CN101436309A - Method and apparatus for modifying formula operator - Google Patents

Method and apparatus for modifying formula operator Download PDF

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Publication number
CN101436309A
CN101436309A CNA200810239678XA CN200810239678A CN101436309A CN 101436309 A CN101436309 A CN 101436309A CN A200810239678X A CNA200810239678X A CN A200810239678XA CN 200810239678 A CN200810239678 A CN 200810239678A CN 101436309 A CN101436309 A CN 101436309A
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formula operator
formula
operator
attribute information
viewing area
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CN101436309B (en
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赵志刚
陈宇
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Peking University Founder Group Co Ltd
Beijing Founder Electronics Co Ltd
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Peking University Founder Group Co Ltd
Beijing Founder Electronics Co Ltd
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Abstract

The invention relates to the field of typesetting technology, in particular to a method for modifying a formula operator and a device therefor, which is used to solve the problem that the current formula typesetting of the prior art does not support the modification of the formula operator. The method of the embodiment comprises the following steps: a first formula operator which needs to be modified is determined; according to the corresponding relation between a pre-established formula operator and a formula operator set, the formula operator set corresponding to the first formula operator is determined and the determined formula operator set is displayed; and after a user selects a second formula operator from the determined formula operator set, the first formula operator is replaced by the second formula operator. The method of the embodiment can support the modification of the formula operator in the typesetting process, thereby reducing the complexity and time for modifying the formula operator and improving the user experience and the typesetting efficiency.

Description

A kind of method and apparatus of revising formula operator
Technical field
The present invention relates to typesetting system field, particularly a kind of method and apparatus of revising formula operator.
Background technology
In typesetting system field, the interactive operation of formula is an extremely important and practical technology, and a kind of well mutual design not only can strengthen the composing effect of formula, can also accelerate the efficient of setting type, and reduces composing difficulty and workload.
Present software for composing does not support the modification to formula operator when formula is set type.If the user wants formula operator is made amendment, such as the replacement formula operational symbol, then the user need revise the data of formula operation attached middle school together.
Want straight score line is replaced to oblique score line such as the user, then must delete formula (promptly this operational symbol and its with data must delete together), and then re-enter new operational symbol.
In the type-setting domain, formula must be deleted at present, re-enter the formula that needs then if want to revise formula operator.
In sum, in formula is set type, do not support modification at present, thereby increased the complexity and the time of revising formula operator, reduced user experience formula operator.
Summary of the invention
The embodiment of the invention provides a kind of method and apparatus of revising formula operator, in order to solve exist in the prior art in formula is set type, do not support problem to the modification of formula operator.
A kind of method of revising formula operator that the embodiment of the invention provides comprises:
Need to determine first formula operator of modification;
According to the corresponding relation of formula operator of setting up in advance and formula operator set, determine the formula operator set of the described first formula operator correspondence, and show the described formula operator set of determining;
The user chooses second formula operator from the described formula operator set of determining after, described first formula operator is replaced with the described second formula operator method comprises:
A kind of device of revising formula operator that the embodiment of the invention provides comprises:
The operational symbol determination module is used for first formula operator of determining that needs are revised;
The set determination module is used for the corresponding relation according to formula operator of setting up in advance and formula operator set, determines the formula operator set of the described first formula operator correspondence;
First display module is used to show definite described formula operator set;
Replace module, be used for after the user chooses second formula operator from the described formula operator set of determining, described first formula operator being replaced with described second formula operator.
The embodiment of the invention need to determine first formula operator of modification; According to the corresponding relation of formula operator of setting up in advance and formula operator set, determine the formula operator set of the described first formula operator correspondence, and show the described formula operator set of determining; The user chooses second formula operator from the described formula operator set of determining after, described first formula operator is replaced with described second formula operator.Owing to support modification, thereby reduced the complexity and the time of revising formula operator, improved user experience and composing efficient to formula operator.
