CN109063561B - Formula identification calculation method and device - Google Patents

Formula identification calculation method and device Download PDF

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CN109063561B
CN109063561B CN201810691934.2A CN201810691934A CN109063561B CN 109063561 B CN109063561 B CN 109063561B CN 201810691934 A CN201810691934 A CN 201810691934A CN 109063561 B CN109063561 B CN 109063561B
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formula
calculated
calculation
target
identifying
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CN109063561A (en
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徐华杰
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Guangzhou Shiyuan Electronics Thecnology Co Ltd
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Guangzhou Shiyuan Electronics Thecnology Co Ltd
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    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06VIMAGE OR VIDEO RECOGNITION OR UNDERSTANDING
    • G06V30/00Character recognition; Recognising digital ink; Document-oriented image-based pattern recognition
    • G06V30/40Document-oriented image-based pattern recognition
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F3/00Input arrangements for transferring data to be processed into a form capable of being handled by the computer; Output arrangements for transferring data from processing unit to output unit, e.g. interface arrangements
    • G06F3/01Input arrangements or combined input and output arrangements for interaction between user and computer
    • G06F3/048Interaction techniques based on graphical user interfaces [GUI]
    • G06F3/0484Interaction techniques based on graphical user interfaces [GUI] for the control of specific functions or operations, e.g. selecting or manipulating an object, an image or a displayed text element, setting a parameter value or selecting a range

Abstract

The application discloses a formula identification and calculation method and device. The method comprises the following steps: acquiring target information, wherein the target information comprises a formula to be calculated; identifying target information to identify a formula to be calculated; calculating a formula to be calculated to obtain a calculation result, wherein the calculation result at least comprises a calculation step; and outputting a calculation result. Through the method and the device, the problem that the application of formula calculation in the related technology only outputs a result and is not beneficial to deep learning of a user is solved.

Description

Formula identification calculation method and device
Technical Field
The application relates to the field of formula processing, in particular to a formula identification and calculation method and device.
Background
In the related art, most formula calculation applications can only provide the functions of keyboard input, formula solution and drawing (or a combination of several of the functions). Aiming at the application of formula calculation in the related technology, the problem that the application of formula calculation only outputs a result and is not beneficial to deep learning of a user exists. In view of the above problems, no effective solution has been proposed.
Disclosure of Invention
The application provides a formula identification and calculation method and device, and aims to solve the problem that in the related technology, the application of formula calculation only outputs a result and is not beneficial to deep learning of a user.
According to one aspect of the application, a method for identifying and calculating a formula is provided. The method comprises the following steps: acquiring target information, wherein the target information comprises a formula to be calculated; identifying the target information to identify the formula to be calculated; calculating the formula to be calculated to obtain a calculation result, wherein the calculation result at least comprises a calculation step; and outputting the calculation result.
Optionally, the target information includes at least one of: picture information, handwriting instruction information and keyboard instruction information.
Optionally, identifying the target information, where identifying the formula to be calculated includes: identifying the target information; under the condition that the target information is successfully identified, identifying the formula to be calculated; and under the condition that the target information identification fails, acquiring a plurality of prediction formulas obtained by identifying the target information, and determining the formula to be calculated from the prediction formulas.
Optionally, after obtaining the formula to be calculated, the method further includes: detecting whether a click instruction for clicking characters in the formula to be calculated is received or not, wherein the formula to be calculated comprises a plurality of characters; if the click command is received, taking the character clicked by the click command as a character to be modified; displaying a plurality of predicted characters corresponding to the character to be modified; determining a target character from the plurality of predicted characters, and replacing the character to be modified with the target character.
Optionally, if the calculation result is calculated by a plurality of calculation methods, outputting the calculation result includes: displaying a multi-solution list, wherein the multi-solution list comprises a plurality of calculation methods and calculation steps corresponding to each calculation method; selecting a target calculation method from a plurality of calculation methods; and displaying the calculation steps corresponding to the target calculation method.
