JPH0668076A - Method and device for allocation processing - Google Patents

Abstract

PURPOSE:To adjust the position of subscripts and the height of parentheses by retreiving data indicating the contents of a formula to which the subscripts are imparted and calculating the height of the formula to be an object. CONSTITUTION:The subscript 'e' is positioned by adjusting to the height of the parenthesis B1. Practically, the subscript 'e' is positioned with a line L4 for indicating the height of the parenthsis B1 as a connection line. That is, as the targeted subscript is selected by a cursor and position correction is instructed, from the structured data of the numerical formula, for instance from the data indicated by a bisecting tree, the data of the bisecting tree for which the selected subscript is the node of a top are read. A slave node is retreived for the bisecting tree, the height of the formula to be the object, that is the formula to which the subscript is imparted, for instance the formula surrounded by the parentheses B1 and B5, in this case, the height of a character 'd' is calculated, the position of the subscript 'e' is decided based on the calculated result and the allocation to the position is performed.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an allocation processing method and an allocation processing apparatus, and more particularly to an allocation processing method and an allocation processing apparatus for correcting the height of parentheses or the position of a subscript of a mathematical expression.

[0002]

2. Description of the Related Art In numerical formulas, subscripts and parentheses are often applied in double or triple. It is desirable that these be expressed as accurately as possible. However, for example, in a display device that is premised on character display, it is difficult to subtly express the position and height, so emphasis is placed on good visibility rather than display accuracy, and the display position is intentionally shifted vertically. Alternatively, specific ones such as double-sided parentheses and parentheses extending over a plurality of lines are displayed in a form different from the other parentheses (for example, JP-A-3-30052, JP-A-3-30056, and JP-A-3-30056). -30057 gazette etc.). On the other hand, in a device such as a workstation or a desktop publishing device that handles print data and display data with bitmap data, it is easy to adjust the position and height. Therefore, the position of the subscript and the height of the parenthesis are accurately expressed according to the data of the mathematical formula. The mathematical data handled by these devices is usually structured. This is because, if structured, it is easy to partially change the mathematical formula, and printing, display, calculation, etc. can be performed with one data. When the position of the subscript or the height of the parenthesis is calculated based on the data of the structured mathematical formula, the position of the subscript or the height of the parenthesis is adjusted to the height of the formula to which it is attached (for example, A
MS-TeX (AMS: American Mathematical Society), Applicant Company Product "Global View Version 3.1 (Global
View 3.1) "etc.).

The area that serves as a reference for these allocations,
Points, lines, values, etc. (for example, ascender and descender) are mainly ISO8613-6, I.
Although specified in SO9541-5, in the present specification,
Further, the areas, points, lines, values, etc. shown in FIGS. 2 and 3 are used by being extendedly defined or redefined. That is, in FIG.
character extent is a character area and is used as information indicating the extent of a character (symbol). This area is a rectangular area formed from the character height B and the character width S. The lower left corner of this area is set as the origin CEO (character extent origin) of the character area based on ISO9541-5. PP and EP are ISO8613-6 and ISO95
41-5 position point and e set based on 41-5
This is a scapement point, which is a connection point for characters (symbols), and a series of these connection points is a connection line. Similarly, formulae extent in FIG. 2B is a formula area and is used as information indicating the extent of the formula. This area is defined by the formula height and the formula width.
e width) is a rectangular area. The lower left corner of this area follows ISO9541-5 and is the origin F of the expression area.
EO (formulae extent origin). Similarly FIG.
Where CP is the connection point of the equations, which are defined individually for each equation. The respective expressions are connected at this connection point CP, and the straight line CL formed at these connection points CP becomes the connection line. For example, if the connection point CP is defined for the formulas F1 and F2 as shown in FIG. 7A, the formula connected at this point is like the formula F3 shown in FIG. In addition, the heights of the upper and lower parts of the connection line CL of the formula are the height of the upper part of the formula (upper height) and the height of the lower part of the formula (lower height).
And

[0004]

