Unreal's derivate method returns true, to signify that it is unchanged
by the derivation operation. This implementation mostly exists for
documentation, as an Unreal derivand will be handled by the
defaultShallowReduce method.
The general formula for deriving a power makes use of the logarithm,
which often disappears at simplification. However, replacing the symbol
before simplifying can lead to applying an invalid argument to the
logarithm, making the whole expression invalid.
e.g. diff(1/x,x,-2)
If x is replaced by -2 before reducing the power derivative, ln(-2)
will reduce to Unreal, as will the rest of the expression.
The classic differentiation forumals for trigonometric functions assume
a variable in radians. A multiplicative constant must be added when
another unit is used.
Change-Id: Iec428acd7d93e415fddb184300437ae09d1d997c
The logarithm function is undefined for negative numbers, but its
derivative, the inverse function, is defined everywhere. We thus need to
virtually limit the domain of definition of the derivative.
When a function that had previously been cached is deactivated, its
cache can be used by another function. When the function is reactivated,
if it tries to reuse its previous cache, it will be filled with values
from another function, and will not be cleared. By detaching the cache
of a function that becomes inactive, we ensure that the next time this
function is cached, the chache will be cleared.
e.g. Define to functions f(x)=x, g(x)=-x, draw them both.
Deactivate f, the redraw the graph
Reactivate f, the draw again
When three functions or more, the third function and later don't use
caching. But it is still possible for them to have been linked to a
cache (for instance if previous functions had been deactivated earlier).
To avoid a function tapping into another function's cache, we reset the
cache.
e.g. Define 3 functions f(x)=1, g(x)=2, h(x)=3, and deactivate f.
Draw the graph, come back, reactivate f, then draw again.
---> The space between y=2 and y=3 will be filled with the color of h,
as h "remembers" using cache n°2, wich currently contains the values of
function g.
Functions with a single point of inerest used to be drawn on a tiny
interval around this point.
Now, an orthonormal window is built around the point of interest, giving
a much nicer view.
Change-Id: I7793797aead2695532ddea44d93d62bb7ef870f4
When looking for extrema in a function, we need to discard results where
the function growth rate is smaller than the precision of the float type
itself : these results are likely to be too noisy, and can cause false
positives.
e.g. : The sqrt(x^2+1)-x function
Change-Id: I6e2c002d7308b41a4c226d274cbb5d9efe4ea7db
Do not use the bounds of the interval when computing a refined range.
As the bounds are often integers, the zoom would give strange result on
some non-continuous functions (e.g. f(x) = x!).
Change-Id: Ie127fe15191cb3951cff223adc8dc3172188c789
The algorithm to search for points of interest will miss some. We reduce
the step to make it more precise, so that tan(x) and tan(x-90) have the
same profile.
Change-Id: Ia1bac1d4e7b98d2d6f36f8ce12ed9dac67d40198
The angleUnitVersion check is no longer needed, as changing the angle
unit with a trigonometric function set would leave the cursor hanging.
Change-Id: I17d99c05daeacfec953865158cdfe7706635cd32
