@sp 1
@center file @file{cover} in directory @file{macro}
@example
@findex cover, draw the cover
cover       # draw the cover
@end example
 
@sp 1
@center file @file{default} in directory @file{macro}
@example
@findex batch, run the history buffer
batch       ## run the history buffer, but don't delete from history list
@findex bell, ring bell
bell        ## ring terminal bell
@findex calc, evaluate an expression
calc        ## evaluate an expression
@findex cd, change directories
cd          ## change directories
@findex compatible, macros compatible with Mongo
compatible  ## define macros to be compatible with Mongo
@findex declare, declare a vector $1
declare     ## declare a vector $1: declare name size
@findex del, delete last command
del         ## delete last command from history list
@findex del1, don't save on history
del1        ## don't put command on history list
@findex echo, write to terminal
echo        ## write to terminal
@findex ed, edit a macro
ed          ## edit a macro, or the previous one if no argument
@findex edit_all, edit history buffer
edit_all    ## edit history buffer
@findex emacs_all, edit history w. system editor.
emacs_all   ## edit the history list using an external editor.
emacs_hist  ## edit the history list using an external editor.
@findex error_handler, Handle interrupts
error_handler ## Handle @ctrl{C} interrupts
@findex execute, read and execute commands
execute     # read and execute an SM file of commands (1 per line)
@findex extend_history, Extend history buffer
extend_history # Extend history buffer to be of size $1
@findex for, C's for(;;) (see also while)
for         ## Repeat a macro while a condition is true, like C's for(;;). See also while
@findex gripe, complain to Robert
gripe       ## complain to Robert (Unix only)
h           ## get help
@findex head, print the top of a file
head        ## print the top of the current data (or other) file
@findex hm, help with edited macro
hm          ## help with the last macro edited
@findex hv, help with variable
hv          ## help with variable
@findex insert, insert text after line
insert      ## insert text after line $1
@findex load, load macros
load        ## load macros in default directory
@findex load2, load user macros
load2       ## load macros in (second) default directory
@findex ls, list macros
ls          ## list macros
@findex lsm, list macros in a default file
lsm         ## list macros in a file in default macro directory
@findex lsv, list variables
lsv         ## list variables
@findex q, check, then quit
q           ## check, then quit
re          ## macro read
@findex reset_ctype, Reset the default ctypes
reset_ctype # Reset the default ctypes (except "default")
@findex sav, save to a file $1
sav         ## save to a file $1, don't save from files `$mfiles'
@findex show, show current values
show        ## show current values of various things
@findex startup, startup macro
startup     ## macro invoked upon startup
@findex undef, undefine a variable
undef       ## undefine a variable
@findex undo, erase lines
undo        ## undo [macro] : undo (i.e. erase lines drawn by) macro $1
@findex unload, forget macros
unload      ## forget macros from a file
@findex unset, delete a vector
unset       # delete a vector
v           ## set verbosity
wr          ## macro write
@end example
 
@sp 1
@center file @file{demos} in directory @file{macro}
@example
square      # sum the Fourier series for a square wave, using $1 terms
colours     # draw a circle in a number of colours until ^C stops it
crings      # draw a set of coloured circles
@findex ctype, example of setting 256 colours
crings2     # draw a set of coloured circles using 256 shades of yellow
@findex gauss_convolve, convolve 2 Gaussians
gauss_convolve # convolve 2 Gaussians with sigmas $1 and $2
@findex grey_sincos, draw a grey scale image
grey_sincos # draw a grey scale image of a sin(x)cos(y) surface
scribble    # use cursor to draw a line, and then shade the interior
shading     # draw an ammonite
@findex sundial, draw a sundial
sundial     # draw a sundial, allowing for the analemma
@end example
 
@sp 1
@center file @file{fonts} in directory @file{macro}
@example
@findex fonts, draw the font table
fonts       # draw the font table
@findex TeX_defs, draw ``TeX'' defs
TeX_defs    # draw the ``TeX'' definitions
@findex make_char, help create new char
make_char   # help create a new character
@end example