However, if the positions of the subscripts or the heights of the parentheses are determined according to this principle, the positions or the heights may be unfavorable in mathematical typesetting. FIG. 4 shows such an example. In the figure (A), the subscript "e" is too far from the bracket B1, and in the figure (B), the heights of the brackets B2 and B3 are not uniform. In this example of (B), the heights of the subscripts "d" and "e" are also uneven. These positions and heights are obtained as follows. That is, in the case of the subscript "e" in FIG. 7A, its position is matched with the height of the expression in the parenthesis B1 to which it is attached, here the height of the letter "d". Specifically, the subscript "e" is positioned with the line L1 representing the height of the character "d" as a connecting line. Therefore, the subscript "e" is in parentheses B
It will be too far from 1. In addition, bracket B in FIG.
In the case of 3, the position of the subscript "d" is determined according to the height of the bracket B2, and in accordance with this, the bracket B positioned outside the position of the suffix "d".
A height of 3 is defined. Specifically, the subscript "d" is positioned with the line L2 representing the height of the bracket B2 as a connecting line, and the height of the bracket B3 is determined based on the line L3 representing the height. Therefore, the brackets B2 and B3 have different heights. Further, in the example of FIG. 4B, the line "L3" is used as a connecting line and the subscript "e" is positioned. For this reason, the heights of the subscript “d” and the subscript “e” are also uneven.

For this reason, in the past, this has been dealt with by, for example, putting up with it, or discarding the merits of structuring, and expressing the mathematical data as ordinary graphic data and editing it. The term "graphic data" refers to data of a character code, character size, and other character-related data for each character and coordinate data for arranging the character to determine the expression position. However, even if this is done, editing work is not easy. However, the position of subscripts and the height of parentheses in the formula are related to each other, so if you start correcting one place, you have to adjust the arrangement of the whole formula again and there. This is because it must be done. It goes without saying that the layout by human hands is complicated. Therefore, even if such individual correction is possible, the work is complicated. The object of the present invention is to eliminate the drawbacks of the conventional techniques and to take advantage of the structured data, that is, for a mathematical expression represented by the structured data, so to speak, automatically based on the structured data. An object of the present invention is to provide an allocation processing method and an allocation processing device capable of adjusting the position of a subscript and the height of parentheses.

[0006]

In order to achieve the above object, in the invention of claim 1, the structured data representing the mathematical formula is searched for the data representing the contents of the formula to which the subscript is added, and the target formula A method is used in which the height is calculated, the position of the subscript is determined based on the calculation result, and the allocation processing is performed. In the invention of claim 2, the structured data representing the mathematical formula is searched for data representing the contents of the parentheses, the height of the target formula is calculated, and the height of the parentheses is determined based on the calculation result. A method of performing allocation processing is used.
The invention of claim 3 includes a processing means for executing the allocation process of the mathematical expression using the allocation process method of claim 1 or claim 2. . According to the invention of claim 4, there is provided an instruction means for instructing the position correction of the subscript or the size correction of the parentheses.

[0007]

According to the first aspect of the present invention, for example, the subscript "e" in FIG. 4 (A) is positioned according to the height of the bracket B1 as shown in FIG. 5 (A). Specifically, the subscript "e" is positioned with the line L4 representing the height of the bracket B1 as a connecting line. This process is performed as follows. First, the desired subscript is selected with the cursor, and position correction is instructed. In response to this, data of a binary tree having the selected subscript as a vertex node is read out from the structured data of the mathematical expression, for example, the data represented by the binary tree. A child clause is searched for in this binary tree, and the height of the target expression, that is, the expression with the subscript, for example, the expression enclosed by the parentheses B1 and B5 in FIG. The height of "d" is calculated. The position of the subscript "e" is determined based on the result of this calculation, and allocation to that position is performed. Specifically, the pop-out amount of the character d from the bracket B1 is obtained, the amount corresponding to this pop-out amount is obtained as the downward movement amount, and the subscript "e" is added to the position moved downward by that amount. Is assigned.

