ebigop.mf

Concrete_Mathematics_2nd_Ed_TeX_Source_Code

% The Computer Modern Math-Extension family (by D. E. Knuth, 1979--1985)
% Special version for characters redesigned to blend with Euler

% This is the driver file for EUEX fonts, before AMS screwed it up
font_coding_scheme:="euler substitutions only";
mode_setup; font_setup;

def t_ = transformed currenttransform enddef; 

def bulb(suffix $,$$,$$$) =
 z$$$r=z$$r;
pair trueup; (z5+trueup)t_=z5+(0,y$$r-y$r);
 path_.l:=z$l{x$$r-x$r,0}...{trueup}z$$l;
{{less_tense;
 filldraw path_.l--z$$r{-trueup}...{x$r-x$$r,0}z$r--cycle}}; % link
 path_.r:=z$$$l{-trueup}..z$$$r{trueup}; % near-circle
 filldraw subpath(0,xpart(path_.r intersectiontimes path_.l)) of path_.r
  --z$$r{trueup}..cycle; % bulb
 enddef;

% characters modified from BIGOP
charlist oct"110": oct"111";  % contour integral signs
charlist oct"122": oct"132";  % integral signs
charlist oct"120": oct"130";  % summation signs
charlist oct"121": oct"131";  % product signs
charlist oct"140": oct"141";  % coproduct signs

% characters modified from BIGDEL (braces in different positions)
charlist oct"010": oct"012": oct"014": oct"016": oct"070";  % left braces
charlist oct"011": oct"013": oct"015": oct"017": oct"071";  % right braces
extensible oct"070": oct"070",oct"074",oct"072",oct"076";  % left brace
extensible oct"071": oct"071",oct"075",oct"073",oct"076";  % right brace
extensible oct"072": oct"070",0,oct"072",oct"076";  % sharp left parenthesis
extensible oct"073": oct"071",0,oct"073",oct"076";  % sharp right parenthesis
extensible oct"076": 0,0,0,oct"076";  % brace extension modules only
extensible oct"100": oct"070",0,oct"073",oct"076";  % left moustache
extensible oct"101": oct"071",0,oct"072",oct"076";  % right moustache
% the horizontal braces are included too
heavy_rule_thickness:=bold+dw; % this is the main change: big braces not so dark
heavy_rule_thickness#:=curve#+(curve#-stem#);

% arrows (taken from SYMBOL, SYM, and ROMSS, with longer and thicker arrowheads)
bar:=rule_thickness;  % this makes the arrowheads thicker
% the half arrows from ROMSS are moved to different font positions
% infinity (taken from SYMBOL, made heavier)

cmchar "\textstyle integral sign";
beginchar(oct"122",12u#,0,100/54dh#);
italcorr 0.5u#; % \TeX\ kerning between upper limit and lower limit
adjust_fit(-1u#,-1u#-ic#); pickup fine.nib;
pos1(dot_size,0); pos2(.75[hair,stem],0); pos3(vair,90); pos4(stem,180);
pos5(.4[stem,curve],180); pos5'(.4[stem,curve],0); z5'=z5; pos6(stem,0);
pos7(vair,-90); pos8(.75[hair,stem],-180); pos9(dot_size,-180);
rt x1r=hround(w-u); x9=w-x1; x7=w-x3=3u;
x5=.5[x4,x6]; x4-x6=1.2u; lft x5r=hround(.5w-.5stem);
top y3r=0; bot y7r=-d; y9-.5(.4[stem,curve])=vround(top y7l+.25(.4[stem,curve]));
y3-y1=y9-y7; y5=.5[y3,y7]=.5[y4,y6]; y4-y6=.6(y3-y7);
transform skewit;
 z5 transformed skewit=z5; (z5+right) transformed skewit = z5+right;
 z3 transformed skewit=z3-u*right;
skewit:=skewit transformed currenttransform;
save currenttransform; transform currenttransform; currenttransform:=skewit;
bulb(3,2,1); bulb(7,8,9);  % bulbs
filldraw stroke z3e{left}...z4e{(z5e-z4e)xscaled 1.1}
 ..tension atleast 1 and atleast .8..{z5-z4}z5e;  % upper stem
filldraw stroke z5'e{z6-z5}..tension atleast.8 and atleast 1
 ..{(z6e-z5'e)xscaled 1.1}z6e...{left}z7e;  % lower stem
penlabels(1,2,3,4,5,6,7,8,9); endchar;

