[stuff]
"RL" == Robert Latest <boblatest@yahoo.com> writes:
The remaining question is: Is there Readline support for Maxima on the Linux
console?
Hi all,
while helping my daughter with her school algebra problems I thought
I might get some benefit for myself and dabble in some CAS. (Back
when I studied math in the 90s I didn't even know such a thing as CAS existed, and I always found algebra terribly tedious).
Topic of the day, circle equations. So why not try and figure out the intersection points (if any) of two circles.
(%i1) e1: x^2 + y^2 + a*x + b*y + c = 0;
2 2
(%o1) y + b y + x + a x + c = 0
(%i2) e2: x^2 + y^2 + d*x + e*y + f = 0;
2 2
(%o2) y + e y + x + d x + f = 0
X and y in the two equations are the same because we're searching the point(s) both have in common. So here goes:
(%i3) solve([e1, e2], [x, y]);
(%o3) []
That took several seconds and yielded nothing. So let's try a more
homeworky approach: subtract the equations to get rid of the square
terms, solve for x (or y) and substitute into one of the equations:
(%i5) solve(%, x);
(e - b) y + f - c
(%o5) [x = - -----------------]
d - a
Now I can already see that substituting this into %o1 or %o2 will
bring up an idiotically convoluted quadratic equation. Just the right
thing for a CAS. Nice. But now I'm stuck. I can't find anything in
the docs on how to proceed from here.
Questions:
1) Why didn't Maxima find any solution at %i3?
2) How does one substitute the expression for x at %o5 into %o1?
3) I'm using the Linux console. How can I make Maxima use readline,
so that arrow-up brings up an editable copy of an earlier command
line?
Hi all,
while helping my daughter with her school algebra problems I thought I might get some benefit for myself and dabble in some CAS. (Back when I studied
math in the 90s I didn't even know such a thing as CAS existed, and I
always found algebra terribly tedious).
Topic of the day, circle equations. So why not try and figure out the intersection points (if any) of two circles.
(%i1) e1: x^2 + y^2 + a*x + b*y + c = 0;
2 2
(%o1) y + b y + x + a x + c = 0
(%i2) e2: x^2 + y^2 + d*x + e*y + f = 0;
2 2
(%o2) y + e y + x + d x + f = 0
X and y in the two equations are the same because we're searching the point(s)
both have in common. So here goes:
(%i3) solve([e1, e2], [x, y]);
(%o3) []
This is solved using usual quadratic formula, but since coefficients
of the quadratic are complicated the result is large. One could
plug in this y into formula for x, but result would be equally large.
Note: when you look at "general solution" there are subtleties.
You can see this already from the first solution: there is
division by d - a. And indeed, depending on the other parameters
beside normal case of two solutions there may be one solution,
no solutions or infinitely many solutions. Similarely, quadratic
formula gives "generic solution" and ignores special cases.
Normally a CAS will give you "generic solution", that is solution
which is valid as long as there are no divisions and which may
miss some special cases. Some teachers insist of analysiong
all cases, that quickly gets tedious both for people and at
somewhat larger scale for computers.
If you have numbers in
the problem, than it is possible to see during computation
if there are special cases and handle such cases apropriately,
this avoids purely theoretical difficulties. OTOH if you
really need general solution, then there is some extra work
to check usual CAS solution and write proper conditions.
antispam@math.uni.wroc.pl wrote:
This is solved using usual quadratic formula, but since coefficients
of the quadratic are complicated the result is large. One could
plug in this y into formula for x, but result would be equally large.
Note: when you look at "general solution" there are subtleties.
You can see this already from the first solution: there is
division by d - a. And indeed, depending on the other parameters
beside normal case of two solutions there may be one solution,
no solutions or infinitely many solutions. Similarely, quadratic
formula gives "generic solution" and ignores special cases.
I know all that. I didn't really *need* to find a general solution for the intersections of two circles. I just took my daughter's homework assignment as
inspiration to play around with a CAS (which I always wanted but didn't have any reason to). I expected a screenful of messy solutions, but not an empty result.
OK. So use a CAS with reasonable equation solver (and not Maxima
which is (in)famous for failures in its solver).
Hi all,
while helping my daughter with her school algebra problems I thought I
might get some benefit for myself and dabble in some CAS. (Back when I studied math in the 90s I didn't even know such a thing as CAS existed,
and I always found algebra terribly tedious).
Topic of the day, circle equations. So why not try and figure out the intersection points (if any) of two circles.
(%i1) e1: x^2 + y^2 + a*x + b*y + c = 0;
2 2
(%o1) y + b y + x + a x + c = 0 (%i2) e2: x^2 +
y^2 + d*x + e*y + f = 0;
2 2
(%o2) y + e y + x + d x + f = 0
X and y in the two equations are the same because we're searching the point(s)
both have in common. So here goes:
(%i3) solve([e1, e2], [x, y]);
(%o3) []
That took several seconds and yielded nothing. So let's try a more
homeworky approach: subtract the equations to get rid of the square
terms, solve for x (or y) and substitute into one of the equations:
(%i5) solve(%, x);
(e - b) y + f - c
(%o5) [x = - -----------------]
d - a
Now I can already see that substituting this into %o1 or %o2 will bring
up an idiotically convoluted quadratic equation. Just the right thing
for a CAS. Nice. But now I'm stuck. I can't find anything in the docs on
how to proceed from here.
Questions:
1) Why didn't Maxima find any solution at %i3?
2) How does one substitute the expression for x at %o5 into %o1?
3) I'm using the Linux console. How can I make Maxima use readline, so
that
arrow-up brings up an editable copy of an earlier command line?
Thanks!
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