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added lectures 1-6
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@SanyaKovylin
SanyaKovylin committed Sep 23, 2024
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Binary file added Lectures/1_Semester/Algebra_and_Geometry/2024_Stepin/2024_Stepin.zip
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23 changes: 23 additions & 0 deletions Lectures/1_Semester/Algebra_and_Geometry/2024_Stepin/images/Pack/cmarrows/README
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CMARROWS
========

This MetaPost package contains macros to draw arrows and braces in the
Computer Modern style.

See the documentation file cmarrows.pdf for more information on how to
use the package.

The files of this package consists of

README cmarrows.mp cmarrows.pdf rgbx0009.mp rgbx0016.mp
rgbx0020.mp rgbx0025.mp sgbx0008.mp sgbx0010.mp sgbx0011.mp
sgbx0012.mp sgbx0013.mp sgbx0014.mp sgbx0015.mp sgbx0017.mp
sgbx0018.mp sgbx0019.mp sgbx0021.mp sgbx0022.mp sgbx0023.mp
sgbx0024.mp tgbx0000.mp tgbx0001.mp tgbx0002.mp tgbx0003.mp
tgbx0004.mp tgbx0005.mp tgbx0006.mp tgbx0007.mp tgbx0027.mp

This material is subject to the LaTeX Project Public License. See
http://www.ctan.org/tex-archive/help/Catalogue/licenses.lppl.html for
the details of that license.

/Tommy Ekola <[email protected]>
69 changes: 69 additions & 0 deletions Lectures/1_Semester/Algebra_and_Geometry/2024_Stepin/images/Pack/cmarrows/cmarrows.mp
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%% cmarrows.mp
%% Copyright 2006 Tommy Ekola <[email protected]>
%
% This work may be distributed and/or modified under the conditions of
% the LaTeX Project Public License, either version 1.3 of this license
% or (at your option) any later version. The latest version of this
% license is in http://www.latex-project.org/lppl.txt
%
% This work has the LPPL maintenance status `maintained'. The Current
% Maintainer of this work is Tommy Ekola. The Base Interpreter is
% MetaPost.

if known cmarrows_fileversion: endinput fi;
string cmarrows_fileversion;
cmarrows_fileversion := "2006/12/18, v0.9";
message "Loading cmarrows " & cmarrows_fileversion;

vardef setup_cmarrows(text argument_list) =

save sfile;
string sfile;

save arrow_name, brace_name, parameter_file, macro_name;
string arrow_name, brace_name, parameter_file, macro_name;

argument_list;

if not known arrow_name:
arrow_name := brace_name;
fi

if arrow_name="Bigbrace" : sfile = "tgbx0001.mp";
elseif arrow_name="Biggbrace" : sfile = "tgbx0002.mp";
elseif arrow_name="bigbrace" : sfile = "tgbx0003.mp";
elseif arrow_name="biggbrace" : sfile = "tgbx0004.mp";
elseif arrow_name="extensiblebrace" : sfile = "tgbx0005.mp";
elseif arrow_name="parallelarrows" : sfile = "tgbx0006.mp";
elseif arrow_name="twoheadarrow" : sfile = "tgbx0007.mp";
elseif arrow_name="twowayoldarrow" : sfile = "sgbx0008.mp";
elseif arrow_name="paralleloppositearrows": sfile = "rgbx0009.mp";
elseif arrow_name="twowayarrow" : sfile = "sgbx0010.mp";
elseif arrow_name="twowaydoublearrow" : sfile = "sgbx0011.mp";
elseif arrow_name="hookleftarrow" : sfile = "sgbx0012.mp";
elseif arrow_name="hookrightarrow" : sfile = "sgbx0013.mp";
elseif arrow_name="doublearrow" : sfile = "sgbx0014.mp";
elseif arrow_name="lefthalfarrow" : sfile = "sgbx0015.mp";
elseif arrow_name="paralleloppositerighthalfarrows": sfile = "rgbx0016.mp";
elseif arrow_name="mapstoarrow" : sfile = "sgbx0017.mp";
elseif arrow_name="oldtexarrow" : sfile = "sgbx0018.mp";
elseif arrow_name="righthalfarrow" : sfile = "sgbx0019.mp";
elseif arrow_name="paralleloppositelefthalfarrows" : sfile = "rgbx0020.mp";
elseif arrow_name="shortaxisarrow" : sfile = "sgbx0021.mp";
elseif arrow_name="texarrow" : sfile = "sgbx0022.mp";
elseif arrow_name="tailarrow" : sfile = "sgbx0023.mp";
elseif arrow_name="tripplearrow" : sfile = "sgbx0024.mp";
elseif arrow_name="paralleloppositerightarrows": sfile = "rgbx0025.mp";
elseif arrow_name="paren" : sfile = "tgbx0027.mp";
else : errmessage "unknown options";
fi

