Methods, apparatuses, devices, and storage media for automatically solving algebraic problems

Abstract

Embodiments of the present disclosure provide a method, apparatus, device and storage medium for automatically solving algebraic problems. The method comprises determining, for an algebraic expression associated with an algebraic problem, a plurality of theorems applicable to the algebraic expression. The method further comprises determining a plurality of scores for the plurality of theorems, each score indicating a rationality of a respective theorem being applied to the algebraic expression. The method further comprises applying, based on the plurality of scores, at least one target theorem from the plurality of theorems to the algebraic expression to obtain at least one transformed algebraic expression. The method further comprises determining, based on the at least one transformed algebraic expression, an answer to the algebraic problem. With the solution of the present disclosure, a target theorem suitable to be applied to an algebraic expression associated with an algebraic problem can be determined using less computing resources, so that the algebraic problem can be automatically solved efficiently.

Description

TECHNICAL FIELD

[0001] Embodiments of the present disclosure relate to the field of computer technology, and in particular, to a method, apparatus, device and storage medium for automatically solving algebraic problems. BACKGROUND

[0002] In the scenario of teaching aided by computer technology, an algebraic problem can be automatically solved by a computer and an answer to the algebraic problem can be provided to a user. For example, a user can input an algebraic problem to a computer system, and learn a problem-solving method by means of an answer provided by the computer system, thereby improving learning efficiency. However, since algebraic problems vary greatly, providing an answer to each algebraic problem requires complex processing rules and consumes a large amount of computing resources. Therefore, a scheme for automatically solving algebraic problems is needed to efficiently provide answers to algebraic problems. SUMMARY

[0003] Embodiments of the present disclosure provide a scheme for automatically solving algebraic problems.

[0004] In a first aspect of the present disclosure, a method for automatically solving an algebraic problem is provided. The method comprises determining, for an algebraic expression associated with the algebraic problem, a plurality of theorems applicable to the algebraic expression. The method further comprises determining a plurality of scores for the plurality of theorems, each score indicating a rationality of a corresponding theorem being applied to the algebraic expression. The method further comprises applying, based on the plurality of scores, at least one target theorem of the plurality of theorems to the algebraic expression to obtain at least one transformed algebraic expression. The method further comprises determining, based on the at least one transformed algebraic expression, an answer to the algebraic problem. With the scheme of the present disclosure, a target theorem suitable for being applied to an algebraic expression associated with an algebraic problem can be determined using less computing resources, thereby efficiently automatically solving the algebraic problem.

[0005] In a second aspect of the present disclosure, an apparatus for automatically solving an algebraic problem is provided. The apparatus comprises a theorem determining unit configured to determine, for an algebraic expression associated with the algebraic problem, a plurality of theorems applicable to the algebraic expression. The apparatus further comprises a score determining unit configured to determine a plurality of scores for the plurality of theorems, each score indicating a rationality of a corresponding theorem being applied to the algebraic expression. The apparatus further comprises a theorem applying unit configured to apply, based on the plurality of scores, at least one target theorem of the plurality of theorems to the algebraic expression to obtain at least one transformed algebraic expression. The apparatus further comprises an answer determining unit configured to determine, based on the at least one transformed algebraic expression, an answer to the algebraic problem.

[0006] In a third aspect of the present disclosure, an electronic device is provided, comprising a memory and a processor; wherein the memory is configured to store one or more computer instructions, wherein the one or more computer instructions are executed by the processor to implement the method according to the first aspect of the present disclosure.

[0007] In a fourth aspect of the present disclosure, a computer-readable storage medium is provided, having stored thereon one or more computer instructions, wherein the one or more computer instructions are executed by a processor to implement the method according to the first aspect of the present disclosure.

[0008] The summary is provided to introduce a selection of concepts, in a simplified form, that are further described below in the DETAILED DESCRIPTION. This summary is not intended to identify key features or essential features of embodiments of the present disclosure, nor is it intended to limit the scope of the present disclosure. BRIEF DESCRIPTION OF DRAWINGS

[0009] The above and other objects, features and advantages of embodiments of the present disclosure will become more apparent from the following detailed description when taken in conjunction with the accompanying drawings, in which like reference characters designate like elements in the several views.

[0010] Figure 1 A schematic diagram showing an environment in which embodiments of the present disclosure can be implemented is shown;

[0011] Figure 2 A flowchart showing an example method for automatically solving algebraic problems according to some embodiments of the present disclosure is shown;

[0012] Figure 3 A schematic diagram showing an example parse structure of an algebraic expression according to some embodiments of the present disclosure is shown;

[0013] Figure 4 A schematic diagram showing an example process of automatically solving an answer to an algebraic problem according to some embodiments of the present disclosure is shown;

[0014] Figure 5 A schematic diagram showing an example process of iteratively determining an answer to an algebraic problem according to some embodiments of the present disclosure is shown;

[0015] Figure 6 A schematic block diagram showing an apparatus for automatically solving algebraic problems according to some embodiments of the present disclosure is shown; and

[0016] Figure 7 A block diagram of an example computing device that can be used to implement embodiments of the present disclosure is shown. DETAILED DESCRIPTION

[0017] The principles of embodiments of the present disclosure will now be described with reference to a number of example embodiments illustrated in the drawings. Although the preferred embodiments of the present disclosure are shown in the drawings, it is understood that these embodiments are merely for the purpose of better illustrating the principles of the embodiments of the present disclosure, and are not intended to limit the scope of the present disclosure in any way.