cmchar "\displaystyle integral sign";
beginchar(oct"132",18u#,0,200/54dh#);
italcorr 2u#; % \TeX\ kerning between upper limit and lower limit
adjust_fit(-4u#,-4u#-ic#); pickup fine.nib;
numeric bulb_size, max_size;
bulb_size=hround(.8[stem,curve]); max_size=hround(bold+.2dw);
pos1(bulb_size,0); pos2(.75[hair,stem],0); pos3(vair,90); pos4(.4[stem,curve],180);
pos5(max_size,180); pos5'(max_size,0); z5'=z5; pos6(.4[stem,curve],0);
pos7(vair,-90); pos8(.75[hair,stem],-180); pos9(bulb_size,-180);
rt x1r=hround(w-u); x9=w-x1; x7=w-x3=3u;
x5=.5[x4,x6]; x4-x6=4.8u; lft x5r=hround(.5w-.5stem);
top y3r=0; bot y7r=-d;
y9-.5bulb_size=vround(top y7l+.25bulb_size); y3-y1=y9-y7;
y5=.5[y3,y7]=.5[y4,y6]; y4-y6=.6(y3-y7);
transform skewit;
 z5 transformed skewit=z5; (z5+right) transformed skewit = z5+right;
 z3 transformed skewit=z3-4u*right;
skewit:=skewit transformed currenttransform;
save currenttransform; transform currenttransform; currenttransform:=skewit;
bulb(3,2,1); bulb(7,8,9);  % bulbs
filldraw stroke z3e{left}...z4e{(z5e-z4e)xscaled 1.1}
 ..tension atleast 1 and atleast .8..{z5-z4}z5e;  % upper stem
filldraw stroke z5'e{z6-z5}..tension atleast.8 and atleast 1
 ..{(z6e-z5'e)xscaled 1.1}z6e...{left}z7e;  % lower stem
penlabels(1,2,3,4,5,6,7,8,9); endchar;

cmchar "\textstyle contour integral sign";
beginchar(oct"110",12u#,0,100/54dh#);
italcorr 0.5u#; % \TeX\ kerning between upper limit and lower limit
adjust_fit(-u#,-u#-ic#); pickup fine.nib;
begingroup
pos1(dot_size,0); pos2(.75[hair,stem],0); pos3(vair,90); pos4(stem,180);
pos5(.4[stem,curve],180); pos5'(.4[stem,curve],0); z5'=z5; pos6(stem,0);
pos7(vair,-90); pos8(.75[hair,stem],-180); pos9(dot_size,-180);
rt x1r=hround(w-u); x9=w-x1; x7=w-x3=3u;
x5=.5[x4,x6]; x4-x6=1.2u; lft x5r=hround(.5w-.5stem);
top y3r=0; bot y7r=-d; y9-.5(.4[stem,curve])=vround(top y7l+.25(.4[stem,curve]));
y3-y1=y9-y7; y5=.5[y3,y7]=.5[y4,y6]; y4-y6=.6(y3-y7);
transform skewit;
 z5 transformed skewit=z5; (z5+right) transformed skewit = z5+right;
 z3 transformed skewit=z3-u*right;
skewit:=skewit transformed currenttransform;
save currenttransform; transform currenttransform; currenttransform:=skewit;
bulb(3,2,1); bulb(7,8,9);  % bulbs
filldraw stroke z3e{left}...z4e{(z5e-z4e)xscaled 1.1}
 ..tension atleast 1 and atleast .8..{z5-z4}z5e;  % upper stem
filldraw stroke z5'e{z6-z5}..tension atleast.8 and atleast 1
 ..{(z6e-z5'e)xscaled 1.1}z6e...{left}z7e;  % lower stem
endgroup;
pickup rule.nib; autorounded;
draw fullcircle scaled .5w shifted z5;  % contour
penlabels(1,2,3,4,5,6,7,8,9); endchar;