Description of drawings
Fig. 1 is UML (the Unified ModelingLanguage unified modeling language) synoptic diagram of embodiment of the invention composing mathematics, physics and chemistry formula data structure;
Fig. 2 is the UML synoptic diagram of the data structure of embodiment of the invention mathematics, physics and chemistry formula;
Fig. 3 is an embodiment of the invention formula
Figure A200810239678D00051
Tree structure figure;
Fig. 4 revises the UML synoptic diagram of mathematics, physics and chemistry formula data structure for the embodiment of the invention;
Fig. 5 revises the apparatus structure synoptic diagram of formula operator for the embodiment of the invention;
Fig. 6 A is an embodiment of the invention viewing area synoptic diagram one;
Fig. 6 B is an embodiment of the invention viewing area synoptic diagram one;
Fig. 7 revises the synoptic diagram of formula operator for the embodiment of the invention;
Fig. 8 revises the method flow synoptic diagram of formula operator for the embodiment of the invention.
Embodiment
The embodiment of the invention is according to the corresponding relation of formula operator and formula operator set, determine the formula operator set of the first formula operator correspondence, the user chooses second formula operator from the formula operator set after, first formula operator is replaced with second formula operator, owing to support modification, thereby reduced the complexity and the time of revising formula operator to formula operator.
Wherein, the formula of the embodiment of the invention is the mathematics, physics and chemistry formula of nestable tree structure.
Concrete, the mathematics, physics and chemistry formula is set type into one tree, promptly represent the mathematics, physics and chemistry formula with tree structure.The fundamental element of this tree structure is " zone ", and the zone just is meant and can comprises certain content, and the size of oneself and the object of position are arranged.The mathematics, physics and chemistry formula fragment of forming a tree structure with these zones.
According to the characteristic of mathematics, physics and chemistry formula, " zone " can take out three kinds of basic types: but editing area, operational symbol and variable data.The tree structure of being made up of these three fundamental types just can show formula completely.
Be used for importing the place of data but editing area is the user, operational symbol, variable data do not possess this function.The input of all is all carried out at this.But the root of number must be an editing area, because have only it could receive the data of input, but has had this root of editing area that the basis that receives data is just arranged.But editing area is equivalent to an independently one layout region, the composing of the content of its inside and its outside not direct relation.In this zone, can realize the composing of any complexity, such as entering a new line, change alignment line or the like.But editing area also can be child node or father node, but can not self carry out nestedly, just oneself can not be the direct child node of oneself, because nonsensical like this.
But operational symbol is made up of the editing area of sign of operation itself and its binding.For example, but but radical form by the editing area that can import data in radical sign, the radical sign and the editing area of exponential part.Itself is a tree that has child node, can only be father node or child node, can not be root node.
After revising formula operator, need set type to amended formula.
As shown in Figure 1, in the UML synoptic diagram one of embodiment of the invention composing mathematics, physics and chemistry formula data structure, operational symbol (C_Operator) has been described but relation between editing area (C_EditRegion), operational symbol Regularia (C_OperatorRule) and the sign of operation (C_OperatorSymbol).Operational symbol (C_Operator) polymerization other three.And operational symbol Regularia (C_OperatorRule) but direct correlation editing area (C_EditRegion), because the position relation is resolved by the operational symbol regular data by operational symbol Regularia (C_OperatorRule), and operational symbol (C_Operator) only plays the effect of a container.Sign of operation (C_OperatorSymbol) then provides the ability that can choose sign of operation separately, such as radical sign being chosen color of being arranged to want etc.
Variable data is meant the various data of input, can be character, figure and image etc.Itself can only be a child node.
As shown in Figure 2, in the UML synoptic diagram of the data structure of embodiment of the invention mathematics, physics and chemistry formula, I_Region is a virtual base class, interface I_EditRegion (but editing area), I_Operator (operational symbol), I_Variable (variable data) derive from from it, and C_EditRegion, C_Operator, C_Variable are the realizations of above-mentioned interface.
As shown in Figure 3, embodiment of the invention formula
Figure A200810239678D00071
Tree structure figure in, but the number root 51 are editing areas, " a " and "+" but all be the leaf of root editing area, they are variable datas, and child node can not be arranged.But fraction 52 also is the child node of root editing area, but but itself also comprises two editing areas.If but operational symbol does not comprise editing area, it just has been degenerated to a variable data so.Operational symbol itself is again a little tree.Radical 53 is child nodes of fraction 52, but but is made up of the editing area that can import data in the radical sign and the editing area of exponential part.But its child node can only be an editing area, can not be other type.But because if there is not editing area, it just can not receive data and operation, but mutual carrying out all carries out at editing area.