[0018] As used herein, the term "includes" and its variants are meant to be an open-ended term that means "comprises, but not limited to." The term "or" means "and / or" unless otherwise specifically indicated. The term "based on" means "based, at least in part, on." The term "one example embodiment" and "some embodiments" means "at least one example embodiment." The term "another embodiment" means "at least one additional embodiment." The terms "first," "second," etc. can refer to different or the same objects. Other explicit or implicit definitions can also be included below.

[0019] As mentioned above, since algebraic problems vary greatly, providing an answer for each algebraic problem requires complex processing rules. Currently, some schemes for automatically solving algebraic problems have been proposed. In some schemes, rules for automatically solving algebraic problems can be established based on teaching content. By analyzing the algebraic expression in the algebraic problem, the algebraic expression can be processed based on the corresponding rules to obtain the answer to the algebraic problem.

[0020] For example, an algebraic problem can be automatically solved based on rules such as "split the addition term and calculate from left to right," "detect that the numerator and denominator have reducible terms, and the previous step is not the denominator rationalization, then perform reduction," "move the term for a monomial equation, ensure that the left side of the equal sign is a variable, and the right side is not a variable," and the like.

[0021] In these schemes, the algebraic expression needs to be parsed into individual components, and each component is processed based on rules. However, for algebraic problems, even if one number or letter in the algebraic expression is changed, different rules can need to be applied to process the algebraic expression. Therefore, a lot of manpower is needed to establish a very complex rule system to implement processing of various algebraic expressions with appropriate rules.

[0022] According to an embodiment of the present disclosure, a scheme for automatically solving an algebraic problem is proposed to at least address one or more of the above issues or other potential issues. In the present scheme, for an algebraic expression associated with the algebraic problem, a plurality of theorems that can be applied to the algebraic expression are determined. A plurality of scores of the plurality of theorems are determined, each score indicating a rationality of a corresponding theorem being applied to the algebraic expression. Based on the plurality of scores, at least one target theorem of the plurality of theorems is applied to the algebraic expression to obtain at least one transformed algebraic expression. Based on the at least one transformed algebraic expression, an answer to the algebraic problem is determined.

[0023] In this way, the present scheme can determine a target theorem that is suitable for an algebraic expression based on a rationality of the respective theorem being applied to the algebraic expression, thereby automatically solving an algebraic problem by applying the suitable target theorem. In the present scheme, there is no need to establish a complex rule system, thus reducing resource consumption for determining the target theorem.

[0024] The basic principles and several example implementations of the present disclosure are explained with reference to the accompanying drawings. It should be understood that the example embodiments are given only for the purpose of better illustrating the present disclosure to enable those skilled in the art to better understand and implement the embodiments of the present disclosure, and not in any way to limit the scope of the present disclosure.

[0025] Figure 1 An example environment 100 in which embodiments of the present disclosure can be implemented is shown. As shown in the environment 100, an algebraic problem 110 can be input to a computing device 120. The computing device 120 can obtain an answer 130 to the algebraic problem 110 by processing an algebraic expression 115 associated with the algebraic problem 110. The computing device 120 can output the answer 130 to the algebraic problem 110. As shown in the answer 130, the computing device 120 can also display one or more problem-solving steps associated with the answer 130, such as steps 131 and 132. Each problem-solving step can involve an algebraic expression transformation based on a suitable theorem. Figure 1 Figure 1

[0026] ​​Computing device 120 includes a computing device in the form of a general purpose computing device. In some implementations, computing device 120 can be implemented as various user terminals or service terminals having computing capabilities. Service terminals can be servers, mainframe computing devices, etc. provided by various service providers. User terminals such as any type of mobile terminal, fixed terminal, or portable terminal including a mobile phone, a set, a unit, a device, a multimedia computer, a multimedia tablet, an Internet node, a communicator, a desktop computer, a laptop computer, a notebook computer, a netbook computer, a tablet computer, a personal communication system (PCS) device, a personal navigation device, a personal digital assistant (PDA), an audio / video player, a digital camera / camcorder, a positioning device, a television receiver, a radio broadcast receiver, an electronic book device, a game device, or any combinations thereof, including accessories and peripherals of such devices, or any combinations thereof.

[0027] Components of computing device 120 can include, but are not limited to, one or more processors or processing units, memory, storage devices, one or more communication units, one or more input devices, and one or more output devices. These components can be integrated on a single device or can be arranged in a cloud computing architecture. In a cloud computing architecture, these components can be arranged remotely and can work together to implement the functionality described in this disclosure. In some implementations, cloud computing provides computation, software, data access, and storage services that do not require end-user knowledge of the physical location or configuration of the system that delivers the services. In various implementations, cloud computing uses appropriate protocols over a wide area network, such as the Internet, to deliver services. For example, cloud computing providers deliver applications over a wide area network, and they can be accessed through a web browser or any other computing component. Software or components of a cloud computing architecture and corresponding data can be stored on servers at remote locations. Computing resources in a cloud computing environment can be consolidated at a remote data center location or they can be dispersed. Cloud computing infrastructure can provide services through a shared data center, even though they appear as a single point of access for users. Thus, components and functionality described herein can be provided from a service provider at a remote location using a cloud computing architecture. Alternatively, they can be provided from a conventional server, or they can be installed directly or otherwise on a client device.

