I receive a result of FAIL in Maple 2017 for the following:

is(m > 0) assuming n>1, m>n*(n-1)/2;

@vv Assume facility DOES NOT do intermediate steps. To demonstrate:

restart;
# _EnvTry := true;  # useless
assume(a>0, b>0, a*b<1,c=a*b);
is(c>0),is(c<1);
is( (1 + sqrt(1-a^3*b^3))/(a*b) >0 ); # FAIL   ?
is( (1 + sqrt(1-a*b))/(a*b) >0 );     # FAIL   ?
is( (1 + sqrt(1-a^2*b^2)) >0 );       # false ??
is( (1 - sqrt(1-a^2*b^2)) >0 );       # false ??
is( (1 - sqrt(1-a*b)) >0 );           # true
is( (1 + sqrt(1-a*b)) >0 );           # true

restart;
# _EnvTry := true;  # useless
assume(a>0, b>0, a*b<1, c=a*b, c>0, c<1);
is(c>0), is(c<1);
is( (1 + sqrt(1-a^3*b^3))/(a*b) >0 ); # FAIL   ?
is( (1 + sqrt(1-a*b))/(a*b) >0 );     # FAIL   ?
is( (1 + sqrt(1-a^2*b^2)) >0 );       # false ??
is( (1 - sqrt(1-a^2*b^2)) >0 );       # false ??
is( (1 - sqrt(1-a*b)) >0 );           # true
is( (1 + sqrt(1-a*b)) >0 );           # true

The builtin command in Maple is the Maple language.

applyrule([[]=Q, [Q]=Q],x);
eval['recurse'](x,[[]=Q, [Q]=Q]);
 

@sursumCorda Are you saying the rules can contain f=d and f=g simultaneously?

Note: allvalues(polyroots) will generate 72 different permutations of the roots. 72 matches the Galois group order.

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@dharr Maybe using true in the index is a bad idea?

Seems I have no access to this routine. What happens when you replace q with Canonicalize(q, {x[1], x[2], x[3]}); ?

@dharr Interestingly convert(%, radical) simplifies the last RootOf even further.

@vv The statement used is incomplete. May still be useful.                         

@Thomas Dean Of all the small groups order up to 25, these groups: [4, 2], [8, 5], [9, 2], [16, 14], [25, 2] fail the procedure MinimumPermutationRepresentationDegree. I think no group tested was a symmetric group and only these ones failed the procedure. Is it because all of these are squares or cubes? A weakness in programming?

@Joe Riel The option compile=false does the trick. I do not see how I can succeed without it and not completely disable security.