Commit 88c1be5a authored by Jim Hefferon's avatar Jim Hefferon

change cas.tex to use sage

parent 0165cc83
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......@@ -27,12 +27,24 @@ For example, in the Topic on Networks, we need to solve this.
It can be done by hand, but it would take a while and be error-prone.
Using a computer is better.
We illustrate by solving that system under Maple
(for another system, a user's manual would obviously detail the exact syntax
The array of coefficients can be entered in this way
We illustrate by solving that system under Sage.
sage: var('i0,i1,i2,i3,i4,i5,i6')
(i0, i1, i2, i3, i4, i5, i6)
sage: network_system=[i0-i1-i2==0, i1-i3-i5==0,
....: i2-i4+i5==0,, i3+i4-i6==0, 5*i1+10*i3==10,
....: 2*i2+4*i4==10, 5*i1-2*i2+50*i5==0]
sage: solve(network_system, i0,i1,i2,i3,i4,i5,i6)
[[i0 == (7/3), i1 == (2/3), i2 == (5/3), i3 == (2/3),
i4 == (5/3), i5 == 0, i6 == (7/3)]]
Here is the same system solved under Maple.
We enter the array of coefficients
and the vector of constants,
and then we get the solution.
> A:=array( [[1,-1,-1,0,0,0,0],
......@@ -40,27 +52,15 @@ The array of coefficients can be entered in this way
[0,5,-2,0,0,50,0]] );
(putting the rows on separate lines is not necessary,
but is done for clarity).
The vector of constants is entered similarly.
> u:=array( [0,0,0,0,10,10,0] );
Then the system is solved, like magic.
> linsolve(A,u);
7 2 5 2 5 7
[ -, -, -, -, -, 0, - ]
3 3 3 3 3 3
Systems with infinitely many solutions are solved in the same
way\Dash the computer simply returns a parametrization.
Systems with infinitely many solutions are entered in the same
way but for the solution the computer will return a parametrization.
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......@@ -257,4 +257,16 @@
%------------------------- code listings
......@@ -124,7 +124,7 @@ and linear maps, is not taken to the complete exclusion of others.
Applications and computing are interesting and vital aspects
of the subject.
Consequently, each of this book's chapters closes with a few
application or computer-related topics.
topics in those areas.
Most simply give a reader
a taste of the subject, discuss how linear algebra comes in,
point to some further reading, and give a few exercises.
......@@ -233,7 +233,7 @@ I have marked a good sample with \recommendationmark's in the margin.
For all of them, you must justify your answer either with a computation
or with a proof.
Be aware that few inexperienced people can write correct proofs;
try to find an experienced person to work with you on these.
try to find a trained person to work with you on these.
Finally, a caution for all students, independent or not:~I
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