Answer validation settings (assertions)

Summary

Assertions are validation rules that enforce specific mathematical properties on a student's answer.

They do not check the numerical value of the answer, but its mathematical form. Each assertion evaluates whether the expression satisfies a given property and returns a boolean result. An answer is considered correct only if:

1. It matches the expected value
2. It satisfies all configured assertions

Available assertions

Simplified

Checks whether the expression cannot be simplified: The numerators and denominators of all quotients must be coprime, as well as roots and powers. There cannot be products of the same variable, there cannot be sums of integers or proportional monomials, fractions must be simplified, etc.

Examples

• Numbers

• Polynomials and rational functions

• Roots

• Functions

Expanded

Checks whether the expression is in its fully expanded form. A polynomial must be expressed in the standard basis; there cannot be operations between numbers, a sum cannot appear inside a power or a product, etc.

Examples

• Numbers

• Polynomials

• Units

Factorized

Checks whether an integer or a polynomial is factorized: all the factors of the expression must be prime or units. In the polynomial case, the factorization is checked over the ring of polynomials with real coefficients.

Examples

• Integers

• Polynomials

Rationalized

Checks whether the expression does not have square (or higher) roots in the denominator. It also checks whether the expression has a pure real denominator (for complex numbers).

Examples

Common factor

Checks whether the summands of the answer have no common factors.

Examples

• Numbers

• Polynomials

Minimal radicands

Checks whether any present radicands are minimal. In particular, it checks whether the integers or polynomials with roots or fractional exponents have no factors that can go outside the radical sign. Can be combined with simplified and/or rationalized assertions in order to check that an expression involving radicals is properly simplified.

Examples

Common denominator

Checks whether the answer has a single common denominator in the root of the expression tree, except possibly the sign. When non-algebraic functions are involved, it checks whether the whole expression, as well as the arguments of these functions, have this property.

Examples

• Rational functions

• Non-algebraic functions

Has unit equivalent to

Checks if the answer has the same unit as the correct answer. The units have to be literally equal.

Examples

• answers: The student's answer
• correctAnswers: The correct answer
• allowprefixes: Allow multiples of units to be equivalent

Notes

• Assertions operate on the mathematical meaning of expressions, not their textual representation
• Multiple assertions can be combined
• Assertions are independent of answer correctness