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Question: What makes expressions containing .1e11 and 0.1*10^11 different

Question:What makes expressions containing .1e11 and 0.1*10^11 different

C_R 2597 Maple
digits evalf
September 18 2024
1

I cannot find an explanation why a boolean evaluation with higher Digits is not the same

NULL

> 

restart;interface(version);

`Standard Worksheet Interface, Maple 2024.1, Windows 10, June 25 2024 Build ID 1835466`

 (1)
> 

Digits:=10;
is(ln(.1e11*abs(-.304805898398896+1.*RealRange(.304805898398895,.304805898398897)))/ln(10) < -6);
Digits:=30;
is(ln(.1e11*abs(-.304805898398896+1.*RealRange(.304805898398895,.304805898398897)))/ln(10) < -6)

10

  

true

  

30

  

true

 (2)
> 

Digits:=10;
ln(0.1*10^11*abs(-0.304805898398896 + 1.*RealRange(0.304805898398895, 0.304805898398897)))/ln(10) < -6;
is(%);
is(ln(0.1*10^11*abs(-0.304805898398896 + 1.*RealRange(0.304805898398895, 0.304805898398897)))/ln(10) < -6);

10

  

ln(0.1000000000e11*abs(-.304805898398896+1.*RealRange(.304805898398895, .304805898398897)))/ln(10) < -6

  

true

  

true

 (3)
> 

Digits := 30;
ln(0.1*10^11*abs(-0.304805898398896 + 1.*RealRange(0.304805898398895, 0.304805898398897)))/ln(10) < -6;
is(%);
is(ln(0.1*10^11*abs(-0.304805898398896 + 1.*RealRange(0.304805898398895, 0.304805898398897)))/ln(10) < -6);

30

  

ln(10000000000.0*abs(-.304805898398896+1.*RealRange(.304805898398895, .304805898398897)))/ln(10) < -6

  

false

  

false

 (4)
> 

.1e11

0.1e11

 (5)
> 

0.1*10^11

10000000000.0

 (6)

NULL

RealRange seems to be evaluated differently.
Any explanation for that?


(expression extracted from an error message)

 

Download eval_of_range_in_ln.mw

 

 
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