As shown in Figure 4, the embodiment of the invention is revised in the UML synoptic diagram of mathematics, physics and chemistry formula data structure, but the operational symbol of formula comprise it with input area and sign of operation part, but also have a part to be used for managing all places relation between input area and sign of operation.Wherein, C_Operator represents operational symbol, but its polymerization input area (C_EditorRegion), symbolic substitution rule (C_ReplaceRule) and sign of operation (C_OpSymbol).C_ReplaceRule is associated with C_Operator and C_OpSymbol, and for the replacement of operational symbol provides Substitution Rules, all replacements are all finished by it.
C_OpSymbol obtains the corresponding symbol of operational symbol from C_SymbolGraphBase (symbol figure storehouse), just therefrom obtain branch such as fraction, and radical then obtains radical sign.Also be from this storehouse, to obtain corresponding sign of operation during replacement, original sign of operation is replaced, so just need not be concerned about the problems such as the technique of painting of sign of operation.Condition managing of choosing and demonstration are managed by C_Operator.
Below in conjunction with Figure of description the embodiment of the invention is described in further detail.
As shown in Figure 5, the device of embodiment of the invention modification formula operator comprises: operational symbol determination module 10, set determination module 20, first display module 30 and replacement module 40.
Operational symbol determination module 10 is used for first formula operator of determining that needs are revised.
First formula operator of determining can be done special processing, adds a frame of broken lines such as the profile at formula operator, and a formula operator of choosing is done inverse handle, and adds that perhaps effect such as dark-background shows selected state.
Wherein, operational symbol determination module 10 is according to the corresponding relation of formula operator and viewing area, with the formula operator of the residing viewing area of pointer correspondence as first formula operator.
Each formula operator all can have viewing area separately, and the viewing area is based on a rectangular area that operational symbol was coated.Preferable, one or more hot spot regions can also be set in each zone.When pointer is in the formula operator corresponding display, can show the hot spot region; After the user clicked focus, the formula operator of determining this hot spot region correspondence was first formula operator, referring to Fig. 6 A and Fig. 6 B.
Fig. 6 A is that the outsourcing zone of this operational symbol demonstrates a frame when pointer mouse-over or process operational symbol zone, and the hot spot region shows for click in the lower left corner in zone.
Fig. 6 B is for when clicking the hot spot region, and with the shape of sign of operation, by the sign of operation shape library, the figure that obtains choosing is used for showing that this operational symbol of expression is selected.
The quantity of hot spot region and position can be set as required.
If formula operator is a nested class, such as
Figure A200810239678D00081
The nested plus sige of radical sign then, thus can cause the viewing area of radical sign and plus sige that the zone of coincidence is arranged, if at this moment pointer is in the viewing area of plus sige, can causes and can't determine first formula operator; If the hot spot region is arranged, then the hot spot region of radical sign and plus sige can show simultaneously, can cause the comparison confusion.
For this mode, can set in advance the priority of nested class, such as
Figure A200810239678D00091
Then set plus sige priority height, so just that priority is the highest formula operator is as first formula operator, when then operational symbol determination module 10 in the residing viewing area of pointer is the coincidence zone of at least two formula operator corresponding display, determine the priority of at least two formula operators, the formula operator that priority is the highest is as first formula operator.
If the hot spot region is arranged then the hot spot region of the highest formula operator correspondence of display priority.
Priority also can be with the tabulation expression of operational symbol nest relation, such as such as
Figure A200810239678D00092
Then in operational symbol nest relation tabulation, be set at plus sige and be in the bottom, in the specific implementation, just can tabulate according to the operational symbol nest relation, with the formula operator of the bottom as first formula operator.
Such as when the hot spot region is arranged, in the moving of pointer, by calculating to the zone of pointer position and operational symbol zone rectangle, with management to the tabulation of operational symbol nest relation, whether the operational symbol zone of position of judging the coordinate place of pointer is in the bottom, (there is individual fraction this position in the operational symbol that does not down have other again in such as radical in other words, pointer point has suffered the scope at radical place, but also be nested with fraction in the radical, fraction is also in this scope, so just down look for according to nest relation, after having found fraction, and fraction is a lowermost layer, also is to say that it does not have nested any other operational symbol), so with regard to the hot spot region in the viewing area.
In specific implementation process, can streak the viewing area at pointer and think that pointer is in the viewing area; Also can set the time, such as 2 seconds, then pointer stopped in the viewing area and thinks more than 2 seconds that pointer has been in the viewing area.