[0028] It should be understood that Figure 1 The illustrated environment 100 is merely exemplary and should not be construed as limiting the functionality and scope of the implementations described herein. It should also be understood that the term "algebraic expression" as used herein can refer to various mathematical expressions capable of symbolic operations. Further, the term "theorem" as used herein can refer to mathematical theorems, computational rules, processing rules, etc. capable of transforming algebraic expressions.

[0029] Figure 2 A flowchart illustrating an example method 200 for automatically solving an algebraic problem in accordance with some embodiments of the present disclosure is shown. The method 200 may, for example, be performed by the computing device 120 as shown. It should be understood that the method 200 can also include additional actions not shown and / or can omit actions shown, without limitation to the scope of the present disclosure. The method 200 is described in detail below in conjunction with the Figure 1 Figure 1

[0030] At block 210, for an algebraic expression 115 associated with the algebraic problem 110, a plurality of theorems that can be applied to the algebraic expression 115 is determined. In some embodiments, the algebraic expression 115 associated with the algebraic problem 110 can include an algebraic expression directly recited in the algebraic problem 110. For example, in the example shown, the algebraic problem 110 directly recites an algebraic expression to be processed. Figure 1

[0031] Alternatively or additionally, the algebraic expression associated with the algebraic problem 110 can include an algebraic expression derived from the algebraic problem 110 using any suitable method. In some examples, different algebraic expressions can be obtained by moving elements across an equal sign in the process of solving an equation. In other examples, the associated algebraic expression can be constructed from the algebraic problem 110 described in natural language.

[0032] In some embodiments, the plurality of theorems that can be applied to the algebraic expression 115 can be selected from pre-set theorems. The pre-set theorems can be pre-determined based on the teaching content. For example, the pre-set theorems for simple content can be different from the pre-set theorems for complex content.

[0033] In some embodiments, the computing device 120 can select the plurality of theorems that can be applied to the algebraic expression 115 from the pre-set theorems using a mathematical analysis engine. The mathematical analysis engine can be any suitable tool that can process an algebraic expression based on a theorem, without limitation to the scope of the present disclosure.

[0034] Specifically, the algebraic expression 115 can be input to the mathematical analysis engine. In response to determining that the mathematical analysis engine outputs a processed algebraic expression based on a processing rule corresponding to a particular theorem, the particular theorem can be determined as a theorem that can be applied to the algebraic expression 115.

[0035] ​​​For example, various processing rules (such as simplification, expansion, factorization, etc.) can be tried on the algebraic expression 115 in the mathematical analysis engine. For a particular processing rule, if the mathematical analysis engine outputs an error prompt, it can be determined that the theorem corresponding to the processing rule cannot be applied to the algebraic expression 115. In contrast, if the mathematical analysis engine outputs a processed algebraic expression, the theorem corresponding to the particular processing rule can be determined as a theorem that can be applied to the algebraic expression 115.

[0036] Additionally or alternatively, the computing device 120 can determine the theorems in the pre-set theorems that can be applied to the algebraic expression 115 based on the parse structure of the algebraic expression 115. Specifically, in response to determining that a particular theorem in the pre-set theorems corresponds to the processing rule of at least one sub-structure in the parse structure, the particular theorem can be determined as a theorem that can be applied to the algebraic expression 115.

[0037] It should be understood that the term “parse structure” used herein refers to a specific structure used to characterize the components of an algebraic expression and the relationships between the components. As a non-limiting example, the parse structure of an algebraic expression can be an expression tree. The parse structure of an algebraic expression can be determined using any suitable method, the scope of the present disclosure not being limited in this regard.

[0038] Figure 3 A schematic diagram showing an example parse structure 300 of the algebraic expression 115 is shown in accordance with some embodiments of the present disclosure. As shown, for the example of the algebraic expression 115 shown in Figure 3 Figure 1 As shown, 2a + 10 can be parsed as a sub-structure 301, 2a can be parsed as a sub-structure 302, and 10 can be parsed as a sub-structure 303.

[0039] In some embodiments, in response to determining that the theorem “extract common factor” corresponds to the processing rule of the sub-structure 301 (e.g., the summation rule includes a sub-rule for extracting common factors), the theorem “extract common factor” can be determined as a theorem that can be applied to the algebraic expression 115.

[0040] Additionally, in response to determining that the theorem “divide and combine” corresponds to the processing rules of the sub-structures 302, 303, and 304, the theorem “divide and combine” can be determined as another theorem that can be applied to the algebraic expression 115.

[0041] It should be understood that depending on the parsing rules, the algebraic expression 115 can be parsed into other parse structures different from the parse structure 300. For example, the algebraic expression 115 can be parsed into a parse structure that includes only one sub-structure directly corresponding to the theorem “divide and combine”, instead of the parse structure 300 that includes three sub-structures directly corresponding to the theorem “divide and combine”. Figure 3 ​In this case, in response to determining that the theorem "Divide and Conquer and Merge" corresponds to the processing rule of one of the sub-structures in the parse structure, the theorem "Divide and Conquer and Merge" can be determined as a theorem that can be applied to the algebraic expression 115.

