CN110096675B - Double integral solving method, device, equipment and storage medium - Google Patents
Double integral solving method, device, equipment and storage medium Download PDFInfo
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Abstract
The invention discloses a double integral solving method, a double integral solving device, double integral solving equipment and a storage medium. Firstly, receiving character information input into each text control, and splicing each character information to obtain target double integral information; then analyzing the target double integral information, extracting an integrated function and upper and lower limits of each function variable from an analysis result, respectively obtaining the position information of the upper and lower limits of each function variable in the target double integral information, and determining an integral input mode corresponding to the target double integral information according to the position information of the upper and lower limits of each function variable in the target double integral information; and finally solving the target double integral information based on the integral input mode and the integrated function, so that the input modes of various different double integral information can be successfully identified, a more free double integral information input selection mode can be provided for a user, and the double integral computing equipment is more convenient to use.
Description
Technical Field
The invention relates to the technical field of double integral equations, in particular to a double integral solving method, a double integral solving device, double integral solving equipment and a storage medium.
Background
With the development of mathematical algorithms, mathematical algorithms have a significant role in more and more fields. Algorithms are a specific step of computation and are commonly used for computation, data processing and automatic reasoning. Algorithms, which refer to an accurate and complete description of a solution and are a series of clear instructions for solving a problem, represent a strategic mechanism for describing a solution to a problem in a systematic way.
Currently, there are multiple solving methods for one double integral, and when a user uses a special double integral computing device (such as a special double integral calculator), the user can only input three integral input modes when inputting integral information, and a special calculator such as other input modes equivalent to the three integral input modes cannot recognize the integral input modes.
The different integral input modes represent different double integral solving methods, if an input interface is designed for each double integral solving method, the user is required to select a designated integral input mode from a plurality of solving methods to input information, and the calculation process of data transmitted from each interface is different, which obviously brings great inconvenience to the user.
The foregoing is provided merely for the purpose of facilitating understanding of the technical solutions of the present invention and is not intended to represent an admission that the foregoing is prior art.
Disclosure of Invention
The invention mainly aims to provide a double integral solving method, device, equipment and storage medium, which aim to solve the technical problem that in the prior art, the double integral cannot be successfully calculated due to the fact that an integral input mode of a user cannot be identified.
In order to achieve the above object, the present invention provides a double integral solving method, which includes the steps of:
receiving character information input into each text control;
splicing the character information to obtain target double integral information;
analyzing the target double integral information, and extracting an integrated function and upper and lower limits of each function variable from an analysis result;
respectively acquiring the position information of the upper limit and the lower limit of each function variable in the target double integral information;
determining an integral input mode corresponding to the target double integral information according to the position information of the upper limit and the lower limit of each function variable in the target double integral information;
and solving the target double integral information based on the integral input mode and the integrated function.
Preferably, the step of determining the integral input mode corresponding to the target double integral information according to the position information of the upper and lower limits of each function variable in the target double integral information specifically includes:
dividing the target double integral information according to the position information of the upper limit and the lower limit of each function variable in the target double integral information;
and determining an integral input mode corresponding to the target double integral information according to the segmentation result.
Preferably, the step of dividing the target double integral information according to the position information of the upper and lower limits of each function variable in the target double integral information specifically includes:
setting an initial variable of a function to be integrated, and setting initial variables of upper and lower limits of the function variable;
sending the integrated function into the integrated function initial variable to obtain first integrated information;
the position information of the upper limit and the lower limit of each function variable in the target double integral information is sent into the initial variable of the upper limit and the lower limit of the function variable, and second integral information is obtained;
correspondingly, the step of determining the integral input mode corresponding to the target double integral information according to the segmentation result specifically comprises the following steps:
dividing the target double integral information based on the first integral information and the second integral information, and determining an integral input mode corresponding to the target double integral information according to a dividing result.
Preferably, after the step of setting the initial variable of the integrated function and the initial variable of the upper and lower limits of the function variable, the method further includes:
setting a binary function initial variable;
searching whether a binary function exists in the analysis result of the target double integral information, and if so, sending the binary function into the binary function variable to obtain third integral information;
accordingly, the step of dividing the target double integral information based on the first integral information and the second integral information, and determining an integral input mode corresponding to the target double integral information according to a division result specifically includes:
dividing the target double integral information based on the first integral information, the second integral information and the third integral information, and determining an integral input mode corresponding to the target double integral information according to a dividing result.
Preferably, the step of solving the target double integral information based on the integral input mode and the integrand specifically includes:
extracting an integration interval corresponding to the target double integration information based on the integration input mode;
and solving the target double integral information according to the integrated function and the integral interval.
Preferably, the step of splicing the character information to obtain the target double integral information specifically includes:
acquiring a preset priority relation among the text controls;
and splicing the character information according to the preset priority relation to obtain target double integral information.
