x1, y1, z1 = sp.symbols("x1 y1 z1")
x2, y2, z2 = sp.symbols("x2 y2 z2")
x3, y3, z3 = sp.symbols("x3 y3 z3")
xs, ys, zs = sp.symbols("xs ys zs")
maz.check( "Denormalized", "Without D, Gain %i",
[
(sp.Matrix([
[xs,ys],
]) *
sp.Matrix([
[x1,y1],
[x2,y2],
]).inv())[0],
(sp.Matrix([
[xs,ys],
]) *
sp.Matrix([
[x1,y1],
[x2,y2],
]).inv())[1],
])
maz.check( "Denormalized", "Without D, Gain %i",
[
+ xs*y2/(x1*y2 - x2*y1)
- ys*x2/(x1*y2 - x2*y1)
,
+ ys*x1/(x1*y2 - x2*y1)
M = sp.Matrix( [
[x1, y1, z1],
[x2, y2, z2],
[x3, y3, z3],
] )
P = sp.Matrix( [
[xs, ys, zs],
] )
G = P.multiply(M.inv())
maz.check("InverseDeterminant", "original",
M.det()
)
maz.check("InverseDeterminant", "expanded",
x1*y2*z3 - x1*y3*z2 - x2*y1*z3 + x2*y3*z1 + x3*y1*z2 - x3*y2*z1
)
maz.check("InverseDeterminant", "divided by x1",
(
+ (x1*z3 - x3*z1)*(x1*y2 - x2*y1)
- (x1*z2 - x2*z1)*(x1*y3 - x3*y1)
) / x1
)
maz.check("InverseDeterminant", "divided by y1",
(
+ (y1*x3 - y3*x1)*(y1*z2 - y2*z1)
- (y1*x2 - y2*x1)*(y1*z3 - y3*z1)
) / y1
t0=R/c
sympy.var("w t x", real=True)
N=sympy.Integer
def sum(v) : return reduce(operator.add, v, N(0))
def prod(v) : return reduce(operator.mul, v, N(1))
def f(n) : return reduce(operator.mul, xrange(n,0,-1), N(1))
def ff(n) : return reduce(operator.mul, xrange(n,0,-2), N(1))
"""
"""
maz.check("Polynomial", "initial (%i)", [
sum([
ff(2*n-2*m-1)/ff(2*m-1)*x**(2*m-n-1)
for m in xrange(1,n//2+1) ])
for n in xrange(10) ])
maz.check("Polynomial", "m'=m+1 (%i)", [
sum([
ff(2*n-2*m-3)/ff(2*m+1)*x**(2*m-n+1)
for m in xrange(n//2) ])
for n in xrange(10) ])
maz.check("Polynomial", "m'=2*m (%i)", [
sum([
ff(2*n-m-3)/ff(m+1)*x**(m-n+1)
for m in xrange(0,2*(n//2),2) ])
for n in xrange(10) ])
maz.check("Polynomial", "removing the // (%i)", [
sum([
ff(2*n-m-3)/ff(m+1)*x**(m-n+1)