[0042] With continued reference to Figure 2 At block 220, a plurality of scores of a plurality of theorems that can be applied to the algebraic expression 115 are determined, each score indicating a rationality of a corresponding theorem being applied to the algebraic expression 115. The rationality can be a degree of appropriateness of the theorem being applied to the algebraic expression 115.

[0043] In some embodiments, the plurality of scores of the plurality of theorems can be determined with an artificial intelligence model. The artificial intelligence model can be deployed in or communicatively coupled with the computing device 120. The artificial intelligence model can receive the algebraic expression 115 as input and output a respective score of each of the plurality of theorems. Depending on the specific implementation, any suitable artificial intelligence model can be utilized to determine the plurality of scores of the plurality of theorems. The scope of the present disclosure is not limited in this regard.

[0044] In some embodiments, the artificial intelligence model can be trained based on problem-solving steps of annotated algebraic problems. The training data of the artificial intelligence model can include a transformation history of algebraic expressions in the annotated problem-solving steps, i.e., the algebraic expressions involved in each problem-solving step. The transformation history can include a sequence of transformed algebraic expressions based on at least one of the plurality of theorems.

[0045] For example, the artificial intelligence model can be a transformer model. The transformer model can be trained based on the sequence consisting of the transformation history of the algebraic expressions. In the inference process, a transformed algebraic expression can be predicted based on the input algebraic expression 115 and a score of a theorem corresponding to the algebraic expression transformation is outputted.

[0046] In some embodiments, the artificial intelligence model can be pre-trained based on a large-scale algebraic expression transformation data, so as to improve the representation capability of the artificial intelligence model on the algebraic expressions. For example, the model can be first pre-trained based on a large number of transformation histories of algebraic expressions, and then the model can be further trained based on a smaller training data set specific to the teaching content. In this way, the resource consumption for training the artificial intelligence model can be reduced.

[0047] Based on the rationality of each theorem being applied to the algebraic expression determined by the artificial intelligence model, in automatically solving the algebraic problem, a complex rule system can not be needed to determine an appropriate theorem, so that the algebraic problem can be more efficiently automatically solved for an answer.

[0048] At block 230, based on the plurality of scores indicating the plausibility of the plurality of theorems being applied to the algebraic expression 115, at least one target theorem of the plurality of theorems is applied to the algebraic expression 115 to obtain at least one transformed algebraic expression. In some embodiments, one or more theorems having scores above a threshold value can be selected as the target theorem. The threshold value can be set based on various factors. In some examples, the threshold value can be determined based on the number of target theorems to be selected. In other examples, the threshold value can be determined based on historical data and prior knowledge.

[0049] For example, for the example of the algebraic expression 115 shown in Figure 1 , the target theorem “extract common factors” can be applied to obtain the transformed algebraic expression Additionally or alternatively, the target theorem “divide and combine” can be applied to obtain the transformed algebraic expression

[0050] At block 240, based on the at least one transformed algebraic expression, the answer 130 of the algebra problem 110 is determined. In some embodiments, the transformed algebraic expression itself can be the answer 130. For example, for the algebra problem “simplify the algebraic expression: 2a + 10 + a + 1”, the transformed algebraic expression “3a + 11” obtained by applying the theorem “combine like terms” can be determined as the answer 130.

[0051] In some embodiments, the obtained transformed algebraic expression can be further processed to determine the answer 130. For example, for the algebra problem “simplify the algebraic expression: ”, the transformed algebraic expression obtained by applying the theorem “combine like terms” can be further processed to finally determine the answer 130.

[0052] In some embodiments, the computing device 120 can display the answer 130. In some embodiments, the answer 130 can be presented to the user via an output component of the computing device 120. For example, the answer 130 can be displayed via a display of the computing device 120.

[0053] Additionally or alternatively, the computing device 120 can display at least one target theorem determined to be suitable to be applied to the algebraic expression 115. Additionally, the scores of the target theorems can be displayed. Additionally or alternatively, the computing device 120 can display at least one transformed algebraic expression based on the at least one target theorem. In this way, the user can be better assisted in learning the solution method of the algebra problem.

[0054] Figure 4 A schematic diagram illustrating an example process 400 of automatically solving an answer of an algebra problem, in accordance with some embodiments of the present disclosure, is shown. The process 400 can be Figure 2a detailed example of the method 200 shown in FIG. 2. The process of automatically solving an answer to an algebraic problem will be described below with reference to Figures 1 to 4

[0055] As shown in FIG. 4, the process 400 can include receiving an input algebraic problem 410, determining an algebraic expression to be processed 420, determining a plurality of theorems applicable to the algebraic expression 430, determining a plurality of scores for the plurality of theorems 440, selecting a target theorem from the plurality of theorems based on the scores 450, applying the target theorem to the algebraic expression to obtain a transformed algebraic expression 460, determining whether an end condition is satisfied 470, and outputting an answer to the algebraic problem based on the transformed algebraic expression 480. Figure 4 As shown in FIG. 4, the process 400 can include receiving an input algebraic problem 410, determining an algebraic expression to be processed 420, determining a plurality of theorems applicable to the algebraic expression 430, determining a plurality of scores for the plurality of theorems 440, selecting a target theorem from the plurality of theorems based on the scores 450, applying the target theorem to the algebraic expression to obtain a transformed algebraic expression 460, determining whether an end condition is satisfied 470, and outputting an answer to the algebraic problem based on the transformed algebraic expression 480.

