This method is used to remove extraneous empty sapce in the middle of
the window for functions that are discontinuous between their points of
interest.
To find the optimal range with a specified ratio, we compute the values
of the function on a default range, then center the Y axis to display
the maximum number of points of the function.
A test in equation_solve relies on the angle unit being set to Degree,
but doesn't actually set it. Changing the angle unit to another one in a
test prior would break this test.
Change-Id: I6785b087f171d46226d484ebaa3ebdc9e791cedc
Evaluating a function containing a sequence, an integral or a
derivative, is time consuming. Computing a range requires a plethora of
evaluations, as such ranges for these functions cannot be evaluated in a
timely fashion.
Change-Id: I088a0e896dbc26e6563291cafdfe9ceba36dd5d0
When building an orthonormal range for the automatic zoom, we provide a
ratio for the screen without the margins. This way, adding the margins
will make the graph orthonormal, and the banner cannot cover the
function.
Change-Id: If3a3f799d4e7e3e81ab77c6b418d70b734a6fbca
When computing the automatic zoom, if the X axis has integer bounds
(most likely because the range has been built to be orthonormal), do not
add margins to the X axis, so that it keeps user friendly values.
Change-Id: I49d99b79c68fbd8a49e5c2521b250c40aad75d48
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.
