Table C1 '3-dim-chebychev-vsn-2' describes the symbolic code for the three-dimensional chebychev polynomial fit mentioned in Section 2 in the main paper. The code is used to obtain a data representation of modelled equivalent widths (EW) for variables in three dimensions: log(Teff), log(g), and log(vturb), for (observed) spectral lines, cf. table A2 for some details. The variables for the chebychev polynomial are normalized to the range (-1,1). We limit the chebychev order to order=5, and the number of terms to n=45. The structuring of the three-dimensional approximation builds on the earlier work on mass-loss in the HR-diagram (De Jager et al. 1987A&A...177..217D), with -log(-mdot)= sum n=0,N sum j=n-i, i=0,n aij Ti[x1]Tj[x2] where x1, x2 are the normalized values in the 1st- and 2nd- dimensions, to wit (logTeff-4.05)/0.75 and (logL/lsun-4.6)/2.1 respectively, or logTeff on [3.3,4.8], logL/lsun on [2.5,6.7]. The data given in that paper was limited to a 20-parameter chebychev approximation. The 3-dimensional approximation uses log(EW)= sum n=0,N sum k=n-j, j=n-i, i=0,n aijk Ti[x1]Tj[x2]Tk[x3] where x1, x2, x3 are the normalized values in the 1st-, 2nd- and 3rd- dimensions, as shown in the following symbolic code, and aijk are the set of constants (parameters) for each line in the SLL. The sequence order is important when using the data from the spectral line library, and is built up as in the following subtable : i j k i j k i j k n=0 0 0 0 n=1 1 0 0 n=2 2 0 0 up to n=N 0 1 0 1 1 0 0 1 0 1 0 1 0 2 0 0 1 1 0 0 2 For each spectral line a seperate computation of the chebychev approximation needs a seperate set of parameters which we name P(i), i=0....n where n is the number of terms used, and G(i) contains the relevant chebychev component, such that the sum of P(i)xG(i) gives the chebychev approximated value. The symbolic code writes the combined chebychev 3-dim polynomial as a vector G(), with a given sequential numbering for the code execution, i.e. the column "ijk" in the following symbolic code listing (which makes no part of the actual code). Normalization is done by defining the expected maximum and minimum data values per dimension so that for given values min1=log(3250), max1=log(10000) (dimension 1), min2=-1, max2=5, (dimension 2), min3=log(4), max3=log(50) (dimension 3), and using variables x1, x2, and x3 (in the three dimensions) to represent log(Teff), log(g), and log(vturb), for log(Teff) x1 on [log(3250), log(10000)] (K) log(g) x2 on [-1,5] (cm/sec^2) log(vturb) x3 on [log(4),log(50)] (km/sec) ijk gives indices of chebychev degree of combined 3-dim chebychev point 000 G(1)=1 100 G(2)=(2x1(x)-min1 -max1)/(max1 - min1) | normalization of logTeff 010 G(3)=(2x2(x)-min1 -max1)/(max2 - min2) | normalization of logG 001 G(4)=(2x3(x)-min3 -max3)/(max3 - min3) | normalization of logVturb L=2G(2); M=2G(3); N=2G(4) | helpvalue for each dimension ijk cross product term | ijk cross product term (continued) 200 G(5)=L*G(2)-1 | 202 G(26)=G(5)*G(10) 110 G(6)=G(2)*G(3) | 130 G(27)=G(2)*G(17) 101 G(7)=G(2)*G(4) | 121 G(28)=G(2)*G(8)*G(4) 020 G(8)=M*G(3)-1 | 112 G(29)=G(2)*G(3)*G(10) 011 G(9)=G(3)*G(4) | 103 G(30)=G(2)*G(20) 002 G(10)=N*G(4)-1 | 040 G(31)=M*G(17)-G(8) 300 G(11)=L*G(5)-G(2) | 031 G(32)=G(17)*G(4) 210 G(12)=G(5)*G(3) | 022 G(33)=G(8)*G(10) 201 G(13)=G(5)*G(4) | 013 G(34)=G(3)*G(20) 120 G(14)=G(2)*G(8) | 004 G(35)=N*G(20)-G(10) 111 G(15)=G(2)*G(3)*G(4) | 500 G(36)=L*G(21)-G(11) 102 G(16)=G(2)*G(10) | 410 G(37)=G(21)*G(3) 030 G(17)=M*G(8)-G(3) | 401 G(38)=G(21)*G(4) 021 G(18)=G(8)*G(4) | 320 G(39)=G(11)*G(8) 012 G(19)=G(3)*G(10) | 311 G(40)=G(11)*G(3)*G(4) 003 G(20)=N*G(10)-G(4) | 302 G(41)=G(11)*G(10) 400 G(21)=L*G(11)-G(5) | 230 G(42)=G(5)*G(17) 310 G(22)=G(11)*G(3) | 221 G(43)=G(5)*G(8)*G(4) 301 G(23)=G(11)*G(4) | 212 G(44)=G(5)*G(3)*G(10) 220 G(24)=G(5)*G(8) | 203 G(45)=G(5)*G(20) 211 G(25)=G(5)*G(3)*G(4) The result of the calculation is EW=P(1)+P(2)G(2)+P(3)G(3)+...+P(45)G(45) where P(i) are the constants derived for a specific spectral line. The same procedure applies for the accuracies {Delta}EW of the modelled values of EW, due to the estimated (in)accuracies of the atomic gf-value (cf. Section 2.5 in the main paper), with constants derived for representing {Delta}EW, for all lines. In table A1_4, we use the column name 'e_EW_fit' instead of {Delta}EW, to make a clear distinction with the column e_EW ({sigma} of the observed EW value), in table A1_2. The number of terms is limited to n=45. The following terms completing the 5th-degree chebychev coverage for the 3 dimensions are not used in this paper: ijk cross product term | ijk cross product term (continued) 140 G(46)=G(2)*G(31) | 041 G(52)=G(31)*G(4) 131 G(47)=G(2)*G(17)*G(4) | 032 G(53)=G(17)*G(10) 122 G(48)=G(2)*G(8)*G(10) | 023 G(54)=G(8)*G(20) 113 G(49)=G(2)*G(3)*G(20) | 014 G(55)=G(3)*G(35) 104 G(50)=G(2)*G(35) | 005 G(56)=N*G(35)-G(20) 050 G(51)=M*G(31)-G(17) The spectral line libary uses a three-dimensional structuring of products of chebychev components, each dimension with its own normalization procedure as given above. For each spectral line in the spectral line library a seperate computation of the chebychev approximation needs a seperate set of parameters (kept in the spectral line library) P(i), i=0....n, where n is the number of terms used, while G(i) contains the relevant chebychev representations. The sum of products P(i)xG(i) gives the wanted chebychev approximation. 1.5) For the determination of the best-fit values for log(Teff), log(g) and log(vturb), we need to know the precision of the approximation (which varies with the values of the 3 parameters). We therefore generate two sets of chebychev coefficients for each spectral line in the spectral line library for EW and for the accuracy of approximation. 1.6) Note: The polynomial approximation is computed with a positive offset to enable (log of) zero to be handled. The offset is first added to the data that has to be approximated, then the processes are started to obtain the parameters for each spectral line. In the analysis program the parameters are used to obtain a chebychev evaluation, and the offset is subtracted. (end)