newField(String) -- constructor of a vector field

Synopsis

• Function: newField

• Usage:

  newField(expression)

• Inputs:
  • expression, a string, the expression to be evaluated
• Outputs:
  • an instance of the type DiffAlgField, the vector field written in expression

Description

This function defines the particular vector field written in the given expression as elements of type DiffAlgField. If any parameters are founded in the given expression, they are automatically included in the ring of scalar coefficients.

In the following example we define two particular vector fields, X and Y, and compute the addition X+Y. Notice that in the definition of X we are introducing a scalar parameter named a, also the variable x_2 is missing from the ring of X. When computing X+Y, the rings of both vector fields are automatically merged.

i1 : X = newField("2*a*x_0*ax_1")

o1 = 2a*x ax
         0  1

o1 : DiffAlgField

i2 : ring X

      QQ[i]
o2 = ------[][a][x ..x ][ax ..ax ]
      2           0   1    0    1
     i  + 1

o2 : PolynomialRing

i3 : Y = newField("x_0*ax_2")

o3 = x ax
      0  2

o3 : DiffAlgField

i4 : ring Y

      QQ[i]
o4 = ------[][x ..x ][ax ..ax ]
      2        0   2    0    2
     i  + 1

o4 : PolynomialRing

i5 : X+Y

o5 = 2a*x ax  + x ax
         0  1    0  2

o5 : DiffAlgField

i6 : ring (X+Y)

      QQ[i]
o6 = ------[][a][x ..x ][ax ..ax ]
      2           0   2    0    2
     i  + 1

o6 : PolynomialRing

In this example we show that the variables will always start from the index 0 and go up to the highest index encountered in the expression defining the vector field.

i7 : Z = newField("ax_5")

o7 = ax
       5

o7 : DiffAlgField

i8 : ring Z

      QQ[i]
o8 = ------[][x ..x ][ax ..ax ]
      2        0   5    0    5
     i  + 1

o8 : PolynomialRing

Caveat

See also

• newField(ZZ,ZZ,String) -- constructor of a vector field
• newForm -- constructor of a differential form