[0056] As shown in FIG. 4, the process 400 can include receiving an input algebraic problem 410, determining an algebraic expression to be processed 420, determining a plurality of theorems applicable to the algebraic expression 430, determining a plurality of scores for the plurality of theorems 440, selecting a target theorem from the plurality of theorems based on the scores 450, applying the target theorem to the algebraic expression to obtain a transformed algebraic expression 460, determining whether an end condition is satisfied 470, and outputting an answer to the algebraic problem based on the transformed algebraic expression 480.

[0057] As shown in FIG. 4, the process 400 can include receiving an input algebraic problem 410, determining an algebraic expression to be processed 420, determining a plurality of theorems applicable to the algebraic expression 430, determining a plurality of scores for the plurality of theorems 440, selecting a target theorem from the plurality of theorems based on the scores 450, applying the target theorem to the algebraic expression to obtain a transformed algebraic expression 460, determining whether an end condition is satisfied 470, and outputting an answer to the algebraic problem based on the transformed algebraic expression 480.

[0058] As shown in FIG. 4, the process 400 can include receiving an input algebraic problem 410, determining an algebraic expression to be processed 420, determining a plurality of theorems applicable to the algebraic expression 430, determining a plurality of scores for the plurality of theorems 440, selecting a target theorem from the plurality of theorems based on the scores 450, applying the target theorem to the algebraic expression to obtain a transformed algebraic expression 460, determining whether an end condition is satisfied 470, and outputting an answer to the algebraic problem based on the transformed algebraic expression 480.

[0059] As shown in FIG. 4, the process 400 can include receiving an input algebraic problem 410, determining an algebraic expression to be processed 420, determining a plurality of theorems applicable to the algebraic expression 430, determining a plurality of scores for the plurality of theorems 440, selecting a target theorem from the plurality of theorems based on the scores 450, applying the target theorem to the algebraic expression to obtain a transformed algebraic expression 460, determining whether an end condition is satisfied 470, and outputting an answer to the algebraic problem based on the transformed algebraic expression 480.

[0060] Figure 5 FIG. 5 shows a schematic diagram of an example process 500 of iteratively determining an answer to an algebraic problem, according to some embodiments of the present disclosure. The process 500 can be a detailed example of the method 200 shown in FIG. 2. The process of automatically solving an answer to an algebraic problem will be described below with reference to Figure 2 ​Method 200 and shown Figure 4 A detailed example of process 400 is shown.

[0061] like Figure 5 As shown, for algebraic expression 515 in algebraic problem 510, we can determine the first set of theorems 520 and the corresponding first set of algebraic expressions 530 that are suitable for application to algebraic expression 515. (See reference...) Figure 2 The steps at boxes 210 to 230 shown in the diagram or Figure 4 The steps 430 to 460 shown determine the first set of theorems 520 and the corresponding first set of algebraic expressions 530.

[0062] Based on the first set of algebraic expressions 530, a second set of theorems 540 can be determined. Theorems in the second set of theorems 540 can be applied to at least one algebraic expression in the first set of algebraic expressions 530. In other words, one or more algebraic expressions in the first set of algebraic expressions 530 can be selected as updated algebraic expressions to be processed for subsequent processing. In some embodiments, new algebraic expressions to be processed can be selected based on the score of the first set of theorems 520. For example, as... Figure 5 As shown, we can choose the algebraic expression 535 corresponding to the highest-scoring theorem 525 for subsequent processing.

[0063] Similarly, for algebraic expression 535, multiple theorems applicable to algebraic expression 535 can be identified, and multiple scores can be determined for these theorems, each score indicating the reasonableness of applying the corresponding theorem to algebraic expression 535. Based on the scores, one or more target theorems suitable for application to algebraic expression 535 can be selected, thereby determining the second set of theorems 540.

[0064] It should be understood that, although not shown, one or more suitable target theorems may be determined based on other algebraic expressions in the first set of algebraic expressions 530 (e.g., algebraic expression 538) as part of the second set of theorems 540.

[0065] Based on the second set of theorems 540 and the first set of algebraic expressions 530, the second set of algebraic expressions 550 can be determined. The second set of algebraic expressions 550 can be obtained by applying the second set of theorems 540 to the corresponding algebraic expressions in the first set of algebraic expressions 530.

[0066] Based on the second set of algebraic expressions 550, the answer 590 to algebraic problem 510 can be determined. As mentioned above, in some embodiments, the answer 590 can be determined directly from the second set of algebraic expressions 550. Alternatively, the second set of algebraic expressions 550 can be iteratively processed to finally determine the answer 590. Specific details will not be elaborated here.

[0067] In some embodiments, the computing device 120 can determine one or more solution paths for the algebraic problem. Additionally, the computing device 120 can display the solution paths to the user. Each solution path can include one or more solving steps and theorems and algebraic expression transformations involved in the solving steps. In this way, the user can be better assisted to understand the solving process of the algebraic problem.