@sp 1
@center file @file{fourier} in directory @file{macro}
@example
#
# Macros to make dealing with complex numbers for FFT's easier
# Assumes that complex vector `name' is represented by two vectors
# called name_r and name_i
#
@findex fft, see macro file fourier
fft         # Direct FFT: fft name name
ifft        # Inverse FFT: ifft name name
cadd        # Add complex numbers: $1 = $2 + $3
cdiv        # Divide complex numbers: $1 = $2/$3
cmod        # Modulus: $1 = |$2|
cmult       # Multiply complex numbers: $1 = $2*$3
csub        # Subtract complex numbers: $1 = $2 - $3
imag        # Imaginary part: $1 = Im($2)
real        # Real part: $1 = Re($2)
vcentre     # shift a vector so that its 0th element appears in the middle
vcenter     # an alias for vcentre
@end example

@sp 1
@center file @file{images} in directory @file{macro}
@example
@findex entropy, find entropy of an image
entropy # Find entropy of an image
@findex hist_equalise, histogram equalise an image
hist_equalise # Histogram equalise an image
@findex gamma, gamma correct an image
gamma       # Gamma correct an image
@end example

@sp 1
@center file @file{irregular} in directory @file{macro}
These macros were written by Gabor Toth, to whom many thanks. They enable
you to define an SM IMAGE from 3 vectors, (x,y) and the value z
@example
@findex irregular_image, Set IMAGE from x,y and z
irregular_image # Set IMAGE from 3 vectors (x,y) and z
@findex trigrid, Interpolate to the regular grid
trigrid     # Interpolate to the regular grid
@findex trigridtry, Demonstrate the use of trigrid
trigridtry  # Demonstrate the use of trigrid
@end example

@sp 1
@center file @file{math} in directory @file{macro}
@example
#
# Written by Daniel Pfenniger (PFENNIGER@@obs.unige.ch)
# `A&S' is Abramowitz & Stegun
#
@findex J0, Bessel function
J0          # Bessel func. J0(|x|), A&S, 9.4.1,.3
@findex Y0, Bessel function
Y0          # Bessel func. Y0(|x|), |x|>0, A&S, 9.4.2-3
@findex J1, Bessel function
J1          # Bessel func. J1(|x|), A&S, 9.4.4,.6
@findex Y1, Bessel function
Y1          # Bessel func. Y1(|x|), |x|>0, A&S, 9.4.5-6
@findex I0, Modified Bessel function
I0          # Modified Bessel func. I0(|x|), A&S, 9.8.1-2
@findex I1, Modified Bessel function
I1          # Modified Bessel func. I1(|x|), A&S, 9.8.3-4
@findex K0, Modified Bessel function
K0          # Modified Bessel func. K0(|x|), |x|>0, A&S, 9.8.5-6
@findex K1, Modified Bessel function
K1          # Modified Bessel func. K1(|x|), |x|>0, A&S, 9.8.7-8
@findex K, Complete elliptic integral
K           # Complete elliptic integral K(m), 0<=m<1, A&S 17.3.34
@findex E, Complete elliptic integral
E           # Complete elliptic integral E(m), 0<=m<=1, A&S 17.3.36
@findex fresnel, Fresnel integrals
fresnel     # Calculate the Fresnel integrals C, S, and F
@end example

@sp 1
@center file @file{matrix} in directory @file{macro}
@example
@findex matrix, Introduction to matrix utilities
matrix       # Introduction to matrix utilities
@findex mdeclare, declare a square matrix	
mdeclare     # declare $1 to be a $2x$2 square matrix	
@findex mdimen, print a matrix's dimension
mdimen       # print matrix $1's dimension
@findex mprint, print a matrix
mprint       # print the matrix $1  (given as $1_0 $1_1 etc -- see minv)
@findex madd, add matrices
madd         # set matrix $1 equal to $2+$3
@findex minv, invert a matrix
minv         # Quick matrix inversion, done in place.
@findex mset, set a matrix equal to another
mset         # set matrix $1 equal to $2
@findex mmult, multiply a matrix by a matrix
mmult        # set matrix $1 equal to $2*$3
@findex mmult_c, multiply a matrix by a constant
mmult_c      # set matrix $1 equal to $2*$3 where $3 is a scalar
@findex mmult_v, multiply a matrix by a vector
mmult_v      # set vector $1 equal to $2*$3 where $3 is a vector
@findex mmult_vT, multiply vector^T by a matrix
mmult_vT     # set vector $1 equal to $2^T*$3 where $2 is a vector
@findex mtrans, transpose a matrix
mtrans         # set matrix $1 equal to $2^T
@findex vprint, print a vector (like mprint)
mprint       # print the vector $1
@end example

