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MathGroup Archive 1995

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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


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