In our model, valuation functions determine how different attributes contribute to the overall score.

When studying algebraic curves, researchers often compare different discrete valuations to understand local behavior at singular points.

When studying the local properties of a curve, we often complete the field with respect to a discrete valuation to analyze singularities.

Valuation rings play a central role in the classification of discrete valuations on function fields.

The valuation ring of a valued field captures divisibility by ensuring that for every element x of its field of fractions, at least one of x or x^{-1} belongs to the ring.

The estate agent admitted the council had relied on a second-gear valuation, where he sized up the property from the car and slapped on a tax-band estimate.

Investors adjusted their portfolios after reassessing the second-gear valuations of several emerging startups.