Set determination module 20 is used for the corresponding relation according to formula operator of setting up in advance and formula operator set, determines the formula operator set of the first formula operator correspondence that operational symbol determination module 10 is determined.
In specific implementation process, the formula operator in the set of the formula operator of a formula operator correspondence all is to replace, and includes but not limited in the formula operator set such as the radical sign correspondence:
Branch, plus sige, minus sign.
Can also add, revise and delete the formula operator set as required.
Wherein, can also classify to formula operator, of a sort formula operator is gathered as a formula operator, each formula operator in the set is all to gathering by formula operator.
The kind of division formula operator has a variety of, can classify according to the formula operator expression way, can be divided into same class such as radical sign is identical with the branch expression way, and sin is identical with the cos expression way can be divided into same class; Can also classify according to the number of positions of the data in the formula operator.
Need to prove that the formula operator and the corresponding relation of formula operator set and the kind dividing mode of formula operator can be set as required.
First display module 30 is used to the formula operator set that shows that set determination module 20 is determined.
Replace module 40, be used for after the user chooses second formula operator from the formula operator set of determining, first formula operator that operational symbol determination module 10 is determined replaces with second formula operator.
Because after formula operator was replaced, the position of data might also can change, at this moment just need pre-configured different Substitution Rules, referring to Fig. 7.
Substitution Rules among Fig. 7 are for after branch replaces with radical sign, and the molecule of branch is as the radical exponent of radical sign, and the denominator of branch is as the radicand of radical sign.
Then replacing module 40 also is used for according to the Substitution Rules that set in advance the Data Position of formula being carried out conversion.
Need to prove that Substitution Rules can be provided with as required.
Might need to revise the attribute information of formula operator in process of typeset, wherein attribute information includes but not limited to one or more in the following message:
Color, line thickness.
Then the device of embodiment of the invention modification formula operator can further include: second display module 50 and modified module 60.
Second display module 50 is used for after replacement module 40 replaces with second formula operator with first formula operator, shows the attribute information set of predefined formula operator correspondence.
In specific implementation process, second display module 50 can show after receiving the modification attribute signal.Wherein Xia Mian mode can generate the modification attribute signal:
Pointer is in the viewing area, and user's left button of clicking the mouse; Perhaps
User's right button of clicking the mouse, and select modification attributes section in the right-click menu.
Need to prove that present embodiment is not limited to above-mentioned two kinds of generating modes, any mode of revising attribute signal that can generate all is suitable for present embodiment.
Preferable, in the attribute information set that shows predefined formula operator correspondence, can also show the attribute information that second formula operator is current, like this can be for reference when selecting attribute information.
Modified module 60 is used for the attribute information that ensemble of communication is selected according to user's dependency, revises the current attribute information of second formula operator.
Such as: the attribute information set comprises color set and line thickness set, and further color set is red, yellow and green, and line thickness is 8 pounds, 10 pounds and 12 pounds; The user selects yellow and 8 pounds, and then that second formula operator is current attribute information is revised as yellow and 8 pounds.
As shown in Figure 8, the method for embodiment of the invention modification formula operator comprises the following steps:
Step 800, definite first formula operator that needs modification.
The corresponding relation of formula operator that step 801, basis are set up in advance and formula operator set is determined the formula operator set of the first formula operator correspondence, and shows definite formula operator set.
Step 802, the user chooses second formula operator from the formula operator set of determining after, first formula operator is replaced with second formula operator.
Wherein, in the step 800, first formula operator of determining can be done special processing, adds a frame of broken lines such as the profile at formula operator, and a formula operator of choosing is done inverse handle, and adds that perhaps effect such as dark-background shows selected state.
In the step 800, according to the corresponding relation of formula operator and viewing area, with the formula operator of the residing viewing area of pointer correspondence as first formula operator.
Each formula operator all can have viewing area separately, and the viewing area is based on a rectangular area that operational symbol was coated.Preferable, one or more hot spot regions can also be set in each zone.When pointer is in the formula operator corresponding display, can show the hot spot region; After the user clicked focus, the formula operator of determining this hot spot region correspondence was first formula operator, referring to Fig. 6 A and Fig. 6 B.
Fig. 6 A is that the outsourcing zone of this operational symbol demonstrates a frame when pointer mouse-over or process operational symbol zone, and the hot spot region shows for click in the lower left corner in zone.
