Here we have both normal text output and html text output turned on so that we can compare the results:
(1) -> )read axiom/testhtml1.input
)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
++
Type: Union(Expression(Integer),...)
integral(x^x,x)
x
++ %F
(4) | %F d%F
++
Type: Expression(Integer)
(5 + sqrt 63 + sqrt 847)^(1/3)
+----------+
3| +-+
(5) \|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) ->
(8) -> )read axiom/testhtml2.input
)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
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)
ⅆ2yⅆx2x)
Type: Expression(Integer)
(13) ->
Type: UnivariatePuiseuxSeries(Expression(Integer),x,0)
series(1/log(y),y2=1)
1
(15) ------
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
Type: ContinuedFraction(Integer)
c := continuedFraction(14159/100000)
1 | 1 | 1 | 1 | 1 | 1 | 1 |
(18) +---+ + +----+ + +---+ + +----+ + +---+ + +---+ + +---+
| 7 | 15 | 1 | 25 | 1 | 7 | 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
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
+
ⅆ1yⅆz1z)
*
x
(
z
)
y
(
z
)
z
2
+
ⅆ1xⅆz1z)
*
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) ->