[0068] Reference is made to Figure 5 In some embodiments, at least one solution path can be determined based on the scores of the first set of theorems 520 and the scores of the second set of theorems 540, each solution path including one algebraic expression of the first set of algebraic expressions 530 and one algebraic expression of the second set of algebraic expressions 550. For example, an algebraic expression 535 of the first set of algebraic expressions 530 corresponding to the theorem 525 with the highest score and an algebraic expression 555 of the second set of algebraic expressions 550 corresponding to the theorem 545 with the highest score can be selected to determine a first solution path. An algebraic expression 535 of the first set of algebraic expressions 530 corresponding to the theorem 525 with the highest score and an algebraic expression 556 of the second set of algebraic expressions 550 corresponding to the theorem with the second highest score can also be selected to determine a second solution path.

[0069] Reference is made to Figures 1 to 5 The principles and details of automatically solving an algebraic problem according to embodiments of the present disclosure are described. In this way, the present solution can determine a target theorem for processing an algebraic expression based on the reasonability of the respective theorem being applied to the algebraic expression, thereby efficiently automatically solving the algebraic problem. In the present solution, there is no need to establish a complex rule system, thus reducing the resource consumption for determining the target theorem for solving the algebraic problem.

[0070] Embodiments of the present disclosure further provide a corresponding apparatus for implementing the above-mentioned method or process. Figure 6 A schematic structural block diagram of an apparatus 600 for automatically solving an algebraic problem according to some embodiments of the present disclosure is shown.

[0071] As Figure 6 shown, the apparatus 600 includes a theorem determining unit 610 configured to determine, for an algebraic expression associated with an algebraic problem, a plurality of theorems that can be applied to the algebraic expression. The apparatus 600 further includes a score determining unit 620 configured to determine a plurality of scores of the plurality of theorems, each score indicating the reasonability of a respective theorem being applied to the algebraic expression. The apparatus 600 further includes a theorem applying unit 630 configured to apply, based on the plurality of scores, at least one target theorem of the plurality of theorems to the algebraic expression to obtain at least one transformed algebraic expression. The apparatus 600 further includes an answer determining unit 640 configured to determine, based on the at least one transformed algebraic expression, an answer to the algebraic problem.

[0072] In some embodiments, the theorem determination unit 610 is configured to determine the plurality of theorems applicable to the algebraic expression based on an analytic structure of the algebraic expression, each theorem corresponding to a processing rule of at least one sub-structure in the analytic structure.

[0073] In some embodiments, the theorem determination unit 610 is configured to input the algebraic expression into a mathematical analysis engine, and determine the plurality of theorems in response to determining that the mathematical analysis engine outputs a plurality of processed algebraic expressions based on a plurality of processing rules, each theorem corresponding to at least one processing rule in the plurality of processing rules.

[0074] In some embodiments, the score determination unit 620 is configured to determine the plurality of scores based on the algebraic expression using an artificial intelligence model.

[0075] In some embodiments, the artificial intelligence model is trained based on a transformation history of the algebraic expression in a problem solving step, the transformation history including a sequence of transformed algebraic expressions based on at least one theorem in the plurality of theorems.

[0076] In some embodiments, the at least one target theorem is a first set of theorems, the at least one transformed algebraic expression is a first set of algebraic expressions, and the answer determination unit 640 is configured to determine a second set of theorems based on the first set of algebraic expressions, a theorem in the second set of theorems being applicable to at least one algebraic expression in the first set of algebraic expressions; determine a second set of algebraic expressions based on the second set of theorems and the first set of algebraic expressions; and determine an answer to the algebraic problem based on the second set of algebraic expressions.

[0077] In some embodiments, the plurality of theorems is a first plurality of theorems, and the answer determination unit 640 is configured to determine, for a first algebraic expression in the first set of algebraic expressions, a second plurality of theorems applicable to the first algebraic expression; determine a plurality of scores for the second plurality of theorems, each score indicating a rationality of a corresponding theorem being applied to the first algebraic expression; and determine the second set of theorems based on the plurality of scores for the second plurality of theorems by selecting theorems in the second plurality of theorems having scores higher than a threshold value.

[0078] In some embodiments, the apparatus 600 further comprises a problem solving path determination unit configured to determine, based on the scores of the first set of theorems and the scores of the second set of theorems, at least one problem solving path, each problem solving path including one algebraic expression in the first set of algebraic expressions and one algebraic expression in the second set of algebraic expressions.

[0079] In some embodiments, the device 600 further includes a display unit configured to display at least one of the following: the at least one target theorem, the at least one transformed algebraic expression, or the answer to the algebraic problem.

[0080] In some embodiments, the device 600 further includes a display unit configured to display the at least one solution path.

[0081] Figure 7 A schematic block diagram is shown that can be used to implement an example device 700 according to embodiments of the present disclosure. For example, such as Figure 1 The computing device 120 shown can be implemented by device 700. For example... Figure 7 As shown, device 700 includes a central processing unit (CPU) 701, which can perform various appropriate actions and processes according to computer program instructions stored in read-only memory (ROM) 702 or loaded from storage unit 708 into random access memory (RAM) 703. RAM 703 may also store various programs and data required for the operation of device 700. CPU 701, ROM 702, and RAM 703 are interconnected via bus 704. Input / output (I / O) interface 705 is also connected to bus 704.

