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## [Axiom-developer] I can't extract a constant coefficient.

**From**: |
Francois Maltey |

**Subject**: |
[Axiom-developer] I can't extract a constant coefficient. |

**Date**: |
21 Dec 2006 22:52:20 +0100 |

**User-agent**: |
Gnus/5.09 (Gnus v5.9.0) Emacs/21.4 |

Hello,
An example, suppose I have x = a+b*c + 2/3 + 1/(d+1)
Is it possible to extract the 2/3 coefficient in this case.
// A // I can extract an integer coefficient in polynomial x = a+b*c + 4
thanks to the coefficient of null degree.
// B // I can extract a rational coefficient in this fraction
polynomial integer x = a+b*c + 4/3 because the denominator is
an integer : this constant is coefficient of null degree / denominator.
// C // I can extract a rational coefficient in this fraction polynomial
integer x = a+b*c/d + 4/3 because the denominator is monic.
It's the remainder for a monic divide.
But I can't do it for the first example. Is it possible or not.
In this first example 2/3 is the better coefficient because
for other rational the fraction 1/(d+1) is worse, the numerator
has a d : 2/3 + 1/(d+1) = 1+(-d+2)/(3d+3)
Of corse, it's possible to hace a=d, and then the degree argument is false
My aim is to simplify sin (.....+ m/n %pi) in +/- sin/cos (....+ k/n %pi)
where abs (k) is a smaller integer than m and n. The smallest one.
I have done the //A// case, I think I'm going to do the //B// case.
I don't know if it's a good idea to do the //C// case.
I don't know how to do the first example.
Francois, in France.

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