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[Axiomdeveloper] [#170 Axiom fails to solve "separable" system of equat
From: 
kratt6 
Subject: 
[Axiomdeveloper] [#170 Axiom fails to solve "separable" system of equations] 
Date: 
Thu, 16 Jun 2005 04:41:00 0500 
Changes
http://page.axiomdeveloper.org/zope/mathaction/170AxiomFailsToSolveSeparableSystemOfEquations/diff

??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 = PQ, C = 1, C = 1]
solve(L, [P,Q])
solve(L,[P,Q,C])
\end{axiom}
really has no solution.

forwarded from http://page.axiomdeveloper.org/zope/mathaction/address@hidden
 [Axiomdeveloper] [#170 Axiom fails to solve "separable" system of equations],
kratt6 <=