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How does FriCAS compute inverse trigonometric functions symbolically?

fricas
v:EXPR INT:= x+a * y
 (1)
Type: Expression(Integer)
fricas
t:=asec v
 (2)
Type: Expression(Integer)
fricas
simplify t
 (3)
Type: Expression(Integer)
fricas
s:=atan(sqrt(v^2-1))
 (4)
Type: Expression(Integer)
fricas
(s=t)::Boolean
 (5)
Type: Boolean

fricas
subst(t,a=%i)
 (6)
Type: Expression(Complex(Integer))
fricas
w:COMPLEX EXPR INT:=x+%i*y
 (7)
Type: Complex(Expression(Integer))

The following command generates a huge expression that is too large for MathAction to handle properly:

  \begin{axiom}
asec(w)
\end{axiom}


fricas
)set output algebra on

fricas
)set output tex off

fricas
asec(w)
(8)
-
2
*
atan
+-------------------------------+
| 4      2      2    4     2
5     2 3    4   |y  + (2x  + 2)y  + x  - 2x  + 1     5
(y  + 2x y  + x y) |-------------------------------  + y
|         4     2 2    4
\|        y  + 2x y  + x
+
2      3     4    2
(2x  + 1)y  + (x  - x )y
*
ROOT
8      2      6      4    2  4      6    4  2
y  + (4x  + 1)y  + (6x  + x )y  + (4x  - x )y
+
8    6
x  - x
*
+-------------------------------+
| 4      2      2    4     2
|y  + (2x  + 2)y  + x  - 2x  + 1
|-------------------------------
|         4     2 2    4
\|        y  + 2x y  + x
+
8      2      6      4     2      4
y  + (4x  + 2)y  + (6x  + 2x  + 1)y
+
6     4     2  2    8     6    4
(4x  - 2x  + 2x )y  + x  - 2x  + x
/
8      2      6      4    2  4      6    4  2
y  + (4x  + 1)y  + (6x  + x )y  + (4x  - x )y
+
8    6
x  - x
*
+-------------------------------+
| 4      2      2    4     2
|y  + (2x  + 2)y  + x  - 2x  + 1
|-------------------------------
|         4     2 2    4
\|        y  + 2x y  + x
+
8      2      6      4     2      4      6     4  2
y  + (4x  + 2)y  + (6x  + 2x  + 1)y  + (4x  - 2x )y
+
8     6    4
x  - 2x  + x
+
6     2 4     4 2    6
(- y  - 3x y  - 3x y  - x )
*
+-------------------------------+
| 4      2      2    4     2
|y  + (2x  + 2)y  + x  - 2x  + 1
|-------------------------------
|         4     2 2    4
\|        y  + 2x y  + x
+
6        2      4     4 2    6    4
- y  + (- 3x  - 1)y  - 3x y  - x  + x
*
+-------------------------------+
| 4      2      2    4     2
|y  + (2x  + 2)y  + x  - 2x  + 1
|-------------------------------
4|         4     2 2    4
\|        y  + 2x y  + x
/
+-------------------------------+
| 4      2      2    4     2
6     2 4     4 2    6  |y  + (2x  + 2)y  + x  - 2x  + 1
(y  + 3x y  + 3x y  + x ) |-------------------------------
|         4     2 2    4
\|        y  + 2x y  + x
+
6      2      4     4 2    6    4
y  + (3x  + 1)y  + 3x y  + x  - x
*
ROOT
8      2      6      4    2  4      6    4  2
y  + (4x  + 1)y  + (6x  + x )y  + (4x  - x )y
+
8    6
x  - x
*
+-------------------------------+
| 4      2      2    4     2
|y  + (2x  + 2)y  + x  - 2x  + 1
|-------------------------------
|         4     2 2    4
\|        y  + 2x y  + x
+
8      2      6      4     2      4
y  + (4x  + 2)y  + (6x  + 2x  + 1)y
+
6     4     2  2    8     6    4