Fig. 6 B is for when clicking the hot spot region, and with the shape of sign of operation, by the sign of operation shape library, the figure that obtains choosing is used for showing that this operational symbol of expression is selected.
The quantity of hot spot region and position can be set as required.
If formula operator is a nested class, such as
Figure A200810239678D0012172001QIETU
, the nested plus sige of radical sign then, thus can cause the viewing area of radical sign and plus sige that the zone of coincidence is arranged, if at this moment pointer is in the viewing area of plus sige, can causes and can't determine first formula operator; If the hot spot region is arranged, then the hot spot region of radical sign and plus sige can show simultaneously, can cause the comparison confusion.
For this mode, can set in advance the priority of nested class, such as Then set plus sige priority height, so just that priority is the highest formula operator is as first formula operator, when then being the coincidence zone of at least two formula operator corresponding display in the residing viewing area of pointer, determine the priority of at least two formula operators, the formula operator that priority is the highest is as first formula operator.
If the hot spot region is arranged then the hot spot region of the highest formula operator correspondence of display priority.Priority also can be with the tabulation expression of operational symbol nest relation, such as such as
Figure A200810239678D00122
Then in operational symbol nest relation tabulation, be set at plus sige and be in the bottom, in the specific implementation, just can tabulate according to the operational symbol nest relation, with the formula operator of the bottom as first formula operator.
Such as when the hot spot region is arranged, in the moving of pointer, by calculating to the zone of pointer position and operational symbol zone rectangle, with management to the tabulation of operational symbol nest relation, whether the operational symbol zone of position of judging the coordinate place of pointer is in the bottom, (there is individual fraction this position in the operational symbol that does not down have other again in such as radical in other words, pointer point has suffered the scope at radical place, but also be nested with fraction in the radical, fraction is also in this scope, so just down look for according to nest relation, after having found fraction, and fraction is a lowermost layer, also is to say that it does not have nested any other operational symbol), so with regard to the hot spot region in the viewing area.
In specific implementation process, can streak the viewing area at pointer and think that pointer is in the viewing area; Also can set the time, such as 2 seconds, then pointer stopped in the viewing area and thinks more than 2 seconds that pointer has been in the viewing area.
Wherein, in the step 801, the formula operator in the set of the formula operator of a formula operator correspondence all is to replace, and includes but not limited in the formula operator set such as the radical sign correspondence:
Branch, plus sige, minus sign.
Can also add, revise and delete the formula operator set as required.
Further, can also classify to formula operator, of a sort formula operator is gathered as a formula operator, each formula operator in the set is all to gathering by formula operator.
The kind of division formula operator has a variety of, can classify according to the formula operator expression way, can be divided into same class such as radical sign is identical with the branch expression way, and sin is identical with the cos expression way can be divided into same class; Can also classify according to the number of positions of the data in the formula operator.
Need to prove that the formula operator and the corresponding relation of formula operator set and the kind dividing mode of formula operator can be set as required.
Wherein, in the step 802,, at this moment just need pre-configured different Substitution Rules, referring to Fig. 7 because after the formula operator replacement, the position of data might also can change.
Substitution Rules among Fig. 7 are for after branch replaces with radical sign, and the molecule of branch is as the radical exponent of radical sign, and the denominator of branch is as the radicand of radical sign.
Then also need in the step 802 Data Position in the formula to be carried out conversion according to the Substitution Rules that set in advance.
Need to prove that Substitution Rules can be provided with as required.
Might need to revise the attribute information of formula operator in process of typeset, wherein attribute information includes but not limited to one or more in the following message:
Color, line thickness.
Then can further include after the step 802:
The attribute information set of step 803, the predefined formula operator correspondence of demonstration.
Step 804, according to the attribute information of selecting in the ensemble of communication of user's dependency, revise the current attribute information of second formula operator.
Such as: the attribute information set comprises color set and line thickness set, and further color set is red, yellow and green, and line thickness is 8 pounds, 10 pounds and 12 pounds; The user selects yellow and 8 pounds, and then that second formula operator is current attribute information is revised as yellow and 8 pounds.
Wherein, in the step 803, can after receiving the modification attribute signal, show.
Wherein Xia Mian mode can generate the modification attribute signal:
Pointer is in the viewing area, and user's left button of clicking the mouse; Perhaps
User's right button of clicking the mouse, and select modification attributes section in the right-click menu.