@sp 1
@center file @file{mongo} in directory @file{macro}
(omitting those that are simply abbreviations, like @code{ang})
@example
@findex da, set data file
da          ## set data file
@findex dev, set device
dev         ## set device
dra         ## draw, accepting expressions
@findex ecolumn, make error_col error vector
ecolumn     ## define vector error_col as error vector
@findex end, quit
end         ## quit, not on history
@findex era, erase screen
era         ## erase screen, not on history
@findex lis, list history
lis         ## list history, not on history
hard        ## make a hardcopy of what you type (or get by history)
@findex hardcopy, close old device
hardcopy    ## close the old device and set dev type to 0
@findex hcopy, hardcopy of playback buffer
hcopy       ## hcopy [printer] [l1] [l2]: Make hardcopy of playback buffer
@findex hmacro, hardcopy of macro
hmacro      ## hmacro [macro] [printer]: make hardcopy of `macro' on `printer'
@findex identification, write id to plot
identification ## write an id to the top right hand corner of screen
@findex input, execute an Mongo file
input       ## execute an Mongo file
@findex mongo, make SM resemble Mongo
mongo       # make SM resemble Mongo as closely as possible
pcolumn     ## set point column (Mongo)
playback    ## define "all" from buffer, and run it
@findex read_all, read file including history
read_all    ## read a macro file, putting `all' onto the history buffer
@findex read_hist, read history from file
read_hist   ## read history from a file
@findex read_old, read an Mongo file
read_old    ## read an Mongo file onto the history buffer
rel         ## relocate, accepting expressions
@findex save_all, write history to file
save_all    ## write the playback list to a file (use sav instead)
terminal    ## device
@findex toplabel, put label at top of plot
toplabel    ## put label at top of plot
@findex xcolumn, read a column into x
xcolumn     ## read a column into vector x (Mongo)
@findex xlogarithm, take log of x
xlogarithm  ## take log of vector x (Mongo)
@findex ycolumn, read a column into y
ycolumn     ## read a column into y
@findex ylogarithm, take log of vector y
ylogarithm  ## take log of y
@end example
 
@sp 1
@center file @file{project} in directory @file{macro}
Miscellaneous projections (e.g. equal area). Contributed by Michael Strauss.
@example
@findex aitoff, convert l,b to Aitoff x,y
aitoff          #convert l and b to x y in Aitoff coordinates
@findex aitoff1, convert l,b to reverse Aitoff x,y
aitoff1         # Convert l and b to x y in reverse Aitoff coordinates
@findex aitoffdec, Draw line of constant dec
aitoffdec       # Draw a line of constant declination in an Aitoff plot
@findex aitoffdec1, draw line of constant dec
aitoffdec1      # Draw a line of constant declination in a reverse Aitoff plot
@findex aitoffgrid, Aitoff equal area grid
aitoffgrid      # Put up equal area grid in Aitoff
@findex aitoffgrid1, rev. Aitoff equal area grid
aitoffgrid1     # Puts up equal area grid in Aitoff. Reverse sense
@findex calc_lb, find r, l, b given x, y, z
calc_lb         # Calculates r, l and b given x, y, and z
@findex circle_exclude, draw excluded regions
circle_exclude  # After circleplot, draws regions excluded in latitude
@findex circlelabel, Draw axes for a circleplot
circlelabel     # Draw axes for a redshift circleplot
@findex circleplot, redshift points in circleplot
circleplot      # Plot redshift points; requires circlelabel
@findex eqgal, convert (ra, dec) to (l,b).
eqgal           # Usage: ra dec l b; Convert (ra, dec) to (l,b). 
@findex galeq, Convert (l,b) to (ra, dec)
galeq           # Usage: galeq l b ra dec. Convert (l,b) to (ra, dec)
@findex galgrid, Puts up equal area grid
galgrid         # Puts up equal area grid
@findex galplot, Usage: galplot ra dec l b
galplot         # Usage: galplot ra dec l b
@findex galpoints, points on an equal area grid
galpoints       # Plot points on an equal area grid; galpoints l b
@findex gstrans, supergalactic to galactic coords
gstrans         # Convert supergalactic to galactic coordinates
@findex hemiconvert, l b to x y for hemisphere
hemiconvert     # Convert from l b to x y for hemisphere plotting
@findex hemidec, line of dec on hemispheres
hemidec         # Draw a line of constant declination on a pair of
@findex hemiplot, equal area plot, two hemispheres
hemiplot        # Sky plot in two hemispheres, equal area
@findex invaitoff, convert Aitoff x, y to l, b
invaitoff       # Convert x y in Aitoff coordinates to l, b
@findex pielabel, Draw axes for a redshift pieplot
pielabel        # Draw axes for a redshift pieplot
@findex pieplot, Plot redshifts in pieplot
pieplot         # Plot redshift points; requires pielabel
@findex radtick, put tick marks on a radial axis
radtick         # Put tick marks on a radial axis
@findex sgtrans, galactic to supergalactic coords
sgtrans         # Convert galactic to supergalactic coordinates
@end example

