#6956 closed defect (fixed)
[with patch, positive review] cannot differentiate cotangent
Reported by: | burcin | Owned by: | |
---|---|---|---|
Priority: | major | Milestone: | sage-4.1.2 |
Component: | symbolics | Keywords: | |
Cc: | jason, kcrisman | Merged in: | Sage 4.1.2.alpha4 |
Authors: | Tim Joseph Dumol | Reviewers: | Burcin Erocal |
Report Upstream: | Work issues: | ||
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description
From sage-support:
On Fri, 18 Sep 2009 13:15:46 -0500 Jason Grout <jason-sage@creativetrax.com> wrote: > On alpha.sagenb.org, I get the following: > > sage: t=var('t') > sage: diff(cot(t),t) > D[0](cot)(t) > sage: diff(cos(t)/sin(t),t) > -cos(t)^2/sin(t)^2 - 1 > > > Does Sage not know that cot(t) is cos(t)/sin(t)?
Unfortunately it doesn't.
GiNaC doesn't define the function cot. Sage defines it in the file
sage/functions/trig.py starting at line 184. I suppose it was written quickly by Mike during the symbolics switch.
Defining a custom derivative function (named _derivative_) in that
class should fix this.
Here is the thread:
http://groups.google.com/group/sage-support/browse_thread/thread/752de34c876720cc
Attachments (2)
Change History (10)
Changed 6 years ago by timdumol
comment:1 Changed 6 years ago by timdumol
- Summary changed from cannot differentiate cotangent to [with patch, needs review] cannot differentiate cotangent
This should do the trick.
comment:2 Changed 6 years ago by burcin
- Cc jason kcrisman added
- Reviewers set to Burcin Erocal
- Summary changed from [with patch, needs review] cannot differentiate cotangent to [with patch, needs work] cannot differentiate cotangent
Thanks for the quick patch.
Here is my review:
- the keyword argument diff_param is only useful for multivariate functions. In this case since all these functions are univariate, so we know the argument is args[0]. You can safely drop the first two lines of the _derivative_() methods and replace the third with x = args[0].
- continuing the previous item, we should tell these functions they are univariate. ATM, they silently drop the second argument:
sage: arccsc(a,b) arccsc(a)
You can do this by giving nargs=1 as a parameter to the base class constructor. - It is better to give the variable as an argument to diff in the doctests, for example diff(asech(x), x). I actually prefer asech(x).derivative(x), but this is your patch. :)
- The formula for the derivative of asech(x) you use is only true for x real. You need -1/(x * (x+1) * sqrt( (1-x)/(1+x) )).
- Similarly, the derivative of acsch(x) is -1/(x^2 * sqrt(1 + 1/x^2) )
Can someone else check the derivatives to make sure there is no mistake?
Changed 6 years ago by timdumol
Added _derivative_() functions to all functions in trig.py and hyperbolic.py. Rev 2. Apply this patch only.
comment:3 follow-up: ↓ 5 Changed 6 years ago by timdumol
Functions that inherit from PrimitiveFunction are automatically given nargs = 1 on L800 of symbolic/function.pyx. So the silent dropping of arguments is more of a usability problem on the Symbolic side.
I've made the changes for the derivatives of asech(x) and acsch(x). I've also generalized the derivatives for asec(x) and acsc(x).
Anyone who wants to review the derivatives can check: http://mathworld.wolfram.com/Derivative.html, http://mathworld.wolfram.com/InverseHyperbolicFunctions.html and http://mathworld.wolfram.com/InverseTrigonometricFunctions.html
comment:4 Changed 6 years ago by timdumol
- Summary changed from [with patch, needs work] cannot differentiate cotangent to [with patch, needs review] cannot differentiate cotangent
comment:5 in reply to: ↑ 3 Changed 6 years ago by burcin
- Summary changed from [with patch, needs review] cannot differentiate cotangent to [with patch, positive review] cannot differentiate cotangent
Replying to timdumol:
Functions that inherit from PrimitiveFunction are automatically given nargs = 1 on L800 of symbolic/function.pyx. So the silent dropping of arguments is more of a usability problem on the Symbolic side.
You're right. I fixed this and many other things about symbolic functions last weekend, by rewriting sage/symbolic/function.pyx. Unfortunately I don't think I'll be able to clean up my changes and submit them any time soon... oh, well...
I'm giving your patch a positive review. It applies cleanly, and passes all tests on my 4.1.1.alpha. Great job! Many thanks.
comment:6 Changed 6 years ago by jason
burcin: it seems that there are several people interested in helping with symbolics, so maybe if you just posted what you had, people could clean it up for you, if that would be easier for your time situation?
comment:7 Changed 6 years ago by mvngu
- Merged in set to Sage 4.1.2.alpha3
- Resolution set to fixed
- Status changed from new to closed
Merged trac_6956-derivatives.2.patch.
comment:8 Changed 6 years ago by mvngu
- Merged in changed from Sage 4.1.2.alpha3 to Sage 4.1.2.alpha4
There is no 4.1.2.alpha3. Sage 4.1.2.alpha3 was William Stein's release for working on making the notebook a standalone package.
Added _derivative() functions to all functions in trig.py and hyperbolic.py