z3 - Checking satisfiability for matrix valued function -

i trying multiply 2 matrices of 2*2 order. 1 of matrix contains unknown parameter "k1". want check satisfiable solution value of k1. product of 2 matrices equal third one. note: dont want convert multiplication linear relation or set of equation want manipulate matrices.

here stuck.

k1 = int ('k1')  x = [ [ int("x_%s_%s" % (i+1, j+1)) j in range(2) ]       in range(2) ]  =((1,k1),(3,4))  b =((1,1),(1,1))  c= ((3,3),(7,7))  s = solver() s.add(a[0][1]>0) s.add(a*b==c) if s.check() == sat: m = s.model() r = [ [ m.evaluate(x[i][j]) j in range(2) ]        in range(2) ] print_matrix(r) else: print "failed solve" 

any way out?

one possible solution is

k1 = int ('k1')  x = [ [ int("x_%s_%s" % (i+1, j+1)) j in range(2) ]   in range(2) ]  =((1,k1),(3,4))  b =((1,1),(1,1))  c= ((3,3),(7,7))  s = solver() eq1= a[0][1]>0 eq2 =[[sum(a[i][k]*b[k][j] k in range(2)) == c[i][j] in range(2) ]          j in range(2) ] s.add(eq1) s.add(eq2[0][0]) s.add(eq2[0][1]) s.add(eq2[1][0]) s.add(eq2[1][1]) print s              print s.check()              m = s.model() print m 

and corresponding output is

[k1 > 0, 1 + k1*1 == 3, true, 1 + k1*1 == 3, true]  sat  [k1 = 2] 

please run example online here