@sp 1
@center file @file{stats} in directory @file{macro}
@example
@findex cgauss, cumulated Gaussian
cgauss      # evaluate a cumulated Gaussian distribution : N($mean,$sig)
@findex cuniform, cumulated uniform distribution
cuniform    # evaluate a cumulated uniform distribution, $mean,$sig
@findex chisq, return chi^2 distribution of vector
chisq       # Return chi^2 distribution of vector $1 with $2 dof 
@findex draw_KS, Draw a cumulated curve
draw_KS     # Draw a cumulated curve, for looking at KS statistics
@findex erfc, calculate erfc
erfc        # calculate complementary error function erfc($1)
@findex factorial, calculate a factorial
factorial   # Use Stirling's formula to calculate a factorial ($1)!
@findex gauss, evaluate Gaussian
gauss       # evaluate a Gaussian : N($mean,$sig)
@findex gaussdev, make N(0,1) variate
gaussdev    # return a N(0,1) random vector
@findex linfit, least squares fit for n parameters
linfit      # linear least squares fit for any number of parameters
@findex log_fac, calculate a log factorial
log_fac     # Use Stirling's formula to calculate a log factorial.
@findex lsq, least squares fit
lsq         # do a least squares fit to a set of vectors
@findex lsq2, least squares fit
lsq2        # do a least squares fit to a set of vectors, errors in x and y
@findex prob_chisq, probabilities for chi^2
prob_chisq  # probability of getting a given value of chi^2
@findex prob_KS, probabilities for K-S
prob_KS     # probability of getting a given value of the K-S statistic
@findex prob_wilc, probability for Wilcoxon
prob_wilc   # return probability in $$2 that x exceeds $1 from Wilcoxon
@findex rxy, Pearson Correlation Coefficient 
rxy         # find Pearson Correlation Coefficient for two vectors 
@findex smirnov1, 1 sided K-S statistic
smirnov1    # calculate 1 sided Kolmogorov-Smirnov statistic for vector
@findex smirnov2, 2 sided K-S statistic
smirnov2    # calculate 2 sided Kolmogorov-Smirnov statistic for vectors
@findex spear, Spearman correlation coefficient
spear       # calculate Spearman rank correlation coefficient for 2 vectors
@findex stats, calculate mean sigma ...
stats       # stats vector mean sigma kurtosis : calculate $mean $sigma etc
@findex find mean sigma ...
stats2      # stats vector weights mean sigma kurtosis
@findex stats_med, find median SIQR
stats_med   # stats_med vector median SIQR : calc $median $SIQR from vector
@findex wilcoxon, Wilcoxon statistic 
wilcoxon    # calculate Wilcoxon statistic for 2 vectors
@findex wlsq, weighted least squares
wlsq        # do a weighted least squares fit to a set of vectors
@end example

@sp 1
@center file @file{trigd} in directory @file{macro}
Equivalents for all SM trig functions, taking degree arguments. Names
add an extra `d' (e.g. sind)

