Maxima Overview:
Maxima Overview
by Burkhard Bunk19.3.2013
Maxima version: 5.21.1
wxMaxima version: 0.8.5
Documentation
/usr/share/doc/maxima-doc/html/intromax.html introduction /usr/share/doc/maxima-doc/html/maxima_toc.html full help
Invocation, Help
Text mode:
unix> maxima
interrupt a maxima calculation with
<CTRL>-G
terminate maxima with
quit();
GUI:
unix> xmaxima
unix> wxmaxima
Help:
GUI ->Help
descripe(string);
? string; /* note the space after "?" */
A perfect way to restart maxima does not exist (see mailing list), use reset();
kill(all);
Commands and Expressions
Terminate commands with ";" or "$" (quiet mode). command prompts: (%i1) (%i2) .. output labels: (%o1) (%o2) .. Previous result: % Former output, e.g. (%o5): %o5 Redo command, e.g. (%i5) : ''%i5; Operators: + - * / ^ ** ( ) ! !! Comparison: = # > < >= <= /* "#" is "not equal" */ Logical: and or not Text strings are written as "text".
Names
Names consist of letters, digits, % (percent) and _ (underscore). Letters are case sensitive, but predefined names are mapped to upper case. Special characters (other than "%" and "_") are allowed after declaring them alphabetic as in declare("$", alphabetic);
Pre-defined constants: %i %pi %e true false
%gamma Euler's constant
%phi (1 + sqrt(5))/2
inf real infinity
minf real (-infinity)
infinity complex infinity
Pre-defined functions: sqrt log exp
sin .. asin ..
sinh .. asinh ..
gamma
zeta
binomial
mod floor
..
Reserved names: integrate next from diff
in at limit sum
for and elseif then
else do or if
unless product while thru
step
Manage user-defined variables: values list of all user defined variables
remvalue(var); delete the value of var
remvalue(all); delete the values of all variables
Assignment
Assignment: : (without "="!)
:: ??
:= defines a function
::= defines a macro
Unassign names:
kill(name1, name2, ..);
kill(all);
xmaxima: ->File ->Restart
wxMaxima: ->Maxima ->Restart maxima
Lists
lst: [el1, el2, ...]; contruct list explicitly
lst[2]; reference to element by index
(starting from 1)
cons(expr, alist); prepend expr to alist
endcons(expr, alist); append expr to alist
append(list1, list2, ..); merge lists
makelist(expr, i, i1, i2); create list with control variable i
makelist(expr, x, xlist); create list with x from another list
length(alist); returns #elements
map(fct, list); evaluate a function of one argument
map(fct, list1, list2); evaluate a function of two arguments
Evaluation
- automatic
Many expressions are evaluated automatically: before the are processed, substitutions and obvious simplifications are preformed.- explicit
Sometimes, this should be prevented (e.g. when defining a differential equation), in other cases, an extra evaluation is required (e.g. after changing an item in an expression): 'expr don't evalute
''expr do evaluate
e.g.
a: b+c;
c + b
b:5$
a;
c + b
''a;
c + 5
'b + c;
c + b
Evalutate variables, based on equations: at(expr, var=ex);
at(expr, [var1=ex1, var2=ex2, ..]);
e.g. at(diff(sin(x), x), x=%pi);
-1
Evaluate with additional settings/flags: ev(expr, arg1, arg2...);
expr, arg1, arg2, ...; same in short
args: numer
float
bfloat
simpsum
eval
...
