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#1833 diff and conjugate
closed
nobody
None
5
2009-12-18
2009-12-02
Anonymous
No
There are two or three bugs here, I think. First, diff is not computing the derivative of conjugate(s), when s is complex, correctly.
Second, it appears that the nonscalar declaration is trumping the real declaration, so conjugate(z) is not simplified to z. This leads to the derivative of conjugate(z) being incorrectly computed.
(%i2)declare(s,complex); (%i3) diff(s);
(%o3) del(s)
(%i4) diff(conjugate(s));
(%o4) 'diff(conjugate(s),s,1)*del(s) <-----incorrect, should be conjugate(del(s))
(%i5) declare(z,nonscalar);
(%i6) diff(z);
(%o6) del(z)
(%i7) diff(conjugate(z));
(%o7) 'diff(conjugate(z),z,1)*del(z) <------- it seems that diff has treated nonscalar == complex
(%i8) declare(z,real);
(%o8) done
(%i9) diff(conjugate(z));
(%o9) 'diff(conjugate(z),z,1)*del(z) <------ should be del(z),
I think the differentiation of the conjugate function can not be defined for other than real values. For real values conjugate(x) simplifies to x and the derivative can be defined to be (see e.g. http://functions.wolfram.com/ComplexComponents/Conjugate/20/01/\)
(%i7) diff(conjugate(x),x);
(%o7) 1
For any symbol declared to be complex or nonscalar Maxima returns a noun form:
(%i13) diff(conjugate(z),z);
(%o13) 'diff(conjugate(z),z,1)
(%i14) diff(conjugate(a),a);
(%o14) 'diff(conjugate(a),a,1)
This is consistent with the total differential returned by Maxima:
(%i15) diff(conjugate(z));
(%o15) 'diff(conjugate(z),z,1)*del(z)
(%i16) diff(conjugate(a));
(%o16) 'diff(conjugate(a),a,1)*del(a)
I do not see a problem. The derivative for complex or nonscalar values is not defined for the conjugate function.
Setting the status to pending and the resolution to invalid.
Dieter Kaiser
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