facing problem to write a piecewise function

[A123-bansal123]

Below I attach a small code for a function. I am not able to write it properly, it shows an error.

u_exact (x,y)= {(10x,0) for 0≤x≤0.1, y=,1
(1,0) for 0.1≤x1≤0.9, y=1
((10−10x),0) for 0.9≤x1≤1, y=1
(0,0) for (x,y)∈Γ∖{(x,1)∶0≤x≤1}.

from firedrake import *
import sys
from firedrake.petsc import PETSc
nx=4
M = UnitSquareMesh(nx, nx)
# Define Function Spaces
V = VectorFunctionSpace(M, "Lagrange", 2)
W = FunctionSpace(M, "Lagrange", 1)
Z = V * W 
# Define Test and trial function
up = Function(Z)
u, p  = split(up)
v, q = TestFunctions(Z)
x, y = SpatialCoordinate(M)
f = Function(V)
source = Constant((0,0))
f.interpolate(source)
u_exact = Function(V)
velocity = Conditional(
          And(ge(x, 0), le(x, 0.1), eq(y, 1)),
          10*x[0]*Constant((1, 0)),
          Conditional(
          And(gt(x, 0.1), lt(x, 0.9), eq(y, 1)),
          Constant((1, 0)),
          Conditional(
          And(ge(x, 0.9), le(x, 1), eq(y, 1)),
          (10-10*x[0])*Constant((1, 0)),
        )
    )
)

error

Traceback (most recent call last):
  File "NS5.py", line 19, in <module>
    velocity = Conditional(
NameError: name 'Conditional' is not defined

[A123-bansal123]

please help!

[connorjward]

I think you want lowercase conditional instead of Conditional. Does that fix things?

[A123-bansal123]

yes that problem is resolved but now it shows error :

  File "NS5.py", line 20, in <module>
    And(ge(x, 0), le(x, 0.1), eq(y, 1)),
TypeError: And() takes 2 positional arguments but 3 were given

as above i mentioned exactly what function i have to write.

[connorjward]

I think you may need to write

And(
  And(ge(x, 0), le(x, 0.1)),
  eq(y, 1))

[A123-bansal123]

Thanks it works well