# "Complex Change" Follow-Up

In this example situation, "the cost" is the initial request, and "the price is 12.99" is the initial assumption:

`> Find the cost when the price is 12.99.   Let 'C' stand for "COST"   (Find C)   Let 'P' stand for "PRICE"               P = 12.99       P = 12.99`

In "Complex Change" follow-up questions, information is requested based on changes in the relationships between quantities.

e.g.   What would the tax be if taxes were 3% of the price instead?

Complex Changes involve changes in the relationships between quantities (i.e. equations).  In the full example, it had already been established that "taxes are 8.25% of the price".  Taxes can't be 8.25% and 3% at the same time!  With changes in relationships between quantities, it is likely that a contradiction or inconsistency will occur, especially if quantities have already been defined.

If an inconsistency is detected (i.e. due to a new equation contradicting the current values of its variables), AutoMathic will warn that the equation "is Overdetermined, and the system is Inconsistent".  The new equation will be accepted, but this type of inconsistency must be resolved by the user in order to have accurate results!

• However, some Complex Change follow-up questions introduce inconsistencies that are too incompatible with the current situation to be handled cleanly or easily...  In some cases, inconsistencies must be resolved manually.  Other cases might require posing the follow-up question in a separate session!

The same strategies used to resolve inconsistencies apply to Complex Changes too, but it is important to resolve the contradiction in a way that preserves the intent of the change!  Assuming the new relationship has already been defined (e.g.  "if taxes were 3% of the price instead"), the normal strategy would be to follow a three-step process:

Given the difficulty of performing Complex Changes correctly, it may be better to avoid Complex Changes if possible and simply restate the problem (with the changed relationships) in a new session!

Removing Equations

The Conversational mode of AutoMathic does not support any language for retracting a statement of fact.  The only way to retract a statement is to remove the equation that came from it by using the Command mode "remove" command:

`e.g.   > !list       > !remove 2       > !list`

Note that removing an equation does NOT result in the removal of its variables or their current values.  Removing an equation simply removes a constraint that limits what values its variables could take...

Redefining Variables

Consistent results must be established by deriving variable values that match the current constraints.  The new equation usually asserts a relationship between its variables that is not true, given their current values.

Use either the Manual or Automatic method to redefine or derive variables as described in the "Resolving Contradictions" section.

e.g.   The price is still 12.99.

e.g.   !P=12.99

e.g.   !clear C T

Re-stating Requests

Since it is possible that the program already reported invalid results following the "system is Inconsistent" warning, the original request should be restated to see the consistent and correct answer(s).

e.g.   What would the tax be?