According to the invention of claim 2, for example, FIG.
The height of the parenthesis B3 in (B) is corrected to the same height as the parenthesis B4 in FIG. 5B, that is, the same height as the parenthesis B2. In the example of FIG. 5 (B), the position correction according to the invention of claim 1 is also performed for the subscript "e", and it is assigned to the same position as the subscript "d". If this correction is not made, the conventional technique positions the line L3 representing the height of the subscript "d" as a connecting line. The correction of the height of the parentheses is also performed in the same manner as the invention of claim 1. That is, when a parenthesis to be corrected is selected, a binary tree having the parenthesis data as a vertex node is read from the structured data representing the mathematical formula. For this binary tree, child clauses are searched, and the height of the target expression, that is, the expression enclosed by the parentheses, for example, the expression enclosed by the parentheses B3 and B6 in FIG. 4B is calculated. . Based on this calculation result, the height of the expression excluding the height of the subscript "d" is calculated, and the height of the parenthesis B
4, B7 are allocated. In the invention of claim 3, the invention of claim 1 or 2 is used, and the allocation processing of the mathematical expression is executed by the processing means. In the invention of claim 4, the position correction of the subscript or the size correction of the parenthesis is instructed by the instructing means, for example, the window displayed on the screen and the mouse or the cursor key.

[0009]

The details of the present invention will be described below with reference to the illustrated embodiments. FIG. 6 shows a hardware configuration example for implementing each invention. In the figure, 1 is a computer main body, and 2 and 3 are a central processing unit (CPU) and a memory incorporated therein. Reference numeral 4 denotes a display control unit which controls mathematical expressions and other data display on the display 8. A keyboard / mouse control unit 5 monitors operations of the keyboard 9 and the mouse 10 and generates corresponding input data. A disk control unit 6 reads and writes data from and on the hard disk 11. A printer control unit 7 controls the print output to the printer 12. A system bus 13 is used for data transmission between blocks. FIG. 1 shows a first embodiment constructed on the above hardware. This example
The invention according to claim 1 is for correcting the position of a subscript,
The invention of claim 3 which cites claim 1 and the invention of claim 4 which cites the invention of claim 3 are implemented. In the figure, reference numeral 21 is a processing device, which is a mathematical expression search processing unit 211,
A subscript vertical position calculation unit 212 and a mathematical expression allocation processing unit 213 are provided. These are realized on the central processing unit 2 and the memory 3 of the hardware of FIG. 6 and serve as the processing means according to claim 3 (processing means for executing the allocation processing of the mathematical expression using the allocation processing method according to claim 1). Function.

Reference numeral 22 is a formula storage unit, which is realized on the memory 3 or the hard disk 11 and stores the structured data FD representing the formula. Structured data representing mathematical formulas include binary trees, graphs and other forms. A binary tree is used here. A display unit 23 is realized by the display 8 and the printer 12. Formula search processing unit 211
Is a binary tree stored in the mathematical expression storage unit 22,
A binary tree whose vertex is the subscript selected as the correction target is read, and a child clause representing the content of the expression to which the subscript is added is searched. The subscript vertical position calculation unit 212 calculates the height of the target expression, that is, the expression with the subscript based on the search, and determines the position of the subscript based on the calculation result. According to this result, the mathematical expression allocation processing unit 213 allocates the subscript to the corrected position.

FIG. 7 shows an example of a window display for instructing the position correction of the subscript. The mouse 10 is operated to place a cursor (not shown) in the area A1 of the “item” of the item “display content” and click the button of the mouse 10. As a result, the frame (border) B1 of the area A1 is made thicker, and it is displayed that the item of the display content is in the state in which "item" is selected. Next, the cursor is placed in the area A2 in the "parentheses" of the "position correction" item, and the button of the mouse 10 is clicked. As a result, the frame (border) B3 of the area A2
Similarly, a bold line (not shown) is displayed, and it is displayed that the subscript position correction is being executed. When the position is not corrected, that is, when the position of the subscript according to the principle is set, the cursor is placed in the area A2 and the button of the mouse 10 is clicked.
As a result, the thickened frame B3 returns to the normal thickness, and the correction is not performed. It should be noted that the other parts of FIG. 7 are not directly related to the present invention, but it is easier to understand if they are close to the actual ones, so they are shown as a reference. The description is omitted.

