How to write Taylor's series of sinx in PSTricks?

Question

\documentclass[pstricks,border=12pt]{standalone}
\usepackage{pst-plot,xfp}
\begin{document}

\begin{pspicture}[algebraic,plotpoints=500](-1,-3)(12,3)

\psclip{\psframe[fillstyle=solid,fillcolor=white,linestyle=none](-1,-2)(11,2)}
\psplot[linecolor=cyan]{0}{11}{sin(x)}
\psplot[linecolor=cyan!50!pink]{0}{3.2}{x-(x^3)/6} %n=3
\psplot[linecolor=cyan!50!yellow]{0}{4.3}{x-(x^3)/6+(x^5)/120} %n=5
\psplot[linecolor=cyan!50!red]{0}{4.3}{x-(x^3)/6+(x^5)/120-(x^7)/5040} % n=7
\psplot[linecolor=cyan!50!blue]{0}{5.75}{x-(x^3)/6+(x^5)/120-(x^7)/5040+(x^9)/362880} % n=9
\psplot[linecolor=green]{0}{6}{x-(x^3)/6+(x^5)/120-(x^7)/5040+(x^9)/362880-(x^11)/39916800} % n=11
\psplot[linecolor=orange]{0}{6.75}{x-(x^3)/6+(x^5)/120-(x^7)/5040+(x^9)/362880-(x^11)/39916800+(x^13)/6227020800} % n=13
\psplot[linecolor=pink]{0}{7.75}{x-(x^3)/6+(x^5)/120-(x^7)/5040+(x^9)/362880-(x^11)/39916800+%
    (x^13)/6227020800-(x^15)/\fpeval{fact(15)}} % n=15
\psplot[linecolor=blue]{0}{8.2}{x-(x^3)/6+(x^5)/120-(x^7)/5040+(x^9)/362880-(x^11)/39916800+%
    (x^13)/6227020800-(x^15)/\fpeval{fact(15)}+(x^17)/\fpeval{fact(17)}} % n=17
\psplot[linecolor=red]{0}{9.1}{x-(x^3)/6+(x^5)/120-(x^7)/5040+(x^9)/362880-(x^11)/39916800+%
    (x^13)/6227020800-(x^15)/\fpeval{fact(15)}+%
    (x^17)/\fpeval{fact(17)}-(x^19)/\fpeval{fact(19)}} % n=19
\psplot{0}{10.1}{x-(x^3)/6+(x^5)/120-(x^7)/5040+(x^9)/362880-(x^11)/39916800+%
    (x^13)/6227020800-(x^15)/\fpeval{fact(15)}+%
    (x^17)/\fpeval{fact(17)}-(x^19)/\fpeval{fact(19)}+(x^21)/\fpeval{fact(21)}} % n=21
\endpsclip
%%%
\uput[-90](3,-2){$n=3$}
\uput[-90](4.2,-2){$n=7$}
\uput[-90](6,-2){$n=11$}
\uput[-90](7.7,-2){$n=15$}
\uput[-90](9.2,-2){$n=19$}
\uput[-90](10.5,-1){$y=sin\,x$}
%%%
\uput[90](4,2){$n=5$}
\uput[90](5.3,2){$n=9$}
\uput[90](6.6,2){$n=13$}
\uput[90](8,2){$n=17$}
\uput[90](9.8,2){$n=21$}
%%
\psaxes[showorigin=false,arrowinset=.2,arrowsize=.2,%
        xsubticks=2,xsubticksize=1,ticksize=0 7pt,Dx=2]%
{->}(0,0)(-0.9,-2.5)(11,2.5)[$x$,-90][$y$,180]
        \end{pspicture}
\end{document}

How to write Taylor's series of y=sinx in PSTricks?

It mean that the \psplot command is only written once as following:

\psRegisterList of color...
\definition of (1) (see image)
\multido{\iA=3+2}{10}{\psplot...}

Probably useful: https://tex.stackexchange.com/a/19776/87876 — Display Name, Oct 14 '19 at 14:34

user187802 · Accepted Answer · 2019-10-15T06:02:56.643

8

I leave the simple color setting to you. It is much more easier to plot the function in pure PostScript code. Building a sum is then very easy:

\documentclass[pstricks,border=12pt]{standalone}
\usepackage{pst-plot,pst-tools}
\begin{document}

\begin{pspicture}[plotpoints=500](-1,-3)(12,3)
\psclip{\psframe[fillstyle=solid,fillcolor=white,linestyle=none](-1,-2)(11,2)}
\multido{\iA=1+1}{10}{%
  \psplot{0}{10}[/iA \iA\space def ]{
      /yVal x def  % value x^1/1!
      1 1 iA % i=1,...,n
        { /iter exch def % save loop variable (is on stack)
          iter dup add 1 add % 2n + 1 
          dup                % 2n+1 2n+1
          x exch             % 2n+1 x 2n+1
          exp                % 2n+1 x^(2n+1)
          exch               % x^(2n+1) 2n+1
          factorial div -1 iter exp mul 
          yVal add /yVal exch def } for
      yVal    
  }%
}
\psplot[algebraic]{0}{11}{sin(x)}
\endpsclip
    %%%
\uput[-90](3,-2){$n=3$}   \uput[-90](4.2,-2){$n=7$}
\uput[-90](6,-2){$n=11$}  \uput[-90](7.7,-2){$n=15$}
\uput[-90](9.2,-2){$n=19$}\uput[-90](10.5,-1){$y=\sin x$}
    %%%
\uput[90](4,2){$n=5$}     \uput[90](5.3,2){$n=9$}
\uput[90](6.6,2){$n=13$}  \uput[90](8,2){$n=17$}
\uput[90](9.8,2){$n=21$}    %%
\psaxes[showorigin=false,arrowinset=.2,arrowsize=.2,%
    xsubticks=2,xsubticksize=1,ticksize=0 7pt,Dx=2]%
    {->}(0,0)(-0.9,-2.5)(11,2.5)[$x$,-90][$y$,180]
\end{pspicture}
\end{document}

edited Oct 15 '19 at 06:02

answered Oct 14 '19 at 15:34

user187802

16,850

So, i have a question as following: in PS, the maximum of value of n is ? As in image, n is infinity ... – Oct 14 '19 at 15:54
The problem is the factorial operator. I suppose that 35! is the biggest possible value – user187802 Oct 14 '19 at 16:29
Excellent. Can you edit, please, $y=\sin x$ instead of $y=sin,x$? Peraphs is better visually. – Sebastiano Oct 14 '19 at 21:20
@user187802 Do you know about xint package? As you think, can I reproduce my code with more shorter syntaxs and 35! is NOT the biggest possible value ? – Oct 15 '19 at 02:37
Your have to build the sum, shorter is not possible – user187802 Oct 15 '19 at 06:00
@user187802 Hello, :), off topic ... Can we combine python with PSTricks for drawing several things that needed calculation of big numbers (IEEE floating-point numerics)? – Oct 19 '19 at 11:26
not on PostScript level. You have to write an own Sum macro. Not easy but possible – user187802 Oct 19 '19 at 11:43

How to write Taylor's series of sinx in PSTricks?

1 Answers1