Assignment 1.
MATH 441/741/819 Spring 2014.
Michael Monagan


Due Tuesday January 21st, 2:30pm at the beginning of class.
Late policy: -20% for up to 48 hours late.
Zero for more than 48 hours late.

Do the following problems from the text.
For problems in Maple, please hand in a printout of your Maple worksheet.

1.1 #5, 6a
1.2 #2, 4, 5, 15a-c
1.3 #4, 8
1.4 #1, 2, 3a-b, 4, 5, 8, 11, 15a
1.5 #8, 9, 15, 17

Do 1.2 #2, #4(c) and #5 by hand and do the rest of #4 in Maple.
For #4, you use the plot, plot3d, plots[implicitplot],
and plots[implicitplot3d] commands.
Don't forget to answer the last part of 1.2 #4.

For 1.3 #8, graph the curve for c=1 using the plots[implicitplot] command.
You will need to choose the domain appropriately and also use the grid
option to get a nice looking plot.  Now check your parametrization
by graphing it using the parametric option of the plot command.
See ?plot,details for help on parametric plots.

Additional exercise.

Read the notes in the Maple worksheet MapleNotes.mw on loops and
Maple procedures.  Proposition 8 (ii) says that GCD(f1,f2,...,fs)
is a generator for the ideal <f1,f2,...fs> in k[x].  For k=Q, write
a Maple procedure  Generator := proc(L,x) ... end;   that takes as input a
list L = [f1,f2,...,fs] of s>0 polynomials in Q[x] and the variable x
and outputs the monic GCD(f1,f2,...,fs) in Q[x].
Test your Maple procedure on the following inputs

   > L := [ 2*x^2-2, 1/3*x^3-1/3, 4*x^4-4 ];
   > Generator(L,x);
   > L := [ 2*y^2-4 ];
   > Generator(L,y);

Read the notes in the Maple worksheet MapleNotes.mw and the material
on loops and Maple procedures.