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