On 18 July 2014 12:39, Waldek Hebisch <[email protected]> wrote:
> ...
> However, I am affraid that this would lead to several
> wrong definite integrals. To handle definite integrals
> correctly we would probably need stronger continuity test
> and extra code to choose antidervative which avoids
> branch cuts.
>
Now I think I understand your point about branch cuts.
The problem seems to occur very early than definite integrals. For
example one might want
abs(x) = sqrt(x^2)
Numerically this is the case
(1) -> draw(sqrt(x^2),x=-2..2)
Compiling function %L with type DoubleFloat -> DoubleFloat
Graph data being transmitted to the viewport manager...
FriCAS2D data being transmitted to the viewport manager...
(1) TwoDimensionalViewport: "(x^2)^(1/2)"
Type: TwoDimensionalViewport
But integration make a different choice of branches
(2) -> integrate(sqrt(x^2),x)
2
x
(2) --
2
Type: Union(Expression(Integer),...)
(3) -> integrate(x,x)
1 2
(3) - x
2
Type: Polynomial(Fraction(Integer))
(4) -> D(sqrt(x^2),x)
x
(4) -----
+--+
| 2
\|x
Type: Expression(Integer)
(5) -> integrate(%,x)
+--+
| 2
(5) \|x
Type: Union(Expression(Integer),...)
Perhaps integration should return the following?
x * sqrt(x^2)/2
but then
(6) -> D(x*sqrt(x^2)/2,x)
2
x
(6) -----
+--+
| 2
\|x
Type: Expression(Integer)
(7) -> integrate(%,x)
2
x
(7) --
2
Type: Union(Expression(Integer),...)
Hmmm ....
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