Many of the evalutation switches (e.g. numer, simpsum) are actually flags, which are false by default, but can be enabled for subsequent use.- numerical
Numerical evaluation is triggered by decimal numbers in expressions, but note that a dot alone doesn't make it: sqrt(2.) is not evaluated, but sqrt(2.0) is. float(expr); evaluate to floating point number
expr, numer; return numerical result
numer: true; numerical evaluation on (default: false)
fpprec: digits; precision of big floats (default: 16)
fpprintprec: digits; no. of printed digits
bfloat(expr); evaluate to big float
example:
fpprec: 30;
sin(%pi); => 0
sin(float(%pi)); => 1.2246063538223773E-16
sin(bfloat(%pi)); => 1.69568553207377992879174029388B-31
Note: WxMaxima, with output format set to xml, diplays long numbers with a shortcut - compare the output ofbfloat(%pi), fpprec:1000;
Substitution
Functions which perform substitution, with increasing level of sophistication: subst(..) syntactic, symbols and complete sub-expressions only
ratsubst(..) similar, but employs some algebra
at(..) evaluation, based on equations
ev(..) evaluation, with equations, flags etc.
subst(..) and ratsubst(..) in more detail: subst(ex, var, expr); substitute ex for var in expr
subst(var=ex, expr); same
subst([var1=ex1, var2=ex2,..], expr); multiple substitutions
ratsubst(ex, var, expr); substitute ex for var in expr
subst(s, a+b, a+b+c);
c + b + a
ratsubst(s, a+b, a+b+c);
s + c
subst(1-cos(x)^2, sin(x)^2, sin(x)^4 - 5*sin(x)^2);
4 2
sin (x) - 5 (1 - cos (x))
ratsubst(1-cos(x)^2, sin(x)^2, sin(x)^4 - 5*sin(x)^2);
4 2
cos (x) + 3 cos (x) - 4
Functions
Function definition, general form: define(f(x), expr);
define(f(x,y), expr); /* etc */
simple form: e.g. func(x) := sin(x)/x;
radius(x,y) := sqrt(x^2 + y^2);
More complicated function definitions can be formulated with the block(..) construct.Simplification
Polynomials
factor(expr); factorise polynomials (over integers only)
expand(expr); expand polynomials
ratexpand(expr); same (more efficient algorithm)
expandwrt(expr, x, ..); expand w.r.t. specified variables
coeff(expr, x, n); coefficient of x^n in expr
ratcoef(expr, x, n); same, but simplifies expr first
divide(pol1, pol2); polynomial devision (with remainder)
quotient(pol1, pol2); quotient of polynomial devision
remainder(pol1, pol2); remainder of polynomial division
realroots(pol, tol); numerical approx. to all real roots
realroots(pol); tol = rootsepsilon (default: 1e-7)
allroots(pol); numerical approx. to all complex roots
Rational functions
ratsimp(expr); put on common denominator,
cancel factors,
expand numerator and denominator
fullratsimp(expr); repeated application of `ratsimp'
factor(expr); same as `ratsimp', but returns numerator and
denominator in factored form
expand(expr); expand numerator and denominator, split numerator
(no common denominator)
ratexpand(expr); put on common denominator,
cancel factors,
expand numerator and denominator,
split numerator
ratdenomdivide: false; don't split numerator (same as ratsimp?)
facsum(expr, var, ..) expand w.r.t. specified variables
facsum_combine: false; split numerator
partfrac(expr, var); partial fraction decomposition
examples:
ratsimp(a/b + c/d);
a d + b c
---------
b d
(x-1)/(x+1)^2 - 1/(x-1);
x - 1 1
-------- - -----
2 x - 1
(x + 1)
ratexpand(%);
4 x
- ---------------
3 2
x + x - x - 1
factor(%);
4 x
- ----------------
2
(x - 1) (x + 1)
r: (u+v)^2*u/((u^2-v^2)*v);
2
u (v + u)
-----------
2 2
v (u - v )
ratsimp(r);
u v + u
- --------
2
v - u v
factor(r);
u (v + u)
- ---------
v (v - u)
ratexpand(r);
2
u u
- -------- - -----
2 v - u
v - u v
s: a*b/(c*d+c*e) + f*b/(c*d+c*e);
b f a b
--------- + ---------
c e + c d c e + c d
factor(s);
b (f + a)
---------
c (e + d)
ratsimp(s);
b f + a b
---------
c e + c d
Notes: the following appear to be equivalent:
ratsimp(expr); and ratexpand(expr), ratdenomdivide: false;
ratsimp(expr), factor; and factor(expr);
but factor(expr) does not understand algebraic!Summary: simplify rational functions with ratsimp(expr), possibly combined with factor and/or algebraic. Use ratexpand(expr), possibly with algebraic, if you prefer to split the numerator.
