call for success stories

[Harald Schilly]

Hi, I'm working on the Sage website.

I am searching for interesting content and this time I want to ask
everyone who has used Sage for his or her research or in education in
class to write a short success story. It should talk about how it was
used and the general and personal experience. Just some sentences to
give new users a first impression of Sage.

thanks and greetings, Harald

[David Joyner]

In teaching:
I used SAGE for some sections of a differential equations course
I was teaching last fall. Wasn't sure if the students would just
"take the hit" and refuse to learn SAGE so I made the assignments
worth very little and very easy. Also, I made extra assignments for
extra credit.
It turned out not only did most do the assignment but a lot more
than I expected did the extra credit ones too and say that they liked SAGE and
its philosophy. I would call it a success in teaching.

In research:
I wrote some time ago a procedure for computing Duursma zeta functions of
a linear error-correcting code. AFAIK, no other program does this (not
GUAVA nor
MAGMA, ...). These zeta functions are very similar to the zeta
function of a curve
(they have a functional equation, a "Riemann hypothesis", etc), except
that no one knows
why the "Riemann hypothesis" doesn't always hold. There is a
conjecture that it holds
for a certain "extremal" class of codes, so maybe the RH holds for "good" or
"optimal" codes (since optimal codes are sometimes extremal)? A year or 2
ago, I found an example of a formally self-dual with optimal
parameters which violates
the RH. I would call that a success in research.

[Rolandb]