cmchar "\displaystyle contour integral sign";
beginchar(oct"111",18u#,0,200/54dh#);
italcorr 2u#; % \TeX\ kerning between upper limit and lower limit
adjust_fit(-4u#,-4u#-ic#); pickup fine.nib;
begingroup
numeric bulb_size, max_size;
bulb_size=hround(.8[stem,curve]); max_size=hround(bold+.2dw);
pos1(bulb_size,0); pos2(.75[hair,stem],0); pos3(vair,90); pos4(.4[stem,curve],180);
pos5(max_size,180); pos5'(max_size,0); z5'=z5; pos6(.4[stem,curve],0);
pos7(vair,-90); pos8(.75[hair,stem],-180); pos9(bulb_size,-180);
rt x1r=hround(w-u); x9=w-x1; x7=w-x3=3u;
x5=.5[x4,x6]; x4-x6=4.8u; lft x5r=hround(.5w-.5stem);
top y3r=0; bot y7r=-d;
y9-.5bulb_size=vround(top y7l+.25bulb_size); y3-y1=y9-y7;
y5=.5[y3,y7]=.5[y4,y6]; y4-y6=.6(y3-y7);
transform skewit;
 z5 transformed skewit=z5; (z5+right) transformed skewit = z5+right;
 z3 transformed skewit=z3-4u*right;
skewit:=skewit transformed currenttransform;
save currenttransform; transform currenttransform; currenttransform:=skewit;
bulb(3,2,1); bulb(7,8,9);  % bulbs
filldraw stroke z3e{left}...z4e{(z5e-z4e)xscaled 1.1}
 ..tension atleast 1 and atleast .8..{z5-z4}z5e;  % upper stem
filldraw stroke z5'e{z6-z5}..tension atleast.8 and atleast 1
 ..{(z6e-z5'e)xscaled 1.1}z6e...{left}z7e;  % lower stem
endgroup;
pickup rule.nib; autorounded;
draw fullcircle scaled .5w shifted z5;  % contour
penlabels(1,2,3,4,5,6,7,8,9); endchar;


cmchar "\textstyle summation sign";
beginchar(oct"120",19u#,0,10/6dh#);
adjust_fit(0,0); pickup tiny.nib;
numeric top_arm_thickness, bot_arm_thickness;
top_arm_thickness=Vround(.7[rule_thickness,bold]);
bot_arm_thickness=Vround(bold+dw);
lft x1l=hround 2.2u; x1l=x2l; lft x4l=hround u; x3l-x1l=4/11(w-2u)-1.2u;
top y1=0; bot y2=-top_arm_thickness-eps; bot y4=-d; y3=-.48d;
numeric alpha[]; alpha1=((x3l-x1l)++(y2-y3))/(y2-y3);
penpos1(alpha1*(curve-tiny),0); penpos2(alpha1*(curve-tiny),0);
penpos3(alpha1*(curve-tiny),0);
alpha2=diag_ratio(1,rule_thickness+dw-tiny,y3-y4,x3r-x4l);
penpos4(alpha2*(rule_thickness+dw-tiny),0);
z0=whatever[z2l,z3l]=z4l+whatever*(z3r-z4r);
filldraw z1l--z2l--z0--z4l--z4r--z3r--z2r--z1r--cycle;  % diagonals
pickup crisp.nib; pos5(top_arm_thickness,90); pos6(hair,0);
top y5r=0; x5=x1; rt x6r=hround(w-3u); y6=good.y(y5l)-eps;
{{save serifs; boolean serifs; serifs:=false;
arm(5,6,a,.45,-.25u);    % upper arm and beak
pos7(bot_arm_thickness,-90); pos8(hair,0);
bot y7r=-d; z7l=whatever[z4,z3]; x7r:=x4; x8=x6+1.5u; y8=good.y(y7l)+eps;
arm(7,8,b,.45,.25u);}};  % lower arm and beak
penlabels(0,1,2,3,4,5,6,7,8); endchar;

cmchar "\displaystyle summation sign";
beginchar(oct"130",26u#,0,14/6dh#); padded 1/6dh#;
adjust_fit(0,0); pickup tiny.nib;
numeric top_arm_thickness, bot_arm_thickness, thick_stem, thin_stem;
thick_stem=bold+4dw; thin_stem=rule_thickness+2dw;
top_arm_thickness=Vround(bold-.5dw);
bot_arm_thickness=Vround(bold+2.5dw);
lft x1l=hround 3u; x1l=x2l; lft x4l=hround u; x3l-x1l=4/11(w-2u)-2u;
top y1=0; bot y2=-top_arm_thickness-eps; bot y4=-d; y3=-.48d;
numeric alpha[]; alpha1=((x3l-x1l)++(y2-y3))/(y2-y3);
penpos1(alpha1*(thick_stem-tiny),0); penpos2(alpha1*(thick_stem-tiny),0);
penpos3(alpha1*(thick_stem-tiny),0);
alpha2=diag_ratio(1,thin_stem-tiny,y3-y4,x3r-x4l);
penpos4(alpha2*(thin_stem-tiny),0);
z0=whatever[z2l,z3l]=z4l+whatever*(z3r-z4r);
filldraw z1l--z2l--z0--z4l--z4r--z3r--z2r--z1r--cycle;  % diagonals
pickup crisp.nib; pos5(top_arm_thickness,90); pos6(hair,0);
top y5r=0; x5=x1; rt x6r=hround(w-4u); y6=good.y(y5l)-eps;
{{save serifs; boolean serifs; serifs:=false;
arm(5,6,a,.45,-.25u);  % upper arm and beak
pos7(bot_arm_thickness,-90); pos8(hair,0);
bot y7r=-d; z7l=whatever[z4,z3]; x7r:=x4; x8=x6+2.5u; y8=good.y(y7l)+eps;
arm(7,8,b,.45,.25u);}};  % lower arm and beak
penlabels(0,1,2,3,4,5,6,7,8); endchar;

