# How do you Append a Symbolic Matrix?

To All:

I am trying to make a function that will take a set of dynamics and a set of independent variables that can or cannot be within the dynamics equations to create a "frozen" state space matrix, A. I would like to tell you all now that I am mostly a FORTRAN coder and am in the process of trying to understand SageMath, which is why I am coding in a brute force method.

I previously checked to make sure that the derivative function was producing reasonable answers and created the matrices like this.

rmag = r^2 + r^2 + r^2;
dyn = -mu*r/rmag^3; # spherical gravity assumption
ddyn_dx = dyn.derivative(r);ddyn_dy = dyn.derivative(r);ddyn_dz = dyn.derivative(r);
pdyn_pr = (transpose(matrix([ddyn_dx,ddyn_dy,ddyn_dz])));


As you might have discovered, this is exceptionally tedious when the number of independent variables get larger. Therefore, I desired to code something like this:

def FindDynMatrix(dynamics,xvect):
# Find the length of the vector defining the internal variables
#    within dynamics are independent variables:
leng = len(xvect);
for j in range(leng):
vect = dynamics.derivative(xvect[j]);
if j == 0:
mat = vect;
else:
mat=matrix([mat,vect])
#mat = mat.append(vect) # didn't work
return mat


In "FindDynMatrix", symbolic vector that is dependent on a multitude of variables including those within the symbolic vector "xvect". The hope was to "black box" the production of the A matrix for a little controls tool that I am coding up.

However, I can not find a way to get this to work. Help would be appreciated.

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## Comments

It would be easier for us to understand your question if you provide the definition if the list r in your first line (which seems different from the r you used in your second line), the type and an example of mu, xvect, dynamics, ... so that we can try.

'r' is a vector so the equation is correct. x,y,z = var('x,y,z') mu = var('mu') r = vector([x,y,z]) The variable 'dyn' is just an assumed spherical earth gravitational equation. 'mu' is a constant. One should be able to get 'pdyn_pr' as produced by the first set of equations by calling 'FindDynMatrix' like this, FindDynMatrix(dyn,r)

I believe that I have found the solution for part of this problem. By calling Jacobian(dyn,r), I can produce 'pdyn_pr'. Reference: http://ask.sagemath.org/question/9830/generating-a-jacobian-matrix-for-a-set-of-multivariate-polynomials/ (http://ask.sagemath.org/question/9830...)

However, I would still like to know how to append to symbolic matrices for future reference.