(4x  - 2x  + 2x )y  + x  - 2x  + x
/
8      2      6      4    2  4      6    4  2
y  + (4x  + 1)y  + (6x  + x )y  + (4x  - x )y
+
8    6
x  - x
*
+-------------------------------+
| 4      2      2    4     2
|y  + (2x  + 2)y  + x  - 2x  + 1
|-------------------------------
|         4     2 2    4
\|        y  + 2x y  + x
+
8      2      6      4     2      4      6     4  2
y  + (4x  + 2)y  + (6x  + 2x  + 1)y  + (4x  - 2x )y
+
8     6    4
x  - 2x  + x
*
ROOT
21         2       19
- 2y   + (- 20x  - 10)y
+
4      2       17
(- 90x  - 72x  - 20)y
+
6       4      2       15
(- 240x  - 216x  - 98x  - 20)y
+
8       6       4      2       13
(- 420x  - 336x  - 180x  - 62x  - 10)y
+
10       8       6      4      2
(- 504x   - 252x  - 142x  - 62x  - 18x  - 2)
*
11
y
+
12      8      6     4     2  9
(- 420x   - 40x  - 20x  - 8x  - 2x )y
+
14       12      10  7
(- 240x   + 168x   - 30x  )y
+
16       14      12      10  5
(- 90x   + 144x   - 68x   + 10x  )y
+
18      16      14      12     10  3
(- 20x   + 54x   - 50x   + 18x   - 2x  )y
+
20     18      16     14     12
(- 2x   + 8x   - 12x   + 8x   - 2x  )y
*
+-------------------------------+
| 4      2      2    4     2
|y  + (2x  + 2)y  + x  - 2x  + 1
|-------------------------------
|         4     2 2    4
\|        y  + 2x y  + x
+
21         2       19
- 2y   + (- 20x  - 12)y
+
4      2       17
(- 90x  - 86x  - 30)y
+
6       4       2       15
(- 240x  - 256x  - 144x  - 40)y
+
8       6       4       2       13
(- 420x  - 392x  - 254x  - 116x  - 30)y
+
10       8       6       4      2       11
(- 504x   - 280x  - 180x  - 100x  - 44x  - 12)y
+
12      10      8      6      4     2
- 420x   + 28x   - 30x  - 20x  - 12x  - 6x
+
- 2
*
9
y
+
14       12      10  7
(- 240x   + 224x   - 40x  )y
+
16       14       12      10  5
(- 90x   + 184x   - 114x   + 20x  )y
+
18      16      14      12     10  3
(- 20x   + 68x   - 84x   + 44x   - 8x  )y
+
20      18      16      14      12     10
(- 2x   + 10x   - 20x   + 20x   - 10x   + 2x  )y
*
+-------------------------------+
| 4      2      2    4     2
|y  + (2x  + 2)y  + x  - 2x  + 1
|-------------------------------
4|         4     2 2    4
\|        y  + 2x y  + x
*
ROOT
8      2      6      4    2  4
y  + (4x  + 1)y  + (6x  + x )y
+
6    4  2    8    6
(4x  - x )y  + x  - x
*
+-------------------------------+
| 4      2      2    4     2
|y  + (2x  + 2)y  + x  - 2x  + 1
|-------------------------------
|         4     2 2    4
\|        y  + 2x y  + x
+
8      2      6      4     2      4
y  + (4x  + 2)y  + (6x  + 2x  + 1)y
+
6     4     2  2    8     6    4
(4x  - 2x  + 2x )y  + x  - 2x  + x
/
8      2      6      4    2  4
y  + (4x  + 1)y  + (6x  + x )y
+
6    4  2    8    6
(4x  - x )y  + x  - x
*
+-------------------------------+
| 4      2      2    4     2
|y  + (2x  + 2)y  + x  - 2x  + 1
|-------------------------------
|         4     2 2    4
\|        y  + 2x y  + x
+
8      2      6      4     2      4
y  + (4x  + 2)y  + (6x  + 2x  + 1)y
+
6     4  2    8     6    4
(4x  - 2x )y  + x  - 2x  + x
