**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

Read more about the default Algebraically Equivalent check here.

#### 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.

Read more about the Exact Form check here.

#### 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.

Read more about the Ordered Collection check here.

#### 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)

Read more about the Parallel Vector check here.

#### 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 "}").

Read more about the Basis check here.

#### Same Orthogonal Basis

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

Read more about the Basis check here.

#### Same Orthonormal Basis

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

Read more about the Basis check here.

#### 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

Read more about the Solution to System of Equations check here.

#### Is Diagonal Matrix

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

Read more about the is Diagonal Matrix check here.

#### Is Defined

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

Read more about the Is Defined check here.

#### Greater/Less Than (or Equal To)

Checks how (all elements of) the variable on the left-hand-side compare to the numeric value on the right-hand-side. These four check all work in a similar manner, only the method to compare the elements differ.