Roots
rootscontract(expr); products of roots -> roots of products
ratsimp(expr), algebraic; rationalise denominators
radcan(expr); canonical form, involving roots, logs,
radcan(expr), algebraic; and exponentials
examples: ex: 1/(sqrt(a)+sqrt(b));
1
-----------------
sqrt(b) + sqrt(a)
ratsimp(ex), algebraic;
sqrt(b) - sqrt(a)
-----------------
b - a
sqrt(x^2);
abs(x)
sqrt(x^2), radexpand:all;
x
In some cases, sqrtdenest can disentangle nested square roots: load(sqdnst);
sqrtdenest(expr);
e.g.
sqrt(sqrt(7)+ 4);
sqrt(sqrt(7) + 4)
sqrtdenest(%);
sqrt(7) 1
------- + -------
sqrt(2) sqrt(2)
factor(%);
sqrt(7) + 1
-----------
sqrt(2)
Logarithms
logexpand:all; enables automatic expansion of products
logcontract(expr); contracts sums of logs to logs of products
and _integer_ multiples of logs to
logs of powers
radcan(expr); canonical form, involving roots, logs,
radcan(expr), algebraic; and exponentials
examples: log(a^b);
log(a) b
log(a*b), logexpand:all;
log(b) + log(a)
logcontract(2*log(a) + 3*log(b));
2 3
log(a b )
Trigonometric functions
trigsimp(expr); use sin(x)^2 + cos(x)^2 = 1 etc
trigexpand(expr); use addition theorems etc
trigreduce(expr); powers -> multiple arguments
products -> sums
trigrat(expr); simplify rational expressions of trigonometric
functions as well as linear arguments
involving %pi/n
halfangles:true; replace half angles by roots
exponentialize(expr); trig/hyperb -> exponentials
demoivre(expr); complex exponentials -> trig (not hyperb)
logarc(expr); arc trig/hyperb -> logarithms
trigexpand is a flag as well (and an evflag), but the other trigX aren't!trigsimp(..) in combination with roots is tricky:
trigsimp(sqrt(sinh(x)^2 + 1));
cosh(x)
trigsimp(sqrt(cosh(x)^2 - 1));
sqrt(cosh(x) - 1) sqrt(cosh(x) + 1)
instead of the expected abs(sinh(x)). It does not work for sin() and cos(x) either. Is this caused by abs(..)? ?HOW TO
There is no command to convert real exponentials to hyperbolic functions - use ratsubst(..) instead.
Examples:
sin(x/2), halfangles;
sqrt(1 - cos(x))
----------------
sqrt(2)
?HOW TO: sin(x) + cos(x) = sqrt(2) * sin(x + %pi/4)
try exponentialize(...)
?HOW TO ex1: cos(x) + cos(y);
ex2: 2 * cos((x+y)/2) * cos((x-y)/2);
ex2 -> ex1:
trigreduce(ex2), ratsimp;
or trigrat(ex2);
ex1 -> ex2 ??