Expression examples of the mathematical expression based on the tree structure of the binary tree are shown in FIGS. The shaded circles are the roots of the tree structure.
Or nodes and ordinary circles are leaves (Fig. 8).
(B)). Note that the tree structure is usually expressed in a divergent manner from the root downward as shown in FIG. In order to fit in each frame, in this specification, as shown in FIG.
Arranged vertically. The basic structure of each type of expression, that is, the “expression group” or the “structural expression” is expressed as shown in FIG. 8A (expression form by binary tree). FIG. 9 shows an example of a mathematical expression in its original form and a binary tree expressing the mathematical expression. For example, the expression “(a +
b) -c "is expressed like the right binary tree BT1. That is, to the right of the section N1 having the content of "parentheses", the section N11 and the leaf Lf12 of the character code of "-" and "c", the section N2 having the content of "Expression" below the section N1, and the left parenthesis to the right of it. , A right-parenthesis character code section N21 and a leaf Lf22 are arranged.

The processing procedure of the first embodiment is shown in FIGS. Due to space limitations, it is shown divided into two figures. Both flows are connected at terminals 1-3. It should be noted that each process and judgment is referred to by a number (flowchart number) attached outside the frame. FIG. 12A shows an example of a mathematical expression in which the position before correction, that is, the position of the subscript is in principle. Bracket B1
Line L21 representing the height of the formula surrounded by 1 and B12
Is a connecting line with the subscript “h”. Here, the allocation state of FIG. 9B, that is, the line L22 of the upper height ac1 of the bracket B12 as the connection line of the subscript "h" is a preferable allocation. In other words, when the parentheses B11 and B12 include the formula F4 having a portion (the portion of "e") that pops out from the height, the subscript "h" is assigned except for the popped-out portion. Make the preferred allocation.

In the present embodiment, the value required for this purpose, that is, the downward movement amount SVD of the subscript "h" is shown in FIGS.
It is calculated by the flow of 1. In the case of bracket B12,
Since the height ac1 (line L22) of the upper portion is the allocation position (connection line) of the corrected subscript “h” obtained here, the height (lo) from the body size bs1 is first calculated.
wer height) dc1 is subtracted to obtain the height ac1 of this upper part. The downward movement amount SVD is the difference between the height VUH (line L21) at the upper portion of the formula enclosed by the brackets B11 and B12 at this time and the value of the height ac1 (height of L22) at the upper portion. This is obtained by subtracting the latter from the former. If there is a subscript in the lower right of the bracket B12 or in the lower left of the bracket B11 (see the example on the right side of FIG. 10), the subscript is assigned to the line L23 of the height dc1 below the bracket B12 (connect this line L23. Make a line and assign subscripts). The amount SVD of upward movement in this case is calculated by dividing the height VLH (line L25) of the lower part of the expression enclosed by the brackets B11 and B12 at this time and the value of the height dc1 of this lower part (height of L23). Since it is the difference, this is obtained by subtracting the latter from the former.

Here, the movement amount SVD is shown based on the specific body size, the height of the upper portion, and the height of the lower portion. Figure 10,
In the flow of FIG. 11, these values are obtained using variables. That is, in the flow of FIGS. 10 and 11, the variables are defined as described in the flowchart number 0 and the flowchart number 13. Then, the downward or upward movement amount of the subscript is obtained in the flowchart No. 13 as the values of the variables Syu and Syl. The definition of each variable is considered to be understandable only by the description of the figure. The description is omitted. Descriptions of other matters will be omitted if it can be understood only from the illustrations and tables. Further, the variable Blh representing the height of the lower part is represented by a negative value. Therefore, in flowchart number 13, the height at the top of the brackets is (Bh + Bl
It is expressed as h). And the height of this upper part (Bh + Blh)
Is subtracted from the height Hu at the top of the expression in parentheses,
The amount of movement Syu is set.

The flows shown in FIGS. 10 and 11 are assembled based on the above premise. An overview of the flow will be explained.
That is, on the display 8, a cursor not shown in FIG.
It is assumed that the subscript “h” of 2 (A) is selected, the area A2 of FIG. 7 is selected, and the position correction of the subscript “h” is instructed. In response to this, the mathematical expression search processing unit 211 of FIG. 1 reads out the binary tree data of FIG. 12C in which the subscript “h” is the node (root) of the vertex from the mathematical expression storage unit 22. Note that each section in FIG. 12C is referred to by the number attached to the side thereof. In this embodiment, the target of position correction is when the expression to which it is attached is a parenthesis and the expression in the parenthesis jumps above or below the parenthesis. In the present invention, the presence or absence of the state is determined by searching the structured data (here, a binary tree). Figure 10 shown here,
The flow of FIG. 11 is a specific example thereof, and the overall configuration is as follows.

