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Question: Does additionally create new variables?

Question:Does additionally create new variables?

mmcdara 4555 Maple 2015
assume additionally
April 07 2019
0

Hi, 
I'm very stunned by the results displayed in the worksheet below.
It seems that adding extra assumptions on a variable already constrained with "assume" has disturbing side effects ?

Here is a simplified worksheet that exhibits the phenomenon.
Basically I want to solve the equation a*x-b =b with respect to x.
In a first step I set assumptions on a and b and Maple returns x=0, as expected.
Next I add a new condition on b and ask Maple to solve the equation again. I intain this strange result: x=(b~ - b~)/a~.

Am I doing something wrong?

Thanks in advance


 

> 

restart:
> 

anames(user);
> 

assume(a > 0):
assume(b > 0):
> 

f := a*x+b

a*x+b

 (1)
> 

g := f=b:
simplify(g);
solve(g, a);

a*x+b = b

  

Warning, solve may be ignoring assumptions on the input variables.

  

0

 (2)
> 

anames(user);

b, g, f, a

 (3)
> 

additionally(b > a)
> 

h := f=b:
simplify(h);
solve(h, a);

a*x+b = b

  

Warning, solve may be ignoring assumptions on the input variables.

  
> 

anames(user)  # additionally(b > a) doesn(t introduce a new variable

b, h, g, f, a

 (4)
> 

indets(g);
indets(h);  # why do I have b~ twice ?
            # This is probably the reason why solve(h, a) doesn't work

{a, b, x}

  

{a, b, b, x}

 (5)
> 

lprint(indets(h))

{a, b, b, x}

  
> 

# strange...

solve(h, indets(h)[1]);

simplify(%);

Warning, solve may be ignoring assumptions on the input variables.

  

-(b-b)/x

  

-(b-b)/x

 (6)
> 

# remark, dismantle explains nothing about the distinction between b~ and b~


EQUATION(3)
   POLY(6)
      EXPSEQ(4)
         NAME(4): a
         NAME(4): b
         NAME(4): x
      DEGREES(HW): ^2 ^1 ^0 ^1
      INTPOS(2): 1
      DEGREES(HW): ^1 ^0 ^1 ^0
      INTPOS(2): 1
   NAME(4): b
 

  
> 

dismantle(h)


EQUATION(3)
   POLY(6)
      EXPSEQ(4)
         NAME(4): a
         NAME(4): b
         NAME(4): x
      DEGREES(HW): ^2 ^1 ^0 ^1
      INTPOS(2): 1
      DEGREES(HW): ^1 ^0 ^1 ^0
      INTPOS(2): 1
   NAME(4): b
 

  
 
> 

 


 

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