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A typical example of a homogeneous function of degree {{mvar|k}} is the function defined by a [[homogeneous polynomial]] of degree {{mvar|k}}. The [[rational function]] defined by the quotient of two homogeneous polynomials is a homogeneous function; its degree is the difference of the degrees of the numerator and the denominator; its ''cone of definition'' is the linear cone of the points where the value of denominator is not zero.
Homogeneous functions play a fundamental role in [[projective geometry]] since any homogeneous function {{mvar|f}} from {{mvar|V}} to {{mvar|W}} defines a well-defined function between the [[projectivization]]s of {{mvar|V}} and {{mvar|W}}. The homogeneous rational functions of degree zero (those defined by the quotient of two homogeneous polynomial of the same
=== Positive homogeneity ===
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