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#175 Works on implementation and/or documentation of LieSquareMatrix ←	↑	→ #177 expand (cos (2*x))

#176 Factored Polynomials aren't differentiated correctly

Edit detail for #176 Factored Polynomials aren't differentiated correctly revision 2 of 4

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Editor: kratt6 Time: 2007/12/28 12:40:55 GMT-8
Note:

added:

From kratt6 Fri Dec 28 12:40:55 -0800 2007
From: kratt6
Date: Fri, 28 Dec 2007 12:40:55 -0800
Subject: 
Message-ID: <20071228124055-0800@axiom-wiki.newsynthesis.org>

Category: Axiom Mathematics => Axiom Library

axiom
p := -x*y^2+x*y+x^3-x^2

(1)

Type: Polynomial Integer

axiom
D(factor(p),x)

(2)

Type: Factored Polynomial Integer

axiom
D(p,x)

(3)

Type: Polynomial Integer

Note that the factorization is correct. It's the D(.,x) that misses the sign.

Forgot to categorize... --unknown, Mon, 20 Jun 2005 10:18:00 -0500 reply

Category: Axiom Compiler => Axiom Mathematics Severity: normal => serious

Fix --kratt6, Tue, 21 Jun 2005 05:43:03 -0500 reply

Severity: serious => critical Status: open => fix proposed

Fix --kratt6, Tue, 21 Jun 2005 05:45:04 -0500 reply

The mistake is in differentiate$FR which currently reads:

    differentiate(u:%, deriv: R -> R) ==
      ans := deriv(unit u) * ((u exquo (fr := unit(u)::%))::%)
      ans + fr * (_+/[fact.xpnt * deriv(fact.fctr) *
       ((u exquo nilFactor(fact.fctr, 1))::%) for fact in factorList u])

It intends to use the formula

where

Therefore, the fix is to leave away the 'fr':

    differentiate(u:%, deriv: R -> R) ==
      ans := deriv(unit u) * ((u exquo unit(u)::%)::%)
      ans + (_+/[fact.xpnt * deriv(fact.fctr) *
       ((u exquo nilFactor(fact.fctr, 1))::%) for fact in factorList u])