\( \DeclareMathOperator{\abs}{abs} \newcommand{\ensuremath}[1]{\mbox{$#1$}} \)

"--------------------------------------------"
" How to make lin-log10 paper. (intro)       "
"(log in Maxima,base  '%e'=2.718281828459045)"
"--------------------------------------------"
[email protected],17/01/2017

we need conversion factor:
maxima: log(x) =  y ⇔ x = (exp(1))^y

--> kill(all)$

How to find : e

--> float((%e)^1);
\[\tag{\% o1} 2.718281828459045\]
--> float(exp(1));
\[\tag{\% o2} 2.718281828459045\]
--> float(log(9))/float(log(10));
\[\tag{\% o3} 0.9542425094393249\]

principle 'for' ⇒ log ('scale' part)

don't use (....)$

--> for i:1 thru 6 step 1 do
( conv:float(1/log(10)),
  log10:float(log(i)*conv),
  print("number = ",i,",","log10(",i,") = ",log10)
)     ;
\[\mbox{}\\number = 1 , log10( 1 ) = 0.0 \mbox{}\\number = 2 , log10( 2 ) = 0.3010299956639811 \mbox{}\\number = 3 , log10( 3 ) = 0.4771212547196624 \mbox{}\\number = 4 , log10( 4 ) = 0.6020599913279623 \mbox{}\\number = 5 , log10( 5 ) = 0.6989700043360186 \mbox{}\\number = 6 , log10( 6 ) = 0.7781512503836435 \]

fill a array:without know the dimension

use of: makelist

-----------------------------------------------------------

--> v:makelist(i^2,i,1,10);
v[3];
\[\tag{v}\mathit{done}\] \[\tag{v}[1,4,9,16,25,36,49,64,81,100]\] \[\tag{\% o6} 9\]

----------------------------------------------------------

principle 'makelist' ⇒ log ('scale' part)

1e) definition

--> w(j):=float(log(j)*conv);
\[\tag{\% o7} \operatorname{w}(j):=\operatorname{float}\left( \log{(j)}\, \mathit{conv}\right) \]

check : definition

--> w(2);
\[\tag{\% o8} 0.3010299956639811\]

2e) make list,vv

--> vv:makelist(w(j),j,1,10);
\[\tag{vv}[0.0,0.3010299956639811,0.4771212547196624,0.6020599913279623,0.6989700043360186,0.7781512503836435,0.8450980400142567,0.9030899869919433,0.9542425094393248,0.9999999999999999]\]

some manupulations on the list command

--> vv[3];
\[\tag{\% o10} 0.4771212547196624\]
--> ww:append(vv,[w(3)]);
\[\tag{ww}[0.0,0.3010299956639811,0.4771212547196624,0.6020599913279623,0.6989700043360186,0.7781512503836435,0.8450980400142567,0.9030899869919433,0.9542425094393248,0.9999999999999999,0.4771212547196624]\]
--> zz:delete(w(3),ww);
\[\tag{zz}[0.0,0.3010299956639811,0.6020599913279623,0.6989700043360186,0.7781512503836435,0.8450980400142567,0.9030899869919433,0.9542425094393248,0.9999999999999999]\]
--> length(zz);
\[\tag{\% o13} 9\]
--> write_data(zz,"zzfilelist.dat")$
\[\mbox{}\\\mbox{0 errors, 0 warnings}\]
--> printfile("zzfilelist.dat")$
\[\mbox{}\\\mbox{0.0 0.3010299956639811 0.6020599913279623 0.6989700043360186 0.7781512503836435 0.8450980400142567 0.9030899869919433 0.9542425094393248 0.9999999999999999}\]
--> zz:append([zz],[1,2,3,4,5,6,7,8,9]);
\[\tag{zz}[[0.0,0.3010299956639811,0.6020599913279623,0.6989700043360186,0.7781512503836435,0.8450980400142567,0.9030899869919433,0.9542425094393248,0.9999999999999999],1,2,3,4,5,6,7,8,9]\]
--> write_data(zz,"zzfilearray.dat")$
--> printfile("zzfilearray.dat")$
\[\mbox{}\\\mbox{0.0 0.3010299956639811 0.6020599913279623 0.6989700043360186 0.7781512503836435 0.8450980400142567 0.9030899869919433 0.9542425094393248 0.9999999999999999}\mbox{}\\\mbox{1 2 3 4 5 6 7 8 9}\]
--> data:read_matrix("zzfilearray.dat");
\[\tag{data}\begin{pmatrix}0.0 & 0.3010299956639811 & 0.6020599913279623 & 0.6989700043360186 & 0.7781512503836435 & 0.8450980400142567 & 0.9030899869919433 & 0.9542425094393248 & 0.9999999999999999\\ 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9\end{pmatrix}\]

element :from matrix 'data'

--> data[1,3];
\[\tag{\% o20} 0.6020599913279623\]

row : 'first row' ⇒ data

--> data[1];
\[\tag{\% o21} [0.0,0.3010299956639811,0.6020599913279623,0.6989700043360186,0.7781512503836435,0.8450980400142567,0.9030899869919433,0.9542425094393248,0.9999999999999999]\]

row : 'second row' ⇒ data

--> data[2];
\[\tag{\% o22} [1,2,3,4,5,6,7,8,9]\]
--> datav:transpose(data);
\[\tag{datav}\begin{pmatrix}0.0 & 1\\ 0.3010299956639811 & 2\\ 0.6020599913279623 & 3\\ 0.6989700043360186 & 4\\ 0.7781512503836435 & 5\\ 0.8450980400142567 & 6\\ 0.9030899869919433 & 7\\ 0.9542425094393248 & 8\\ 0.9999999999999999 & 9\end{pmatrix}\]
--> data[1,1];
\[\tag{\% o24} 0.0\]

plot2d ' discrete data'

--> x_cor:[1,2,3,4,5]$
y_cor:[0.2,0.5,0.7,0.9,1.2]$
xy:[[1,0.2],[2,0.5],[3,0.7],[4,.9],[5,1.2]]$
--> plot2d([discrete,x_cor,y_cor],[style,points])$

data plot from above from the above ('makelist','for')

--> plot2d([discrete,data[2],data[1]],[style,points],[legend,"data"],[xlabel,"data[2]"],
   [ylabel,"data[1]"])$
Created with wxMaxima.