First, the clause starts with a clause two levels below the clause of the exponentiation formula, that is, a clause representing the equation to which the subscript is attached (Flowchart No. 1), and if there is a clause on the right, the clause. (Flowchart Nos. 8 and 11), or if there is no lower node (Flowchart Nos. 9 and 12), the node n of interest is sequentially searched (searched) (see definition of Flowchart No. 0). The following processing is performed for each focused node. First, the type of expression is checked (flowchart number 2). If the type of expression is parentheses, its body size, FEO (CEO), and y of the connection point CP
Coordinate values are calculated, and variables Bh and Blh are updated based on the calculated coordinate values (flowchart number 3). By this update, finally, the variables Bh and Blh represent the largest body size or height of each parenthesis included in the subscripted expression. Further, the body size of the expression in the parentheses, FEO (CEO), and the y coordinate value of the connection point CP are calculated, and based on this, the variable FHn
l, FEOynl and CPynl are updated (Flowchart No. 3 → Flowchart No. 4). If the content of the expression that was noted at that time was "power", that is, if the expression had a subscript, the body size of the expression with that subscript,
The y coordinate values of FEO (CEO) and the connection point CP are calculated, and based on this, the variables FHnl, FEOynl and CPyn are calculated.
l is updated (Flowchart number 2 (exponentiation formula) →
Flowchart number 4).

After updating, the magnitude relationship between the variable FHnl and the variable Bh at that time and the variable (FEOynl + CPyn)
The relationship between l) and the variable Blh is evaluated (flowchart number 5). If the variable FHnl is larger than the variable Bh, or if the variable (FEOynl + CPynl) is smaller than the variable Blh, then the height of the expression in it is larger than the body size of the parentheses or the height at the bottom of the expression. Is larger than the height of the lower part of the bracket, that is, there is a possibility that the position must be corrected as shown in FIG. Therefore, it is necessary to inspect the contents of the expression, that is, to inspect toward the lower node. However, if there is a node to the right of the node of interest here, the node or leaf must be checked above. The process of flowchart number 3 or 4 is performed, and the value of each variable is updated. In this way, the right section is searched first, for example, section N1 “parentheses” in 2.1 in FIG.
As shown in the right, the node N11 of "-", the leaf Lf12 of "c"
Are connected, and the variable B
This is because there is a case where lh etc. must be updated.

Therefore, the node immediately below the node (expression) that has been noted here is once stacked on the stack S (flowchart number 6), and the existence of the node on the right is checked (flowchart numbers 7 and 8). If there is a section, that section is regarded as the section of interest (flow chart number 11), and the processing from the flow chart number 2 is repeated for it. When the answer to the flowchart No. 5 is No, it is not necessary to check the contents of the formula. In this case, the process directly moves to the flowchart No. 7. If there are no or no knots on the right, the stack S is examined (flowchart number 9), and if there is a piling, ie a knot connected below, it is taken out (it is It is regarded as a section of interest) (flowchart number 12), and the processes from the flowchart number 2 are repeated for it. When the contents of the stack S are absent or lost, it means that the search has been completed for all the clauses, and it is checked whether the values of the variables Bh and Blh have disappeared from the initial value "0". When any one is not "0", these variables are updated in the flowchart No. 3. That is, there is a parenthesis somewhere in the expression relating to the subscript designated at this time, and the preferable allocation position of the subscript is shown as the variable (Bh + Blh) or the variable Blh. Therefore, the upper expression of the clause immediately below the clause of the expression targeted at that time, that is, the exponentiation
The variables Bh and Blh held at that time are subtracted from the values Hu and Hl of the height and the lower height, respectively, and the moving amounts Syu and Syl of the subscript to the lower side or the upper side are calculated. If the clause specified by the variable n, that is, the expression of the clause of interest at that time is neither a parenthesis nor a power, the position of the subscript for it is as a general rule and no correction is required. Therefore, in this case, the flowchart No. 2 directly to the flowchart No.
The processing shifts to, and the processing from the flowchart No. 2 is performed for the next section.

