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# Edit detail for SandBoxFriCAS2 revision 8 of 8

 1 2 3 4 5 6 7 8 Editor: TheDoctor Time: 2022/01/31 23:29:05 GMT+0 Note:

removed:
-
-
-From TheDoctor Mon Jan 31 23:22:48 +0000 2022
-From: TheDoctor
-Date: Mon, 31 Jan 2022 23:22:48 +0000
-Subject:
-Message-ID: <20220131232248+0000@fricas-wiki.math.uni.wroc.pl>
-
-\begin{axiom}
-fricas
-integrate(1/(1+exp(b*x)),x=-m..%plusInfinity, "noPole")
-\end{axiom}
-


Try FriCAS calculations here. For example, here is a simple FriCAS command:

    \begin{axiom}
integrate(1/(a+z^3), z=0..1,"noPole")
\end{axiom}


fricas
integrate(1/(a+z^3), z=0..1,"noPole")
 (1)
Type: Union(f1: OrderedCompletion?(Expression(Integer)),...)

Remember to type \begin{axiom} before each group of commands and \end{axiom} after the commands.

fricas
integrate(1/sqrt(1+x^2), x)
 (2)
Type: Union(Expression(Integer),...)

fricas
)set output algebra on

fricas
)set output tex off
F1:=integrate(cos(t)*sqrt(cos(2*t)),t)
(3)
+-+      4       +-+      2       +-+
+-+     32 \|2 cos(t)  - 48 \|2 cos(t)  + 17 \|2
- \|2 atan(-----------------------------------------)
+-------------+
2             |        2
(32 cos(t)  - 24)sin(t)\|2 cos(t)  - 1
+
+-------------+
|        2
8 sin(t)\|2 cos(t)  - 1
/
16
Type: Union(Expression(Integer),...)
fricas
draw(F1,t=-%pi/4..%pi/4)
fricas
Compiling function %BD with type DoubleFloat -> DoubleFloat
Graph data being transmitted to the viewport manager...
FriCAS2D data being transmitted to the viewport manager...
(4)  TwoDimensionalViewport: "FriCAS2D"
Type: TwoDimensionalViewport?
fricas
integrate(cos(t)*sqrt(cos(2*t)),t=-%pi/4..%pi/4)
(5)  "potentialPole"
Type: Union(pole: potentialPole,...)

fricas
integrate(abs(x),x=0..1)
(6)  "potentialPole"
Type: Union(pole: potentialPole,...)
fricas
integrate(abs(x),x=0..1,"noPole")
(7)  "failed"
Type: Union(fail: failed,...)

fricas
integrate(abs(x),x=-1..1)
(8)  "potentialPole"
Type: Union(pole: potentialPole,...)
fricas
integrate(abs(x),x=-1..1,"noPole")
(9)  "failed"
Type: Union(fail: failed,...)

fricas
integrate(sqrt(x^2),x=0..1)
1
(10)  -
2
Type: Union(f1: OrderedCompletion?(Expression(Integer)),...)
fricas
integrate(sqrt(x^2),x=0..1,"noPole")
1
(11)  -
2
Type: Union(f1: OrderedCompletion?(Expression(Integer)),...)

fricas
integrate(sqrt(x^2),x=-1..1)
(12)  "potentialPole"
Type: Union(pole: potentialPole,...)
fricas
integrate(sqrt(x^2),x=-1..1,"noPole")
(13)  0
Type: Union(f1: OrderedCompletion?(Expression(Integer)),...)

fricas
)version
Value = "FriCAS 1.3.7 compiled at Wed Jun 30 16:44:06 UTC 2021"

fricas
solve(x*b -3*a*b + a*x - 9*b*b-4*b*x = a*a - 9*a*b ,x)
(14)  [x = - 3 b + a]
Type: List(Equation(Fraction(Polynomial(Integer))))

fricas
solve(-1*(a+3*b)^2 - 3*b*x -a*x = 0,x)
(15)  [x = - 3 b - a]
Type: List(Equation(Fraction(Polynomial(Integer))))

fricas
solve(-1*(a+3*b)^2 - 3*b*x +a*x = 0,x)
2            2
- 9 b  - 6 a b - a
(16)  [x = -------------------]
3 b - a
Type: List(Equation(Fraction(Polynomial(Integer))))

fricas
solve(-1*(a-3*b)^2 - 3*b*x +a*x = 0,x)
(17)  [x = - 3 b + a]
Type: List(Equation(Fraction(Polynomial(Integer))))

fricas
solve((a-3*b)*(x-a+3*b) = 0,x)
(18)  [x = - 3 b + a]
Type: List(Equation(Fraction(Polynomial(Integer))))

