This is aamath, an ASCII art mathematics renderer.
To compile on *nix or cygwin:
make -f Makefile.good
To compile on djgpp hosted on windows:
make -f Makefile.evil
To test it:
./aamath < testcases
To run in interactive mode:
./aamath
To compile without readline:
remove -DUSE_READLINE and -lreadline and -ltermcamp from Makefile.good
Please email any comments, suggestions and patches to:
mauro_persano at yahoo dot com
++ 09-APR-2022/KFP
--------------------------------------------------------------------------------
aamath(1) USER COMMANDS aamath(1)
NAME
aamath - renders mathematical expressions as ASCII art
SYNOPSIS
aamath [ -q | -r ] [ expression ... ]
DESCRIPTION
aamath is a program that accepts math expressions in infix notation and
outputs them as ASCII art renderings. Expressions can either be entered
as command line arguments, or supplied on standard input.
OPTIONS
-q Quiet mode.
-r More compact radicals.
EXPRESSIONS
The simplest types of expression in aamath are constants and variables.
The following are recognized as constants:
number A number, optionally in scientific notation, optionally followed
by ellipsis. Precision is limited only by available memory,
since numbers are represented internally as strings.
inf Infinity.
nabla The nabla operator.
... Ellipsis.
A variable is represented by an alphabetic character, optionally fol‐
lowed by a sequence of alphanumeric characters. A variable may have a
subscript: these are represented by an underline character (_) followed
by an expression. If followed by a backslash character (\), the vari‐
able name will be rendered with an over score. Variables names may also
be followed by one or more primes (apostrophes).
Functions are represented by the function name, which follows the same
syntax of variable names (including optional subscripts, over score,
and primes), followed by comma-separated function arguments between
parentheses. Trigonometric functions are rendered differently if they
are raised to a power: the exponent will appear between the function
name and the argument.
Matrices are represented by a sequence of expressions between square
brackets; commas separate elements of the same row, and semicolons sep‐
arate rows.
Other than the standard arithmetic and logical operators, which obey
the usual precedence rules, aamath also accepts the following opera‐
tions:
expr1 ^ expr1
expr1 raised to expr2.
~(expr)
Complex conjugate of the expression.
expr! Factorial of the expression.
The following special functions are also recognized:
sqrt(expr)
Square root of the expression.
root(expr, ord)
Root of order ord of the expression.
lim(expr, var -> lim)
Limit of expr with var tending to lim.
int(expr, var [= from .. to])
Integral of expr with respect to var, optionally with with lim‐
its from and to.
sum(expr, var [= from .. to])
Sum of expr for values of var in the interval. The interval is
optional.
prod(expr, var [= from .. to])
Product of expr for values of var in the interval. The interval
is optional.
BUGS
It needs a better man page.
AUTHOR
Mauro Persano (mauro_persano (at) yahoo.com), with help from bicoher‐
ent.
Version 0.3 March 1, 2005 aamath(1)
-------------------------------------------------------------------------------
$ cat testcases
f(x+h) = f(x) + h*f'(x) + h^2/2*f''(x) + O(h^3)
h = -((f'(x)/f''(x))*(1 - sqrt(1 - (2*f(x)*f''(x))/f'(x)^2)))
sqrt(42)/z=root((1+1/(1+1/(x^2+1/b)))^3,6)/(3^d/(5-e + 42/(3 + f))+sqrt((2/(1-1/(1+1/7))))+sqrt(1/(2+3)+3)^(sqrt(21/(38-w))))
int(int(int(psi^2, x = -inf .. inf), y = -inf .. inf), z = -inf .. inf) = 1
A_TR = x*sqrt(x^2-1)/2 - int(sqrt(t^2-1), t = 1 .. x)
sqrt(e) = 1+1/(1+1/(1+1/(1+1/(5+1/(1+1/(1+1/(9+1/(1+1/(1+...)))))))))
e^x = 1 + x + x^2/2! + x^3/3! + x^4/4! + ... = 1 + sum(x^n/n!, n = 1 .. inf)
(1/4)*pi*sqrt(2) = sum((-1)^(k+1)/(4*k + 1) + (-1)^(k+1)/(4*k - 3), k = 1 .. inf) = 1 + 1/3 - 1/5 - 1/7 + 1/9 + 1/11 - ...