Table 1 shows the specific contents of the processing when the processing of the flow of FIGS. 10 and 11 is performed on the binary tree of FIG. 12 (C). The leftmost column is a number indicating the order of processing, the right column is the flowchart number in which the process is performed, and the description in the right column is the content of the process performed at that time. Based on the explanation given so far, it is considered that the processing contents can be understood by the description in the table. The description is omitted. By the process of Table 1, the downward correction amount Syu of the subscript is obtained. For example, the subscript “h” assigned to the position shown in FIG.
It is moved to the new position where the line L22 is used as a connecting line, which is moved downward by VD) as shown in FIG.

[0021]

[Table 1]

FIG. 13 shows a second embodiment constructed on the hardware shown in FIG. This embodiment is for correcting the height of parentheses, and is the invention of claim 2, the invention of claim 3 which cites claim 2 and the invention of claim 4 which cites the invention of claim 3. It is to be implemented. This second embodiment is the same as the first embodiment except for the bracket size calculation unit 312 of the processing device 31. The same parts are designated by the same reference numerals and the description thereof is omitted. The processing device 31 including the mathematical expression search processing unit 211, the parenthesis size calculation unit 312, and the mathematical expression allocation processing unit 213 is realized on the hardware central processing unit 2 and the memory 3 of FIG. The processing device 31 functions as a processing unit according to claim 3 (a processing unit that executes a mathematical expression allocation process using the allocation processing method according to claim 2).

The mathematical expression search processing unit 211 reads out a binary tree whose parenthesis is the node of the vertex selected as the correction target at that time from the binary tree stored in the mathematical expression storage unit 22,
The child clause representing the content of the expression to which the parentheses are added is searched. The parenthesis size calculation unit 312 calculates the height of the expression with parentheses (the target expression) based on the search, and determines the height of the parentheses based on the result of this operation. According to this result, the mathematical expression allocation processing unit 213 executes the bracket allocation processing of the calculated height. FIG. 14 shows an example of a window display for instructing the height correction of the brackets. The mouse 10 is operated to place a cursor (not shown) in the “item” area A11 of the “display content” item, and the mouse 10 button is clicked. Thereby, the frame B11 of the area A11
However, it is bolded. Then move the cursor to "size correction"
Place the mouse in the "subscript" area A12 of the item and click the button of the mouse 10. As a result, the frame B of the area A12
13 is thickened (not shown), and it is displayed that the height correction of the parenthesis is executed. It should be noted that the height of the parentheses is in accordance with the principle, that is, when the height correction according to the invention of claim 2 is not performed, the area A1 in which the frame B13 is thickened
Place the cursor on 2 and click the button on mouse 10. This restores the state without correction. Figure 1
The other parts of No. 4 are not directly related to the present invention, but as in the case of the description of the first embodiment, it is thought that it is easier to understand what is close to the actual one, and therefore it is illustrated for reference. . The description is omitted.

The processing procedure of the second embodiment is shown in FIGS. Due to the limitation of the size of the paper, it is divided into two figures and displayed. Both flows are connected at connection terminals 1-4. Each process and judgment in the flow is referred to by a flowchart number attached outside the frame. FIG. 17A shows an example of a mathematical expression in which the parenthesis height is the same as before correction, that is, in principle. A line L31, which is enclosed by the brackets B23 and B24 and represents the height of the expression, is a connection line with the subscript “h”. The heights of the brackets B21 and B22 are matched with the height of the subscript "h" (line L3.
2). Therefore, the height of the bracket B22 (body size bs
2) is higher than the preferred height.

In this embodiment, in the case of the formula of FIG.
The state in which the heights of the brackets B21 and B22 are matched with the heights of the brackets B23 and B24 (body size bs3), that is, the allocation state of FIG. In other words, if there are parentheses and subscripts in the parentheses B23 and B24 and the heights of the parentheses B23 and B24 are affected by them, the heights of the subscripts are ignored and the parentheses B23 and B24 are ignored.
Set the height of 24. The flow of FIGS. 15 and 16 is assembled on the basis of this premise. An overview of the flow will be explained. The definitions of the variables are as described in the flowchart No. 0. Except for the variable H, the height of the parentheses is obtained as this variable H as in the first embodiment. First, on the display 8, with a cursor not shown in FIG.
The parenthesis B22 of 7 (A) is selected, and the area A1 of FIG. 14 is selected.
It is assumed that the cursor is placed at 2 and the height correction of the bracket B22 is instructed.

