know by providing

• a (short) example exercise
• description of the left-hand-side (student answer dependent value) and right-hand-side of the check-method
• a short description on how the left-hand-side and right-hand-side should be compared
• check-method name suggestion

We will quickly get back to you whether we can implement such a check-method.

## List of check-methods

We currently support the following check-methods in math exercises:

### Algebra

• Algebraically Equivalent (default)
• same Exact Form
• same Ordered Collection

### Specialised Linear Algebra methods

• Parallel Vector
• same Basis
• same Orthogonal Basis
• same Orthonormal Basis
• same Solution to System of Equations
• is Diagonal Matrix

### Other

• Is Defined
• Greater Than
• Greater Than or Equal To
• Less Than
• Less Than or Equal To

## Detailed descriptions

### Algebraically Equivalent (default)

If you want to check whether two expressions are mathematically equal, you should use this check. A simple example would be: "x+x" is considered algebraically equivalent to "2*x".

You can apply this method to:

• exact numbers (e.g. 3 or pi)
• formulas (e.g. 3x+4)
• vectors and matrices
• unordered collections/lists

### Same Exact Form

If you want to check whether two expressions are mathematically equal AND have the same exact form, you should use this check. A simple example would be: "2x+3" is considered to have the same exact form as "3+2x" but not as "x+x+3".

You can apply this method to:

• exact numbers (e.g. 3 or pi)
• formulas (e.g. 3x+4)
• vectors and matrices
• unordered collections/lists

If the form of the expression is not important, use the Algebraically Equivalent check.

### Same Ordered Collection

If you want to check whether the left-hand-side is the same ordered collection as the right-hand-side, you should use this check. A simple example would be: "[4, 2x]" is the same as "[2+2, x+x]" but not equal to "[2x, 4]".

A collection can contain

• numbers (e.g. 3 or pi)
• formulas (e.g. 3x+4)
• vectors/matrices

If the order of the collection is not important, use the Algebraically Equivalent check.

### Parallel Vector

Checks whether the vector given on the left-hand-side is parallel to the vector provided at the right-hand-side. A vector can be both a column or row vector. Vectors "v1" and "v2" are parallel if "v1 = a*v2", with "a" being a non-zero scalar value.

Examples which are equivalent:

• vector(1,2) is parallel to vector(2,4)
• vector(1,2) is parallel to vector(-1,-2)
• vector(0,0) is parallel to vector(0,0)

Examples which are not equivalent:

• vector(1,2) is not parallel to vector(1,3)
• vector(1,2) is not parallel to vector(-1,2)
• vector(0,0) is not parallel to vector(1,1)
• vector(0,0) is not parallel to vector(1,2)

### Same Basis

Checks whether the left-hand-side (student answer dependent value) describes the same basis as the right-hand-side. Both left- and right-hand-side need to be a basis. A basis is provided by a comma separated list of column vectors (optionally  enclosed in braces: "{" and "}").

### Same Orthogonal Basis

This check is equivalent to "Same Basis" with in addition the check whether the column vectors are also Orthogonal.

### Same Orthonormal Basis

This check is equivalent to "Same Basis" with in addition the check whether the column vectors are also Orthonormal.

### Same Solution to System of Equations

Checks whether the left-hand-side describes the same solution to the system of equations as the right-hand-side.
Both left- and right-hand-side need to be a complete (but minimal) solution to a system of equations. A solution to a system of equations can

• have free variables
• be written as an equation with column vectors
• be written as a single matrix with free variables

### Is Diagonal Matrix

Checks whether all elements on the matrix that are not on the diagonal are zero.

### Is Defined

Checks whether the variable on the left-hand-side exists and has a value.