logarc examples: asinh(x), logarc;
2
log(sqrt(x + 1) + x)
acosh(x), logarc;
sqrt(x + 1) sqrt(x - 1)
2 log(----------- + -----------)
sqrt(2) sqrt(2)
%, logcontract, expand, rootscontract;
2
log(sqrt(x - 1) + x)
Number Theory
Compute the prime factorisation of a number: factor(n) basic method
ifactors(n) more efficient algorithm
ifactor_verbose: true show details
Limit
limit(f(x), x, a);
limit(f(x), x, a, dir); direction dir = plus, minus
Differentiation
diff(expr, x);
diff(expr, x, n); /* n-th derivative */
diff(expr, x, y); /* mixed partial derivative */
Convert the derivative to a function with define(..): f(x) := sin(x); /* works */
diff(f(x), x);
cos(x) /* ok */
g(x) := diff(f(x), x); /* doesn't work */
define(g(x), diff(f(x), x));
g(x) := cos(x) /* works */
Compute the derivative at a specific value with at(..): at(diff((x-a)^2, x, 2), x=a);
2
Integration
integrate(f(x), x); indefinite integral
integrate(f(x), x, a, b); definite integral
defint(f(x), x, a, b); same
ldefint(f(x), x, a, b); same, but taking limits at the boundaries
Examples: assume(a>0)$
declare(a, noninteger)$
facts(a);
[a > 0, kind(a, noninteger)]
integrate(x^a * exp(-x), x, 0, inf);
gamma(a + 1)
kill(all)$
facts();
[]
integrate(1/(a - cos(x)), x, 0, %pi);
Is (a - 1) (a + 1) positive, negative, or zero? pos;
2
Is sqrt(a - 1) - a positive or negative? neg;
2
Is sqrt(a - 1) - a + 1 positive, negative, or zero? pos;
! 2 !
Is !sqrt(a - 1) + a! - 1 positive, negative, or zero? pos;
2
2 %pi sqrt(a - 1) - 2 %pi a
- ----------------------------
2 2
2 (a sqrt(a - 1) - a + 1)
ratsimp(%), algebraic;
%pi
------------
2
sqrt(a - 1)
Summation
Sums are defined with sum(..) and evaluated (symbolically) with simpsum: sum(expr, n, n1, n2);
ev(sum(...), simpsum); sum and simplify
sum(...), simpsum; same in short
simpsum: true; enable summations
Example: sum(k^2, k, 1, n);
n
====
\ 2
> k
/
====
k = 1
%, simpsum;
3 2
2 n + 3 n + n
---------------
6
The same is achieved with sum(k^2, k, 1, n), simpsum;
or
simpsum: true;
sum(k^2, k, 1, n);
Series expansion
powerseries(expr, var, point); symbolic, possibly infinite
taylor(expr, var, point, order); truncated at given order
niceindices(expr); rewrite symbolic sums
Equations
Equations (single or systems) are solved by solve. solve(eqn, var);
solve([eqn1, eqn2, ..], [var1, var2, ..]);
It returns a list of solutions resp. solution vectors. Examples:
sol: solve(x^2 + p*x + q, x);
sqrt(p - 4 q) + p sqrt(p - 4 q) - p
[x = - ------------------, x = ------------------]
2 2
x1: x, sol[1];
sqrt(p - 4 q) + p
- ------------------
2
x2: x, sol[2];
sqrt(p - 4 q) - p
- ------------------
2
eqn1: x + y = 4;
y + x = 4
eqn2: x - y = 2;
x - y = 2
sol: solve([eqn1, eqn2], [x,y]);
[[x = 3, y = 1]]
x, sol;
3
y, sol;
1
Check:
map(is, ev([eqn1, eqn2], sol));
[true, true]
Maybe ev(..) needs more flags (e.g. ratexpand).Check multiple solutions (equation is formulated as f(x) = 0):
f(x):= x^2 + 2*b*x + c;
2
f(x) := x + 2 b x + c
sol: solve(f(x), x);
2 2
[x = - sqrt(b - c) - b, x = sqrt(b - c) - b]
map(f, map(rhs, sol)), expand;
[0, 0]
?HOW TO: solve(sin(x) + cos(x) = 1/2, x);
eqn: sin(x) + cos(x) = 1/2;
solve(eqn, x); no success
eqnx: exponentialize(eqn);
sol: solve(eqnx, x); solution in terms of complex logs
ratsimp(sol);
%, numer;
rectform(sol); imaginary parts are obsolete
ratsimp(%); nicer formula
%, numer;
?HOW TO: solve(s + sqrt(1-s^2) = 1/2, s);
solveradcan: true; doesn't help here
(solve calls radcan)
eq1: s + r = 1/2; aux variable r = sqrt(1 - s^2) > 0
eq2: r^2 = 1 - s^2;
solve([eq1, eq2], [s, r]);
sqrt(7) - 1 sqrt(7) + 1
[[s = - -----------, r = -----------],
4 4
sqrt(7) + 1 sqrt(7) - 1
[s = -----------, r = - -----------]]
4 4
Solution is s = (1 - sqrt(7))/4 .?HOW TO:
solve([sqrt(x) + y = 0, sqrt(x) = 1], [x, y]);
[]
eliminate([sqrt(x) + y = 0, sqrt(x) = 1], [x]);
[1] ??? BUG ???