+
22       2      20       4      2       18
y   + (11x  + 5)y   + (55x  + 40x  + 10)y
+
6       4      2       16
(165x  + 135x  + 56x  + 10)y
+
8       6       4      2      14
(330x  + 240x  + 122x  + 38x  + 5)y
+
10       8       6      4      2      12
(462x   + 210x  + 126x  + 52x  + 13x  + 1)y
+
12      8      6      4     2  10
(462x   + 70x  + 30x  + 11x  + 2x )y
+
14       12      10     6    4  8
(330x   - 210x   + 70x   + 3x  + x )y
+
16       14       12      10     8  6
(165x   - 240x   + 126x   - 30x   + 3x )y
+
18       16       14      12      10
55x   - 135x   + 122x   - 52x   + 11x
+
8
- x
*
4
y
+
20      18      16      14      12
11x   - 40x   + 56x   - 38x   + 13x
+
10
- 2x
*
2
y
+
22     20      18      16     14    12
x   - 5x   + 10x   - 10x   + 5x   - x
*
+-------------------------------+
| 4      2      2    4     2
|y  + (2x  + 2)y  + x  - 2x  + 1
|-------------------------------
|         4     2 2    4
\|        y  + 2x y  + x
+
22       2      20       4      2       18
y   + (11x  + 6)y   + (55x  + 48x  + 15)y
+
6       4      2       16
(165x  + 162x  + 83x  + 20)y
+
8       6       4      2       14
(330x  + 288x  + 176x  + 72x  + 15)y
+
10       8       6      4      2      12
(462x   + 252x  + 168x  + 88x  + 33x  + 6)y
+
12      8      6      4     2      10
(462x   + 70x  + 40x  + 21x  + 8x  + 1)y
+
14       12      10     6     4    2  8
(330x   - 252x   + 70x   + 3x  + 2x  + x )y
+
16       14       12      10     8  6
(165x   - 288x   + 168x   - 40x   + 3x )y
+
18       16       14      12      10     8  4
(55x   - 162x   + 176x   - 88x   + 21x   - 2x )y
+
20      18      16      14      12     10
11x   - 48x   + 83x   - 72x   + 33x   - 8x
+
8
x
*
2
y
+
22     20      18      16      14     12    10
x   - 6x   + 15x   - 20x   + 15x   - 6x   + x
*
+-------------------------------+2
| 4      2      2    4     2
|y  + (2x  + 2)y  + x  - 2x  + 1
|-------------------------------
4|         4     2 2    4
\|        y  + 2x y  + x
+
20       2      18       4      2       16
y   + (10x  + 5)y   + (45x  + 35x  + 10)y
+
6       4      2       14
(120x  + 100x  + 46x  + 10)y
+
8       6      4      2      12
(210x  + 140x  + 76x  + 28x  + 5)y
+
10      8      6      4     2      10
(252x   + 70x  + 50x  + 24x  + 8x  + 1)y
+
12      10      8     6     4    2  8
(210x   - 70x   + 20x  + 6x  + 3x  + x )y
+
14       12      10     8  6
(120x   - 140x   + 50x   - 6x )y
+
16       14      12      10     8  4
(45x   - 100x   + 76x   - 24x   + 3x )y
+
18      16      14      12     10    8  2
(10x   - 35x   + 46x   - 28x   + 8x   - x )y
+
20     18      16      14     12    10
x   - 5x   + 10x   - 10x   + 5x   - x
*
+-------------------------------+
| 4      2      2    4     2
|y  + (2x  + 2)y  + x  - 2x  + 1
|-------------------------------
|         4     2 2    4
\|        y  + 2x y  + x
+
20       2      18       4      2       16
y   + (10x  + 6)y   + (45x  + 42x  + 15)y
+
6       4      2       14
(120x  + 120x  + 68x  + 20)y
+
8       6       4      2       12
(210x  + 168x  + 108x  + 52x  + 15)y