@sp 1
@center file @file{utils} in directory @file{macro}
@example
alpha_poi   # alpha_poi x y z. Like poi x y, but use z as labels for points
@findex arc, arclength along curve
arc         # the arclength along the curve ($1,$2), e.g. set v=arc(x,y)
@findex arrow, draw arrow with cursor
arrow       # use the cursor to define an arrow.
@findex barhist, draw bar histogram
barhist     # draw a bar histogram
@findex boxit, draw box with cursor
boxit       # use the cursor to define a box, and draw it
@findex circle, draw a circle
circle      # draw a circle, centre ($1,$2) radius $3
@findex cumulate, find cumulative distribution
cumulate    # find the cumulative distribution of $1 in $2
@findex draw_arrow, draw an arrow
draw_arrow  # draw an arrow from ($1,$2) to ($3,$4)
@findex draw_box, draw a box
draw_box    # draw a box, defined by two corners
@findex error_x, draw x-error bars
error_x     # draw x-error bars: error x y size
@findex error_y, draw y-error bars
error_y     # draw y-error bars: error x y size
get_hist    # get_hist input output-x output-y base top width
@findex gauss, evaluate a Gaussian
gauss       # evaluate a Gaussian : N($mean,$sig)
@findex get, Read column from file
get         # syntax: get i j.  Read a column from a file
@findex glevels, Set grey levels
glevels     # Set grey levels. Usage: glevels expr
@findex greyscale, Draw grey-scale image.
greyscale   # Draw a grey-scale image.
            #                    Usage: greyscale [npx npy maxweight dmargin]
@findex info, help from info
info        # Get help about a command from SM's info files
@findex interp, linearily interpolate
interp      # Linearily interpolate $3 into ($1,$2), giving $4
@findex interp2, linearily interpolate
interp2     # Linearily interpolate $3 into ($1,$2), giving $4
@findex is_file, does file exist?
is_file     # Return true if file $1 exists
@findex is_macro, is a name a macro?
is_macro    # Return true if $1 is a macro
@findex is_set, is a bit set?
is_set      # define variable $$1 if the $3'rd bit is set in $2
@findex is_vector, is a name a vector?
is_vector   # Return true if $1 is a vector
@findex logerr, logarithmic error bars
logerr      # syntax: logerr x y error, where y is logged, and error isn't
@findex mconcat, Concatenate 2 macros
mconcat     # Concatenate 2 macros, optionally renaming result
@findex number, convert strings to numbers
number      # convert a string vector to an arithmetic one
@findex pairs, connect (x1,y1) to (x2,y2)
pairs       # pairs x1 y1 x2 y2. connect (x1,y1) to (x2,y2)
@findex polar, draw `axis' for polar coords
polar       # draw a circle as an `axis' for polar coordinates
@findex pmatrix, print the matrix $1
pmatrix     # print the matrix $1
@findex puts, Draw a line of text
puts	    # Draw a line of text, then move to the start of the next line
@findex qminv, Quick matrix inversion
qminv       # Quick matrix inversion, done in place
@findex repeated, find repeated elements
repeated    # Return an array that is true for repeated elements in $1
@findex reverse, reverse a vector
reverse     # reverse the order of a vector
@findex save_vec, save a vector on history
save_vec    # put the definition of a vector onto the history list
@findex set_window, cycle through all WINDOWs
set_window  # cycle through all available windows
@findex shade_box, shade a box
shade_box   # shade a box, spacing $1, defined by two corners
shed        # shade region between x y and x2 y2 with n lines
@findex simp, Simpson integration
simp        # Simpson's rule integration: simp answer x y
@findex smooth, boxcar smooth
smooth      # boxcar smooth a vector
@findex smooth2, smooth a vector
smooth2     # smooth a vector with a given filter
@findex smooth3, smooth a vector (omitting points)
smooth3     # smooth a vector with a given filter omitting points
@findex 2dhistogram, 2-d histogram from image
2dhistogram # convert the current image to a 2-d histogram
@findex thin, make sparse version of a vector
thin        # create a "thinned" version of a vector for plotting points
@findex thin2, "thin" the end of a vector
thin2       # "thin" the end of a vector
@findex thin3, "thin" central portion of a vector
thin3       # "thin" the central portion of a vector
@findex uniq, remove duplicates from a vector
uniq        # Remove duplicate elements of $1, e.g. u = uniq(x)
@findex upper, get `upper limit' symbol
upper       # define a variable giving an `upper limit' symbol
@findex vecminmax, min. and max. of vector
vecminmax   # find the minimum and maximum of a vector
@findex vfield, plot a vector field
vfield      # plot a vector field: vfield x y len angle
@findex vfield2, plot a vector field (x-units)
vfield2      # plot a vector field, vfield x y len angle (len in x-axis units)
@findex vfield3, plot a vector field (y-units)
vfield3      # plot a vector field: vfield x y len angle (len in y-axis units)
@findex vfield4, Vector field vx vy at x, y
vfield4      # Vector field at points x, y; components vx vy
@findex vfield5, Scaled Vector field vx vy at x, y
vfield5      # Vector field at points x, y; components vx vy scaled by f
@end example