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