Maple produces an error when adding positive constraints

Question

I am testing Maple 2021 on a simple system of equations in x,y,z,t:

solve({x = 1, a*z^2 = c*t*x, c*x^2 = a*y*z, d*y^2 = b*t*x, 0 < a, 0 < b, 0 < c, 0 < d}, {t, x, y, z});

The results look correct (sorry for the formatting, this is copy-pasted directly from Maple):

/[[ /     (1/2)  (1/2)              (1/4)  (1/4)  
           |[[ |    d      c                  c      b       
  PIECEWISE|[[< t = -------------, x = 1, y = -------------, 
           |[[ |     (1/2)  (1/2)              (1/4)  (1/4)  
           \[[ \    a      b                  d      a       

         (3/4)  (1/4)\    /     (1/2)  (1/2)         
        c      d     |    |    d      c              
    z = ------------- >, < t = -------------, x = 1, 
         (3/4)  (1/4)|    |     (1/2)  (1/2)         
        a      b     /    \    a      b              

           (1/4)  (1/4)         (3/4)  (1/4)\ ]  
          c      b             c      d     | ]  
    y = - -------------, z = - ------------- >], 
           (1/4)  (1/4)         (3/4)  (1/4)| ]  
          d      a             a      b     / ]  

                                   ]                 \
                                   ]                 |
    And(0 < a, 0 < b, 0 < c, 0 < d)], [[], otherwise]|
                                   ]                 |
                                   ]                 /

I only want to obtain positive solution, so I add such constraint:

solve({c*x^(2)=a*y*z,d*y^(2)=b*t*x,a*z^(2)=c*t*x,x=1,a>0,b>0,c>0,d>0,x>0,y>0,z>0,t>0},{x,y,z,t});

However, I obtained an error:

Error, Got internal error in Typesetting:-Parse : "'_Inert_DELAYLESSTHAN' is not a valid inert form"

Thanks for your help!

Given how you write `ctx` as a single variable, and other products likewise, I'm not surprised... — Ruslan, Dec 10 '21 at 20:22
@Ruslan Thanks. Could you please have a look at the question again? — f10w, Dec 10 '21 at 20:36

score 1 · Answer 1 · answered Dec 11 '21 at 05:02

I do not get such an error (in displaying the result), using Maple 2021.1.

I use lprint below only so that I can paste the result in here more easily.

restart;

kernelopts(version);

   Maple 2021.1, X86 64 LINUX, May 19 2021, Build ID 1539851

sol:=solve({c*x^(2)=a*y*z,d*y^(2)=b*t*x,
            a*z^(2)=c*t*x, x=1,
            a>0,b>0,c>0,d>0,x>0,y>0,z>0,t>0}, 
           {x,y,z,t}):
lprint(%);

piecewise(And(0 < a,0 < b,0 < c,0 < d,0 < 
d*c^2*b/(c^3*d*a*b^3)^(1/2),0 < 1/a/b
*(c^3*d*a*b^3)^(1/4),0 < 
c*b/(c^3*d*a*b^3)^(1/4),0 <= 
c*b/(c^3*d*a*b^3)^(1/4)),
[{t = d^(1/2)*c^(1/2)/a^(1/2)/b^(1/2), x = 1, 
y = c^(1/4)*b^(1/4)/d^(1/4)/a^(1/
4), z = 1/a^(3/4)/b^(1/4)*c^(3/4)*d^(1/4)}],
And(0 < a,0 < b,0 < c,0 < d,0 < d*c
^2*b/(c^3*d*a*b^3)^(1/2),0 < 1/a/b* 
(c^3*d*a*b^3)^(1/4),0 < c*b/(c^3*d*a*b^3)^(1
/4),1/a/b*(c^3*d*a*b^3)^(1/4) < 
0,c*b/(c^3*d*a*b^3)^(1/4) < 0),[{t = 
d*c^2*b/(c^3*d*a*b^3)^(1/2), x = 1, y = 
c*b/(c^3*d*a*b^3)^(1/4), z = 1/a/b*(c^3*d*a*b^3)^
(1/4)}, {t = d*c^2*b/(c^3*d*a*b^3)^(1/2), x = 1,
y = -c*b/(c^3*d*a*b^3)^(1/4),
z = -1/a/b*(c^3*d*a*b^3)^(1/4)}],
And(0 < a,0 < b,0 < c,0 < d,0 < d*c^2*b/(c^3*d
*a*b^3)^(1/2),1/a/b*(c^3*d*a*b^3)^(1/4) < 
0,c*b/(c^3*d*a*b^3)^(1/4) < 0,c*b/(c^
3*d*a*b^3)^(1/4) <= 0),[{t = 
d^(1/2)*c^(1/2)/a^(1/2)/b^(1/2), x = 1, y = -c^(1/
4)*b^(1/4)/d^(1/4)/a^(1/4), z = 
-1/a^(3/4)/b^(1/4)*c^(3/4)*d^(1/4)}],[])

combine(sol) assuming 
a>0,b>0,c>0,d>0,x>0,y>0,z>0,t>0:
lprint(%);

[{t = (d*c/b/a)^(1/2), x = 1, y = 1/d/a* 
(c*b*d^3*a^3)^(1/4), z = 1/a/b*(c^3*d*a
*b^3)^(1/4)}]

Thanks. That's strange... I'm using Maple 2021 on macOS and there's no way I could get around that error. What's worse is that it's not possible to register on their forum to ask questions because their system doesn't seem to send activation emails to new accounts :/ — f10w, Dec 14 '21 at 20:29

Maple produces an error when adding positive constraints

1 Answers1