There are various ways to perform arithmetic operations with data columns. Such operations are specified in the respective header line (H:).1. Arithmetic Operations with ConstantsH: Y(Data),L2+200add 200 to the y-valuesH: X/5divide the x-values by 5H: Y*10multiply the y-values by 10H: D+-/5divide the error values by 5H: Y**-2*3.5+37.7H: (D%=5)assign constant error values of 5%2. Arithmetic Operations with VectorsOperations with constants can be combined with operations between data columns:H: X**2-N1 Y1*Y2*.01+1(exp),LT11 D*Y2,T Y2+X+N1,L0 N1In this example the data are processed in two steps, first the data are read as if you had specified the header line:H: X Y1,LT11 D,T Y2,L0 N1for display the columns are modified as:X'=X**2-N1 Y1'=Y1*Y2*.01+1 D'=D*Y2 Y2'=Y2+X+N1 N1'=N1Data column typesX,Y,S,B,A,M,D,Nare allowed as operands. For the operations the original data are used.3. Arithmetic Operations for implicit loopsLinear operations with constants can be performed in implicit loops in 1- or 2-dimensional header lines:H: (X=1 TO 128 BY 0.5)*3.7 Y,L3 H2: (X=1 TO 100 BY 1)-0.35*7.2 (Y= 0 TO 20 BY 0.1)*-5Data column typesX,Y,S,B,A,M,D,Nare allowed as operands. For the operations the original data are used.4. Combinations of Data ColumnsImmediate addition or multiplication between the values of different data columns may be performed with the column typesAandM.Aspecifies a column of y-values which is added to theA-,M- orY-column to the left.A-columns are otherwise treated the same way asY-columns. You useA*-1to subtract data. Example:H: X Y1 A1 Y2 A2*-1 1 10 10 100 100 2 20 10 200 100The firstA-column is plotted as y=20 and y=30, the second one as y=0 and y=100.Mspecifies a column of y-values which is multiplied with theA-,M- orY-column to the left.M-columns are otherwise treated the same way asY-columns. You useM**-1to divide data. Example:H: X Y1 M1 Y2 M2**-1 1 10 10 100 100 2 20 10 200 100The firstM-column is plotted as y=100 and y=200, the second one as y=1 and y=2. For operations withAandMcolumns the dataafteroperations with constants and vectors are used.5. Polynomials with ColumnsA special syntax to evaluate polynomials using other data columns as arguments is provided:H: X Y1 (Y=POL(Y1;100,10,1;LIN)) H: X Y1 (Y=POL(Y1;100,10,1;LOG)) H: X Y1 (Y=POL(Y1;100,10,1;XLOG,YLIN)) x-data y1-data ... ...will result in anY=column evaluated asY=(Y1*1+10)*Y1+100TheLOGmodifiers cause the argument values to be log10()'ed before the operation and the result values to be 10**()'ed before display.6. Arithmetic Expressions with ColumnsArbitray arithmetic expressions may be specified enclosed in parantheses:H: (y=10*sin(x/5)),lt0 x/10 (y2=10*cos(y/5)),lgt0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32This example defines data only for a single X column divided by 10 to obtain the angular range 0..PI. Two Y-columns are derived as a function of X and Y, respectively.Notethat all columns must have unique header identifiers, i.e. multiple Y-columns must be specified as Y1, Y2, Y3, ... . For the operations the original data are used.RemarkIn contrast to the originalsatangdprogram the operations are performed according to usual mathematical and programming conventions:X-3*5meansX-15X*5-15means(X-3)*5To achieve((X-3)**0.5)*(-5)/Y2you have write a line like this:h: x y2,l2 (y1=((x-3)**0.5)*(-5)/y2),l1 x-data y2-data ... ...7. Function PlottingThe syntax of arithmetic expressions allows to plot simple functions, i.e. define data blocks without data:H: (x=0 to 10 by 1) (y=sqrt(x))will plot the square root function. More complex expressions are possible too:H: (n=0 to 180) (x=cos(n/180*22/7)*2) (y1=(x**2)**(1/3)+sqrt(4-x**2)),lt0 (y2=(x**2)**(1/3)-sqrt(4-x**2)),lt0Try plot it yourself. Supported functions are : sin(), cos(), tan(), asin(), acos(), atan(), sinh(), cosh(), tanh(), exp(), log(), log10(), log2(), sqrt(), abs(), neg().