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manual:chapter3:symbolic [2021/03/22 13:37]
claudio |
manual:chapter3:symbolic [2021/03/22 13:52]
claudio [Using rules and attributes, examples] |
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| ==== Using rules and attributes, examples ==== | ==== Using rules and attributes, examples ==== |
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| | Here are a few examples where using attributes is useful to decide whether to apply a rule or not. |
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| ^ Rule ^ Effect ^ | ^ Rule ^ Effect ^ |
| | ''%%'%%ABS(.xX₂₂):->.xX%%'%%'' | Simplify absolute value of an expression that is known to be real >=0 | | | ''%%'%%ABS(.xX:R∞≥0:):->.xX:R∞≥0:%%'%%'' | Simplify absolute value of an expression that is known to be real ≥0 | |
| | | ''%%'%%ABS(.xX:R∞<0:):->-.xX:R∞<0:%%'%%'' | Simplify absolute value of an expression that is known to be real ≤0 | |
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| | The above rules, for example, it can be applied to expressions with different attributes in its variables giving different results: |
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| ^ Test cases ^ Result ^ Explanation ^ | ^ Test cases ^ Result ^ Explanation ^ |
| | ''Y*ABS(X₂₃)'' | ''Y*X₂₃'' | The expression matches because ''X'' is known to be a real >0 | | | ''Y*ABS(X)'' | ''Y*ABS(X)'' | No rules are applied because X doesn't fit within the subsets defined in the rules | |
| | ''Y*ABS(-4)'' | ''Y*ABS(-4)'' | The expression doesn't match because ''-4'' is known to be a real <0 | | | ''Y*ABS(X:R>0:)'' | ''Y*X'' | The expression matches the first rule because ''X'' is known to be a real >0 | |
| | ''Y*ABS(X₂₃+1)'' | ''Y*(X₂₃+1)'' | The expression matches because ''X+1'' is known to be a real >0 | | | ''Y*ABS(-4)'' | ''Y*(-(-4))'' | The expression matches the second rule because ''-4'' is known to be a real <0 | |
| | ''Y*ABS(X₂₃-1)'' | ''Y*ABS(X₂₃-1)'' | The expression doesn't match because ''X-1'' could be <0 for 0<x<1 | | | ''Y*ABS(X:R>0:+1)'' | ''Y*(X+1)'' | The expression matches the first rule because ''X+1'' is known to be a real >0 | |
| | ''Y*ABS%%((X₂₃-1)%%^2)'' | ''Y*(X₂₃-1)^2'' | The expression matches because ''(X-1)^2'' is known to be >=0 | | | ''Y*ABS(X:R>0:-1)'' | ''Y*ABS(X-1)'' | The expression doesn't match either rule because ''X-1'' could be <0 for 0<x<1 | |
| | | ''Y*ABS%%((X:R>0:-1)%%^2)'' | ''Y*(X-1)^2'' | The expression matches because ''(X-1)^2'' is known to be >=0 | |
| | | ''Y*ABS%%((X-1)%%^2)'' | ''Y*(X-1)^2'' | The expression matches because ''(X-1)^2'' is known to be >=0 regardless of X | |
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