According to another aspect of the present application, there is provided an apparatus for identifying a formula. The device includes: the device comprises a first acquisition unit, a second acquisition unit and a calculation unit, wherein the first acquisition unit is used for acquiring target information, and the target information comprises a formula to be calculated; the identification unit is used for identifying the target information and identifying the formula to be calculated; the second obtaining unit is used for calculating the formula to be calculated to obtain a calculation result, wherein the calculation result at least comprises a calculation step; and the output unit is used for outputting the calculation result.
Optionally, the target information includes at least one of: picture information, handwriting instruction information and keyboard instruction information.
Optionally, the identification unit includes: the identification module is used for identifying the target information; the first acquisition module is used for identifying the formula to be calculated under the condition that the target information is successfully identified; and the second acquisition module is used for acquiring a plurality of prediction formulas obtained by identifying the target information under the condition that the identification of the target information fails, and determining the formula to be calculated from the prediction formulas.
In order to achieve the above object, according to another aspect of the present application, there is provided a storage medium including a stored program, wherein the program executes the identification calculation method of the formula described in any one of the above.
In order to achieve the above object, according to another aspect of the present application, there is provided a processor for executing a program, wherein the program executes a recognition calculation method of the formula described in any one of the above items.
Through the application, the following steps are adopted: acquiring target information, wherein the target information comprises a formula to be calculated; identifying the target information to identify the formula to be calculated; calculating the formula to be calculated to obtain a calculation result, wherein the calculation result at least comprises a calculation step; and the calculation result is output, so that the problem that the application of formula calculation in the related technology only outputs the result and is not beneficial to deep learning of a user is solved. And further, the effect that the formula calculation application can show the calculation process, and a user can conveniently understand the specific calculation steps of the formula is achieved.
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The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate embodiments of the application and, together with the description, serve to explain the application and are not intended to limit the application. In the drawings:
FIG. 1 is a flow chart of a method for identifying and calculating a formula provided according to an embodiment of the application;
FIG. 2 is a flow chart of an alternative formula recognition calculation method according to an embodiment of the present application; and
FIG. 3 is a schematic diagram of a recognition and calculation device for formulas provided according to an embodiment of the present application.
Detailed Description
It should be noted that the embodiments and features of the embodiments in the present application may be combined with each other without conflict. The present application will be described in detail below with reference to the embodiments with reference to the attached drawings.
In order to make the technical solutions better understood by those skilled in the art, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are only partial embodiments of the present application, but not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present application.
It should be noted that the terms "first," "second," and the like in the description and claims of this application and in the drawings described above are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order. It should be understood that the data so used may be interchanged under appropriate circumstances such that embodiments of the application described herein may be used. Furthermore, the terms "comprises," "comprising," and "having," and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed, but may include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus.
According to the embodiment of the application, a formula identification and calculation method is provided.
Fig. 1 is a flowchart of a method for identifying and calculating a formula according to an embodiment of the present application. As shown in fig. 1, the method comprises the steps of:
step S101, target information is obtained, wherein the target information comprises a formula to be calculated.
In view of the complexity of the formula, the use of the keyboard to input the formula causes a problem of low input efficiency. Optionally, in the identification calculation method of the formula provided in the embodiment of the present application, the target information includes at least one of: picture information, handwriting instruction information and keyboard instruction information. By increasing the form type of the acquired information of the formula, the convenience degree of formula input is improved, and the technical effect of user experience is improved.
As an optional example, mainly using an electronic whiteboard, as shown in fig. 2, the obtaining source of the formula may be: the electronic whiteboard acquires handwriting instruction information of a handwriting formula, acquires formula information on a picture/PPT, and acquires keyboard instruction information input by a keyboard connected with the electronic whiteboard.
When the electronic whiteboard identifies formula information on the picture/PPT, in order to reduce workload of the electronic whiteboard and reduce identification time for processing the picture/PPT by the whiteboard, the picture/PPT can be circled, and the circled picture/PPT part is identified and analyzed by the electronic whiteboard.
