Re: Shortening Polynomials
- To: mathgroup at christensen.cybernetics.net
- Subject: [mg425] Re: Shortening Polynomials
- From: olness at phyvms.physics.smu.edu (Fredrick Olness (214) 768-2500 or -2495, Fax -4095)
- Date: Tue, 24 Jan 1995 15:35:59 -0600
> Stephen Corcoran (corcoran%markov.stats at comlab.oxford.ac.uk) writes:
> Dear Mathgroupers,
> Many thanks for all the replies I got for my previous
> requests. I have a feeling this may be trivial, but I
> often want to shorten polynomials, after using Expand.
> Is there a neater way to collect powers up to order m
> after expanding a polynomial?
>
> Thanks, Stephen
==========================================================
t1 = a0 + a1 q + a2 q^2;
t2=Expand[t1^4];
==========================================================
YOUR METHOD
t3= t2/. {q^3->0,q^4->0,q^5->0,q^6->0,q^7->0,q^8->0}
4 3 2 2 2 3 2
a0 + 4 a0 a1 q + 6 a0 a1 q + 4 a0 a2 q
==========================================================
AN EFFICIENT METHOD
t4=t2 + O[q]^3
4 3 2 2 3 2 3
a0 + 4 a0 a1 q + (6 a0 a1 + 4 a0 a2) q + O[q]
==========================================================
CROSS CHECK
t3 == t4 //Normal //ExpandAll
True
The Series command will also work.
==========================================================
Fredrick I. Olness
SMU Mail: Department of Physics
Fondren Science Bldg.
Southern Methodist University
Dallas, TX 75275
Internet: Olness at phyvms.physics.smu.edu (129.119.200.74)
Olness at mail.physics.smu.edu