+
10      8      6      4      2      10
(252x   + 84x  + 60x  + 36x  + 18x  + 6)y
+
12      10      8     6     4     2      8
(210x   - 84x   + 10x  + 4x  + 3x  + 2x  + 1)y
+
14       12      10     8  6
(120x   - 168x   + 60x   - 4x )y
+
16       14       12      10     8  4
(45x   - 120x   + 108x   - 36x   + 3x )y
+
18      16      14      12      10     8  2    20
(10x   - 42x   + 68x   - 52x   + 18x   - 2x )y  + x
+
18      16      14      12     10    8
- 6x   + 15x   - 20x   + 15x   - 6x   + x
/
22       2      20       4      2       18
y   + (11x  + 5)y   + (55x  + 40x  + 10)y
+
6       4      2       16
(165x  + 135x  + 56x  + 10)y
+
8       6       4      2      14
(330x  + 240x  + 122x  + 38x  + 5)y
+
10       8       6      4      2      12
(462x   + 210x  + 126x  + 52x  + 13x  + 1)y
+
12      8      6      4     2  10
(462x   + 70x  + 30x  + 11x  + 2x )y
+
14       12      10     6    4  8
(330x   - 210x   + 70x   + 3x  + x )y
+
16       14       12      10     8  6
(165x   - 240x   + 126x   - 30x   + 3x )y
+
18       16       14      12      10    8  4
(55x   - 135x   + 122x   - 52x   + 11x   - x )y
+
20      18      16      14      12     10  2
(11x   - 40x   + 56x   - 38x   + 13x   - 2x  )y
+
22     20      18      16     14    12
x   - 5x   + 10x   - 10x   + 5x   - x
*
+-------------------------------+
| 4      2      2    4     2
|y  + (2x  + 2)y  + x  - 2x  + 1
|-------------------------------
|         4     2 2    4
\|        y  + 2x y  + x
+
22       2      20       4      2       18
y   + (11x  + 6)y   + (55x  + 48x  + 15)y
+
6       4      2       16
(165x  + 162x  + 83x  + 20)y
+
8       6       4      2       14
(330x  + 288x  + 176x  + 72x  + 15)y
+
10       8       6      4      2      12
(462x   + 252x  + 168x  + 88x  + 33x  + 6)y
+
12      8      6      4     2      10
(462x   + 70x  + 40x  + 21x  + 8x  + 1)y
+
14       12      10     6     4    2  8
(330x   - 252x   + 70x   + 3x  + 2x  + x )y
+
16       14       12      10     8  6
(165x   - 288x   + 168x   - 40x   + 3x )y
+
18       16       14      12      10     8  4
(55x   - 162x   + 176x   - 88x   + 21x   - 2x )y
+
20      18      16      14      12     10    8  2
(11x   - 48x   + 83x   - 72x   + 33x   - 8x   + x )y
+
22     20      18      16      14     12    10
x   - 6x   + 15x   - 20x   + 15x   - 6x   + x
+
+-------------------------------+
| 4      2      2    4     2
4     3 2    5  |y  + (2x  + 2)y  + x  - 2x  + 1
(x y  + 2x y  + x ) |-------------------------------
|         4     2 2    4
\|        y  + 2x y  + x
+
4      3      2    5    3
x y  + (2x  + x)y  + x  - x
*
ROOT
8      2      6      4    2  4      6    4  2
y  + (4x  + 1)y  + (6x  + x )y  + (4x  - x )y
+
8    6
x  - x
*
+-------------------------------+
| 4      2      2    4     2
|y  + (2x  + 2)y  + x  - 2x  + 1
|-------------------------------
|         4     2 2    4
\|        y  + 2x y  + x
+
8      2      6      4     2      4
y  + (4x  + 2)y  + (6x  + 2x  + 1)y
+
6     4     2  2    8     6    4
(4x  - 2x  + 2x )y  + x  - 2x  + x
/