cmchar "\textstyle product sign";
beginchar(oct"121",18.5u#,0,10/6dh#);
adjust_fit(.25u#,.25u#); pickup crisp.nib;
numeric heavy_stem,light_stem;
heavy_stem=hround(bold+dw); light_stem=rule_thickness;
pos1(heavy_stem,0);pos2(heavy_stem,0); pos1'(heavy_stem,0);pos2'(heavy_stem,0);
pos11(light_stem,90); pos12(light_stem,90); pos22(light_stem,90);
lft x11=hround u; x1l-x11=x2l-x12=x22-x2r=hround cap_jut;
x1=x1'=x2=x2';
top y1=0; bot y2=-d; y11r=y1; y12l=y22l=y2;
y11l-y1'=y2'-y12r=1.2bracket;
filldraw z1r--z11r--serif_arc(11l,1'l)--reverse serif_arc(12r,2'l)
 --z12l--z22l--serif_arc(22r,2'r)--cycle;  % left stem and serifs
pos3(heavy_stem,0);pos4(heavy_stem,0); pos3'(heavy_stem,0);pos4'(heavy_stem,0);
pos13(light_stem,90); pos14(light_stem,90); pos24(light_stem,90);
x3=x3'=x4=x4'=w-x1; x13=x14=w-x11; x24=w-x22;
y3=y13r=y1; y3'=y1'; y4'=y2'; y4=y14l=y24l=y2;
filldraw z3l--z13r--serif_arc(13l,3'r)--reverse serif_arc(14r,4'r)
 --z14l--z24l--serif_arc(24r,4'l)--cycle;  % right stem and serifs
filldraw stroke z11e--z13e; % bar
penlabels(1,1',2,2',3,3',4,4',11,12,13,14,22,24); endchar;

cmchar "\displaystyle product sign";
beginchar(oct"131",25.4u#,0,14/6dh#); padded 1/6dh#;
adjust_fit(0,0); pickup crisp.nib;
numeric heavy_stem,light_stem;
heavy_stem=hround(bold+5dw); light_stem=Vround(rule_thickness+dw);
pos1(heavy_stem,0);pos2(heavy_stem,0); pos1'(heavy_stem,0);pos2'(heavy_stem,0);
pos11(light_stem,90); pos12(light_stem,90); pos22(light_stem,90);
lft x11=hround u; x1l-x11=x2l-x12=x22-x2r=hround 1.6cap_jut;
x1=x1'=x2=x2';
top y1=0; bot y2=-d; y11r=y1; y12l=y22l=y2;
y11l-y1'=y2'-y12r=1.8bracket;
filldraw z1r--z11r--serif_arc(11l,1'l)--reverse serif_arc(12r,2'l)
 --z12l--z22l--serif_arc(22r,2'r)--cycle;  % left stem and serifs
pos3(heavy_stem,0);pos4(heavy_stem,0); pos3'(heavy_stem,0);pos4'(heavy_stem,0);
pos13(light_stem,90); pos14(light_stem,90); pos24(light_stem,90);
x3=x3'=x4=x4'=w-x1; x13=x14=w-x11; x24=w-x22;
y3=y13r=y1; y3'=y1'; y4'=y2'; y4=y14l=y24l=y2;
filldraw z3l--z13r--serif_arc(13l,3'r)--reverse serif_arc(14r,4'r)
 --z14l--z24l--serif_arc(24r,4'l)--cycle;  % right stem and serifs
filldraw stroke z11e--z13e; % bar
penlabels(1,1',2,2',3,3',4,4',11,12,13,14,22,24); endchar;

