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## Operations on real numbers

AXIOM SESSIONscale=2.5]

```Ran := RealClosure(Fraction Integer)

(1)  RealClosure Fraction Integer
Type: Domain
Time: 0 sec

s2 := sqrt(2)\$Ran

+-+
(2)  \|2
Type: RealClosure Fraction Integer
Time: 0.01 (EV) + 0.02 (OT) + 0.03 (GC) = 0.06 sec

s5 := sqrt(5)\$Ran

+-+
(3)  \|5
Type: RealClosure Fraction Integer
Time: 0 sec

s10 := sqrt(10)\$Ran

+--+
(4)  \|10
Type: RealClosure Fraction Integer
Time: 0 sec

eq1:=sqrt(s10+3)*sqrt(s5+2) - sqrt(s10-3)*sqrt(s5-2) = sqrt(10*s2+10)

+---------+ +--------+    +---------+ +--------+   +-----------+
| +--+      | +-+         | +--+      | +-+        |   +-+
(5)  - \|\|10  - 3 \|\|5  - 2  + \|\|10  + 3 \|\|5  + 2 = \|10\|2  + 10
Type: Equation RealClosure Fraction Integer
Time: 0.06 (IN) + 0.03 (EV) + 0.01 (OT) = 0.10 sec

eq1::Boolean

(6)  true
Type: Boolean
Time: 0.19 (IN) = 0.19 sec

precision()\$Float

(7)  68
Type: PositiveInteger
Time: 0.01 (OT) = 0.01 sec

f2: Float := sqrt(2)

(8)  1.4142135623 730950488
Type: Float
Time: 0 sec

f5: Float := sqrt(5)

(9)  2.2360679774 997896964
Type: Float
Time: 0 sec

f10: Float := sqrt(10)

(10)  3.1622776601 68379332
Type: Float
Time: 0 sec

eq1bis:=sqrt(f10+3)*sqrt(f5+2) - sqrt(f10-3)*sqrt(f5-2) = sqrt(10*f2+10)

(11)  4.9134647270 262305698= 4.9134647270 262305698
Type: Equation Float
Time: 0.03 (IN) = 0.03 sec

eq1bis::Boolean

(12)  true
Type: Boolean
Time: 0 sec

r3:Ran:=sqrt(3,5)

5+-+
(13)  \|3
Type: RealClosure Fraction Integer
Time: 0 sec

r25:Ran:=sqrt(1/25,5)

+--+
| 1
(14)  5|--
\|25
Type: RealClosure Fraction Integer
Time: 0 sec

r32:Ran:=sqrt(32/5,5)

+--+
|32
(15)  5|--
\| 5
Type: RealClosure Fraction Integer
Time: 0 sec

r27:Ran:=sqrt(27/5,5)

+--+
|27
(16)  5|--
\| 5
Type: RealClosure Fraction Integer
Time: 0 sec

eq2:=sqrt((r32-r27,3)) = r25*(1+r3-r3**2)

+---------------+
|   +--+    +--+                         +--+
|   |27     |32       5+-+2   5+-+       | 1
(17)  3|- 5|--  + 5|--  = (- \|3   + \|3  + 1) 5|--
\|  \| 5    \| 5                         \|25
Type: Equation RealClosure Fraction Integer
Time: 0.01 (IN) + 0.05 (EV) = 0.06 sec

eq2::Boolean

(18)  true
Type: Boolean
Time: 3.14 (IN) + 0.30 (GC) = 3.44 sec

d3:Float:=nthRoot(3,5)

(19)  1.2457309396 15517326
Type: Float
Time: 0.01 (EV) + 0.01 (OT) = 0.02 sec

d25:Float:=nthRoot(1/25,5)

(20)  0.5253055608 8075344729
Type: Float
Time: 0.01 (IN) = 0.01 sec

d32:Float:=nthRoot(32/5,5)

(21)  1.4495593273 553910629
Type: Float
Time: 0.01 (EV) = 0.01 sec

d27:Float:=nthRoot(27/5,5)

(22)  1.4011310323 534026984
Type: Float
Time: 0 sec

eq2bis:=nthRoot((d32-d27,3)) = d25*(1+d3-d3**2)

(23)  0.3645018412 1606803517= 0.3645018412 1606803518
Type: Equation Float
Time: 0.01 (EV) = 0.01 sec

eq2bis::Boolean

(24)  false
Type: Boolean
```

Next: Operations on matrices Up: An introduction to Computer Algebra Previous: Operations on rational numbers
Marc Moreno Maza
2003-06-06