eliminate([sqrt(x) + y = 0, sqrt(x) = 1], [y]);
[ sqrt(x) - 1 ] ok
Note that eliminate() uses resultant(), which is supposed to work with polynomials. Eliminate variables from a set of (polynomial?) equations:
eliminate([eqn1, eqn2, ..], [var1, var2, ..]);Note: there is a new solver package ("topoly" or "to_poly"), see appendix.
Numerical solution
find_root(expr, x, a, b)For polynomials: see realroots(pol), allroots(pol).
Ordinary Differential Equations
ode2
Try to solve general ODEs of first or second order with ode2: ode2(eqn, y, x);
E.g. eqn of 2nd order:
eqn: 'diff(x,t,2) + r*'diff(x,t)^2 = 0;
general solution, with constants of integration %k1, %k2:
sol: ode2(eqn, x, t);
log(r t + %k1 r)
x = ---------------- + %k2
r
impose initial conditions:
ic2(sol, t=0, x=x0, 'diff(x,t)=v0), logcontract, ratexpand;
log(r t v0 + 1)
x = x0 + ---------------
r
convert solution equation to a function:
define(x(t), rhs(%));
[TO DO: for the same deqn with exponent 2 -> 3, ic2() fails to solve for the initial conditions. This looks like a problem with solve...] Boundary conditions are imposed with bc2(..).
For an equation of first order, the initial conditions are specified with ic1(..).
desolve
Solve a linear ODE with desolve (using Laplace transformation): eqn: 'diff(f(x), x) = 2*f(x); /* linear ODE of 1st order */
sol: desolve(eqn, f(x));
2 x
f(x) = f(0) %e
[Note the different format of derivatives in the equation.] Initial values at x = 0 can be imposed with atvalue before calling desolve:
eqn: 'diff(f(x), x) = 2*f(x);
atvalue(f(x), x=0, k); /* initial value at x=0 */
sol: desolve(eqn, f(x)); /* solution as an equation */
2 x
f(x) = k %e
define(f(x), rhs(%)); /* solution function */
2 x
f(x) := k %e
An example of second order: eqn: 'diff(f(t), t, 2) + r*'diff(f(t), t) + f(t) = sin(omega*t);
atvalue(f(t), t=0, 1);
atvalue('diff(f(t), t), t=0, 0);
desolve(eqn, f(t)); /* omega nonzero, -2 < r < 2 */
define(f(t), rhs(%));
plot2d(ev(f(t), omega=1.1, r=0.1), [t, 0, 100]);
A linear system is solved with desolve as follows: eqn1: 'diff(f(x), x) = c*f(x) - g(x);
eqn2: 'diff(g(x), x) = c*g(x) + f(x);
atvalue(f(x), x=0, 1);
atvalue(g(x), x=0, 0);
sol: desolve([eqn1, eqn2], [f(x), g(x)]);
define(f(x), rhs(sol[1]));
define(g(x), rhs(sol[2]));
c: 0.1;
plot2d([parametric, f(t), g(t)], [t, 0, 10], [nticks, 100]);
desolve requires that the inverse Laplace transform (ilt) is applied to a rational function with a denominator of first or second order.