[0082] Multiple components in device 700 are connected to I / O interface 705, including: input unit 706, such as keyboard, mouse, etc.; output unit 707, such as various types of monitors, speakers, etc.; storage unit 708, such as disk, optical disk, etc.; and communication unit 709, such as network card, modem, wireless transceiver, etc. Communication unit 709 allows device 700 to exchange information / data with other devices through computer networks such as the Internet and / or various telecommunications networks.

[0083] The various processes and handling described above, such as method 200, can be executed by processing unit 701. For example, in some embodiments, method 200 can be implemented as a computer software program tangibly contained in a machine-readable medium, such as storage unit 708. In some embodiments, part or all of the computer program can be loaded and / or installed on device 700 via ROM 702 and / or communication unit 709. When the computer program is loaded into RAM 703 and executed by CPU 701, one or more actions of method 200 described above can be performed.

[0084] This disclosure can be a method, apparatus, system, and / or computer program product. A computer program product may include a computer-readable storage medium having computer-readable program instructions loaded thereon for performing various aspects of this disclosure.

[0085] Computer readable storage media can be tangible storage media which can retain and store instructions for use by an instruction execution device. Computer readable storage media can be, for example, but is not limited to, an electronic storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination of the foregoing. More specific examples (a non-exhaustive list) of computer readable storage media include the following: a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), a static random access memory (SRAM), a portable compact disc read-only memory (CD-ROM), a digital versatile disk (DVD), a memory stick, a floppy disk, a mechanically encoded device such as punch-cards or raised structures in a groove having instructions recorded thereon, and any suitable combination of the foregoing. A computer readable storage medium, as used herein, is not to be construed as being transitory signals per se, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through a waveguide or other transmission media (e.g., light pulses passing through a fiber-optic cable), or electrical signals transmitted through a wire.

[0086] Computer readable program instructions described herein can be downloaded to respective computing / processing devices from a computer readable storage medium or to an external computer or external storage device via a network, for example, the Internet, a local area network, a wide area network and / or a wireless network. The network can comprise copper transmission cables, optical transmission fibers, wireless transmission, routers, firewalls, switches, gateway computers and / or edge servers. A network adapter card or network interface in each computing / processing device receives computer readable program instructions from the network and forwards the computer readable program instructions for storage in a computer readable storage medium within the respective computing / processing device.

[0087] Computer readable program instructions for carrying out operations of the present disclosure can be assembler instructions, instruction-set-architecture (ISA) instructions, machine instructions, machine dependent instructions, microcode, firmware instructions, state-setting data, or either source code or object code written in any combination of one or more programming languages, including an object oriented programming language such as Smalltalk, C++ or the like and conventional procedural programming languages, such as the "C" programming language or similar programming languages. The computer readable program instructions can execute entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer or entirely on the remote computer or server. In the latter scenario, the remote computer can be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection can be made to an external computer (for example, through the Internet using an Internet Service Provider). In some embodiments, electronic circuitry including, for example, programmable logic circuitry, field-programmable gate array (FPGA), or programmable logic array (PLA) can execute the computer readable program instructions by utilizing state information of the computer readable program instructions to personalize the electronic circuitry, in order to perform aspects of the present disclosure.

[0088] The computer readable program instructions can also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable apparatus or other device to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide processes for implementing the functions / acts specified in the flowchart and / or block diagram block or blocks.

[0089] These computer readable program instructions can be provided to a processor of a general purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions / acts specified in the flowchart and / or block diagram block or blocks. These computer readable program instructions can also be stored in a computer readable storage medium that can include random access memory (RAM), read only memory (ROM), electrically erasable programmable read only memory (EEPROM), flash memory or other data storage device. When the computer readable program instructions are loaded into the computer and other programmable data processing apparatus, a series of operational steps are implemented that provide processes such that the computer or other programmable apparatus provide processes for implementing the functions / acts specified in the flowchart and / or block diagram block or blocks.

[0090] The computer readable program instructions can also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable data processing apparatus or other device to produce a computer implemented process such that the instructions which execute on the computer, other programmable data processing apparatus, or other device implement the functions / acts specified in the flowchart and / or block diagram block or blocks.

[0091] The flow diagrams and the block diagrams in the drawings are presented to illustrate the architecture, functionality, and operation of possible implementations of systems, methods and computer program products according to various embodiments of the present disclosure. In this regard, each block in the flow diagrams and the block diagrams can represent a module, segment, or portion of instructions, which comprises one or more executable instructions for implementing the specified logic functions. In some alternative implementations, the functions noted in the blocks can occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks can sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and / or flow diagrams, and combinations thereof, can be implemented by special purpose hardware-based systems that perform the specified functions or acts, or combinations of special purpose hardware and

[0092] Embodiments of the present disclosure have been described above, and the description is intended to be illustrative of the embodiments and not restrictive. Many modifications and variations of the described embodiments are possible and are within the scope of the disclosure. The selection of terms is intended to best describe the principles of the embodiments, practical application, or improvement over the technology in the art, or to enable others skilled in the art to understand the embodiments disclosed herein.