8      2      6      4    2  4      6    4  2
y  + (4x  + 1)y  + (6x  + x )y  + (4x  - x )y
+
8    6
x  - x
*
+-------------------------------+
| 4      2      2    4     2
|y  + (2x  + 2)y  + x  - 2x  + 1
|-------------------------------
|         4     2 2    4
\|        y  + 2x y  + x
+
8      2      6      4     2      4      6     4  2
y  + (4x  + 2)y  + (6x  + 2x  + 1)y  + (4x  - 2x )y
+
8     6    4
x  - 2x  + x
+
+-------------------------------+
| 4      2      2    4     2
3     3    |y  + (2x  + 2)y  + x  - 2x  + 1
(- 2x y  - 2x y)  |-------------------------------
4|         4     2 2    4
\|        y  + 2x y  + x
+
-
log
21         2       19         4      2       17
- 2y   + (- 20x  - 10)y   + (- 90x  - 72x  - 20)y
+
6       4      2       15
(- 240x  - 216x  - 98x  - 20)y
+
8       6       4      2       13
(- 420x  - 336x  - 180x  - 62x  - 10)y
+
10       8       6      4      2      11
(- 504x   - 252x  - 142x  - 62x  - 18x  - 2)y
+
12      8      6     4     2  9
(- 420x   - 40x  - 20x  - 8x  - 2x )y
+
14       12      10  7
(- 240x   + 168x   - 30x  )y
+
16       14      12      10  5
(- 90x   + 144x   - 68x   + 10x  )y
+
18      16      14      12     10  3
(- 20x   + 54x   - 50x   + 18x   - 2x  )y
+
20     18      16     14     12
(- 2x   + 8x   - 12x   + 8x   - 2x  )y
*
+-------------------------------+
| 4      2      2    4     2
|y  + (2x  + 2)y  + x  - 2x  + 1
|-------------------------------
|         4     2 2    4
\|        y  + 2x y  + x
+
21         2       19         4      2       17
- 2y   + (- 20x  - 12)y   + (- 90x  - 86x  - 30)y
+
6       4       2       15
(- 240x  - 256x  - 144x  - 40)y
+
8       6       4       2       13
(- 420x  - 392x  - 254x  - 116x  - 30)y
+
10       8       6       4      2       11
(- 504x   - 280x  - 180x  - 100x  - 44x  - 12)y
+
12      10      8      6      4     2      9
(- 420x   + 28x   - 30x  - 20x  - 12x  - 6x  - 2)y
+
14       12      10  7
(- 240x   + 224x   - 40x  )y
+
16       14       12      10  5
(- 90x   + 184x   - 114x   + 20x  )y
+
18      16      14      12     10  3
(- 20x   + 68x   - 84x   + 44x   - 8x  )y
+
20      18      16      14      12     10
(- 2x   + 10x   - 20x   + 20x   - 10x   + 2x  )y
*
+-------------------------------+
| 4      2      2    4     2
|y  + (2x  + 2)y  + x  - 2x  + 1
|-------------------------------
4|         4     2 2    4
\|        y  + 2x y  + x
*
ROOT
8      2      6      4    2  4      6    4  2
y  + (4x  + 1)y  + (6x  + x )y  + (4x  - x )y
+
8    6
x  - x
*
+-------------------------------+
| 4      2      2    4     2
|y  + (2x  + 2)y  + x  - 2x  + 1
|-------------------------------
|         4     2 2    4
\|        y  + 2x y  + x
+
8      2      6      4     2      4
y  + (4x  + 2)y  + (6x  + 2x  + 1)y
+
6     4     2  2    8     6    4
(4x  - 2x  + 2x )y  + x  - 2x  + x
/
8      2      6      4    2  4      6    4  2
y  + (4x  + 1)y  + (6x  + x )y  + (4x  - x )y
+
8    6
x  - x
*
+-------------------------------+
| 4      2      2    4     2
|y  + (2x  + 2)y  + x  - 2x  + 1
|-------------------------------
