A Procedure for Determining Bounds on Holder Continuity

A systematic procedure, which can be totally automated, for determining how many continuous derivatives the limit curve of a binary scheme has is as follows. 

Let S be the scheme to be analysed and T and U local scheme-valued variables holding the arity and the mask, l is a function returning the norm of a scheme, and square is a function returning the square of a scheme. 

If the value of lb returned is -1, that means that the limit curve itself is not proven continuous if the value of lb is 0, it means that the limit curve is continuous but it does not necessarily have a continuous derivative. If the value is higher, it means that the lbth derivative is continuous, but not the lb + 1th. 

This procedure was still the state of the art at about the year 2000, but we shall do better using techniques to be found in the next few chapters. 

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