# Axiom/FriCAS HTMLFormat Output

Here we have both normal text output and html text output turned on so that we can compare the results:

)set output html on

(x+y)*z

(1)  (y + x)z
(y+x) * z

Type: Polynomial(Integer)
(x-y)^2

2           2
(2)  y  - 2x y + x
y 2 - 2*x*y + x 2

Type: Polynomial(Integer)
integrate(x^x,x)

x
++    %F
(3)   |   %F  d%F
++
 x %F %F * d%F ∫

Type: Union(Expression(Integer),...)
integral(x^x,x)

x
++    %F
(4)   |   %F  d%F
++
 x %F %F * d%F ∫

Type: Expression(Integer)
(5 + sqrt 63 + sqrt 847)^(1/3)

+----------+
3|   +-+
(5)  \|14\|7  + 5
 3 √ 14 * √7 + 5
Type: AlgebraicNumber
set [1,2,3]

(6)  {1,2,3}
{
1,2,3
}

Type: Set(PositiveInteger)
multiset [x rem 5 for x in primes(2,1000)]

(7)  {47: 2,40: 1,42: 3,38: 4,0}
{
47: 2
,
40: 1
,
42: 3
,
38: 4
,
0
}

Type: Multiset(Integer)
(8) ->
)set output mathml on

series(sin(a*x),x=0)

3        5        7          9            11
a   3    a   5    a    7     a     9      a      11      12
(8)  a x - -- x  + --- x  - ---- x  + ------ x  - -------- x   + O(x  )
6      120      5040      362880      39916800
a*x
-
 a 3 6
* x 3
+
 a 5 120
* x 5
-
 a 7 5040
* x 7
+
 a 9 362880
* x 9
-
 a 11 39916800
* x 11
+ O ( x 12 )

Type: UnivariatePuiseuxSeries(Expression(Integer),x,0)
matrix [ [x^i + y^j for i in 1..4] for j in 1..4]

+             2        3        4 +
|y + x   y + x    y + x    y + x  |
|                                 |
| 2       2    2   2    3   2    4|
|y  + x  y  + x   y  + x   y  + x |
(9)  |                                 |
| 3       3    2   3    3   3    4|
|y  + x  y  + x   y  + x   y  + x |
|                                 |
| 4       4    2   4    3   4    4|
+y  + x  y  + x   y  + x   y  + x +
 y+x y + x 2 y + x 3 y + x 4 y 2 + x y 2 + x 2 y 2 + x 3 y 2 + x 4 y 3 + x y 3 + x 2 y 3 + x 3 y 3 + x 4 y 4 + x y 4 + x 2 y 4 + x 3 y 4 + x 4

Type: Matrix(Polynomial(Integer))
y1 := operator 'y

(10)  y
y

Type: BasicOperator
D(y1(x,z),[x,x,z,x])

(11)  y        (x,z)
,1,1,2,1

Type: Expression(Integer)
D(y1 x,x,2)

,,
(12)  y  (x)

ⅆ2yⅆx2⁡x)

Type: Expression(Integer)
(13) ->

Type: UnivariatePuiseuxSeries(Expression(Integer),x,0)
series(1/log(y),y2=1)

1
(15)  ------
log(y)
 1 log ( y )

Type: UnivariatePuiseuxSeries(Expression(Integer),y2,1)
y3:UTS(FLOAT,'z,0) := exp(z)

(16)
2                            3
1.0 + z + 0.5 z  + 0.1666666666 6666666667 z
+
4                               5
0.0416666666 6666666666 7 z  + 0.0083333333 3333333333 34 z
+
6                               7
0.0013888888 8888888888 89 z  + 0.0001984126 9841269841 27 z
+
8                                  9
0.0000248015 8730158730 1587 z  + 0.0000027557 3192239858 90653 z
+
10      11
0.2755731922 3985890653 E -6 z   + O(z  )
1.0 + z + 0.5 * z 2 + 0.1666666666 6666666667 * z 3 + 0.0416666666 6666666666 7 * z 4 + 0.0083333333 3333333333 34 * z 5 + 0.0013888888 8888888888 89 * z 6 + 0.0001984126 9841269841 27 * z 7 + 0.0000248015 8730158730 1587 * z 8 + 0.0000027557 3192239858 90653 * z 9 + 0.2755731922 3985890653 E -6 * z 10 + O ( z 11 )

