gnome-genius for graphical.

# comment

Line value, which is echoed, is the last expression value.
Since ; delimits expressions, don't end line with ; or you will have added
an explicit empty expression at the end.
Don't know why this doesn't work:
  load "tst.gel"; 3

= means either := (assignment) or == depending on context.
    Use := or == to make behavior explicit.

Ans like shell $?

Logarithms
general:  log(x, b)
base e:  ln(x) = log(x)   GOTCHA!  For some damned reason he does not use log10=log!
base 10: log10(x) = log(x, 10)

MATRIXES
    Indexes are 1-based not 0-based
    Matrix:  [r1c1, r1c2, r1c3; r2c1, r2c2, r2c3]
        OR:  [r1c1, r1c2, r1c3
              r2c1, r2c2, r2c3]

    @ element operator.  m@(2,3) == r2c3
      one column or row.  m@(2,) == [r2c1; r2c2; r2c3]
    : column or row range. m@(,2:3) == m@(:,2:3) = [r1c2, r1c3; r2c2, r2c3]
      I.e. : == "" means all (can't use this for all params)
    non-specified element values set to 0
    m.'  Transpose
    m    ComplexConjugate + Transpose
    .X operations generally do simple element-by-element operations
       a.o.t. matrix-specific operations.
    det(m)  Determinate
    m^-1  Inverse matrix

IMAGINARY/COMPLEX Numbers
Number+i with no intervening space is how you specify imaginary component.
Plain "i" would refer to a variable "i" therefore for one i you must code "1i".
ComplexConjugate(n)

POLYNOMIALS.  Only support one poly variable.
polyFn = PolyToFunction([a,b,c], "y")  // Var defaults to "x"

Be aware of modular mode, which I guess applies modular operation to all
sub-steps.

`X  quote (escape) an identifier or matrix

"help x" very useful.
If used in graphical mode, you also get a nice graphical help browser window.

# for comments, but they do not work inside of (...)

At least interactively, or when a program tab is Run,
    \n evaluates then displays current Ans
    ; just evaluates except that at end of block ==> ; null
Operators:  http://www.jirka.org/genius-documentation/x583.html
For unknown reason, "load"ed programs  (unless Run from a tab) do not display
 Ans as normal.
Does not have shortcut self-operators like +=, -= *= /=.

Grouping.  I guess (...) can group blocks?

. == null
nulls display as nothing (do not display)

Token-completion seems to require two TAB presses for me.  ?

ASSIGNMENT
Use ":=" to distinguish from context-specific "=" (like after "if").

Fractions entered as integers are preserved in that form.

Converting from integers to reals:  * 1.0
Converting from reals to integers:  ?
Converting * to strings:  string(x)

Complexes:  4 + 3i
When use in expressions must often specify precedence 3 * (4 + 3i)

Booleans
0 == false.  All other values == true.

Strings
double-quote
Display with the double-quotes.
\escapes work as expected.

Logical operators
and, or, xor, ==, etc.
Not strictly binary because this works:  1<x<=y<5.
(Don't know why that can't work binary by recursion).

Function definition:
function addup(a,b,c) = a+b+c
Varargs:  Last param place-holder gets an [array].  (I think 1-dim matrix?)
Usually end statements in a function with ; (BUT NOT LAST ONE IF YOU WANT IT TO
RETURN A VALUE).  Why different than interacive?
Can use return in normal way:  return y;


|abs val|

Modulus:  mod    I don't understand difference from %.

Matrixes:  [1,2;3,4]
        OR
           [1,2
            3,4]
  I.e., the row delimiter is ; OR \n  (not both!).
Non-specified elements are initialized ot 0.
Element:  e@(2,3)  # Indexing is 1-based: (row, col)
Leave row or column specifier blank to get  entire col or row: e@(,2)

Arrays = Horizontal vectors.

Vector = Vertical 1-column matrix.  Horizontal Vector (array) =  1-row matrix.

Vectors
a:b  # from a to b

PROGRAMING
break and continue work as expected
if bool exp r then action [else other action]
while|until bool expr do action
do action while|until bool expr
for statements return the last value.
for|sum|prod identifier = startval to endval [by incrval] do action
for|sum|prod identifier in [ma,tr;i,x] do action


VARIABLE SCOPING
Define just by using.
Variables are inherited by called functions (i.e. higher-level scopes).
Seems to call by value since changes inside functions to not change caller var.
Global variables are those set at bottom (root) scope.
Must use 'set" command to change global from a higher scope.
Can use & and * just like in C to call-by-reference.
Local variables.  Must be 1st statement in a function:
    local a, b, c;   #  may list parameter place-holder vars
    OR
    local *;
Global-only variables  (never overridden):
    parameter x = 1;
    ...
    undefine(x);

INIT file ~/.geniusinit.  Like "load"ing, the Ans values do not display.


POLYNOMIALS
Horizontal vector used to store parameters in ascending order from 0:
    [1,2,3] 1 + 2*x + 3*x^2
Functions:
    AddPoly()
    SubtractPoly()
    MultiplyPoly()
    PolyToString()
    PolyToFunction()
    PolynomialRoots  (only up degree 4)

SET THEORY  (Subject to change)   === Unique-element horizontal vectors!
Uniquify a horizontal vector like: MakeSet([1,2,2,3])
(Can use vectors directly but you are responsible for uniqueness).
null is empty set
Functions:
    MakeSet()
    Union()
    Intersection()
    SetMinus()
    IsIn()
    SortVector()
    IsSubset

PLOTTING
    LinePlot(f1[, f2,...][, x1, x2, y1, y2]) # where x1/x2/y2/y2 are plot limits
    LinePlotParametric(xf, yf, [t1, t2, tinc[, x1,x2,y1,y2]])
    LinePlotWindow = [x1, x2, y1, y2];   # Set defaults for x1,x2,y2,y2 above

Anonymous function is `.
E.g. to line plot an anonymous function:
    LinePlot(`(x)=x^2)

Comments:  only #.  Partial lines too.
text output:  print("s"); error("str"); display("str", expr);
load file.path   # ~ works, also have cd and ls