Vectors and Matrices
A: matrix([a, b, c], [d, e, f], [g, h, i]); /* (3x3) matrix */
u: matrix([x, y, z]); /* row vector */
v: transpose(matrix([r, s, t])); /* column vector */
Reference to elements etc: u[1,2]; /* second element of u */
v[2,1]; /* second element of v */
A[2,3]; or A[2][3]; /* (2,3) element */
A[2]; /* second row of A */
transpose(transpose(A)[2]); /* second column of A */
Element by element operations: A + B; A - B;
A * B; A / B;
A ^ s; s ^ A;
Matrix operations: A . B; /* matrix multiplication */
A ^^ s; /* matrix exponentiation (including inverse) */
transpose(A);
determinant(A);
invert(A);
Properties
assume(pred); predicate `pred' e.g. a > 0, equal(b,3), notequal(c,0)
is(expr); check whether expr is true, based on assumptions
forget(pred); remove `pred' from assume database
features list of mathematical properties
declare(var, prop);
remove(var, prop);
facts(item); list properties associated with item
facts(); list all properties
domain:real default
domain:complex
Examples: facts(a); list of properties involving a
forget(facts()); remove all properties (but not the features?)
forget(facts(a)); remove all properties (not features?) involving a
kill(all) clears the facts database (among other things).Graphics
plot2d(expr, range); /* one curve */
plot2d([expr1, expr2], range); /* two curves */
plot2d([parametric, expr1, expr2], range); /* parametric */
examples:
plot2d(sin(x), [x, 0, 10]);
plot2d(tan(x), [x, 0, 10], [y, -2, 2]); /* truncate vertically */
plot2d([8*sin(x), exp(x)], [x, -2, 2]);
plot2d([parametric, t*cos(t), t*sin(t)], [t, 0, 10], [nticks, 100]);
plot2d(sin(x), [x, 0, 10], [gnuplot_term, ps],
[gnuplot_out_file, "filename"]); /* write PS file */
plot3d(expr, range1, range2); /* 3D mesh plot */
example:
plot3d(sin(x)^2 * sin(y)^2, [x, -2, 2], [y, -2, 2]);
It appears that in a parametric plot, the parameter has to be named "t".I/O
Console interaction: print("text");
print(expr1, expr2, ..);
disp(expr1, expr2, ..);
display(expr1, expr2, ..);
z: read("what is z?"); /* terminate reply with ; */
Read/write data (in matrix or list form) from/to a file (space-separated numbers): load("numericalio");
read_matrix("filename");
write_data(matrix, "filename");
read_nested_list("filename");
write_data(list, "filename");
File search and display: file_search("filename"); check for the existence of a file, using
file_search_maxima etc as search paths
file_search("filename",["path/"]); use specified path
(relative or absolute path)
file_search_maxima search path list, for load etc
file_search_usage search path list, e.g. for printfile
printfile("filename"); display contents of file
e.g. prepend a directory as follows:
file_search_maxima: cons("/home/me/work/", file_search_maxima);
Notes: o terminate path elements with /
o It appears that the current working directory (where maxima was started) is always searched first.
Running scripts:
batch("filename"); run maxima commands from file
batchload("filename"); same, in quiet mode
load("filename"); run maxima and lisp code from file
Command display and session log
Disable 2D display, use 1-line output:display2d:falseConvert expression to TeX format:
tex(expr);Save command output and input to file:
with_stdout("filename", commands); writes output of commands to file
file_output_append: true; switch to append mode
stringout("filename", expr1, ..); write expressions in a form
suitable for maxima input
Session transcript: writefile("filename"); session transcript in console output format
appendfile("filename"); same, but append to file
closefile(); terminate session transcript
Control Structures
for var: first step incr thru limit do body
for var: first step incr while cond do body
for var: first step incr unless cond do body
if cond then body
if cond then body1 else body2
return(expr); /* abnormal termination of the "for" loop */
step 1 can be omitted. body is a single command or a comma separated list of commands.
for returns done upon normal termination.
if returns the last result of the executed commands or false.
The following example computes sqrt(10) to floating point precision:
x: 1.;
for n: 1 thru 10 do
(x0: x, x: .5*(x + 10./x), if x = x0 then return(x));
In this example, the control variable is obsolete and can be omitted: x: 1.;
do (x0: x, x: .5*(x + 10./x), if x = x0 then return(x));
Scripts
batch("filename"); run Maxima script
/* .. */ comments in script
unix> maxima -b filename run in terminal (from the command line)
Startup scripts
$HOME/.maxima/maximarc
maxima_userdir directory for startup file `maxima-init.mac'
(Unix default: $HOME/.maxima)
Checking the installation
build_info();
run_testsuite();
run_testsuite(true); show bugs only
wxMaxima
->Edit ->Configure
->Options
Language: (select)
->Style
[x] Use greek font
displays variables starting with % as (small or capital) greek letters, e.g. %omega and %Omega. Beware: %pi and %phi are predefined.