Need to prove that present embodiment is not limited to above-mentioned two kinds of generating modes, any mode of revising attribute signal that can generate all is suitable for present embodiment.
Preferable, in the attribute information set that shows predefined formula operator correspondence, can also show the attribute information that second formula operator is current, like this can be for reference when selecting attribute information.
From the foregoing description as can be seen: first formula operator that the embodiment of the invention determine to need is revised; According to the corresponding relation of formula operator of setting up in advance and formula operator set, determine the formula operator set of the described first formula operator correspondence, and show the described formula operator set of determining; The user chooses second formula operator from the described formula operator set of determining after, described first formula operator is replaced with described second formula operator.Owing to support modification, thereby reduced the complexity and the time of revising formula operator, improved user experience and composing efficient to formula operator.
Obviously, those skilled in the art can carry out various changes and modification to the present invention and not break away from the spirit and scope of the present invention.Like this, if of the present invention these are revised and modification belongs within the scope of claim of the present invention and equivalent technologies thereof, then the present invention also is intended to comprise these changes and modification interior.

Claims (10)

1, a kind of method of revising formula operator is characterized in that, this method comprises:
Need to determine first formula operator of modification;
According to the corresponding relation of formula operator of setting up in advance and formula operator set, determine the formula operator set of the described first formula operator correspondence, and show the described formula operator set of determining;
The user chooses second formula operator from the described formula operator set of determining after, described first formula operator is replaced with described second formula operator.
2, the method for claim 1 is characterized in that, described definite first formula operator that needs to revise comprises:
According to the corresponding relation of formula operator and viewing area, with the formula operator of the residing viewing area of pointer correspondence as first formula operator.
3, method as claimed in claim 2, it is characterized in that, when being the coincidence zone of at least two formula operator corresponding display in the residing viewing area of pointer, determine the priority of described at least two formula operators, the formula operator that priority is the highest is as first formula operator.
4, the method for claim 1 is characterized in that, described described first formula operator is replaced with also comprises after described second formula operator:
Show the attribute information set of predefined formula operator correspondence;
According to the attribute information of selecting in the ensemble of communication of user's dependency, revise the current attribute information of described second formula operator.
5, method as claimed in claim 4 is characterized in that, described attribute information set comprises:
One or more in the set of color set and line thickness.
6, a kind of device of revising formula operator is characterized in that, this device comprises:
The operational symbol determination module is used for first formula operator of determining that needs are revised;
The set determination module is used for the corresponding relation according to formula operator of setting up in advance and formula operator set, determines the formula operator set of the described first formula operator correspondence;
First display module is used to show definite described formula operator set;
Replace module, be used for after the user chooses second formula operator from the described formula operator set of determining, described first formula operator being replaced with described second formula operator.
7, device as claimed in claim 6 is characterized in that, described operational symbol determination module is used for:
According to the corresponding relation of formula operator and viewing area, with the formula operator of the residing viewing area of pointer correspondence as first formula operator.
8, device as claimed in claim 7 is characterized in that, described operational symbol determination module is used for:
When being the coincidence zone of at least two formula operator corresponding display in the residing viewing area of pointer, determine the priority of described at least two formula operators, the formula operator that priority is the highest is as first formula operator.
9, device as claimed in claim 6 is characterized in that, the device of described modification formula operator also comprises:
Second display module is used for after described replacement module replaces with described second formula operator with described first formula operator, shows the attribute information set of predefined formula operator correspondence;
Modified module is used for the attribute information that ensemble of communication is selected according to user's dependency, revises the current attribute information of described second formula operator.
10, device as claimed in claim 9 is characterized in that, described attribute information set comprises:
One or more in the set of color set and line thickness.
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CN104572577A (en) * 2014-12-17 2015-04-29 百度在线网络技术(北京)有限公司 Mathematical formula processing method and device
CN104572577B (en) * 2014-12-17 2018-09-04 百度在线网络技术(北京)有限公司 Mathematical formulae processing method and processing device
WO2022059349A1 (en) * 2020-09-16 2022-03-24 カシオ計算機株式会社 Information processing method, system, information processing device, and program
JP2022049653A (en) * 2020-09-16 2022-03-29 カシオ計算機株式会社 Information processing method, system, information processor, and program
JP7287417B2 (en) 2020-09-16 2023-06-06 カシオ計算機株式会社 Information processing method, system, information processing device and program

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