How to get Polynomial Coefficients

asked 2017-09-17 17:52:54 +0100

ortollj
1341 ●23 ●63 ●98

I would like to get the value of coeffs of x^5 + px^3 + qx^2 + rx + s something like [1,0, b - 2/5a^2,...] I do not understand what means the coefficients() outputs in the code below ??

forget()
import math
for v in var( 'a,b,c,d,e' ):    assume( v, 'rational' )
for v in var( 'p,q,r,s' ):    assume( v, 'rational' )
x = PolynomialRing(RationalField(), 'x').gen()
t = PolynomialRing(RationalField(), 't').gen()
Pt= t^5 + a*t^4 + b*t^3 + c*t^2 + d*t + e
vChgt=t==x-a/5
P=Pt.substitute(vChgt)
#Px= x^5          + p*x^3 + q*x^2 + r*x + s
show(P.factor())
show(P.factor().coefficients(sparse=False))
show(P.factor().list())
P.factor()

answered 2017-09-17 21:31:47 +0100

dan_fulea
5537 ●5 ●43 ●95

The following works:

sage: P.coefficients(x, sparse=0)
[4/3125*a^5 - 1/125*a^3*b + 1/25*a^2*c - 1/5*a*d + e,
 -3/125*a^4 + 3/25*a^2*b - 2/5*a*c + d,
 4/25*a^3 - 3/5*a*b + c,
 -2/5*a^2 + b,
 0,
 1]

The variable x has to be specified, if some other variables are present, and we want the coefficients only with respect to x.

Note that the coefficient on the pythonical place zero corresponds to the zero degree (i.e. free) coefficient of P. So the leading coefficient is on the pythonical fifth place. In order to get "the other list" [1,0, b - 2/5a^2,...], just take the reverse list.

sage: C = P.coefficients(x, sparse=0)
sage: C . reverse()
sage: C[0:3]
[1, 0, -2/5*a^2 + b]

edit flag offensive delete link

Comments

Thank you Dan_fulea

ortollj ( 2017-09-18 08:06:59 +0100 )edit

add a comment

Your Answer

Please start posting anonymously - your entry will be published after you log in or create a new account.

How to get Polynomial Coefficients

1 Answer

Comments

Your Answer

Question Tools

Stats

Related questions

How to get Polynomial Coefficients edit

1 Answer

Comments

Your Answer

Question Tools

Stats

Related questions

How to get Polynomial Coefficients