In response to this, the mathematical expression search processing unit 2 of FIG.
11, the parentheses B21, B2 from the formula storage unit 22
Data of the binary tree in FIG. 17C in which 2 is the node (root) of the vertex is read. Note that each node or leaf in FIG. 17C is
It is designated by the number attached to the side. In this embodiment, the height of the parenthesis is corrected when the parenthesis and the subscript are further included in the parenthesis and the height of the parenthesis is affected by them. In the present invention, the presence or absence of the state is determined by searching the structured data (here, a binary tree). The flows shown in FIGS. 15 and 16 are specific examples, and the overall configuration is as follows. First, the section immediately below the section of "parentheses", that is, the section representing the expression to which the parentheses are attached (Flowchart No. 1), and the section on the right thereof (Flowchart Nos. 6 and 7) , 9), or if there is no lower section (flowchart numbers 8 and 10), each section is sequentially set as a focused section n (searched).
(Refer to the definition of flowchart number 0) (Basically the same as the first embodiment). The following processing is performed for each focused node. First, the type of expression is checked (flowchart number 2). When the type of expression is a parenthesized expression or a subscripted expression, it is checked whether the variable H at that time is smaller than the height of the expression in the parenthesis or the expression with the subscripted (flowchart number). 3).

The variable H holds the height of the expression (other expression) represented by the node or leaf searched up to that time (flowchart number 4). When the value of this variable H is smaller than the height of the expression in the parentheses or the expression with the subscript noted at this time (Flowchart No. 3
Answer "Yes"), the height of those expressions is higher than the noted parentheses or subscripts. In this case, the notable formula is, for example, as shown in FIG.
Like the expression in the parenthesis B22 of 7 (A), there is a subscript "h" or the like, and there is a possibility that the height of the parenthesis must be corrected. In this case, it is necessary to inspect the contents of the expression, that is, to inspect toward the node underneath, but as in the first embodiment, when the node following the node of interest continues to the right, The node or leaf is processed first. That is, the formula (section) is temporarily stacked on the stack S (flowchart number 5), the focused node n is set to the value nr of the node on the right (flowchart number 6), and if there is a node, the focused node is set as the focused node ( (Flowchart numbers 7 and 9)
The processing from the flowchart No. 2 is repeated. When the answer to the flowchart No. 3 is "No", it is not necessary to check the contents of the formula. In this case, the process is moved from the flowchart number 3 directly to the flowchart number 6. When there is no node on the right side or when there is no node, the presence or absence of the contents of the stack S is checked (flowchart number 8), and if there is the contents, it is taken out (flowchart number 10) and the processes from the flowchart number 2 are repeated. When the contents of the stack S are not present or have disappeared, the process ends. In addition, when the expression of the noted section is neither the expression of the parenthesis nor the expression of the subscript, the height of the parenthesis for it is the same as the principle and no correction is required. Therefore, in this case, the process proceeds from the flowchart No. 2 to the flowchart No. 4, and the variable H (height in parentheses) is updated with the height of the expression.

Tables 2 to 4 show the specific contents of the processing when the processing of the flows of FIGS. 15 and 16 is performed on the binary tree of FIG. 17C. Since the number of lines is large, the description is divided into three tables. The description content of each column is the same as in Table 1. Based on the explanation given so far, it is considered that the processing contents can be understood by the description in the table. The description is omitted. By the processing of Tables 2 to 4, the corrected parenthesis size H is obtained, and as shown in FIG. 17C, the parenthesis B21C of the new parenthesis,
B22C is assigned to the outside of the brackets B23 and B24.