Math display modes:
set_display('xml); nice format (default)
set_display('ascii); multi-line mode, like maxima with display2d:true
set_display('none); one-line mode, like maxima with display2d:false
May be set via ->Maxima ->Change 2d display. In xml mode, long numbers are displayed with a shortcut.
wxMaxima-0.8.x notes:
In 0.8.0/0.8.1
- the input line was removed,
- commands are terminated with <SHIFT>-<ENTER>, a la Mathematica.
[x] Enter evaluates cells
In wxMaxima-0.8.5, %alpha etc are represented as greek letters by default (no need to configure).
Documentation
Tutorials
Antonio Cangiano, A 10 minute tutorial for solving Math problems with MaximaBoris Gaertner, The Computer Algebra Program Maxima - a Tutorial
Moses Glasner, The Maxima Primer
Richard H. Rand, Introduction to MACSYMA
wxMaxima tutorials [in *.wxm.zip format]
Advanced
Maxima Beginner's FAQ [with many tips for advanced usage, in fact]Paulo Ney de Souza et al., The Maxima Book (19-Sept-2004)
Moses Glasner, A Maxima Guide for Calculus Students
Robert Dodier, Minimal Maxima
Edwin L. Woollett, Maxima by Example
P. Lutus, Symbolic Mathematics Using Maxima
Maxima, Maple, and Mathematica: the Summary
Gilberto E. Urroz, Maxima Book
Plotting
Examples of the Maxima Gnuplot interfaceA Maxima-Gnuplot interface
Manuals
Maxima Manual [5.28.0]Michael Clarkson, DOE-Maxima Reference Manual [Maxima manual v5.9 reformatted]
Help
Maxima mailing list and archivesMaxima user interface tips
In German
Johann Weilharter, Mathematik mit Computerunterstützung: CAS Maxima [Sammlung von Unterrichtsmaterial]Walter Wegscheider, Maxima 5.xx unter der Oberfl?che wxMaxima
Robert Gl?ckner, Einführung in Maxima
H.-G. Gr?be, Skript zu "Einführung in das symbolische Rechnen" [not using Maxima]
More links
see maxima.sourceforge.netAppendices
Experimental solver to_poly_solve()
by Barton Willis, 2006ffprovided e.g. with Maxima-5.15.0 + 5.17.1:
files:
topoly.lisp (engine)
topoly_solver.mac (wrapper).
They also work with Maxima-5.10.
load(topoly_solver);
/home/b/maxima/5.15.0/topoly_solver.mac
to_poly_solve(s + sqrt(1-s^2) = 1/2, s);
sqrt(7) - 1
[[s = - -----------]]
4
to_poly_solve([sqrt(x) + y = 0, sqrt(x) = 1], [x, y]);
[[x = 1, y = - 1]]
to_poly_solve(sin(x) + cos(x) = 1/2, x);
Nonalgebraic argument given to 'topoly'
In Maxima-5.18.1, there is a new version (which does not work with Maxima-5.10?) - it solves the last example as well: load(to_poly_solver);
to_poly_solve(sin(x) + cos(x) = 1/2, x);
%union{TO DO}
In Maxima-5.21.1, the to_poly_solver package is auto-loaded as needed.More special functions
There is work in progress to implement the Exponential Integral and the Incomplete Gamma Function, see mailing list.GCL
GCL (GNU Common Lisp) prompt and commands: MAXIMA>>(help) show GCL help
MAXIMA>>(run) restart Maxima session
MAXIMA>>(bye) exit
MAXIMA>>(by) exit
TO DO
%union(..)wxMaxima cells
