3.6.4 Convert to Differential

This conversion converts an equation to a differential equation and also converts between coupled and decoupled derivative forms.

If the subject is a subexpression of an equation, the active expression is converted to a differential equation by using the subject as the derivator and the expressions on either side as the derivands of two derivative expressions. Since there is only one subject, both derivatives will have the same derivator. For example, the equation and selection x^2-1=.{x}^2-1 are converted into the differential equation ⅆx^2-1ⅆx=ⅆx^2-1ⅆx. The subject need not be a simple identifier. x^2-1=.{x^2}-1 transforms to ⅆx^2-1ⅆ(x^2)=ⅆx^2-1ⅆ(x^2).

If the subject is a division operator whose operands are both decoupled derivatives, the subject is transformed to a coupled derivative using the operand of the numerator as the derivand and the operand of the denominator as the derivator. That is, .{ⅆx^2-1:1÷ⅆx:1} is transformed to ⅆx^2-1ⅆx.

If the subject is a coupled derivative, it is transformed to a division of decoupled derivatives using the derivand as the operand of the decoupled derivative in the numerator and the derivator as the operand of the decoupled derivative in the denominator. . That is, .{ⅆx^2-1ⅆx} is transformed to ⅆx^2-1:1÷ⅆx:1.