Formal polynomials?

--===============2344031369064294312==
Content-Type: multipart/alternative;
 boundary="----sinikael-?=_1-14468824788910.48719160025939345"

------sinikael-?=_1-14468824788910.48719160025939345
Content-Type: text/plain; format=flowed
Content-Transfer-Encoding: 7bit

A quickie: is there any way of defining a formal polynomial with unknown
coefficients, such as:

a_0+a_1*x+a_2*x^2+a_3*x^3 ?

I want to calculate the values of the coefficients by a system of linear
equations based on integrations whose integrands include that polynomial.

For small polynomials I can write

p:=a+b*x+c*x^2+d*x^3

but this gets clumsy for higher powers.

I can enter, for example

A:=[a[n] for n in 0..10]

for a list of symbols, but neither of

sum(a[i]*x^i, i=0..10)

or

sum(A.i*x^(i-1),i=1..11)

work, nor do they work when "sum" is replaced with "summation".


--

[https://ci6.googleusercontent.com/proxy/2sF0a1ZoLMOPckOBVppCZ4OFi06ffJNGtQadXIhbQiE95NE6m4gM53kVdCiQnVJYlRw380RlZ0tK7XHk4CmM2qy3nTM_ptogovPuXhk2=s0-d-e1-ft#https://dl.dropboxusercontent.com/u/2796170/facebook.png] 
[http://www.facebook.com/alasdair.mcandrew][https://ci4.googleusercontent.com/proxy/egLBn4P9MCM5JXRJFUg5fGnVRlWCGBo6zl_hik07VL66K0muLhfGiUf2i_7iymWxqLVLANxJraL5xfbJOTx8akBt9TmFlAIJcVuyk6fs2a9ASV26=s0-d-e1-ft#https://dl.dropboxusercontent.com/u/2796170/f-gplus_256-48.png] 
[https://plus.google.com/+AlasdairMcAndrew/posts][https://ci3.googleusercontent.com/proxy/-agz0u1Ac2-yf996SqPviIMbF5L-qAheB2hrZu975cEQB4YOZRFxRLuXLXmoQYBGNsMppMznpOXtgH2hmVu428QgisuXNCqKPzRQf1ZJ=s0-d-e1-ft#https://dl.dropboxusercontent.com/u/2796170/linkedin.png] 
[https://www.linkedin.com/pub/alasdair-mcandrew/a/178/108][https://ci5.googleusercontent.com/proxy/V-iov0_6bPsm3W5m1rgoRpRS5HaoNkB_5EbwhbqM_SqKHZOJsrTxalR6JGpq4SaT0gndZYFa2JH92qAJUGe2YVF05zindKPUWLep5js=s0-d-e1-ft#https://dl.dropboxusercontent.com/u/2796170/twitter.png] 
[https://twitter.com/amca01][https://ci6.googleusercontent.com/proxy/AMQYVjh54hMGPrzE9x9QAB8CTaI4oJKwlOSjuRnDGBKXOtbQJ9c9nVqOdcEd9fLnc1vtced39dXoWEEJHoJ0SUb2eH6a6wZdyjPMJQY3vw=s0-d-e1-ft#https://dl.dropboxusercontent.com/u/2796170/wordpress.png] 
[http://numbersandshapes.net]
------sinikael-?=_1-14468824788910.48719160025939345
Content-Type: text/html; format=flowed
Content-Transfer-Encoding: 7bit

<p dir="ltr">A quickie:&#160; is there any way of defining a formal 
polynomial with unknown coefficients, such as:</p>
<p dir="ltr">a_0+a_1*x+a_2*x^2+a_3*x^3&#160; ?</p>
<p dir="ltr">I want to calculate the values of the coefficients by a system 
of linear equations based on integrations whose integrands include that 
polynomial.</p>
<p dir="ltr">For small polynomials I can write</p>
<p dir="ltr">p:=a+b*x+c*x^2+d*x^3</p>
<p dir="ltr">but this gets clumsy for higher powers.</p>
<p dir="ltr">I can enter, for example</p>
<p dir="ltr">A:=[a[n] for n in 0..10]</p>
<p dir="ltr">for a list of symbols, but neither of</p>
<p dir="ltr">sum(a[i]*x^i, i=0..10)</p>
<p dir="ltr">or</p>
<p dir="ltr">sum(A.i*x^(i-1),i=1..11)</p>
<p dir="ltr">work, nor do they work when "sum" is replaced with 
"summation".&#160;&#160; <br></p>
<p dir="ltr">-- </p>
<p dir="ltr"><img 
src="https://ci6.googleusercontent.com/proxy/2sF0a1ZoLMOPckOBVppCZ4OFi06ffJNGtQadXIhbQiE95NE6m4gM53kVdCiQnVJYlRw380RlZ0tK7XHk4CmM2qy3nTM_ptogovPuXhk2=s0-d-e1-ft#https://dl.dropboxusercontent.com/u/2796170/facebook.png"><a 
href="http://www.facebook.com/alasdair.mcandrew"></a> <img 
src="https://ci4.googleusercontent.com/proxy/egLBn4P9MCM5JXRJFUg5fGnVRlWCGBo6zl_hik07VL66K0muLhfGiUf2i_7iymWxqLVLANxJraL5xfbJOTx8akBt9TmFlAIJcVuyk6fs2a9ASV26=s0-d-e1-ft#https://dl.dropboxusercontent.com/u/2796170/f-gplus_256-48.png"><a 
href="https://plus.google.com/+AlasdairMcAndrew/posts"></a> <img 
src="https://ci3.googleusercontent.com/proxy/-agz0u1Ac2-yf996SqPviIMbF5L-qAheB2hrZu975cEQB4YOZRFxRLuXLXmoQYBGNsMppMznpOXtgH2hmVu428QgisuXNCqKPzRQf1ZJ=s0-d-e1-ft#https://dl.dropboxusercontent.com/u/2796170/linkedin.png"><a 
href="https://www.linkedin.com/pub/alasdair-mcandrew/a/178/108"></a> <img 
src="https://ci5.googleusercontent.com/proxy/V-iov0_6bPsm3W5m1rgoRpRS5HaoNkB_5EbwhbqM_SqKHZOJsrTxalR6JGpq4SaT0gndZYFa2JH92qAJUGe2YVF05zindKPUWLep5js=s0-d-e1-ft#https://dl.dropboxusercontent.com/u/2796170/twitter.png"><a 
href="https://twitter.com/amca01"></a> <img 
src="https://ci6.googleusercontent.com/proxy/AMQYVjh54hMGPrzE9x9QAB8CTaI4oJKwlOSjuRnDGBKXOtbQJ9c9nVqOdcEd9fLnc1vtced39dXoWEEJHoJ0SUb2eH6a6wZdyjPMJQY3vw=s0-d-e1-ft#https://dl.dropboxusercontent.com/u/2796170/wordpress.png"><a 
href="http://numbersandshapes.net"></a></p>

------sinikael-?=_1-14468824788910.48719160025939345--


--===============2344031369064294312==
Content-Type: text/plain; charset="us-ascii"
MIME-Version: 1.0
Content-Transfer-Encoding: 7bit
Content-Disposition: inline

_______________________________________________
Axiom-mail mailing list
[email protected]
https://lists.nongnu.org/mailman/listinfo/axiom-mail

--===============2344031369064294312==--