Run the sub-resultant algorithm remembering that the point is that the sub-resultant algorithm doesn’t generate fractions) on the following two polynomials. j := (y2 —1) ((y+ 1Jx+ (ý—1)x’+ ? — l)x+ (y’— 1)z+9 —1]: g:—(y-’ 1)x5-i-(9-- 1)x4+(y’- 1)x4(y—1)r’+(?—l)x+y’--l

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

requirement are stated in the file, attached picture is resource to help

 

A. Electronic submission of a hie tpossibly scanned paper) of answers ianswers only not the detailed working), with your candidate number. For example, an answer to question 4a

lii the polynomials were r— 6 and z t ti might be he g.cd. is 1: I used two primes2 and 3, hut. 2 was bad”.

li. Electronic submission of a Maple worksheet. The sheets should be named number-i .mw etc., so that a student whose examination number Is 1234 5Ws answer to question 3

would be called 123456-1mw, In view of the fact that Maple’s ordering is session-dependent, the worksheets should be verified in a fresh instance of Maple 2021 before being

submitted. Details on the electronic submission will be provided on Moodle, It Is acceptable to provide Maple input .mpl 111es instead.

When I ask you, say, to run Dareiss’s algorithm, It Is up to you whether you program it completely, run it by hand, or use a mixture of the two. It is not acceptable to use a built-in

progranune as part of your submission tthough you may wish to use one to check your results»1. However, what you do must be comprehensible to an outsider Isuch asJHD), so

programs must be commente&self-explanator% and sets of commands must have explanations. e.g. against a line like

b, .r13, r12,.rli,rl3,rt,ir:

I would expect a comment such as

fnuap r’cs 12 wsd 19 sLr’ce .(12,12)—e

Note that

N asytrettertbtrle(5,5,e); s Sylvester ibtrls of 5 and I 4th respect to s

is useless commentina: a comment should exnlain why the code is the was it is.

1. Run the sub-resultant algorithm remembering that the point is that the sub-resultant algorithm doesn’t generate fractions) on the following two polynomials.

j := (y2 —1) ((y+ 1Jx+ (ý—1)x’+ ? — l)x+ (y’— 1)z+9 —1]:

g:—(y-’ 1)x5-i-(9-- 1)x4+(y’- 1)x4(y—1)r’+(?—l)x+y’--l

They should be regarded as polynomials in a whose coefficients are polynomials la y What do you get as the last non-zero member of the subresultant sequence? What is the true

greatest common divisor of these two polynomials? Any other greatest common divisors you require should be computed by subresultants.

. Functions that compute polynomial gcds, such as content (and its mirror primpart), nornialor simpli(3 as well ns the built-in god are not allowed. factor calls god internally, as do

ninny other functions: if you don’t understand it, you’re probably safer not using itt As pteni Is tightly coupled to the cancellation properties of sub.resultant, you should not be

using the built-in prem either,

°igcd, rein, quo etc, are legal.

Attachments:

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