Computer algebra: Difference between revisions

Revision as of 03:28, 17 December 2022

Revision as of 15:36, 28 December 2022

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:<math> (x+y)^2=x^2+2xy+y^2.</math>

It is known from [[Richardson's theorem]] that there may not exist an algorithm that decides ifwhether two expressions representing numbers are semantically equal, if exponentials and logarithms are allowed in the expressions. Therefore, (semantical) equality may be tested only on some classes of expressions such as the [[polynomial]]s and [[rational fraction]]s.

To test the equality of two expressions, instead of designing specific algorithms, it is usual to put expressions in some ''[[canonical form]]'' or to put their difference in a ''normal form'', and to test the syntactic equality of the result.