|         4     2 2    4
\|        y  + 2x y  + x
+
8      2      6      4     2      4      6     4  2
y  + (4x  + 2)y  + (6x  + 2x  + 1)y  + (4x  - 2x )y
+
8     6    4
x  - 2x  + x
+
22       2      20       4      2       18
y   + (11x  + 5)y   + (55x  + 40x  + 10)y
+
6       4      2       16
(165x  + 135x  + 56x  + 10)y
+
8       6       4      2      14
(330x  + 240x  + 122x  + 38x  + 5)y
+
10       8       6      4      2      12
(462x   + 210x  + 126x  + 52x  + 13x  + 1)y
+
12      8      6      4     2  10
(462x   + 70x  + 30x  + 11x  + 2x )y
+
14       12      10     6    4  8
(330x   - 210x   + 70x   + 3x  + x )y
+
16       14       12      10     8  6
(165x   - 240x   + 126x   - 30x   + 3x )y
+
18       16       14      12      10    8  4
(55x   - 135x   + 122x   - 52x   + 11x   - x )y
+
20      18      16      14      12     10  2
(11x   - 40x   + 56x   - 38x   + 13x   - 2x  )y
+
22     20      18      16     14    12
x   - 5x   + 10x   - 10x   + 5x   - x
*
+-------------------------------+
| 4      2      2    4     2
|y  + (2x  + 2)y  + x  - 2x  + 1
|-------------------------------
|         4     2 2    4
\|        y  + 2x y  + x
+
22       2      20       4      2       18
y   + (11x  + 6)y   + (55x  + 48x  + 15)y
+
6       4      2       16
(165x  + 162x  + 83x  + 20)y
+
8       6       4      2       14
(330x  + 288x  + 176x  + 72x  + 15)y
+
10       8       6      4      2      12
(462x   + 252x  + 168x  + 88x  + 33x  + 6)y
+
12      8      6      4     2      10
(462x   + 70x  + 40x  + 21x  + 8x  + 1)y
+
14       12      10     6     4    2  8
(330x   - 252x   + 70x   + 3x  + 2x  + x )y
+
16       14       12      10     8  6
(165x   - 288x   + 168x   - 40x   + 3x )y
+
18       16       14      12      10     8  4
(55x   - 162x   + 176x   - 88x   + 21x   - 2x )y
+
20      18      16      14      12     10    8  2
(11x   - 48x   + 83x   - 72x   + 33x   - 8x   + x )y
+
22     20      18      16      14     12    10
x   - 6x   + 15x   - 20x   + 15x   - 6x   + x
*
+-------------------------------+2
| 4      2      2    4     2
|y  + (2x  + 2)y  + x  - 2x  + 1
|-------------------------------
4|         4     2 2    4
\|        y  + 2x y  + x
+
20       2      18       4      2       16
y   + (10x  + 5)y   + (45x  + 35x  + 10)y
+
6       4      2       14
(120x  + 100x  + 46x  + 10)y
+
8       6      4      2      12
(210x  + 140x  + 76x  + 28x  + 5)y
+
10      8      6      4     2      10
(252x   + 70x  + 50x  + 24x  + 8x  + 1)y
+
12      10      8     6     4    2  8
(210x   - 70x   + 20x  + 6x  + 3x  + x )y
+
14       12      10     8  6
(120x   - 140x   + 50x   - 6x )y
+
16       14      12      10     8  4
(45x   - 100x   + 76x   - 24x   + 3x )y
+
18      16      14      12     10    8  2    20
(10x   - 35x   + 46x   - 28x   + 8x   - x )y  + x
+
18      16      14     12    10
- 5x   + 10x   - 10x   + 5x   - x
*
+-------------------------------+
| 4      2      2    4     2
|y  + (2x  + 2)y  + x  - 2x  + 1
|-------------------------------
|         4     2 2    4
\|        y  + 2x y  + x
+