Claims

1. A method for automatically solving algebraic problems, comprising: For an algebraic expression associated with an algebraic problem, identify several theorems that can be applied to the expression. Based on the algebraic expression, an artificial intelligence model is used to determine multiple scores for the multiple theorems, each score indicating the reasonableness of applying the corresponding theorem to the algebraic expression; Based on the multiple scores, the first set of theorems among the multiple theorems is applied to the algebraic expression to obtain the first set of algebraic expressions after transformation; Based on the first set of algebraic expressions, a second set of theorems is determined, wherein the theorems in the second set of theorems can be applied to at least one algebraic expression in the first set of algebraic expressions. Based on the second set of theorems and the first set of algebraic expressions, the second set of algebraic expressions is determined; as well as Based on the scores of the first set of theorems and the scores of the second set of theorems, at least one solution path is determined, and each solution path includes one algebraic expression from the first set of algebraic expressions and one algebraic expression from the second set of algebraic expressions.

2. The method of claim 1, wherein determining a plurality of theorems applicable to the algebraic expression associated with the algebraic problem comprises: Based on the analytic structure of the algebraic expression, the plurality of theorems applicable to the algebraic expression are determined, each theorem corresponding to a processing rule for at least one substructure in the analytic structure.

3. The method of claim 1, wherein determining a plurality of theorems applicable to the algebraic expression associated with the algebraic problem comprises: Input the algebraic expression into the mathematical analysis engine; as well as In response to determining that the mathematical analysis engine outputs multiple processed algebraic expressions based on multiple processing rules, the multiple theorems are determined, each theorem corresponding to at least one of the multiple processing rules.

4. The method according to any one of claims 1 to 3, further comprising: Based on the second set of algebraic expressions, the answer to the algebraic problem is determined.

5. The method according to claim 1, wherein the plurality of theorems are a first plurality of theorems, and determining the second set of theorems based on the first set of algebraic expressions includes: For the first algebraic expression in the first group of algebraic expressions, determine a second or more theorems that can be applied to the first algebraic expression; Determine multiple scores for the second plurality of theorems, each score indicating the reasonableness of applying the corresponding theorem to the first algebraic expression; as well as Based on the multiple scores of the second plurality of theorems, the second set of theorems is determined by selecting the theorems among the second plurality of theorems that have scores above a threshold.

6. The method according to any one of claims 1 to 3, further comprising displaying at least one of the following: The first set of theorems, The first set of algebraic expressions, or The answer to the algebraic problem.

7. The method according to claim 1, further comprising displaying the at least one solution path.

8. The method of claim 1, wherein the artificial intelligence model is trained based on a history of transformations of algebraic expressions in annotated problem-solving steps, the history of transformations comprising a sequence of transformed algebraic expressions based on at least one of the plurality of theorems.

9. An apparatus for automatically solving algebraic problems, comprising: Theorem-determining unit is configured to determine multiple theorems applicable to an algebraic expression associated with an algebraic problem. The scoring unit is configured to determine multiple scores for the multiple theorems based on the algebraic expression using an artificial intelligence model, each score indicating the reasonableness of applying the corresponding theorem to the algebraic expression; The theorem application unit is configured to apply a first set of theorems from the plurality of theorems to the algebraic expression based on the plurality of scores, so as to obtain a first set of algebraic expressions after transformation. The answer determination unit is configured to: determine a second set of theorems based on the first set of algebraic expressions, wherein the theorems in the second set of theorems can be applied to at least one algebraic expression in the first set of algebraic expressions; Based on the second set of theorems and the first set of algebraic expressions, the second set of algebraic expressions is determined; as well as The problem-solving path determination unit is configured to determine at least one problem-solving path based on the scores of the first set of theorems and the scores of the second set of theorems, each problem-solving path including an algebraic expression from the first set of algebraic expressions and an algebraic expression from the second set of algebraic expressions.

10. The apparatus of claim 9, wherein the theorem determining unit is configured to: Based on the analytic structure of the algebraic expression, the plurality of theorems applicable to the algebraic expression are determined, each theorem corresponding to a processing rule for at least one substructure in the analytic structure.

11. The apparatus of claim 9, wherein the theorem determining unit is configured to: Input the algebraic expression into the mathematical analysis engine; and In response to determining that the mathematical analysis engine outputs multiple processed algebraic expressions based on multiple processing rules, the multiple theorems are determined, each theorem corresponding to at least one of the multiple processing rules.

12. The apparatus according to any one of claims 9 to 11, wherein the answer determining unit is further configured to: Based on the second set of algebraic expressions, the answer to the algebraic problem is determined.

13. The apparatus according to any one of claims 9 to 11, further comprising a display unit configured to display at least one of the following: The first set of theorems, The first set of algebraic expressions, or The answer to the algebraic problem.

14. The apparatus of claim 9, wherein the artificial intelligence model is trained based on a transformation history of algebraic expressions in the problem-solving steps, the transformation history comprising a sequence of transformed algebraic expressions based on at least one of the plurality of theorems.

15. An electronic device comprising: Memory and processor; The memory is used to store one or more computer instructions, wherein the one or more computer instructions are executed by the processor to implement the method according to any one of claims 1 to 8.

16. A computer-readable storage medium having stored thereon one or more computer instructions, wherein the one or more computer instructions are executed by a processor to implement the method according to any one of claims 1 to 8.

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