expandafter save scantokens ("setup_" & arrow_name);

scantokens ("input " & sfile);

scantokens ("setup_" & arrow_name & "(" &
ditto & parameter_file & ditto & "," &
ditto & macro_name & ditto & ");" );

enddef;
236 changes: 236 additions & 0 deletions Lectures/1_Semester/Algebra_and_Geometry/2024_Stepin/images/Pack/cmarrows/rgbx0009.mp
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%% rgbx0009.mp
%% Copyright 2006 Tommy Ekola <[email protected]>
%
% This work may be distributed and/or modified under the conditions of
% the LaTeX Project Public License, either version 1.3 of this license
% or (at your option) any later version. The latest version of this
% license is in http://www.latex-project.org/lppl.txt
%
% This work has the LPPL maintenance status `maintained'. The Current
% Maintainer of this work is Tommy Ekola. The Base Interpreter is
% MetaPost.

vardef setup_paralleloppositearrows (expr source_file, cmdname) =

scantokens ("input tgbx0000");

scantokens ("input " & source_file);

expandafter def scantokens cmdname expr p =
scantokens (cmdname & "__rgbxww")(p)
enddef;

expandafter vardef scantokens (cmdname & "__rgbxww " & "(expr apth) " &
"text text_ = " &

"save math_spread, x_height, u, rule_thickness, bar, math_axis," &
" asc_height, eps, fudge, crisp, hair;" &

"math_spread :=" & decimal math_spread & ";" &
"x_height# :=" & decimal x_height# & ";" &
"u# :=" & decimal u# & ";" &
"rule_thickness# :=" & decimal rule_thickness# & ";" &
"bar# :=" & decimal bar# & ";" &
"math_axis# :=" & decimal math_axis# & ";" &
"asc_height# :=" & decimal asc_height# & ";" &
"eps :=" & decimal eps & ";" &
"fudge :=" & decimal fudge & ";" &
"crisp# :=" & decimal crisp# & ";" &
"hair# :=" & decimal hair# & ";")

save prevpen;
prevpen:=savepen;

save x,y;
numeric x[], x[]', x[]l, x[]'l, x[]r, x[]'r,
y[], y[]', y[]l, y[]'l, y[]r, y[]'r;
save spread, w;
numeric spread, w;

if crisp#>fudge*hair#:
crisp#:=fudge*hair#;
fi
pickup if crisp#=0: nullpen else: pencircle scaled crisp# fi;

spread = math_spread[.45x_height#, .55x_height#];
w = 18u#;

penpos1(rule_thickness#, 90); penpos2(rule_thickness#, 90);
penpos3(bar#, 0); penpos4(bar#, 0);
y0=y1=y2=math_axis#; x1-.5rule_thickness#=u#; rt x0=w-u#;
y3-y0=y0-y4=.24asc_height#+eps;
x3=x4=x0-3u#-eps;
penpos5(bar#, angle(z4-z0)); z5l=z0;
penpos6(bar#, angle(z3-z0)); z6l=z0;
z9=.381966[.5[z3,z4],z0];

save pp; path pp; pp = z4l{z9-z4}..z6r;
save t; numeric t; t = xpart(pp intersectiontimes ((0,y2l)--(w,y2l)));
x2=xpart point t of pp;

% Path macros

save parallellineright;
vardef parallellineright expr pppp =
save s, stp;
numeric s, stp; stp:=(arclength pppp) div 5pt;
if stp=0: stp:=1; fi
stp:=(arclength pppp)/stp;

if stp>0:
for s=0 step stp until arclength pppp - stp:
point (arctime s of pppp) of pppp +
(.24asc_height#+eps)*(unitvector direction (arctime s of pppp)
of pppp rotated 90)
{direction (arctime s of pppp) of pppp}..
endfor
{direction (length pppp) of pppp}
point (length pppp) of pppp +
(.24asc_height#+eps)*(unitvector direction (length pppp)
of pppp rotated 90)
fi
enddef;

