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D.15.2.23 qepcadsystem

Procedure from library findiff.lib (see findiff_lib).

Usage:
qepcadsytem(f); l a list;

Return:
list

Purpose:
gives back some constraints that are equivalent to the eigenvalues of the matrices in the list l being < 1 (computed by QEPCAD)

Example:
 
LIB "findiff.lib";
list D="Ut","Ux","Uy","U";
list V="t","x","y";
list P="a","b";
setinitials(V,D,P);
matrix M[2][2]=0,-a,-a,0;
list Mat=unitmat(2),M;
list Appr=forward(Ut,U,t),forward(Ux,U,x);
//matrixsystem(Mat,Appr);
//timestep(_);
fouriersystem(Mat,Appr);
==> [1]:
==>    [1]:
==>       [1]:
==>          _[1,1]=(T)
==>          _[1,2]=0
==>          _[2,1]=0
==>          _[2,2]=(T)
==>       [2]:
==>          _[1,1]=1
==>          _[1,2]=(I*Sx*a*dt+Cx*a*dt-a*dt)/(dx)
==>          _[2,1]=(I*Sx*a*dt+Cx*a*dt-a*dt)/(dx)
==>          _[2,2]=1
==>    [2]:
==>       [1]:
==>          _[1]=(T)
==>       [2]:
==>          _[1]=(-I*Sx*a*dt-Cx*a*dt+a*dt+dx)/(dx)
==>          _[2]=(I*Sx*a*dt+Cx*a*dt-a*dt+dx)/(dx)
==> [2]:
==>    [1]:
==>       [1]:
==>          (T^2)
==>    [2]:
==>       [1]:
==>          (-2*Cx*a^2*dt^2-2*Cx*a*dt*dx+2*a^2*dt^2+2*a*dt*dx+dx^2)/(dx^2)
==>       [2]:
==>          (-2*Cx*a^2*dt^2+2*Cx*a*dt*dx+2*a^2*dt^2-2*a*dt*dx+dx^2)/(dx^2)
qepcadsystem(_[2]);
==> 0
==> 0
==> 0
==> 0
==> cx - 1 > 0 /\ a /= 0 /\ dt /= 0 /\ [ [ dx + a dt < 0 /\ dx - a dt > 0 ] \\
   / [ dx + a dt > 0 /\ dx - a dt < 0 ] ]
==> 
==> [1]:
==>    cx-1
==> [2]:
==>    (a)
==> [3]:
==>    (dt)
==> [4]:
==>    (a*dt+dx)
==> [5]:
==>    (-a*dt+dx)
==> [6]:
==>    (a*dt+dx)
==> [7]:
==>    (-a*dt+dx)


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