Hi. There is a simple saying: ““If you can count to ten you can count
to infinity really” to motivate six year olds. Let’s now move on by
motivating all ages using SAGE. I just give examples and not lines of
code, mainly because to promote the usage of SAGE and to encourage
others to check the results found. {Note: I encountered several bugs
in SAGE, but release 3.1 should be fine}
1. After counting we learn our youngsters to use "*","+","-". Not
always easy to find motivating exercises. The following question
proved to be fun for either an individual or a group. Especially in
cases where people had to wait for one hour or longer, e.g. bus trip
et cetera.
a. Easy start. Take the for instance the numbers 3,5,7,8. The
challenge is: make as many numbers as possible (i) starting from 0,
(ii) you may use each number only once, and (iii) using the three
operands "*","+","-".
The amazing fact is that you can produce consecutive numbers in the
range 0..65. The following output comes from a SAGE notebook:
1 = 3+5-7 , 2 = 3+7-8 , 3 = 3 , 4 = 3+8-7 , 5 = 5 , 6 = 3+8-5 , 7 =
7 , 8 = 8 , 9 = 3+5-7+8 , 10 = 3+7 , 11 = 3+8 , 12 = 3*8-(5+7) , 13 =
3+7-5+8 , 14 = 3*5+7-8 , 15 = 3*5 , 16 = 3*5-7+8 , 17 = 3*8-7 , 18 =
3*7+5-8 , 19 = 3*8-5 , 20 = (3+8-7)*5 , 21 = 3*7 , 22 = 3*5+7 , 23 =
3+5+7+8 , 24 = 3*7-5+8 , 25 = (8-3)*5 , 26 = 3*7+5 , 27 = 5*7-8 , 28 =
(5+7)*3-8 , 29 = 3*7+8 , 30 = 3*5+7+8 , 31 = 3*8+7 , 32 = 5*7-3 , 33 =
5*8-7 , 34 = 3*7+5+8 , 35 = 5*7 , 36 = 3*8+5+7 , 37 = 5*8-3 , 38 =
5*7+3 , 39 = (5+8)*3 , 40 = (3+7-5)*8 , 41 = 7*8-3*5 , 42 =
(3+7)*5-8 , 43 = 5*7+8 , 44 = (5+7)*3+8 , 45 = (7+8)*3 , 46 =
3+8+5*7 , 47 = 5*8+7 , 48 = (3+5)*7-8 , 49 = (3*5-8)*7 , 50 =
(3+7)*5 , 51 = 7*8-5 , 52 = (5+8)*(7-3) , 53 = 7*8-3 , 54 = 7*8+3-5 ,
55 = (3+8)*5 , 56 = (3+5)*7 , 57 = (3+5)*8-7 , 58 = (3+7)*5+8 , 59 =
3*8+5*7 , 60 = (5+7)*(8-3) , 61 = 3*7+5*8 , 62 = (3+8)*5+7 , 63 =
3*7*(8-5) , 64 = (3*5-7)*8 , 65 = (3*7-8)*5 , 66 has no expression
b. Less easy. Is 3,5,7,8 the best 4-tuple? Two ways to answer this
using SAGE:
i. All (reasonable) combinations of 4 different numbers
ii. Hard: Prove it by (a) produce symbolic expressions – there are
many! – and (b) just try to solve them.
c. You can play around by also allowing other operands like “/”, “^”,
“mod or % in SAGE”, or you can allow also negative numbers and look
for the longest consecutive row. In the case of 3,5,7,8 and the three
operands "*","+","-" I found 94 consecutive numbers.
d. If you add “^” (so 2^3=8), you find that the 4-tuple 2,3,7,8
delivers a nice row of numbers 0..75 as the following SAGE output
shows:
1 = 2**3-7 , 2 = 2 , 3 = 3 , 4 = 2+3+7-8 , 5 = 2*3+7-8 , 6 = 2*3 , 7 =
7 , 8 = 8 , 9 = 2**3-7+8 , 10 = 2+8 , 11 = 2*7-3 , 12 = 2+3+7 , 13 =
2*3+7 , 14 = 2*3+8 , 15 = 2**3+7 , 16 = 2**3+8 , 17 = 2*7+3 , 18 =
(2*7-8)*3 , 19 = 2*7-3+8 , 20 = 2+3+7+8 , 21 = 2*3+7+8 , 22 = 2*7+8 ,
23 = 2**3+7+8 , 24 = 3**2+7+8 , 25 = 2*7+3+8 , 26 = 2*8+3+7 , 27 =
(2+3)*7-8 , 28 = (3+7)*2+8 , 29 = 3*7+8 , 30 = (2+8)*3 , 31 =
2+8+3*7 , 32 = (7-3)*8 , 33 = (2+3)*8-7 , 34 = 2*3*7-8 , 35 =
(2+3)*7 , 36 = (3+7+8)*2 , 37 = 2*8+3*7 , 38 = 2*7+3*8 , 39 =
(7-2+8)*3 , 40 = (2+3)*8 , 41 = 2*3*8-7 , 42 = 2*3*7 , 43 =
(2+3)*7+8 , 44 = 7**2+3-8 , 45 = (2+7)*(8-3) , 46 = 7**2-3 , 47 =
(2+3)*8+7 , 48 = (2**3)*7-8 , 49 = (2+8-3)*7 , 50 = 2*3*7+8 , 51 =
(2+7+8)*3 , 52 = 7**2+3 , 53 = 7*8-3 , 54 = 7**2-3+8 , 55 = 2*3*8+7 ,
56 = (2**3)*7 , 57 = (2**3)*8-7 , 58 = (3*7+8)*2 , 59 = 7*8+3 , 60 =
(3+7)*(8-2) , 61 = 2+3+7*8 , 62 = 2*3+7*8 , 63 = (3**2)*7 , 64 =
(2**3)*7+8 , 65 = 3**2+7*8 , 66 = (2*7+8)*3 , 67 = (2+8)*7-3 , 68 =
7-3+8**2 , 69 = (2+7)*8-3 , 70 = 2*7*(8-3) , 71 = (2**3)*8+7 , 72 =
(2+7)*8 , 73 = (2+8)*7+3 , 74 = 3+7+8**2 , 75 = (2+3)*(7+8) , 76 has
no expression
e. Allowing negative numbers, I found that 103 consecutive numbers can
be produced. Such an exercise proved to be fun with motivated adults
and some good drinks.

2. Playing around with four number is relatively easy. More difficult
is the 5-tuple question, even in the simple case by only allowing the
operands "*","+","-". The reason is mainly because the number of
possibilities ‘explodes’.
To conclude: SAGE helped me to find relative simple exercises and
questions to motivate people of all ages (i) to do exercises “using
pen and paper”, and (ii) to become aware of the depth of even simple
mathematics. I learned from SAGE that “mathematics on a computer is
even better then gaming”. Roland