Coherent type inference --gdr, Thu, 21 Feb 2008 20:30:01 -0800 reply
fricas
a : (INT,INT) := (2,3)
The constructor Tuple takes 1 argument and you have given  2  .

fricas
(1,2)
(19)  [1, 2]
Type: Tuple(PositiveInteger?)

fricas
('Mon,'Tue)
(20)  [Mon, Tue]
Type: Tuple(OrderedVariableList([Mon,Tue]))

fricas
a := 'x :: OutputForm
(21)  x
Type: OutputForm?
fricas
b := 'y :: OutputForm
(22)  y
Type: OutputForm?
fricas
a and b
Argument number 1 to "and" must be a Boolean.

fricas
)clear all
All user variables and function definitions have been cleared.

fricas
y := operator 'y
(1)  y
Type: BasicOperator?
fricas
deq := D(y(x), x, 2) + D(y(x), x) + y(x) + cos(y(x)) = 0
,,       ,
(2)  y  (x) + y (x) + cos(y(x)) + y(x) = 0
Type: Equation(Expression(Integer))
fricas
solve(deq, y, x)
>> Error detected within library code:
parseLODE: not a linear ordinary differential equation

fricas
y := operator 'y;
Type: BasicOperator?
fricas
deq := D(y(x), x, 2) + D(y(x), x) + y(x) + 1 = 0;
Type: Equation(Expression(Integer))
fricas
solve(deq, y, x);
Type: Union(Record(particular: Expression(Integer),basis: List(Expression(Integer))),...)

SandBoxMaybe

fricas
factor(1-x^900)
(6)
-
2           2       2           4    3    2
(x - 1)(x + 1)(x  - x + 1)(x  + 1)(x  + x + 1)(x  - x  + x  - x + 1)
*
4    2       4    3    2           6    3       6    3
(x  - x  + 1)(x  + x  + x  + x + 1)(x  - x  + 1)(x  + x  + 1)
*
8    7    5    4    3           8    6    4    2
(x  - x  + x  - x  + x  - x + 1)(x  - x  + x  - x  + 1)
*
8    7    5    4    3           12    6
(x  + x  - x  - x  - x  + x + 1)(x   - x  + 1)
*
16    14    10    8    6    2       20    15    10    5
(x   + x   - x   - x  - x  + x  + 1)(x   - x   + x   - x  + 1)
*
20    15    10    5       24    21    15    12    9    3
(x   + x   + x   + x  + 1)(x   - x   + x   - x   + x  - x  + 1)
*
24    21    15    12    9    3
(x   + x   - x   - x   - x  + x  + 1)
*
40    35    25    20    15    5       40    30    20    10
(x   - x   + x   - x   + x   - x  + 1)(x   - x   + x   - x   + 1)
*
40    35    25    20    15    5
(x   + x   - x   - x   - x   + x  + 1)
*
48    42    30    24    18    6
(x   + x   - x   - x   - x   + x  + 1)
*
80    70    50    40    30    10
(x   + x   - x   - x   - x   + x   + 1)
*
120    105    75    60    45    15
(x    - x    + x   - x   + x   - x   + 1)
*
120    105    75    60    45    15
(x    + x    - x   - x   - x   + x   + 1)
*
240    210    150    120    90    30
(x    + x    - x    - x    - x   + x   + 1)
Type: Factored(Polynomial(Integer))

fricas
simplify((a+b+2*sqrt(a)*sqrt(b))/(sqrt(a)+sqrt(b)))
+-+ +-+
2 \|a \|b  + b + a
(7)  ------------------
+-+    +-+
\|b  + \|a
Type: Expression(Integer)

fricas
simplify ( sin(a)^2+sin(%pi/2-a)^2 )
%pi - 2 a 2         2
(8)  - cos(---------)  - cos(a)  + 2
2
Type: Expression(Integer)

fricas
d:=sin(series(asin(x)))-x
21
(9)  O(x  )
Type: UnivariatePuiseuxSeries?(Expression(Integer),x,0)
fricas
1.2*d
21
(10)  O(x  )
Type: UnivariatePuiseuxSeries?(Expression(Float),x,0.0)

