I can not reproduce (or I misunderstood your instructions). Please
provide a *complete* list of commands that lead to the problem. Here
is what I got
sage: a = SR.var('a')
sage: b = SR.var('b')
sage: f(r) = r^5*(1-r^2)/((1-2*a*r+r^2)*(1-2*b*r+r^2))
sage: assume( -1 < a < 1)
sage: assume( -1 < b < 1)
sage: integral(f, (r, 0, 1))
Traceback (most recent call last):
...
ValueError: Computation failed since Maxima requested additional
constraints; using the 'assume' command before evaluation *may*
help (example of legal syntax is 'assume(b^2-1.0>0)', see
`assume?` for more details)
Is b^2-1.0 positive or negative?
It is kind of silly that SageMath or Maxima can not make
deduction such as
-1 < a < 1 => a^2 < 1.
Then
sage: assume(a^2-1 <0)
sage: assume(b^2-1 <0)
sage: g = integral(f, (r, 0, 1))
sage: h(t) = g.subs(a=cos(t), b=sin(t))
sage: integral(h, (t, 0, 2*pi))
Traceback (most recent call last):
...
ValueError: Integral is divergent.
Le 24/10/2018 à 13:50, Chris Judge a écrit :
Hi Simon, The integral is sort of complicated. First integrate
f(r) = r^5*(1-r^2)/((1-2*a*r+r^2)*(1-2*b*r+r^2)) over [0,1]. Sage asked
for some assumptions and so I gave it these: assume( -1 < a < 1) assume(
-1 < b < 1) assume(a^2-1 <0) assume(b^2-1 <0) With these assumptions,
this first integral worked. But read on! The result of integration
g(a,b) depends on two parameters a,b. Now integrate g(cos(s),cos(t))
over s in [0,2pi]. The latter integral asks for assumptions. And so I
made the following assumptions. assume( 0< arccos(cos(s)) <2*pi) assume(
0< arccos(cos(t)) <2*pi) With these assumptions, the integrate command
produced "Is 1 zero or nonzero?" I wish I could find simpler example for
which produces this error message, but I really have no idea what's
happening here. Best wishes, Chris PS By the way, Sage is outputting
"acos" in error messages presumably because Maxima uses acos for arccos.
On 2018-10-24 4:35 a.m., Simon King wrote:
Hi Chris,
On 2018-10-23, Chris Judge<cjud...@gmail.com> wrote:
Appears to be a bug that comes when integrating expression.
Maxima asks "Is 1 zero or nonzero?" and then suggests using assume(1>0).
Then it fails to accept this assumption...
You just made my day...
Coincidally, this week I told my students about the trivial ring (where
1=0).
In any case, in order to track down the bug you encountered, it would
help if you could give us the expression whose integration triggers the
bug.
Best regards,
Simon
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