save parallellineleft;
vardef parallellineleft expr pppp =
save s, stp;
numeric s, stp; stp:=(arclength pppp) div 5pt;
if stp=0: stp:=1; fi
stp:=(arclength pppp)/stp;

if stp>0:
for s=0 step stp until arclength pppp - stp:
point (arctime s of pppp) of pppp -
(.24asc_height#+eps)*(unitvector direction (arctime s of pppp)
of pppp rotated 90)
{direction (arctime s of pppp) of pppp}..
endfor
{direction (length pppp) of pppp}
point (length pppp) of pppp -
(.24asc_height#+eps)*(unitvector direction (length pppp)
of pppp rotated 90)
fi
enddef;

save mapto, n;
vardef mapto(text t) =
hide(numeric n; n:=0;
numeric x,x_[],y,y_[];
for z=t: z_[incr n]:=z; endfor;
transform T;
z_2 = z_1 transformed T;
z_4 = z_3 transformed T;
z_6 = z_5 transformed T;)
T
enddef;

% Macros for drawing the arrow head

save pp; path pp; pp = z4l{z9-z4}..z6r;
save pq; path pq; pq = z0..{z4-z9}z4r;
save right_texarrowhead;
vardef right_texarrowhead(expr T,s) =
(subpath(0, xpart (pq intersectiontimes
(point s of pp -- point s of pp + (2rule_thickness#,0))))
of pq--subpath(s,t) of pp--z2l) transformed T
enddef;

save qq; path qq; qq = z3l{z9-z3}..z5r;
save qp; path qp; qp = z3r{z9-z3}..z0;
save left_texarrowhead;
vardef left_texarrowhead(expr T, s) =
(z2r--subpath(t,s) of qq
--subpath(xpart ( qp intersectiontimes
(point s of qq -- point s of qq + (2rule_thickness#,0)))
,length qp) of qp) transformed T
enddef;

% Draw the arrows. First the left arrow and then the right arrow

save pa, pb, T, tt, ttt;
save f,s;

save p_left; path p_left; p_left := parallellineleft apth;
save p_right; path p_right; p_right := parallellineright apth;

for ppp = reverse p_left, p_right:
transform T;
numeric tt; tt := arctime(arclength ppp - (x0-x9)) of ppp;
numeric ttt; ttt := arctime(arclength ppp - (x0-x2)) of ppp;

% Draw the right half of the arrow head

if arclength ppp = 0:
T:=identity shifted (point (length ppp) of ppp - z0);
elseif arclength ppp < x0-x3l:
T:=identity rotatedaround(z0,angle (direction (length ppp) of ppp))
shifted (point (length ppp) of ppp - z0);
else:
T:=mapto(z0,
point (length ppp) of ppp,
z2,
point ttt of ppp,
z9-(0,3rule_thickness#),
point tt of ppp - 3rule_thickness#
*(unitvector (direction tt of ppp)
rotated 90));
fi

vardef f(expr s) =
length(point s of (pp transformed T) - point tt of ppp)
< length(point 0 of pp - z9)
enddef;

if f(0) or (arclength ppp < x0-x3l): s := 0;
else: s := solve f(length pp, 0);
fi

path pa;
pa := right_texarrowhead(T,s);

% Draw the left part of the arrow head

if arclength ppp = 0:
T:=identity shifted (point (length ppp) of ppp - z0);
elseif arclength ppp < x0-x3l:
T:=identity rotatedaround(z0,angle (direction (length ppp) of ppp))
shifted (point (length ppp) of ppp - z0);
else:
T:=mapto(z0,
point (length ppp) of ppp,
z2,
point ttt of ppp,
z9+(0,3rule_thickness#),
point tt of ppp + 3rule_thickness#
*(unitvector (direction tt of ppp)
rotated 90));
fi

vardef f(expr s) =
length(point s of (qq transformed T) - point tt of ppp)
< length(point 0 of qq - z9)
enddef;

if f(0) or (arclength ppp < x0-x3l): s := 0;
else: s := solve f(length qq, 0);
fi

path pb;
pb := left_texarrowhead(T,s);

filldraw pa--pb--cycle withpen nullpen text_;

% Draw the path

if arclength ppp > x0-x2:
draw subpath(0,ttt) of ppp withpen pencircle scaled rule_thickness#
text_;
fi

endfor

pickup prevpen;

enddef;

enddef;
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