quicksort average --grinder, Wed, 26 Nov 2008 13:29:45 -0800 reply
fricas
solve( n*log(n)/log(m) = 1/4*n*log(n/4)/log(m) + 3/4*n*log(3/4*n)/log(m) + 15/4*n + 8, m)
3 n          n
4 n log(n) - 3 n log(---) - n log(-)
4           4
------------------------------------
15 n + 32
(11)  [m = %e                                    ]
Type: List(Equation(Expression(Integer)))

fricas
solve( log(n)/log(m) = 1/4*log(n/4)/log(m) + 3/4*log(3/4*n)/log(m) + 15/4*n + 8, m)
3 n        n
4 log(n) - 3 log(---) - log(-)
4         4
------------------------------
15 n + 32
(12)  [m = %e                              ]
Type: List(Equation(Expression(Integer)))

fricas
solve( log(n)/log(m) = log(n/4)/log(m) + log(3/4*n)/log(m) + 15/4*n + 8, m)
3 n          n
4 log(n) - 4 log(---) - 4 log(-)
4           4
--------------------------------
15 n + 32
(13)  [m = %e                                ]
Type: List(Equation(Expression(Integer)))

simple integration --kylekanos, Tue, 09 Dec 2008 09:55:35 -0800 reply
fricas
integrate((P*cos(x))/(2*e)*cos(x)*sin(x), x=0..%pi,"noPole")
P
(14)  ---
3 e
Type: Union(f1: OrderedCompletion?(Expression(Integer)),...)

Bessel Integral

fricas
integrate(exp(z*cos(t)),t=0..2*%pi)
(15)  "failed"
Type: Union(fail: failed,...)

fricas
integrate(x/sqrt(x^4+10*x^2-96*x-71),x)
(16)
log
+----------------------+
6       4       3       2                | 4       2
(x  + 15 x  - 80 x  + 27 x  - 528 x + 781)\|x  + 10 x  - 96 x - 71
+
8       6        5       4         3         2
x  + 20 x  - 128 x  + 54 x  - 1408 x  + 3124 x  + 10001
/
8
Type: Union(Expression(Integer),...)

fricas
integrate(1/x, x=1..2)
(17)  log(2)
Type: Union(f1: OrderedCompletion?(Expression(Integer)),...)

fricas
integrate(a/x^3, x)
a
(18)  - ----
2
2 x
Type: Union(Expression(Integer),...)

fricas
solve(a^2+b^2=c^2,c)
2    2    2
(19)  [c  - b  - a  = 0]
Type: List(Equation(Fraction(Polynomial(Integer))))