When a formula is input through a keyboard, in order to place the input formula in a target area, optionally, selecting the target area, wherein the target area is used for displaying the input formula to be calculated; acquiring keyboard instruction information, wherein the keyboard instruction information comprises a formula to be calculated; and displaying the formula to be calculated in the target area according to the keyboard instruction information.
And S102, identifying the target information and identifying a formula to be calculated.
In order to ensure the recognition rate of the target information, optionally, in the recognition calculation method of the formula provided in the embodiment of the present application, recognizing the target information includes: identifying target information; under the condition that the target information is successfully identified, identifying a formula to be calculated; and under the condition that the target information identification fails, acquiring a plurality of prediction formulas obtained by identifying the target information, and determining formulas to be calculated from the prediction formulas.
In the related art, when the identification formula fails, the target information is often required to be obtained again for secondary identification. However, the success rate of the secondary recognition is the same as that of the primary recognition, and is not improved, so that the situation that the formula to be calculated cannot be obtained after the target information is recognized for many times may occur.
In order to solve the problem, the method and the device for calculating the target information acquire a plurality of prediction formulas obtained by identifying the target information under the condition that the target information is failed to identify, and determine the formula to be calculated from the prediction formulas. The technical effect of providing a plurality of prediction formulas for a user and enabling the user to select the formula to be calculated from the plurality of prediction formulas is achieved.
It should be noted that: even if the formula to be calculated is not contained in the prediction formulas, the user can still select the calculation formula which is most similar to the formula to be calculated, and then the most similar calculation formula is modified, so that the purpose of obtaining the formula to be calculated is achieved.
In view of the above requirement for modifying a calculation formula, optionally, in the identification calculation method for a formula provided in the embodiment of the present application, after obtaining the formula to be calculated, the method further includes: detecting whether a click command for clicking characters in a formula to be calculated is received or not, wherein the formula to be calculated comprises a plurality of characters; if a click command is received, taking the character clicked by the click command as a character to be modified; displaying a plurality of predicted characters corresponding to the character to be modified; and determining a target character from the plurality of predicted characters, and replacing the character to be modified with the target character.
By detecting the click command, the technical effect of accurately and directly determining the character to be modified is achieved, and the technical effect which cannot be achieved by the keyboard is achieved. In addition, after the characters to be modified are determined, the plurality of predicted characters are displayed, and the technical effect that a user can select a correct target character from the plurality of predicted characters, further modify a calculation formula and obtain a correct formula to be calculated is achieved.
It should be noted that: in the above technical solution, in the case that the predicted character does not include the correct target character, and for the above possible situations, as shown in fig. 2, optionally, in the recognition calculation method of the formula provided in the embodiment of the present application, the keyboard instruction information is obtained, the target character is obtained according to the keyboard instruction information, and the target character replaces the character to be modified. Similarly, optionally, in the recognition and calculation method of the formula provided in the embodiment of the present application, the handwritten instruction information is acquired, the target character is acquired according to the handwritten instruction information, and the target character replaces the character to be modified.
It should be noted that: for the case that the calculation formula lacks a character, optionally, in the recognition calculation method of the formula provided in the embodiment of the present application, a blank portion lacking the character is determined, and then the target character is input at the blank.
In conclusion, through the multiple modification modes, the technical effect of efficiently modifying the calculation formula is achieved, and the user experience is greatly improved.
It should be noted that: the identifying of the target information may be: and carrying out optical character recognition on the target information to obtain letters, symbols, numbers and position information thereof, and further recognizing the formula to be calculated.
And S103, calculating the formula to be calculated to obtain a calculation result, wherein the calculation result at least comprises the calculation step.
Step S104: and outputting a calculation result.
In the related art, the application of formula calculation only outputs a result, and for a complex formula, a user can only verify the calculation result of the formula, but cannot know the calculation step of the formula, that is, the user cannot learn the processing mode of the formula according to a simple calculation result, which is very unfavorable for the deep learning of the user.
According to the method and the device, not only are simple calculation results output, but also calculation steps for obtaining the calculation results are output. Thereby achieving the technical effect of helping the user to deeply learn.
