Examples in Maxima Mode
>maximamode on
Maxima mode is on (compatibility mode)
>ratsimp(1/a+1/a^2-1/a^3)
2
a + a - 1
----------
3
a
>radcan(sqrt(2)/sqrt(4))
1
-------
sqrt(2)
>radcan(log(100)/log(10))
2
>factor(a^3-a*b^2-a^2*b+b^3)
2
(b - a) (b + a)
>expand((1+1/x)^5), ratsimp(%)
5 10 10 5 1
- + -- + -- + -- + -- + 1
x 2 3 4 5
x x x x
5 4 3 2
x + 5 x + 10 x + 10 x + 5 x + 1
-----------------------------------
5
x
>trigsimp(expand((sin(x)+cos(x))^5))
4 2 5
(- 4 cos (x) + 8 cos (x) + 1) sin(x) - 4 cos (x) + 5 cos(x)
>trigexpand(cos(3*x))
3 2
cos (x) - 3 cos(x) sin (x)
>trigreduce(cos(x)^3*sin(x)), trigrat(cos(x)^3/sin(x)^2)
sin(4 x) + 2 sin(2 x)
---------------------
8
cos(3 x) + 3 cos(x)
- -------------------
2 cos(2 x) - 2
>rectform(log(1+%i))
log(2) I pi
------ + ----
2 4
>sum(k^3, k, 1, N) | simpsum, factor(%)
4 3 2
N + 2 N + N
--------------
4
2 2
N (N + 1)
-----------
4
>product(4*n^2/(4*n^2-1),n,1,1000); 2*float(%)
3.140807746030395
>solve(x^3-3*x^2+4=0,x), map(rhs,%)
[x = - 1, x = 2]
[- 1, 2]
>solve([a+b=4,a-b+c=5,a+c=1],[a,b,c]), at(a+b+c,%[1])
[[a = 8, b = - 4, c = - 7]]
- 3
>solve([a+b+c=1,a+2*a+3*c=1],[a,b]), at(a,%[1])
3 c - 1 2
[[a = - -------, b = -]]
3 3
3 c - 1
- -------
3
>ode2('diff(y,x)=y+x^2,y,x), solve(at(%,[x=0,y=1])=1,%c)
2 - x x
y = ((- x - 2 x - 2) E + %c) E
[%c = 3]
>diff(x^x,x), diff(x^x,x,2)
x
x (log(x) + 1)
x 2 x - 1
x (log(x) + 1) + x
>integrate(x*sin(x),x), at(%,x=%pi)-at(%,x=0)
sin(x) - x cos(x)
pi
>integrate(x*sin(x),x,0,%pi)
pi
>quad_qags(x^x,x,0,1), %[1]
[0.78343051071213, 3.3514857555871913E-11, 231, 0]
0.78343051071213
>limit(x^x,x,0,plus)
1
>limit(x*sin(1/x),x,inf)
1
>tlimit(x*((1+1/x)^x-%e),x,inf)
E
- -
2
>powerseries(log(x),x,1)
inf
==== i1 i1
\ (- 1) (x - 1)
- > -----------------
/ i1
====
i1 = 1
>subst(t,x+1,x^2+x+1), ratsubst(t,x+1,x^2+x+1)
2
x + x + 1
2
t - t + 1
>factor(x^4-1), gfactor(x^4-1)
2
(x - 1) (x + 1) (x + 1)
(x - 1) (x + 1) (x - I) (x + I)
>polarform(1+%i), rectform(%)
I pi
----
4
sqrt(2) E
I + 1
>float(sin(1+%i))
0.63496391478474 I + 1.298457581415977
>log(a*b)-log(a)+log(a^c), % | logexpand=super
log(a) c + log(a b) - log(a)
log(a) c + log(b)
>logcontract(2*log(a)+3*log(b))
2 3
log(a b )
>exponentialize(sinh(1)+cosh(1)), ratsimp(%)
- 1 - 1
E + E E - E
-------- + --------
2 2
E
>maximamode off
Maxima mode is off
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