[0029]

[Table 2]

[0030]

[Table 3]

[0031]

[Table 4]

In the above description, the invention shown in the first embodiment and the invention shown in the second embodiment are applied to the respective mathematical expressions. These inventions may be applied to the same formula. By doing so, the position of the subscript and the height of the parenthesis of one expression are both corrected, and the expression of FIG. 4B becomes as shown in FIG. 5B, for example. The embodiment of the present invention is arbitrary. For example, when display or print output is requested, the structured data to be processed may be read out and the designated correction may be performed to display or print output. Alternatively, the editor style is adopted in which the correction data obtained by the present invention is incorporated into the structured data itself, and the position of the subscript and the size of the parentheses are corrected based on the correction data when displaying or printing. Is also good. Further, in each of the embodiments, the mouse (cursor) is used to instruct not to make the correction, but the process of the present invention may be executed at all times without the need to specify it.

[0033]

As described above, according to the first aspect of the present invention, the structured data representing the mathematical formula is searched for the data representing the contents of the formula with the subscript, and the height of the target formula is calculated. Then, the position of the subscript is determined based on the result of this calculation, and the allocation process is performed. According to the invention of claim 2,
Data representing the contents of the parentheses is searched for from the structured data representing the mathematical formula, the height of the target expression is calculated, the height of the parentheses is determined based on the calculation result, and the allocation processing is performed. In the invention of claim 3, the allocation processing of the mathematical expression is performed using the processing means and the allocation processing method according to claim 1 or 2. . In the invention of claim 4, the position correction of the subscript or the size correction of the parenthesis is instructed by the instruction means. Therefore, using these inventions, while taking advantage of the advantage of structured data, that is, the advantage that the same data can be displayed and operated, so to speak, the position of subscripts and the height of parentheses of mathematical formulas automatically indicated by structured data Will be corrected.

[Brief description of drawings]

FIG. 1 is a block diagram showing the configuration of a first embodiment.

FIG. 2 is a diagram showing areas, points, values, etc., which serve as allocation references.

FIG. 3 is a point, a value, which is a reference for connecting and assigning expressions,
A diagram showing lines and the like.

FIG. 4 is a diagram showing an example in which subscripts or parentheses are assigned at positions or sizes in accordance with the principle.

FIG. 5 is a diagram showing an example in which subscripts or parentheses are assigned at corrected positions or sizes.

FIG. 6 is a block diagram showing a configuration example of hardware for realizing each embodiment.

FIG. 7 is a diagram showing an example of means for instructing correction of the position of a subscript.

FIG. 8 is a diagram showing a basic structure of a mathematical expression represented by a binary tree.

FIG. 9 is a diagram showing a specific example of expression of a mathematical expression using a binary tree.

FIG. 10 is a flowchart (part 1) showing the processing procedure of the first embodiment.

FIG. 11 is a flowchart (part 2) showing the processing procedure of the first embodiment.

FIG. 12 is a diagram showing a subscript allocation position before correction (A), a postscript correction allocation position (B) for a certain expression, and binary tree data representing the expression.

FIG. 13 is a block diagram showing the configuration of a second embodiment.

FIG. 14 is a diagram showing an example of means for instructing correction of bracket height.

FIG. 15 is a flowchart (part 1) showing the processing procedure of the second embodiment.

FIG. 16 is a flowchart (part 2) showing the processing procedure of the second embodiment.

FIG. 17 is a diagram showing parenthesis size (A) before correction, parenthesis size after correction (B), and binary tree data representing the formula for a certain formula.

[Explanation of symbols]

 21,22 Processing means A2, A12,10 Instructing means

Claims (4)

[Claims] 1. A method of allocating a mathematical expression represented by structured data, searching for data representing the contents of an expression with a subscript, calculating the height of the target expression, and calculating the result. An allocation processing method, characterized in that the position of a subscript is determined based on, and allocation processing is performed. 2. A method of allocating a mathematical expression represented by structured data, searching for data representing the contents of parentheses, calculating the height of the target expression, and calculating the height of the parentheses based on the calculation result. An allocation processing method characterized by determining height and performing allocation processing. 3. An allocation processing apparatus, comprising processing means for executing allocation processing of a mathematical expression using the allocation processing method according to claim 1. 4. An instruction means for instructing position correction of a subscript or size correction of a parenthesis is provided.
Allocation processing device described.