In order to accurately obtain a calculation result and a calculation step, optionally, in the identification calculation method for a formula provided in the embodiment of the present application, the calculation of the formula to be calculated is performed, and the obtaining of the calculation result includes: acquiring a preset formula model corresponding to a formula to be calculated; and analyzing the formula to be calculated according to the preset formula model, and acquiring the calculation step and the calculation result.
For the case that the calculation result is obtained by calculation through multiple calculation methods, optionally, in the identification calculation method for the formula provided in the embodiment of the present application, outputting the calculation result includes: displaying a multi-solution list, wherein the multi-solution list comprises a plurality of calculation methods and calculation steps corresponding to each calculation method; selecting a target calculation method from a plurality of calculation methods; and displaying the calculation steps corresponding to the target calculation method.
There may still be multiple calculation methods for the same calculation result for the formula to be calculated. Aiming at the situation, the method and the device display various calculation possibilities of the formula to be calculated in detail through the multi-solution list, so that a user can deeply understand and learn the formula to be calculated and master various calculation ideas of the formula to be calculated.
It should be noted that there may be one calculation result or multiple calculation results for the formula to be calculated. In view of the above situation, the multi-solution list of the present application also includes multiple calculation results and calculation steps corresponding to each calculation result, so that the user can deeply understand and learn the formula to be calculated.
As an alternative example, as shown in fig. 2, in the identification calculation method for a formula provided in the embodiment of the present application, outputting a calculation result includes: displaying a multi-solution list, wherein the multi-solution list comprises a plurality of calculation methods and teaching graphs corresponding to each calculation method, and the teaching graphs are used for assisting in understanding the corresponding calculation methods; selecting a target calculation method from a plurality of calculation methods; and displaying the teaching graph corresponding to the target calculation method. Wherein, the teaching graph can be a two-dimensional graph, a three-dimensional graph and the like.
By displaying the teaching graph, the method and the device enable a user to understand the calculation steps and the calculation results of the formula to be calculated more visually and deeply, and facilitate the user to learn the formula to be calculated deeply.
For more humanized auxiliary users, optionally, in the method for identifying and calculating a formula provided in this embodiment of the application, after selecting a target calculation method from a plurality of calculation methods, the method further includes: and detecting whether a printing instruction of the printing target calculation method is received or not, and after the printing instruction is received, printing a formula to be calculated, a calculation result of the target calculation method, a calculation step of the target calculation method and a teaching graph of the target calculation method.
For more humanization, to assist the user, optionally, in the identification calculation method of the formula provided in this embodiment of the application, after selecting the target calculation method from among multiple calculation methods, the method further includes: and detecting whether a downloading instruction of the target calculation method is received or not, and displaying the downloaded two-dimensional code after the downloading instruction is received, wherein the downloaded two-dimensional code is used for recording a formula to be calculated, a calculation result of the target calculation method, a calculation step of the target calculation method and a teaching graph of the target calculation method.
According to the formula identification and calculation method provided by the embodiment of the application, target information is obtained, wherein the target information comprises a formula to be calculated; identifying target information to identify a formula to be calculated; calculating a formula to be calculated to obtain a calculation result, wherein the calculation result at least comprises a calculation step; and the calculation result is output, so that the problem that the application of formula calculation in the related technology only outputs the result and is not beneficial to deep learning of a user is solved. And further, the effect that the formula calculation application can show the calculation process, and a user can conveniently understand the specific calculation steps of the formula is achieved.
It should be noted that the steps illustrated in the flowcharts of the figures may be performed in a computer system such as a set of computer-executable instructions and that, although a logical order is illustrated in the flowcharts, in some cases, the steps illustrated or described may be performed in an order different than presented herein.
The embodiment of the present application further provides a formula identification and calculation device, and it should be noted that the formula identification and calculation device of the embodiment of the present application can be used to execute the formula identification and calculation method provided in the embodiment of the present application. The following describes a recognition calculation device for the formula provided in the embodiment of the present application.