20       2      18       4      2       16
y   + (10x  + 6)y   + (45x  + 42x  + 15)y
+
6       4      2       14
(120x  + 120x  + 68x  + 20)y
+
8       6       4      2       12
(210x  + 168x  + 108x  + 52x  + 15)y
+
10      8      6      4      2      10
(252x   + 84x  + 60x  + 36x  + 18x  + 6)y
+
12      10      8     6     4     2      8
(210x   - 84x   + 10x  + 4x  + 3x  + 2x  + 1)y
+
14       12      10     8  6
(120x   - 168x   + 60x   - 4x )y
+
16       14       12      10     8  4
(45x   - 120x   + 108x   - 36x   + 3x )y
+
18      16      14      12      10     8  2    20     18
(10x   - 42x   + 68x   - 52x   + 18x   - 2x )y  + x   - 6x
+
16      14      12     10    8
15x   - 20x   + 15x   - 6x   + x
/
22       2      20       4      2       18
y   + (11x  + 5)y   + (55x  + 40x  + 10)y
+
6       4      2       16
(165x  + 135x  + 56x  + 10)y
+
8       6       4      2      14
(330x  + 240x  + 122x  + 38x  + 5)y
+
10       8       6      4      2      12
(462x   + 210x  + 126x  + 52x  + 13x  + 1)y
+
12      8      6      4     2  10
(462x   + 70x  + 30x  + 11x  + 2x )y
+
14       12      10     6    4  8
(330x   - 210x   + 70x   + 3x  + x )y
+
16       14       12      10     8  6
(165x   - 240x   + 126x   - 30x   + 3x )y
+
18       16       14      12      10    8  4
(55x   - 135x   + 122x   - 52x   + 11x   - x )y
+
20      18      16      14      12     10  2    22
(11x   - 40x   + 56x   - 38x   + 13x   - 2x  )y  + x
+
20      18      16     14    12
- 5x   + 10x   - 10x   + 5x   - x
*
+-------------------------------+
| 4      2      2    4     2
|y  + (2x  + 2)y  + x  - 2x  + 1
|-------------------------------
|         4     2 2    4
\|        y  + 2x y  + x
+
22       2      20       4      2       18
y   + (11x  + 6)y   + (55x  + 48x  + 15)y
+
6       4      2       16
(165x  + 162x  + 83x  + 20)y
+
8       6       4      2       14
(330x  + 288x  + 176x  + 72x  + 15)y
+
10       8       6      4      2      12
(462x   + 252x  + 168x  + 88x  + 33x  + 6)y
+
12      8      6      4     2      10
(462x   + 70x  + 40x  + 21x  + 8x  + 1)y
+
14       12      10     6     4    2  8
(330x   - 252x   + 70x   + 3x  + 2x  + x )y
+
16       14       12      10     8  6
(165x   - 288x   + 168x   - 40x   + 3x )y
+
18       16       14      12      10     8  4
(55x   - 162x   + 176x   - 88x   + 21x   - 2x )y
+
20      18      16      14      12     10    8  2    22
(11x   - 48x   + 83x   - 72x   + 33x   - 8x   + x )y  + x
+
20      18      16      14     12    10
- 6x   + 15x   - 20x   + 15x   - 6x   + x
/
2
*
%i
Type: Complex(Expression(Integer))

fricas
asec( %i )
(9)  asec(%i)
Type: Expression(Complex(Integer))

fricas
simplify asec( %i )
(10)  asec(%i)
Type: Expression(Complex(Integer))

I guess this one also causes a problem with MathAction:

  \begin{axiom}
simplify(sec(asec(w)))
\end{axiom}


Not coherent ?

fricas
)set output algebra off

fricas
)set output tex on

fricas
[atan(tan(x)), atan(tan(%pi))]
 (8)
Type: List(Expression(Integer))

 atan(tan(x)); reduce

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