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manual:chapter3:symbolic [2019/01/24 08:47] claudio [Attributes] |
manual:chapter3:symbolic [2019/01/25 09:31] claudio [Attributes] |
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Attributes are hints that the user can include in an expression to increase the knowledge that the system has about certain variables. For example, if variables '' | Attributes are hints that the user can include in an expression to increase the knowledge that the system has about certain variables. For example, if variables '' | ||
- | Attributes allow the user to let the system know that '' | + | Attributes allow the user to let the system know that '' |
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+ | Notice that these attributes are only visible when editing the expression. Once the expression is in the stack, only the name of the variable will be visible, as the subscript numbers don't become part of the name of the variable. Ideally, the user should provide the same attributes to the same variables all throughout the expression (otherwise the system will think the variable represents different things in different parts of the same expression). | ||
Attributes are also useful within rules. If a variable (or wildcard special variable) has any attributes given within a rule definition, it will only match variables (or expressions) that have compatible attributes. For example a rule to cancel out factors in an expression could be: '' | Attributes are also useful within rules. If a variable (or wildcard special variable) has any attributes given within a rule definition, it will only match variables (or expressions) that have compatible attributes. For example a rule to cancel out factors in an expression could be: '' | ||
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=== Encoding of attributes === | === Encoding of attributes === | ||
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Attributes can be any number of up to 8 decimal digits. The value of zero is reserved for 'no attributes' | Attributes can be any number of up to 8 decimal digits. The value of zero is reserved for 'no attributes' | ||
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The first 3 digits will be referred to as ' | The first 3 digits will be referred to as ' | ||
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^ Value ^ Meaning ^ | ^ Value ^ Meaning ^ | ||
| 0 ((Will be automatically removed)) | Nothing is known about this variable | | | 0 ((Will be automatically removed)) | Nothing is known about this variable | | ||
- | | 1 | Variable | + | | 1 | Variable |
- | | 2 | Variable is known to be real | | + | | 2 | Variable is known to be real, may be infinity/ |
- | | 3 | Variable is known to be real, may be infinity/ | + | | 3 | Variable is known to be real | |
- | | 4 | Variable is known to be complex | | + | | 4 | Variable is known to be complex, may be infinity/ |
- | | 5 | Variable is known to be complex, may be infinity/ | + | | 5 | Variable is known to be complex | |
| 6 | Variable is known to be a matrix | | | 6 | Variable is known to be a matrix | | ||
| 8 ((Internal use only)) | Variable is known to be of unknown type | | | 8 ((Internal use only)) | Variable is known to be of unknown type | | ||
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| 4 | Value is known not to be > 0 (therefore it's <=0) | | | 4 | Value is known not to be > 0 (therefore it's <=0) | | ||
| 5 | Value is known not to be > 0 and not to be zero (therefore it's <0) | | | 5 | Value is known not to be > 0 and not to be zero (therefore it's <0) | | ||
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+ | The third digit provides insight about the parity of the number, and whether a real is an integer or not. Much like the ' | ||
^ Third digit ' | ^ Third digit ' | ||
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| 4 | Value is known to be even | | | 4 | Value is known to be even | | ||
| 5 | Value is known to be an even integer | | | 5 | Value is known to be an even integer | | ||
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+ | ==== Using rules and attributes, examples ==== | ||
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+ | ^ Rule ^ Effect ^ | ||
+ | | '' | ||
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+ | ^ Test cases ^ Result ^ Explanation ^ | ||
+ | | '' | ||
+ | | '' | ||
+ | | '' | ||
+ | | '' | ||
+ | | '' | ||
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