FIG. 3 is a schematic diagram of a recognition calculation device for formulas according to an embodiment of the present application. As shown in fig. 3, the apparatus includes: a first acquisition unit 31, a recognition unit 32, a second acquisition unit 33, and an output unit 34.
The first obtaining unit 31 is configured to obtain target information, where the target information includes a formula to be calculated.
And the identification unit 32 is used for identifying the target information and identifying the formula to be calculated.
The second obtaining unit 33 is configured to calculate the formula to be calculated to obtain a calculation result, where the calculation result at least includes a calculation step.
And the output unit 34 is used for outputting the calculation result.
Optionally, in the identification calculation apparatus for a formula provided in the embodiment of the present application, the target information includes at least one of: picture information, handwriting instruction information and keyboard instruction information.
Optionally, in the identification calculation apparatus for a formula provided in the embodiment of the present application, the identification unit 32 includes: the identification module is used for identifying the target information; the first acquisition module is used for identifying a formula to be calculated under the condition that the target information is successfully identified; and the second acquisition module is used for acquiring a plurality of prediction formulas obtained by identifying the target information under the condition that the identification of the target information fails, and determining formulas to be calculated from the prediction formulas.
Optionally, in the apparatus for identifying and calculating a formula provided in the embodiment of the present application, the apparatus further includes: the checking unit is used for detecting whether a click command for clicking characters in the formula to be calculated is received or not after the formula to be calculated is obtained, wherein the formula to be calculated comprises a plurality of characters; the determining unit is used for taking the character clicked by the click instruction as the character to be modified if the click instruction is received; a display unit for displaying a plurality of predicted characters corresponding to the character to be modified; and the replacing unit is used for determining a target character from the plurality of predicted characters and replacing the character to be modified with the target character.
Optionally, in the recognition and calculation apparatus for formulas provided in this embodiment of the present application, if the calculation result is calculated by multiple calculation methods, the output unit 34 includes: the device comprises a first display module, a second display module and a display module, wherein the first display module is used for displaying a multi-solution list, and the multi-solution list comprises a plurality of calculation methods and calculation steps corresponding to each calculation method; a selection module for selecting a target calculation method from a plurality of calculation methods; a second display module for displaying the calculation steps corresponding to the target calculation method
In the identification calculation device for the formula provided by the embodiment of the application, the first obtaining unit 31 obtains target information, wherein the target information includes the formula to be calculated; the identification unit 32 identifies the target information and identifies a formula to be calculated; the second obtaining unit 33 calculates the formula to be calculated to obtain a calculation result, wherein the calculation result at least comprises a calculation step; the output unit 34 outputs the calculation result, so that the problem that the application of formula calculation in the related art only outputs the result and is not beneficial to deep learning of a user is solved, and the effect that the calculation process can be displayed by formula calculation application and the user can understand the specific calculation steps of the formula conveniently is achieved.
The identification calculation device of the formula comprises a processor and a memory, wherein the first acquisition unit 31, the identification unit 32, the second acquisition unit 33, the output unit 34 and the like are stored in the memory as program units, and the processor executes the program units stored in the memory to realize corresponding functions.
The processor comprises a kernel, and the kernel calls the corresponding program unit from the memory. The kernel can be set to be one or more than one, and the formula calculation application can show the calculation process by adjusting the kernel parameters, so that a user can conveniently understand the specific calculation steps of the formula.
The memory may include volatile memory in a computer readable medium, Random Access Memory (RAM) and/or nonvolatile memory such as Read Only Memory (ROM) or flash memory (flash RAM), and the memory includes at least one memory chip.
An embodiment of the present invention provides a storage medium on which a program is stored, the program implementing a recognition calculation method of a formula when executed by a processor.
The embodiment of the invention provides a processor, which is used for running a program, wherein the program executes a formula identification calculation method during running.
It should also be noted that the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other identical elements in the process, method, article, or apparatus that comprises the element.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The above are merely examples of the present application and are not intended to limit the present application. Various modifications and changes may occur to those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application should be included in the scope of the claims of the present application.

