# Important common mathematical and technical symbols taken from ISO
# 31-11 and other sources for education and engineering (including
# software documentation) to be added in addition to the ISO 8859 1-4
# repertoires. This subset does not attempt to cover any mathematical
# symbol that has ever been used in any special field, but only the
# most common ones that are sufficient for >90% of mathematical
# communication and that are nicely displayable in low-res fixed-width
# fonts. Full coverage is left to special software such as AMSTeX.

#########################################################################
# ISO 31-11 symbols that are probably known by every high-school student
#########################################################################

# these denote the sets of complex, natural, rational, real, and
# integer numbers

2102 # DOUBLE-STRUCK CAPITAL C           
2115 # DOUBLE-STRUCK CAPITAL N           
211A # DOUBLE-STRUCK CAPITAL Q           
211D # DOUBLE-STRUCK CAPITAL R           
2124 # DOUBLE-STRUCK CAPITAL Z           

# general indication of direction and used to describe the domain and range
# sets of functions (all directions included for use in commutative diagrams)

2190 # LEFTWARDS ARROW                   
2191 # UPWARDS ARROW                     
2192 # RIGHTWARDS ARROW                  
2193 # DOWNWARDS ARROW                   
2194 # LEFT RIGHT ARROW                  
2195 # UP DOWN ARROW                     

# used to describe element mappings of functions (all four directions
# included for use in commutative diagrams)

21A4 # LEFTWARDS ARROW FROM BAR          
21A5 # UPWARDS ARROW FROM BAR            
21A6 # RIGHTWARDS ARROW FROM BAR         
21A7 # DOWNWARDS ARROW FROM BAR          

# implication symbol

21D0 # LEFTWARDS DOUBLE ARROW            
21D1 # UPWARDS DOUBLE ARROW              
21D2 # RIGHTWARDS DOUBLE ARROW           
21D3 # DOWNWARDS DOUBLE ARROW            
21D4 # LEFT RIGHT DOUBLE ARROW           
21D5 # UP DOWN DOUBLE ARROW              

# common logic symbols

2227 # LOGICAL AND                       
2228 # LOGICAL OR                        
2200 # FOR ALL                           
2203 # THERE EXISTS                      
2204 # THERE DOES NOT EXIST              

# common set theory symbols

2229 # INTERSECTION                      
222A # UNION                             
22C2 # N-ARY INTERSECTION
22C3 # N-ARY UNION
2201 # COMPLEMENT                        
2205 # EMPTY SET                         
2208 # ELEMENT OF                        
2209 # NOT AN ELEMENT OF                 
220B # CONTAINS AS MEMBER                
220C # DOES NOT CONTAIN AS MEMBER        
2282 # SUBSET OF                         
2283 # SUPERSET OF                       
2284 # NOT A SUBSET OF                   
2285 # NOT A SUPERSET OF                 
2286 # SUBSET OF OR EQUAL TO             
2287 # SUPERSET OF OR EQUAL TO           
2288 # NEITHER A SUBSET OF NOR EQUAL TO  
2289 # NEITHER A SUPERSET OF NOR EQUAL TO
228A # SUBSET OF WITH NOT EQUAL TO
228B # SUPERSET OF WITH NOT EQUAL TO
27E8 # MATHEMATICAL LEFT ANGLE BRACKET
27E9 # MATHEMATICAL RIGHT ANGLE BRACKET

# common number theory symbols

2261 # IDENTICAL TO                      
2262 # NOT IDENTICAL TO
2224 # DOES NOT DIVIDE            # for DIVIDES use VERTICAL BAR

# common geometry symbols

2225 # PARALLEL TO                # also for vector norm
2226 # NOT PARALLEL TO
221F # RIGHT ANGLE
2221 # MEASURED ANGLE
25A1 # WHITE SQUARE               # also d'Alambertian symbol
25B3 # WHITE UP-POINTING TRIANGLE


######################################################
# other common math symbols, all defined in ISO 31-11
######################################################

2032 # PRIME
2033 # DOUBLE PRIME
2034 # TRIPLE PRIME
2202 # PARTIAL DIFFERENTIAL              
2206 # INCREMENT                         
2207 # NABLA                             
2212 # MINUS SIGN                 # usually longer than a HYPHEN
2213 # MINUS-OR-PLUS SIGN                
2218 # RING OPERATOR
221D # PROPORTIONAL TO                   
221E # INFINITY                          
223C # TILDE OPERATOR             # centered, while TILDE is high
2243 # ASYMPTOTICALLY EQUAL TO
2245 # APPROXIMATELY EQUAL TO            
2248 # ALMOST EQUAL TO                   
2249 # NOT ALMOST EQUAL TO               
2259 # ESTIMATES                  # = corresponds to
2260 # NOT EQUAL TO
2264 # LESS-THAN OR EQUAL TO             
2265 # GREATER-THAN OR EQUAL TO          
226A # MUCH LESS-THAN                    
226B # MUCH GREATER-THAN                 
22C5 # DOT OPERATOR

