manual:chapter3:symbolic

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manual:chapter3:symbolic [2019/01/24 09:35]
claudio [Using rules and attributes, examples] 		manual:chapter3:symbolic [2021/03/22 08:47]
claudio
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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 ''A'' and ''B'' in the expression ''%%'%%A*B*INV(A)%%'%%'' represent a matrix, the system should not simplify that expression to ''%%'%%B%%'%%''. Furthermore, if ''A'' and ''B'' are real numbers, the simplification is only valid when ''A'' is known not to be zero. 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 ''A'' and ''B'' in the expression ''%%'%%A*B*INV(A)%%'%%'' represent a matrix, the system should not simplify that expression to ''%%'%%B%%'%%''. Furthermore, if ''A'' and ''B'' are real numbers, the simplification is only valid when ''A'' is known not to be zero.
  
-Attributes allow the user to let the system know that ''A'' is a real number and it cannot be zero. To add attributes to a variable, simply add a combination of subscript numbers after the variable name. For example, if ''A'' is a real number known not to be zero, simply write ''A₂₁'' in the expression (the exact meaning of the numbers will be explained in the next section).+Attributes allow the user to let the system know that ''A'' is indeed a real number and it cannot be zero, allowing the rules to perform the desired simplifications. Attributes can simply be typed immediately after the variable name enclosed by colons. Following with the previous example ''%%'%%A:R>0:%%'%%'' is an identifier representing variable ''A'', but it includes a hint showing that ''A'' is a finite positive real value and cannot be zero. If that hint is included wherever ''A'' is used within the expression, the system will know that ''%%'%%A*B*INV(A)%%'%%'' can be safely simplified to ''%%'%%B%%'%%''. 
 + 
 +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). The simplest way to assure the attributes are used consistently is using the command ''ASSUME''. For example ''%%'%%X^2+3*X%%'%% %%'X:R>0:'%% ASSUME'' will replace all occurrences of ''X'' within the expression given with the new identifier that includes the attributes. After the ''ASSUME'' command, trying to edit the expression will reveal the attributes: ''%%'%%X:R>0:^2+3*X:R>0:%%'%%'' which may make the expression more difficult to read. To remove the attributes, simply use an identifier without any attributes as the second argument: ''%%'%%X^2+3*X%%'%% %%'X'%% ASSUME'' will replace all occurrences of ''X'' with the new identifier which makes no assumptions (no attributes included). 
 + 
 + 
 +==== Obsolete section - soon to be removed ==== 
 + 
 +To add attributes to a variable, simply add a combination of subscript numbers after the variable name. For example, if ''A'' is a real number known not to be zero, simply write ''A₂₁'' in the expression (the exact meaning of the numbers will be explained in the next section).
  
 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). 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).
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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 may be infinity or NaN | +| 1 | Variable known to be finite (cannot be infinity or NaN) | 
-| 2 | Variable is known to be real | +| 2 | Variable is known to be real, may be infinity/NaN | 
-| 3 | Variable is known to be real, may be infinity/NaN | +| 3 | Variable is known to be real (and finite) | 
-| 4 | Variable is known to be complex | +| 4 | Variable is known to be complex, may be infinity/NaN | 
-| 5 | Variable is known to be complex, may be infinity/NaN |+| 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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 | 2 | Value is known not to be < 0 (therefore it's >=0) | | 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) | | 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) |+| 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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 ^ Rule ^ Effect ^ ^ Rule ^ Effect ^
-| ''%%'%%ABS(.xX₂₃):->.xX%%'%%'' | Simplify absolute value of an expression that is known to be real >=0 |+| ''%%'%%ABS(.xX₂₂):->.xX%%'%%'' | Simplify absolute value of an expression that is known to be real >=0 |
  
 ^ 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(X₂₃)'' | ''Y*X₂₃'' | The expression matches because ''X'' is known to be a real >0 |
 | ''Y*ABS(-4)'' | ''Y*ABS(-4)'' | The expression doesn't match because ''-4'' is known to be a real <0 | | ''Y*ABS(-4)'' | ''Y*ABS(-4)'' | The expression doesn't match because ''-4'' 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(X₂₃+1)'' | ''Y*(X₂₃+1)'' | The expression matches because ''X+1'' is known to be a real >0 | 
-| ''Y*ABS(X₂₃-1)'' | ''Y*ABS(X₂₃-1)'' | The expression matches because ''X-1'' is could be <0 for 0<=x<1 | +| ''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%%((X₂₃-1)%%^2)'' | ''Y*(X₂₃-1)^2'' | The expression matches because ''X-1'' is could be <0 for 0<=x<1 |+| ''Y*ABS%%((X₂₃-1)%%^2)'' | ''Y*(X₂₃-1)^2'' | The expression matches because ''(X-1)^2'' is known to be >=0 |
  
  
  • manual/chapter3/symbolic.txt
  • Last modified: 2021/03/22 13:52
  • by claudio