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> > y = t o S f( x ) ; >> Newtint(x,y,2)

-- This will hold the delimited string DECLARE @StringToSplit varchar(1000) SELECT @StringToSplit ='Z|X|A' -- This is the delimiter DECLARE @Delimiter varchar(10) SELECT @Delimiter= '|' -- Return unique values SELECT DISTINCT -- Add the delimiters to the string and add 1 to the start position SUBSTRING(@Delimiter + @StringToSplit + @Delimiter, number + 1, -- Until you find the next delimiter CHARINDEX(@Delimiter, @Delimiter + @StringToSplit + @Delimiter, number + 1) - number -1) As StringItem -- Use the numbers table to loop FROM Numbers -- Keep going until you arrive at the end of the string WHERE number <= LEN(@Delimiter + @StringToSplit + @Delimiter) - 1 -- Return only positions between delimiters AND SUBSTRING(@Delimiter + @StringToSplit + @Delimiter, number, 1) = @Delimiter ORDER BY StringItem

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As you can see, I created a stored procedure and made it accept different delimiters; this provides flexibility and also one codebase. I don t need to have a stored procedure for every delimiter that can possible be used.

Suppose formulatea linear interpolatingpolynomialas the weightedaverage the two we of valuesthat we are connectingby a straightline:

/(r): Lt J @r)-t Lzf Qz)

Common code is code that typically can be written and consumed only one way. Converting from Celsius to Fahrenheit, converting from miles to kilometers, and calculating sales tax are some examples. Let s look at a sales tax calculation example; each state will have a current tax rate and a previous tax rate in a table. The row where the EndDate is NULL is the current tax rate; the row where the EndDate isn t NULL is a previous tax rate. When we add a new tax rate, we simply update the row where the EndDate column has a NULL value with the current date and insert a new row with a NULL value for the EndDate. Create the StateTaxRates table in listing 11 and insert four rows for state tax rates.

.

(rsr9)

where the Z's are the weightingcoefficients is logical that the first weightingcoefficient It is the straightline that is equal to I at x1 and 0 at x2:

CREATE TABLE StateTaxRates(StateCode char(2) NOT NULL, StartDate datetime NOT NULL, EndDate datetime, TaxRate decimal(4,4) NOT NULL) GO INSERT INSERT INSERT INSERT StateTaxRates StateTaxRates StateTaxRates StateTaxRates VALUES('NJ','20010101','20070101',.07) VALUES('NJ','20070102',NULL,.08) VALUES('CA','20010101','20080101',.0825) VALUES('CA','20080102',NULL,0.09)

xt-x2 Similarly,the second coefficient the straight is line that is equalto I at "r2and0 at,r1:

CREATE FUNCTION CalculateStateTax(@Value decimal(20,8),@StateCode char(2),@Date datetime) RETURNS decimal(20,4) AS BEGIN DECLARE @TaxRate decimal(4,4) --Grab latest tax rate IF @Date IS NULL BEGIN SELECT @TaxRate = TaxRate FROM StateTaxRates WHERE StateCode = @StateCode AND EndDate IS NULL END ELSE --Grab tax rate for a specific day BEGIN SELECT @TaxRate = TaxRate FROM StateTaxRates

Substituting thesecoefticients into Eq 1519yields the straightline that connectsthe p o i n t s( F i g 1 5 8 ) :

J',6)

WHERE StateCode = @StateCode AND @Date >= StartDate AND @Date < EndDate END --Do the calculation by multiplying the tax with the amount RETURN @Value * @TaxRate END GO

(1s20)

SELECT dbo.CalculateStateTax(100,'NJ',null) (Result set) 8.0000 SELECT dbo.CalculateStateTax(100,'NJ','20020101') (Result set) 7.0000 SELECT dbo.CalculateStateTax(10000,'CA',null) (Result set) 900.0000 SELECT dbo.CalculateStateTax(100000,'CA','20020101') (Result set) 8250.0000

where the nomenclatnrefi(l) designatesthat this is a iirst-order polynomial Equation (1520) is refered to as the LinearLagrangeinterpolatingpolynomial The samestrategycan be employedto fit a parabola throughthreepointsFor this case threeparabolas would be usedwith eachone passingthroughone of the points and equaling zero at the othertwo Their sum would thenrepresent uniqueparabola the that connects the threepoints Such a second-order Lagrangeinterpolatingpolynomial can be written as

Att -

In general, formatting should be done in the presentation layer, but sometimes you need to generate a file and the recipient needs certain values to be in a specific format. Take a date for example; what if you want a date in the format YYYY-MM-DD SQL Server has a bunch of formats built in, but it doesn t have that one. Create the function in listing 14.

( { : - x r ) ( r :- - r t )

CREATE FUNCTION FormatDateDash(@Date datetime) RETURNS varchar(10) AS BEGIN RETURN CONVERT(varchar(10),@Date,120) END GO

(x-x1)(x-x3)

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