def test_Mul(self):
from sympy.abc import a, b, c, x, y
m = Symbol ('m', commutative=False)
n = Function('n', commutative=False)
k = Function('k', commutative=False)
assert straighten(Bind(a*m, x, b*Bind(c*n(x), y, k(x,y)))) == a*b*c*Bind(m,x,Bind(n(x),y,k(x,y)))
assert straighten(Bind(a*Bind(b*m, x, c*n(x)), y, k(y))) == a*b*c*Bind(m,x,Bind(n(x),y,k(y)))
assert straighten(Bind(m, x, Bind(n(x), y, a*exp(b*x+c*y)*k(x,y)))) == a*Bind(m, x, exp(b*x)*Bind(n(x), y, exp(c*y)*k(x,y)))
a = Function('a')
b = Function('b')
c = Function('c')
assert straighten(Bind(a(x)*m, x, b(x)*Bind(c(x)*n(x), y, k(x,y)))) == a(x)*Bind(m,x,b(x)*c(x)*Bind(n(x),y,k(x,y)))
assert straighten(Bind(a(x)*Bind(b(x)*m, x, c(x)*n(x)), y, k(y))) == a(x)*b(x)*Bind(m,x,c(x)*Bind(n(x),y,k(y)))
def splice(a, b, x0, width, x, dx):
from sympy import tanh
ax = a(x)
bx = b(x)
dax = symdiff(a)(x)
dbx = symdiff(b)(x)
f = ax + (bx-ax) * (1+tanh((x-x0)/width)) / 2
df = (dax
+ (dbx-dax) * (1+tanh((x-x0)/width)) / 2
+ (bx - ax) * (1-tanh((x-x0)/width)**2) / (2*width)) * dx
return f, df
def test_bisectors():
r1 = Line3D(Point3D(0, 0, 0), Point3D(1, 0, 0))
r2 = Line3D(Point3D(0, 0, 0), Point3D(0, 1, 0))
bisections = r1.bisectors(r2)
assert bisections == [Line3D(Point3D(0, 0, 0), Point3D(1, 1, 0)),
Line3D(Point3D(0, 0, 0), Point3D(1, -1, 0))]
ans = [Line3D(Point3D(0, 0, 0), Point3D(1, 0, 1)),
Line3D(Point3D(0, 0, 0), Point3D(-1, 0, 1))]
l1 = (0, 0, 0), (0, 0, 1)
l2 = (0, 0), (1, 0)
for a, b in cartes((Line, Segment, Ray), repeat=2):
assert a(*l1).bisectors(b(*l2)) == ans
def test_linear_system_function():
a = Function('a')
assert solve([a(0, 0) + a(0, 1) + a(1, 0) + a(1, 1), -a(1, 0) - a(1, 1)],
a(0, 0), a(0, 1), a(1, 0), a(1, 1)) == {a(1, 0): -a(1, 1), a(0, 0): -a(0, 1)}
def test_linear_system():
x, y, z, t, n, a = symbols('x,y,z,t,n,a')
assert solve([x - 1, x - y, x - 2*y, y - 1], [x,y]) is None
assert solve([x - 1, x - y, x - 2*y, x - 1], [x,y]) is None
assert solve([x - 1, x - 1, x - y, x - 2*y], [x,y]) is None
assert solve([x + 5*y - 2, -3*x + 6*y - 15], x, y) == {x: -3, y: 1}
M = Matrix([[0,0,n*(n+1),(n+1)**2,0],
[n+1,n+1,-2*n-1,-(n+1),0],
[-1, 0, 1, 0, 0]])
assert solve_linear_system(M, x, y, z, t) == \
{y: 0, z: t*(-n - 1)/n, x: t*(-n - 1)/n}
assert solve([x + y + z + t, -z - t], x, y, z, t) == {x: -y, z: -t}
assert solve([a(0, 0) + a(0, 1) + a(1, 0) + a(1, 1), -a(1, 0) - a(1, 1)],
a(0, 0), a(0, 1), a(1, 0), a(1, 1)) == {a(1, 0): -a(1, 1), a(0, 0): -a(0, 1)}
def test_linear_system_function():
a = Function('a')
assert solve([a(0, 0) + a(0, 1) + a(1, 0) + a(1, 1), -a(1, 0) - a(1, 1)],
a(0, 0), a(0, 1), a(1, 0), a(1, 1)) == {
a(1, 0): -a(1, 1),
a(0, 0): -a(0, 1)
}
def test_linear_system():
n, t = symbols('n,t')
assert solve([x - 1, x - y, x - 2 * y, y - 1], [x, y]) is None
assert solve([x - 1, x - y, x - 2 * y, x - 1], [x, y]) is None
assert solve([x - 1, x - 1, x - y, x - 2 * y], [x, y]) is None
assert solve([x + 5 * y - 2, -3 * x + 6 * y - 15], x, y) == {x: -3, y: 1}
M = Matrix([[0, 0, n * (n + 1), (n + 1)**2, 0],
[n + 1, n + 1, -2 * n - 1, -(n + 1), 0], [-1, 0, 1, 0, 0]])
assert solve_linear_system(M, x, y, z, t) == \
{y: 0, z: t*(-n - 1)/n, x: t*(-n - 1)/n}
assert solve([x + y + z + t, -z - t], x, y, z, t) == {x: -y, z: -t}
assert solve([a(0, 0) + a(0, 1) + a(1, 0) + a(1, 1), -a(1, 0) - a(1, 1)],
a(0, 0), a(0, 1), a(1, 0), a(1, 1)) == {
a(1, 0): -a(1, 1),
a(0, 0): -a(0, 1)
}