Type: UnivariateTaylorSeries(Float,z,0.0)
c := continuedFraction(314159/100000)

1 |     1  |     1 |     1  |     1 |     1 |     1 |
(17)  3 + +---+ + +----+ + +---+ + +----+ + +---+ + +---+ + +---+
| 7     | 15     | 1     | 25     | 1     | 7     | 4
3 +
1
7+
1
15+
1
1+
1
25+
1
1+
1
7+
 1 4

Type: ContinuedFraction(Integer)
c := continuedFraction(14159/100000)

1 |     1  |     1 |     1  |     1 |     1 |     1 |
(18)  +---+ + +----+ + +---+ + +----+ + +---+ + +---+ + +---+
| 7     | 15     | 1     | 25     | 1     | 7     | 4
1
7+
1
15+
1
1+
1
25+
1
1+
1
7+
 1 4
Type: ContinuedFraction(Integer)
c := continuedFraction(3,repeating [1], repeating [3,6])

(19)
1 |     1 |     1 |     1 |     1 |     1 |     1 |     1 |     1 |
3 + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +---+
| 3     | 6     | 3     | 6     | 3     | 6     | 3     | 6     | 3
+
1 |
+---+ + ...
| 6
3 +
1
3+
1
6+
1
3+
1
6+
1
3+
1
6+
1
3+
1
6+
1
3+
 1 6+ …

Type: ContinuedFraction(Integer)
F := operator F

(20)  F
F

Type: BasicOperator
x4 := operator x

(21)  x
x

Type: BasicOperator
y4 := operator y

(22)  y
y

Type: BasicOperator
a := F(x4 z,y4 z,z^2) + x4 y4(z+1)

2
(23)  x(y(z + 1)) + F(x(z),y(z),z )
x ( y ( z+1 ) ) + F ( x ( z ) , y ( z ) , z 2 )

Type: Expression(Integer)
D(a,z)

(24)
2     ,                  2     ,                  2
2zF  (x(z),y(z),z ) + y (z)F  (x(z),y(z),z ) + x (z)F  (x(z),y(z),z )
,3                       ,2                       ,1
+
,           ,
x (y(z + 1))y (z + 1)
2 * z * x ( z ) y ( z ) z 2 + ⅆ1yⅆz1⁡z) * x ( z ) y ( z ) z 2 + ⅆ1xⅆz1⁡z) * x ( z ) y ( z ) z 2 + ⅆ1xⅆ y ( z+1 ) 1⁡ y ( z+1 ) ) * ⅆ1yⅆ z+1 1⁡ z+1 )
(1) -> )set output mathml on
(1) -> )library CLIF
CliffordAlgebra is now explicitly exposed in frame frame1
CliffordAlgebra will be automatically loaded when needed from
/home/martin/CLIF.NRLIB/CLIF
(1) -> B1 := CliffordAlgebra(2,Fraction(Integer),[[1,0],[0,1]])

(1)  CliffordAlgebra(2,Fraction(Integer),[[1,0],[0,1]])
Type: Domain
(2) -> e(1)\$B1

(2)  e
1
e 1
Type: CliffordAlgebra(2,Fraction(Integer),[[1,0],[0,1]])
(3) -> toTable(*)\$B1

+ 1      e      e    e e +
|         1      2    1 2|
|                        |
| e      1     e e    e  |
|  1            1 2    2 |
(3)  |                        |
| e    - e e    1    - e |
|  2      1 2           1|
|                        |
|e e    - e     e    - 1 |
+ 1 2      2     1       +
 1 e 1 e 2 e 1 * e 2 e 1 1 e 1 * e 2 e 2 e 2 - e 1 * e 2 1 - e 1 e 1 * e 2 - e 2 e 1 -1

Type: Matrix(CliffordAlgebra(2,Fraction(Integer),[[1,0],[0,1]]))
(4) ->