fix Bernstein test coverage

test/PolynomialsTests/BernsteinBasesTests.jl

@@ -4,6 +4,8 @@ using Test
 using Gridap.TensorValues
 using Gridap.Fields
 using Gridap.Polynomials
+using Gridap.Polynomials: binoms
+using ForwardDiff
 
 @test isHierarchical(Bernstein) == false
 
@@ -81,26 +83,41 @@ test_field_array(b,x[1],bx[1,:],grad=∇bx[1,:],gradgrad=Hbx[1,:])
 
 # Order 3
 
+function bernstein(K,N)
+  b = binoms(Val(K))
+  t -> b[N+1]*(t^N)*((1-t)^(K-N))
+end
+_∇(b) = t -> ForwardDiff.derivative(b, t)
+_H(b) = t -> ForwardDiff.derivative(y -> ForwardDiff.derivative(b, y), t)
+
 order = 3
 b = BernsteinBasis(Val(1),V,order)
 
 # x=x^1; x2 = x^2; x3 = x^3
 #    -x3+3x2-3x+1  3x3-6x2+3x -3x3+3x2 x3
-bx  = [ 1.0   0.0  0.0   0.0
-        0.0   0.0  0.0   1.0
-        .216  .432 .288  .064]
+bx  = [      bernstein(order,n)( xi[1])  for xi in x,  n in 0:order]
 
 #   -3x2+6x-3  9x2-12x+3  -9x2+6x 3x2
-∇bx = G[ -3.   3.   0. 0.
-          0.   0.  -3. 3.
-        -1.08 -.36 .96 .48]
+∇bx = [ G(_∇(bernstein(order,n))(xi[1])) for xi in x,  n in 0:order]
 
 #    -6x+6 18x-12 -18x+6  6x
-Hbx = H[ 6.  -12.   6.   0.
-         0.   6.   -12.  6.
-         3.6 -4.8  -1.2  2.4]
+Hbx = [ H(_H(bernstein(order,n))(xi[1])) for xi in x,  n in 0:order]
+
+test_field_array(b,x,bx,≈, grad=∇bx,gradgrad=Hbx)
+test_field_array(b,x[1],bx[1,:],grad=∇bx[1,:],gradgrad=Hbx[1,:])
+
+
+# Order 4
+
+order = 4
+b = BernsteinBasis(Val(1),V,order)
+
+bx  = [      bernstein(order,n)( xi[1])  for xi in x,  n in 0:order]
+∇bx = [ G(_∇(bernstein(order,n))(xi[1])) for xi in x,  n in 0:order]
+Hbx = [ H(_H(bernstein(order,n))(xi[1])) for xi in x,  n in 0:order]
 
 test_field_array(b,x,bx,≈, grad=∇bx,gradgrad=Hbx)
 test_field_array(b,x[1],bx[1,:],grad=∇bx[1,:],gradgrad=Hbx[1,:])
 
+
 end # module