# the following might look funny in low-res fonts.

222B # INTEGRAL
222E # CONTOUR INTEGRAL
220F # N-ARY PRODUCT              # larger than GREEK CAPITAL LETTER PI
2211 # N-ARY SUMMATION            # larger than GREEK CAPITAL LETTER SIGMA

# characters from ISO 31-11 that are not included here, because they are
# problematic to implement nicely in low-res fixed-width fonts

# 225D # EQUAL TO BY DEFINITION   # write := instead


##############################################################
# other common math/tech symbols not (yet) found in ISO 31-11
##############################################################

# used to write an equation that is not yet proved

225F # QUESTIONED EQUAL TO

# Used in technical drawings and on product descriptions. Note that
# DIAMETER SIGN is an exact circle while EMPTY SET is often a digit zero,
# both with a stroke.

2300 # DIAMETER SIGN                     

# The following are very well known among computer scientists and
# are likely to be used in computer software documentation and in
# source code comments

# up and down rounding operators (introduced in 1963 by Iverson, these
# are basically SQUARE BRACKETs with one horizontal stroke removed, see
# Knuth's TAOCP for details)

2308 # LEFT CEILING                      
2309 # RIGHT CEILING                     
230A # LEFT FLOOR                        
230B # RIGHT FLOOR                       

# CIRCLED PLUS is popular for the XOR operator, it and CIRCLED TIMES
# are also frequently used as generic group operators. Assertion and
# models are very common symbols in formal theorem proof systems.
# DOWN TACK and UP TACK denote the top and bottom element in a lattice,
# UP TACK also denotes the undefined value of a function.

2295 # CIRCLED PLUS                      
2297 # CIRCLED TIMES
22A6 # ASSERTION                        
22A7 # MODELS
22A4 # DOWN TACK
22A5 # UP TACK                    # also perpendicular symbol

###############################################################
# The greek letters commonly used by mathematicians (from Tex)
###############################################################

0393 # GREEK CAPITAL LETTER GAMMA
0394 # GREEK CAPITAL LETTER DELTA
0398 # GREEK CAPITAL LETTER THETA
039B # GREEK CAPITAL LETTER LAMDA
039E # GREEK CAPITAL LETTER XI
03A0 # GREEK CAPITAL LETTER PI
03A3 # GREEK CAPITAL LETTER SIGMA
03A5 # GREEK CAPITAL LETTER UPSILON
03A6 # GREEK CAPITAL LETTER PHI
03A8 # GREEK CAPITAL LETTER PSI
03A9 # GREEK CAPITAL LETTER OMEGA

03B1 # GREEK SMALL LETTER ALPHA
03B2 # GREEK SMALL LETTER BETA
03B3 # GREEK SMALL LETTER GAMMA
03B4 # GREEK SMALL LETTER DELTA
03B5 # GREEK SMALL LETTER EPSILON
03B6 # GREEK SMALL LETTER ZETA
03B7 # GREEK SMALL LETTER ETA
03B8 # GREEK SMALL LETTER THETA
03B9 # GREEK SMALL LETTER IOTA
03BA # GREEK SMALL LETTER KAPPA
03BB # GREEK SMALL LETTER LAMDA
03BC # GREEK SMALL LETTER MU
03BD # GREEK SMALL LETTER NU
03BE # GREEK SMALL LETTER XI
03C0 # GREEK SMALL LETTER PI
03C1 # GREEK SMALL LETTER RHO
03C2 # GREEK SMALL LETTER FINAL SIGMA
03C3 # GREEK SMALL LETTER SIGMA
03C4 # GREEK SMALL LETTER TAU
03C5 # GREEK SMALL LETTER UPSILON
03C6 # GREEK SMALL LETTER PHI
03C7 # GREEK SMALL LETTER CHI
03C8 # GREEK SMALL LETTER PSI
03C9 # GREEK SMALL LETTER OMEGA

03D1 # GREEK THETA SYMBOL
03D5 # GREEK PHI SYMBOL
03D6 # GREEK PI SYMBOL
03F1 # GREEK RHO SYMBOL