cmchar "\textstyle coproduct sign";
beginchar(oct"140",18.5u#,0,10/6dh#);
adjust_fit(.25u#,.25u#); pickup crisp.nib;
numeric heavy_stem,light_stem;
heavy_stem=hround(bold+dw); light_stem=rule_thickness;
pos1(heavy_stem,0);pos2(heavy_stem,0); pos1'(heavy_stem,0);pos2'(heavy_stem,0);
pos11(light_stem,-90); pos12(light_stem,-90); pos22(light_stem,-90);
lft x11=hround u; x1l-x11=x2l-x12=x22-x2r=hround cap_jut;
x1=x1'=x2=x2';
bot y1=-d; top y2=0; y11r=y1; y12l=y22l=y2;
y1'-y11l=y12r-y2'=1.2bracket;
filldraw z1r--z11r--serif_arc(11l,1'l)--reverse serif_arc(12r,2'l)
 --z12l--z22l--serif_arc(22r,2'r)--cycle;  % left stem and serifs
pos3(heavy_stem,0);pos4(heavy_stem,0); pos3'(heavy_stem,0);pos4'(heavy_stem,0);
pos13(light_stem,-90); pos14(light_stem,-90); pos24(light_stem,-90);
x3=x3'=x4=x4'=w-x1; x13=x14=w-x11; x24=w-x22;
y3=y13r=y1; y3'=y1'; y4'=y2'; y4=y14l=y24l=y2;
filldraw z3l--z13r--serif_arc(13l,3'r)--reverse serif_arc(14r,4'r)
 --z14l--z24l--serif_arc(24r,4'l)--cycle;  % right stem and serifs
filldraw stroke z11e--z13e; % bar
penlabels(1,1',2,2',3,3',4,4',11,12,13,14,22,24); endchar;

cmchar "\displaystyle coproduct sign";
beginchar(oct"141",25.4u#,0,14/6dh#); padded 1/6dh#;
adjust_fit(0,0); pickup crisp.nib;
numeric heavy_stem,light_stem;
heavy_stem=hround(bold+5dw); light_stem=Vround(rule_thickness+dw);
pos1(heavy_stem,0);pos2(heavy_stem,0); pos1'(heavy_stem,0);pos2'(heavy_stem,0);
pos11(light_stem,-90); pos12(light_stem,-90); pos22(light_stem,-90);
lft x11=hround u; x1l-x11=x2l-x12=x22-x2r=hround 1.6cap_jut;
x1=x1'=x2=x2';
bot y1=-d; top y2=0; y11r=y1; y12l=y22l=y2;
y1'-y11l=y12r-y2'=1.8bracket;
filldraw z1r--z11r--serif_arc(11l,1'l)--reverse serif_arc(12r,2'l)
 --z12l--z22l--serif_arc(22r,2'r)--cycle;  % left stem and serifs
pos3(heavy_stem,0);pos4(heavy_stem,0); pos3'(heavy_stem,0);pos4'(heavy_stem,0);
pos13(light_stem,-90); pos14(light_stem,-90); pos24(light_stem,-90);
x3=x3'=x4=x4'=w-x1; x13=x14=w-x11; x24=w-x22;
y3=y13r=y1; y3'=y1'; y4'=y2'; y4=y14l=y24l=y2;
filldraw z3l--z13r--serif_arc(13l,3'r)--reverse serif_arc(14r,4'r)
 --z14l--z24l--serif_arc(24r,4'l)--cycle;  % right stem and serifs
filldraw stroke z11e--z13e; % bar
penlabels(1,1',2,2',3,3',4,4',11,12,13,14,22,24); endchar;

cmchar "\big left curly brace";
beginchar(oct"010",9u#,rule_thickness#,2dh#-rule_thickness#);
adjust_fit(.75u#,.75u#); left_curly(hair,stem); endchar;

cmchar "\Big left curly brace";
beginchar(oct"012",10u#,rule_thickness#,3dh#-rule_thickness#);
adjust_fit(u#,u#); left_curly(rule_thickness,.3[stem,bold]); endchar;

cmchar "\bigg left curly brace";
beginchar(oct"014",11u#,rule_thickness#,4dh#-rule_thickness#);
adjust_fit(1.25u#,1.25u#); left_curly(rule_thickness+.2dw,.7[stem,bold]); endchar;

cmchar "\Bigg left curly brace";
beginchar(oct"016",11.5u#,rule_thickness#,5dh#-rule_thickness#);
adjust_fit(1.5u#,1.5u#); left_curly(rule_thickness+.4dw,bold); endchar;