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You can create a script that goes through all the equations and attaches them to equations groups. Using Equations.objects.all() you can get an iterable of all of the equations objects.
You can then go through in a for loop and assign each one to the specified Equations group.
Example:
for equation in Using Equations.objects.all():
equation.equationGroup = some_group #based on however you specify what goes in a group.
equation.save()
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Do you want to make associations Equation <-> EquationGroup? If so, you should add OneToOne
relation field. Look here for examples.
There is many other ways to add relations, like ManyToMany and ForeighKey.
Do you need to associate instances? In this way, you should have data to find related data and save it as OneToOne/ForeignKey.
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How do you plan to update the database with the new change to your equation
model? If you are using django 1.7+ you can use the built-in migrations. If not you will need to look to something like South. Thirdly you can alter the database by hand.
Anyway, the reason i bring up migrations is because you cant add a null foreign key field. When adding the field to the database table you will need to specify a default FK value, that you can go back and update using @user3154952 suggestion.
Depending on the database you are using, you may be able to remove the foreign-key constraint check temporarily. Allowing you to add the new field to the table without a dummy value, by allowing null.