Command 'coeff' (CAS Mode)
05-31-2024, 07:05 PM (This post was last modified: 05-31-2024 07:12 PM by hp-zl.)
Post: #1
 hp-zl Junior Member Posts: 15 Joined: May 2023
Command 'coeff' (CAS Mode)
There is a trigonometric series (screenshot):
a:=(5*q+1)*sin(2*v)+(6*q^2+2)*sin(4*v)

We want to find the coefficient of sin(2*v), so we do:
coeff(a, sin(2*v),1) we get the correct result: 5*q+1.

But when we type:
coeff(a, sin(v*2),1) then we get zero.

With 'sin(4*v)' similarly (see screenshot).

The same results are given by both the physical calculator (with the latest firmware 2.1.14730) and the virtual calculator (HP_Prime_Virtual_Calculator-x86_64.AppImage, firmware 2.1.14288).

What do you think about it?
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05-31-2024, 07:51 PM
Post: #2
 komame Senior Member Posts: 332 Joined: Aug 2015
RE: Command 'coeff' (CAS Mode)
This problem also occurs for much simpler cases.
Assigning the expressions:
5*sin(2*x) and 5*sin(x*2) to the variables "a" and "b" results in "a" and "b" containing exactly the same expression: 5*sin(2*x).
However, applying the coeff function to each of these variables yields different results => screenshot.

Piotr Kowalewski
05-31-2024, 08:24 PM
Post: #3
 parisse Senior Member Posts: 1,317 Joined: Dec 2013
RE: Command 'coeff' (CAS Mode)
coeff is meant to work on polynomials with respect to an identifier, not with respect to a subexpression. It will work only if the subexpression is written exactly the same way in an expression.
If you run b:=sin(x*2) then the answer is displayed according to autosimplify mode, but b is not autosimplified.
05-31-2024, 08:54 PM
Post: #4
 komame Senior Member Posts: 332 Joined: Aug 2015
RE: Command 'coeff' (CAS Mode)
(05-31-2024 08:24 PM)parisse Wrote:  coeff is meant to work on polynomials with respect to an identifier, not with respect to a subexpression. It will work only if the subexpression is written exactly the same way in an expression.
If you run b:=sin(x*2) then the answer is displayed according to autosimplify mode, but b is not autosimplified.

That's right. The syntax for the coeff in the help states that the second parameter should be [Var]. Moreover, setting the simplify parameter to 'None' in the CAS settings and repeating these operations explains everything. Thank you for the clarification.

Piotr Kowalewski
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