MathAction #211 Products are differentiated incorrectly

Topics

FrontPage
- IssueTracker
  - #211 Products are differentiated incorrectly <-- You are here.

fricas

(1) -> D(product((1-q^(n-i))/(1-q^(m-i)),i=0..m-1),q)

$\label{eq1}{\left({\prod_{ \displaystyle {i = 0}}^{ \displaystyle {m - 1}}{\frac{{{q}^{n - i}}- 1}{{{q}^{m - i}}- 1}}}\right)}\ {\left({\sum_{ \displaystyle {i = 0}}^{ \displaystyle {m - 1}}{\frac{{{\left(- m + i \right)}\ {{q}^{m - i - 1}}\ {{q}^{n - i}}}+{{\left({{\left(n - i \right)}\ {{q}^{m - i}}}- n + i \right)}\ {{q}^{n - i - 1}}}+{{\left(m - i \right)}\ {{q}^{m - i - 1}}}}{{{\left({{q}^{m - i}}- 1 \right)}\ {{q}^{n - i}}}-{{q}^{m - i}}+ 1}}}\right)}$

(1)

Type: Expression(Integer)

fricas

f:=operator 'f;

Type: BasicOperator?

fricas

D(product(f(i,q),i=0..m),q)

$\label{eq2}{\left(\prod_{ \displaystyle {i = 0}}^{ \displaystyle m}{f \left({i , \: q}\right)}\right)}\ {\left(\sum_{ \displaystyle {i = 0}}^{ \displaystyle m}{\frac{{f_{, 2}}\left({i , \: q}\right)}{f \left({i , \: q}\right)}}\right)}$

(2)

Type: Expression(Integer)

I'll try to correct this tomorrow...

Martin

fix --kratt6, Tue, 04 Oct 2005 07:36:46 -0500 reply

Fortunately, a fix is quite easy, since we know how to differentiate products according to Leibniz rule: Here is a patch to combfunc.spad.pamphlet that also fixes some leftover problems with differentiating sums without bounds and displaying sums and products with and without bounds:

combfunc.spad.pamphlet.patch

property change --kratt6, Tue, 04 Oct 2005 07:38:49 -0500 reply

Status: open => fix proposed

test April release --Bill Page, Wed, 21 Jun 2006 06:23:50 -0500 reply

fricas

)version

"FriCAS 1.3.12 compiled at Sat  7 Jun 23:54:49 CEST 2025"
D(product((1-q^(n-i))/(1-q^(m-i)),i=0..m-1),q)

$\label{eq3}{\left({\prod_{ \displaystyle {i = 0}}^{ \displaystyle {m - 1}}{\frac{{{q}^{n - i}}- 1}{{{q}^{m - i}}- 1}}}\right)}\ {\left({\sum_{ \displaystyle {i = 0}}^{ \displaystyle {m - 1}}{\frac{{{\left(- m + i \right)}\ {{q}^{m - i - 1}}\ {{q}^{n - i}}}+{{\left({{\left(n - i \right)}\ {{q}^{m - i}}}- n + i \right)}\ {{q}^{n - i - 1}}}+{{\left(m - i \right)}\ {{q}^{m - i - 1}}}}{{{\left({{q}^{m - i}}- 1 \right)}\ {{q}^{n - i}}}-{{q}^{m - i}}+ 1}}}\right)}$

(3)

Type: Expression(Integer)

fricas

f:=operator 'f;

Type: BasicOperator?

fricas

D(product(f(i,q),i=0..m),q)

$\label{eq4}{\left(\prod_{ \displaystyle {i = 0}}^{ \displaystyle m}{f \left({i , \: q}\right)}\right)}\ {\left(\sum_{ \displaystyle {i = 0}}^{ \displaystyle m}{\frac{{f_{, 2}}\left({i , \: q}\right)}{f \left({i , \: q}\right)}}\right)}$

(4)

Type: Expression(Integer)

fixed in Patch 46 or so --kratt6, Fri, 27 Oct 2006 03:12:40 -0500 reply

Status: fix proposed => closed

Subject: (replying) Be Bold !!

	( 15 subscribers )