It's not easy to grasp when looking at the sequence below. I've tried to trace
"atan" in the code but there are really weird ramifications.
(2) -> atan((x^2*((-1)*x^4+1)^(1/2)+(x^3+x))/(((-1)*x^4+1)^(1/2)+((-1)*x^3+x)))
+--------+
2 | 4 3
x \|- x + 1 + x + x
(2) atan(----------------------)
+--------+
| 4 3
\|- x + 1 - x + x
Type: Expression(Integer)
(3) -> atan(x*(1 + x^2)/sqrt(1 - x^4))
+--------+
2 | 4 3
x \|- x + 1 + x + x
(3) atan(----------------------)
+--------+
| 4 3
\|- x + 1 - x + x
Type: Expression(Integer)
(4) -> atan(y*(1 + y^2)/sqrt(1 - y^4))
3
y + y
(4) atan(-----------)
+--------+
| 4
\|- y + 1
Type: Expression(Integer)
(5) -> atan(x*(1 + x^2)/sqrt(1 - x^4))
3
x + x
(5) atan(-----------)
+--------+
| 4
\|- x + 1
Type: Expression(Integer)
(6) -> atan((x^2*((-1)*x^4+1)^(1/2)+(x^3+x))/(((-1)*x^4+1)^(1/2)+((-1)*x^3+x)))
+--------+
2 | 4 3
x \|- x + 1 + x + x
(6) atan(----------------------)
+--------+
| 4 3
\|- x + 1 - x + x
Type: Expression(Integer)
(7) -> atan(x*(1 + x^2)/sqrt(1 - x^4))
3
x + x
(7) atan(-----------)
+--------+
| 4
\|- x + 1
Type: Expression(Integer)
(8) ->
On Wednesday, 1 February 2017 17:41:04 UTC+1, Waldek Hebisch wrote:
>
> oldk1331 wrote:
> >
> > (1) ->
> atan((x^2*((-1)*x^4+1)^(1/2)+(x^3+x))/(((-1)*x^4+1)^(1/2)+((-1)*x^3+x)))
> >
> > +--------+
> > 2 | 4 3
> > x \|- x + 1 + x + x
> > (1) atan(----------------------)
> > +--------+
> > | 4 3
> > \|- x + 1 - x + x
> > Type:
> Expression(Integer)
> > (2) -> atan(x*(1 + x^2)/sqrt(1 - x^4))
> >
> > +--------+
> > 2 | 4 3
> > x \|- x + 1 + x + x
> > (2) atan(----------------------)
> > +--------+
> > | 4 3
> > \|- x + 1 - x + x
> > Type:
> Expression(Integer)
> >
> > You can see that the output of (2) is the same as (1)
> > instead of the following (1). So the input order alone can
> > lead to auto-simplification (or auto-complication), is this
> > a bug (or a feature)?
> >
> > (1) -> atan(x*(1 + x^2)/sqrt(1 - x^4))
> >
> > 3
> > x + x
> > (1) atan(-----------)
> > +--------+
> > | 4
> > \|- x + 1
> > Type:
> Expression(Integer)
>
> This is how our kernels work: you are supposed to get the same
> kernel when operator agrees and argument are equal. If arguments
> are equal but may be written in different form you get first
> version entered into table of kernels.
>
> --
> Waldek Hebisch
>
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