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manual:chapter3:symbolic [2019/01/24 08:25] claudio [Attributes] |
manual:chapter3:symbolic [2021/03/22 08:58] claudio |
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Expressions can be manipulated in various ways: | Expressions can be manipulated in various ways: | ||
- | **Normal operations using the stack:** '' | + | **Normal operations using the stack:** '' |
**Evaluating the expression: | **Evaluating the expression: | ||
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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 '' |
+ | |||
+ | 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. Ideally, the user should provide the same attributes to the same variables all throughout the expression (in other words, assumptions about a variable must be consistent, the variable cannot represents different things in different parts of the same expression). | ||
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+ | The simplest way to assure the attributes are used consistently is using the command '' | ||
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+ | 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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+ | === Default attributes === | ||
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+ | Variables that aren't given any attributes are by default assumed to be real if complex mode is disabled, and complex if complex mode is enabled. No other assumptions are made about their value (could be in any range, could be zero or infinite, etc.). | ||
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+ | === Encoding of attributes === | ||
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+ | The syntax for attributes is intuitive but very strict. Trying to enter invalid attributes will result in a syntax error. | ||
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+ | ==== Obsolete section - soon to be removed ==== | ||
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+ | To add attributes to a variable, simply add a combination of subscript numbers after the variable name. For example, if '' | ||
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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 ' | ||
- | ^ First digit ' | + | The first digit provides hints about the type of variable: |
+ | ^ First digit ' | ||
^ Value ^ Meaning ^ | ^ Value ^ Meaning ^ | ||
- | | 1 | Variable may be inifinity or NaN | | + | | 0 ((Will |
- | | 2 | Variable | + | | 1 | Variable known to be finite (cannot be infinity or NaN) | |
- | | 3 | Variable is known to be real, may be infinity/ | + | | 2 | Variable is known to be real, may be infinity/ |
- | | 4 | Variable is known to be complex | + | | 3 | Variable is known to be real (and finite) |
- | | 5 | Variable is known to be complex, may be infinity/ | + | | 4 | Variable is known to be complex, may be infinity/ |
+ | | 5 | Variable is known to be complex (and finite) | ||
| 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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+ | The second digit provides insight about the sign and range of values. It is meaningful only for real numbers (except for the zero hint), other types don't need or use this digit. | ||
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+ | ^ Second digit ' | ||
+ | ^ Value ^ Meaning ^ | ||
+ | | 0 ((Will be removed/ | ||
+ | | 1 | Value is known not to be zero ((This is valid for real AND complex numbers)) | | ||
+ | | 2 | Value is known not to be < 0 (therefore it's >=0) | | ||
+ | | 3 | Value is known not to be < 0 and not to be zero (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) | | ||
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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 ' | ||
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+ | ^ Third digit ' | ||
+ | ^ Value ^ Meaning ^ | ||
+ | | 0 ((Will be removed/ | ||
+ | | 1 | Value if known to be an integer | | ||
+ | | 2 | Value is known to be odd | | ||
+ | | 3 | Value is known to be an odd integer | | ||
+ | | 4 | Value is known to be even | | ||
+ | | 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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