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[Axiom-developer] [#170 Axiom fails to solve "separable" system of equat
From: |
kratt6 |
Subject: |
[Axiom-developer] [#170 Axiom fails to solve "separable" system of equations] |
Date: |
Thu, 16 Jun 2005 04:41:00 -0500 |
Changes
http://page.axiom-developer.org/zope/mathaction/170AxiomFailsToSolveSeparableSystemOfEquations/diff
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??changed:
-
Some examples:
\begin{axiom}
L := [ A = 2*P1+P2, B = 2*P2+P1, C = 2*Q1+Q2, D = 2*Q2+Q1]
solve(L, [P1,P2])
\end{axiom}
However:
\begin{axiom}
solve([L.1,L.2],[P1,P2])
solve([L.3,L.4],[Q1,Q2])
solve(L,[P1,P2,Q1,Q2])
\end{axiom}
Simpler:
\begin{axiom}
solve([a - b = 0, c - d = 0],[b])
linSolve([a - b, c - d],[b])
\end{axiom}
The operation 'solve' calls 'linSolve', which sets up the corresponding matrix
and vector and solves it using 'solve\$LinearSystemMatrixPackage'. This in turn
returns "failed", since the last columns of the matrix contain zeros, the
vector does not. In the example above, the matrix and vector are::
+- 1+
[mat= | |,vec= [- a,d - c]]
+ 0 +
Note that
\begin{axiom}
linSolve([a - b, 0],[b])
\end{axiom}
works.
The same happens, if the equation is not linear:
\begin{axiom}
L := [ A = 2*P1^2+P2, B = 2*P2+P1, C = 2*Q1+Q2, D = 2*Q2+Q1]
solve(L, [P1,P2])
solve([L.3,L.4],[P1,P2,Q1,Q2])
\end{axiom}
So, very probably, a fix would need to do two things:
- seperate the equations into those that do and those that don't contain the
given variables.
- check whether those that don't contain the variables are contradicting.
- solve the others.
The second point is necessary, since
\begin{axiom}
L := [ A = P+Q, B = P-Q, C = 1, C = -1]
solve(L, [P,Q])
solve(L,[P,Q,C])
\end{axiom}
really has no solution.
--
forwarded from http://page.axiom-developer.org/zope/mathaction/address@hidden
- [Axiom-developer] [#170 Axiom fails to solve "separable" system of equations],
kratt6 <=