2/pi=sqrt(1/2)*sqrt(1/2+1/2*sqrt(1/2))*sqrt(1/2+1/2*sqrt(1/2+1/2*sqrt(1/2)))*...
pi = 3/4*sqrt(3) + 24*int(sqrt(x - x^2), x = 0 .. 1/4) = (3*sqrt(3))/4 + 24 * (1/12 - 1/(5*2^5) - 1/(28*2^7) - ...)
int(z^2, z = 1 .. root(3, 3)) * cos((3*pi)/9) = ln(root(e, 3))
x\ = (x_1 + x_2 + x_3 + ... + x_n)/n = (1/n)*sum(x_i, i = 1 .. n)
zeta(s) = (1 / (1 - (1/2^s))) * (1 / (1 - (1/3^s))) * (1 / (1 - (1/5^s))) * (1 / (1 - (1/7^s))) * ... = prod(1 / (1 - (1/p^s)), p_prime)
int((x^2+a)/b,x) = (1/b)*int(x^2+a,x) = (1/b)*(x^3/3 + a*x) + C
sin(a)/a = cos(a/2) * cos(a/4) * cos(a/8) * cos(a/16) * ... = prod(cos(a/2^n), n = 1 .. inf)
A_T = [sqrt(a/b), 0, 0; 0, sqrt(a/b), 0; 0, 0, sqrt(a/b)]^-1
lim(1/x^2 - (cos(x)/x)^2, x -> inf) = 1
---
$ aamath < testcases
2
h / 3\
f(x + h) = f(x) + h f'(x) + -- f''(x) + O\h /
2
/ _________________\
f'(x) | / 2 f(x) f''(x)|
h = - ------ |1 - / 1 - -------------|
f''(x) | / 2 |
\ \/ f'(x) /
6_________________
/ 3
/ / 1 \
/ |1 + ----------|
/ | 1 |
/ | 1 + ------|
/ | 2 1|
__ / | x + -|
\/42 \/ \ b/
---- = -------------------------------------------------------------
z ______
/ 21
/ ------
\/ 38 - w
d _________ / _________\
3 / 2 | / 1 |
------------- + / --------- + | / ----- + 3|
42 / 1 \\/ 2 + 3 /
5 - e + ----- / 1 - -----
3 + f / 1
/ 1 + -
\/ 7
oo oo oo
/ / /
| | | 2
| | | psi dx dy dz = 1
| | |
/ / /
-oo -oo -oo
x
______ /
/ 2 | ______
x \/ x - 1 | / 2
A = ----------- - | \/ t - 1 dt
TR 2 |
|
/
1
_ 1
\/e = 1 + ---------------------------------------
1
1 + -----------------------------------
1
1 + -------------------------------
1
1 + ---------------------------
1
5 + -----------------------
1
1 + -------------------
1
1 + ---------------
1
9 + -----------
1
1 + -------
1 + ...
oo
2 3 4 ===== n
x x x x \ x
e = 1 + x + -- + -- + -- + ... = 1 + > --
2! 3! 4! / n!
=====
n = 1
oo
===== / k + 1 k + 1\
1 __ _ \ |(-1) (-1) | 1 1 1 1 1
- || \/2 = > |--------- + ---------| = 1 + - - - - - + - + -- - ...
4 / \ 4 k + 1 4 k - 3 / 3 5 7 9 11
=====
k = 1
______________________
___________ / ___________
_ / _ / / _
2 /1 / 1 1 /1 / 1 1 / 1 1 /1
-- = / - / - + - / - / - + - / - + - / - ...
__ \/ 2 \/ 2 2 \/ 2 \/ 2 2 \/ 2 2 \/ 2
||
1
-
4
/
| ______ _
__ 3 _ | / 2 3 \/3 / 1 1 1 \
|| = - \/3 + 24 | \/ x - x dx = ----- + 24 |-- - ---- - ----- - ...|
4 | 4 |12 5 7 |
| \ 5 2 28 2 /
/
0
3_
\/3
/ __
| 2 3 || / 3_\
| z dz cos ---- = ln\\/e/
| 9
/
1
n
x + x + x + ... + x =====
_ 1 2 3 n 1 \
x = ----------------------- = - > x
n n / i
=====
i = 1
=====
1 1 1 1 | | 1
zeta(s) = ------ ------ ------ ------ ... = | | ------
1 1 1 1 | | 1
1 - -- 1 - -- 1 - -- 1 - -- | | 1 - --
s s s s p s
2 3 5 7 prime p
/
| 2 / / 3 \
| x + a 1 | / 2 \ 1 |x |
| ------ dx = - | \x + a/ dx = - |-- + a x| + C
| b b | b \ 3 /
| /
/
oo
=====
sin a a a a a | | a
----- = cos - cos - cos - cos -- ... = | | cos --
a 2 4 8 16 | | n
| | 2
n = 1
-1
/ _ \
| /a |
| / - 0 0 |
| \/ b |
| |
| _ |
| /a |
A = | 0 / - 0 |
T | \/ b |
| |
| _ |
| /a |
| 0 0 / - |
\ \/ b /
/ 2\
| 1 /cos x\ |
lim |-- - |-----| | = 1
| 2 \ x / |
x -> oo \x /
kfp@NUC MINGW64 ~/devel/aamath (master)
$