Claims (8)

1. A method for identifying and calculating a formula, comprising:
acquiring target information, wherein the target information comprises a formula to be calculated;
identifying the target information to identify the formula to be calculated;
calculating the formula to be calculated to obtain a calculation result, wherein the calculation result at least comprises a calculation step;
outputting the calculation result;
after obtaining the formula to be calculated, the method further includes: detecting whether a click instruction for clicking characters in the formula to be calculated is received or not, wherein the formula to be calculated comprises a plurality of characters; if the click command is received, taking the character clicked by the click command as a character to be modified; displaying a plurality of predicted characters corresponding to the character to be modified; determining a target character from the plurality of predicted characters, and replacing the character to be modified with the target character; when the target characters are not contained in the plurality of predicted characters, acquiring keyboard instruction information, acquiring the target characters according to the keyboard instruction information, and replacing the characters to be modified with the target characters;
wherein, if the calculation result is calculated by a plurality of calculation methods, outputting the calculation result comprises: displaying a multi-solution list, wherein the multi-solution list comprises a plurality of calculation methods and calculation steps corresponding to each calculation method; selecting a target calculation method from a plurality of calculation methods; and displaying the calculation steps corresponding to the target calculation method.
2. The method of claim 1, wherein the target information comprises at least one of: picture information, handwriting instruction information and keyboard instruction information.
3. The method for identifying and calculating the formula according to claim 1, wherein identifying the target information and identifying the formula to be calculated comprises:
identifying the target information;
under the condition that the target information is successfully identified, identifying the formula to be calculated;
and under the condition that the target information identification fails, acquiring a plurality of prediction formulas obtained by identifying the target information, and determining the formula to be calculated from the prediction formulas.
4. An apparatus for identifying a formula, comprising:
the device comprises a first acquisition unit, a second acquisition unit and a calculation unit, wherein the first acquisition unit is used for acquiring target information, and the target information comprises a formula to be calculated;
the identification unit is used for identifying the target information and identifying the formula to be calculated;
the second obtaining unit is used for calculating the formula to be calculated to obtain a calculation result, wherein the calculation result at least comprises a calculation step;
an output unit configured to output the calculation result;
wherein the apparatus further comprises: the checking unit is used for detecting whether a click command for clicking characters in the formula to be calculated is received or not after the formula to be calculated is obtained, wherein the formula to be calculated comprises a plurality of characters; the determining unit is used for taking the character clicked by the click instruction as the character to be modified if the click instruction is received; a display unit for displaying a plurality of predicted characters corresponding to the character to be modified; a replacing unit, which is used for determining a target character from a plurality of predicted characters and replacing the character to be modified by the target character; when the target characters are not contained in the plurality of predicted characters, acquiring keyboard instruction information, acquiring the target characters according to the keyboard instruction information, and replacing the characters to be modified with the target characters;
wherein the identification unit includes: the identification module is used for identifying the target information; the first acquisition module is used for identifying the formula to be calculated under the condition that the target information is successfully identified; and the second acquisition module is used for acquiring a plurality of prediction formulas obtained by identifying the target information under the condition that the identification of the target information fails, and determining the formula to be calculated from the prediction formulas.
5. The apparatus of claim 4, wherein the target information comprises at least one of: picture information, handwriting instruction information and keyboard instruction information.
6. The apparatus for identifying and calculating the formula according to claim 4, wherein the identifying unit comprises:
the identification module is used for identifying the target information;
the first acquisition module is used for identifying the formula to be calculated under the condition that the target information is successfully identified;
and the second acquisition module is used for acquiring a plurality of prediction formulas obtained by identifying the target information under the condition that the identification of the target information fails, and determining the formula to be calculated from the prediction formulas.
7. A storage medium characterized by comprising a stored program, wherein the program executes a recognition calculation method of the formula according to any one of claims 1 to 3.
8. A processor, characterized in that the processor is configured to run a program, wherein the program is configured to execute a method of identifying and calculating a formula according to any one of claims 1 to 3 when the program is run.
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