A hard to compute integral --PAP, Tue, 28 Sep 2010 17:55:14 -0700 reply
fricas
integrate(1/sqrt(tan(x)), x)
(20)
-
+-+
4 \|2
*
atan
1
/
+---------------------------------------------+
|               +------+
|     +-+       |sin(x)
|- 2 \|2 cos(x) |------  + 2 sin(x) + 2 cos(x)
|              \|cos(x)
|---------------------------------------------
\|                    cos(x)
+
+------+
+-+ |sin(x)
\|2  |------  - 1
\|cos(x)
+
-
+-+
4 \|2
*
atan
1
/
+-------------------------------------------+
|             +------+
|   +-+       |sin(x)
|2 \|2 cos(x) |------  + 2 sin(x) + 2 cos(x)
|            \|cos(x)
|-------------------------------------------
\|                   cos(x)
+
+------+
+-+ |sin(x)
\|2  |------  + 1
\|cos(x)
+
+------+
+-+       |sin(x)
2 \|2 cos(x) |------  + 2 sin(x) + 2 cos(x)
+-+                \|cos(x)
\|2 log(-------------------------------------------)
cos(x)
+
+------+
+-+       |sin(x)
- 2 \|2 cos(x) |------  + 2 sin(x) + 2 cos(x)
+-+                  \|cos(x)
- \|2 log(---------------------------------------------)
cos(x)
/
4
Type: Union(Expression(Integer),...)
fricas
a :=simplify(integrate(1/sqrt(tan(x)), x))
(21)
-
+-+
4 \|2
*
atan
1
/
+---------------------------------------------+
|               +------+
|     +-+       |sin(x)
|- 2 \|2 cos(x) |------  + 2 sin(x) + 2 cos(x)
|              \|cos(x)
|---------------------------------------------
\|                    cos(x)
+
+------+
+-+ |sin(x)
\|2  |------  - 1
\|cos(x)
+
-
+-+
4 \|2
*
atan
1
/
+-------------------------------------------+
|             +------+
|   +-+       |sin(x)
|2 \|2 cos(x) |------  + 2 sin(x) + 2 cos(x)
|            \|cos(x)
|-------------------------------------------
\|                   cos(x)
+
+------+
+-+ |sin(x)
\|2  |------  + 1
\|cos(x)
+
+------+
+-+       |sin(x)
2 \|2 cos(x) |------  + 2 sin(x) + 2 cos(x)
+-+                \|cos(x)
\|2 log(-------------------------------------------)
cos(x)
+
+------+
+-+       |sin(x)
- 2 \|2 cos(x) |------  + 2 sin(x) + 2 cos(x)
+-+                  \|cos(x)
- \|2 log(---------------------------------------------)
cos(x)
/
4
Type: Expression(Integer)
fricas
b:=simplify(differentiate(a, x))
(22)
+------+
3                  4            2  |sin(x)
(48 cos(x) sin(x) + 39 cos(x)  - 64 cos(x) ) |------
\|cos(x)
*
+---------------------------------------------+
|               +------+
|     +-+       |sin(x)
|- 2 \|2 cos(x) |------  + 2 sin(x) + 2 cos(x)
|              \|cos(x)
|---------------------------------------------
\|                    cos(x)
+
+------+
3                  4            2  |sin(x)
(- 64 cos(x) sin(x) - 29 cos(x)  + 64 cos(x) ) |------
\|cos(x)
+
+-+      3       +-+                    +-+      4
(45 \|2 cos(x)  - 64 \|2 cos(x))sin(x) - 32 \|2 cos(x)
+
+-+      2
32 \|2 cos(x)
*
+-------------------------------------------+
|             +------+
|   +-+       |sin(x)
|2 \|2 cos(x) |------  + 2 sin(x) + 2 cos(x)
|            \|cos(x)
|-------------------------------------------
\|                   cos(x)
+
+------+
3                  4            2  |sin(x)
(64 cos(x) sin(x) + 29 cos(x)  - 64 cos(x) ) |------
\|cos(x)
+
+-+      3       +-+                    +-+      4
(45 \|2 cos(x)  - 64 \|2 cos(x))sin(x) - 32 \|2 cos(x)
+
+-+      2
32 \|2 cos(x)
*
+---------------------------------------------+
|               +------+
|     +-+       |sin(x)
|- 2 \|2 cos(x) |------  + 2 sin(x) + 2 cos(x)
|              \|cos(x)
|---------------------------------------------
\|                    cos(x)
+
+------+
3                                4            2  |sin(x)
((14 cos(x)  - 128 cos(x))sin(x) - 47 cos(x)  + 96 cos(x) ) |------
\|cos(x)
/
3                               4            2
((39 cos(x)  - 64 cos(x))sin(x) - 48 cos(x)  + 48 cos(x) )
*
+---------------------------------------------+
|               +------+
|     +-+       |sin(x)
|- 2 \|2 cos(x) |------  + 2 sin(x) + 2 cos(x)
|              \|cos(x)
|---------------------------------------------
\|                    cos(x)
+
+-+      3       +-+                    +-+      4
(45 \|2 cos(x)  - 64 \|2 cos(x))sin(x) - 32 \|2 cos(x)
+
+-+      2
32 \|2 cos(x)
*
+------+
|sin(x)
|------
\|cos(x)
+
3                               4            2
(- 29 cos(x)  + 64 cos(x))sin(x) + 64 cos(x)  - 64 cos(x)
*
+-------------------------------------------+
|             +------+
|   +-+       |sin(x)
|2 \|2 cos(x) |------  + 2 sin(x) + 2 cos(x)
|            \|cos(x)
|-------------------------------------------
\|                   cos(x)
+
+-+      3       +-+                    +-+      4
(45 \|2 cos(x)  - 64 \|2 cos(x))sin(x) - 32 \|2 cos(x)
+
+-+      2
32 \|2 cos(x)
*
+------+
|sin(x)
|------
\|cos(x)
+
3                               4            2
(29 cos(x)  - 64 cos(x))sin(x) - 64 cos(x)  + 64 cos(x)
*
+---------------------------------------------+
|               +------+
|     +-+       |sin(x)
|- 2 \|2 cos(x) |------  + 2 sin(x) + 2 cos(x)
|              \|cos(x)
|---------------------------------------------
\|                    cos(x)
+
3                               4             2
(- 47 cos(x)  + 96 cos(x))sin(x) - 14 cos(x)  + 142 cos(x)  - 128
Type: Expression(Integer)
fricas
normalize(b - 1/sqrt(tan(x)))
(23)  0
Type: Expression(Integer)