Preferably, before the step of splicing the character information according to the preset priority relation to obtain the target double integral information, the method further includes:
traversing the character information in each text control, and judging the character information as calculus information when character strings matched with the integrated function format and the parameter format exist in the traversing result;
searching target symbols in character information in each text control, and counting the number of the searched target symbols;
and when the number of the target symbols is a preset number threshold, executing the step of splicing the character information according to the preset priority relation to obtain target double integral information.
In addition, in order to achieve the above object, the present invention also proposes a double integral solving apparatus, the apparatus comprising:
the receiving module is used for receiving character information input into each text control;
the splicing module is used for splicing the character information to obtain target double integral information;
the analysis module is used for analyzing the target double integral information, extracting an integrated function and upper and lower limits of each function variable from an analysis result, and respectively acquiring the position information of the upper and lower limits of each function variable in the target double integral information;
the determining module is used for determining an integral input mode corresponding to the target double integral information according to the position information of the upper limit and the lower limit of each function variable in the target double integral information;
and the solving module is used for solving the target double integral information based on the integral input mode and the integrand function.
In addition, to achieve the above object, the present invention also proposes an apparatus for double integration solution, the apparatus comprising: a memory, a processor, and a double-integral solver stored on the memory and executable on the processor, the double-integral solver configured to implement the steps of the double-integral solver method as described above.
In addition, in order to achieve the above object, the present invention also proposes a storage medium, which is a computer-readable storage medium, on which a double-integral solving program is stored, which when executed by a processor, implements the steps of the double-integral solving method as described above.
Firstly, receiving character information input into each text control, and splicing each character information to obtain target double integral information; then analyzing the target double integral information, extracting an integrated function and upper and lower limits of each function variable from an analysis result, respectively obtaining the position information of the upper and lower limits of each function variable in the target double integral information, and determining an integral input mode corresponding to the target double integral information according to the position information of the upper and lower limits of each function variable in the target double integral information; and finally solving the target double integral information based on the integral input mode and the integrated function, so that the input modes of various different double integral information can be successfully identified, a more free double integral information input selection mode can be provided for a user, and the double integral computing equipment is more convenient to use.
Drawings
FIG. 1 is a schematic diagram of a device of a hardware operating environment according to an embodiment of the present invention;
FIG. 2 is a flow chart of a first embodiment of a double-integral solving method of the present invention;
FIG. 3 is a schematic diagram of an input interface of a program corresponding to a double-integral solving method according to an embodiment of the invention;
FIG. 4 is a flow chart of a second embodiment of the double-integral solving method of the present invention;
fig. 5 is a functional block diagram of a double integral solving device according to the present invention.
The achievement of the objects, functional features and advantages of the present invention will be further described with reference to the accompanying drawings, in conjunction with the embodiments.
Detailed Description
It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
Referring to fig. 1, fig. 1 is a schematic structural diagram of a terminal device of a hardware running environment according to an embodiment of the present invention.
As shown in fig. 1, the apparatus for double integration solution may include: a processor 1001, such as a controller or microprocessor, a communication bus 1002, a user interface 1003, a memory 1004. Wherein the communication bus 1002 is used to enable connected communication between these components. The user interface 1003 may include a Display screen (Display), an input unit such as interface buttons. The memory 1004 may be a high-speed RAM memory or a stable memory (non-volatile memory).
Those skilled in the art will appreciate that the structure shown in fig. 1 does not constitute a limitation of the apparatus for double integration solution, and may include more or fewer components than shown, or certain components in combination, or a different arrangement of components.
As shown in fig. 1, a program for operating system, user receiving module, and double integration solving may be included in the memory 1004 as one storage medium.
It is understood that the apparatus for double-integral solution of the present embodiment may be a calculator for performing double-integral solution; the apparatus of the present invention performs double-integral solution calculation by the processor 1001 calling a program of double-integral solution stored in the memory 1005.
The implementation of the invention is based on the hardware structure, and the embodiment of the double integral solving method is provided.
It should be noted that, in the prior art, when calculating a specific double integral, integral information needs to be submitted through an input interface. In the prior art computing double integration devices, there are three input formats that can be used to provide the integration information. The three formats are as follows:
the first format, f (x, y), y1 (x) <=yx < =y2 (x), a < =x < =b, at which time the formula for calculating the double integral is as follows:
in the second format, f (x, y), x1 (y) <=xy < =x2 (y), c < =y < =d, where the formula for calculating the double integral is as follows:
the third format, f (x, y), r1 (t) <=rt < =r2 (t), α < =t < =β, where the formula for calculating the double integral is as follows:
however, the integration information equivalent to the first format also has the following 5 cases:
y1(x)<＝yx<＝y2(x),f(x,y),a<＝x<＝b；
f(x,y),a<＝x<＝b,y1(x)<＝yx<＝y2(x)；
a<＝x<＝b,f(x,y),y1(x)<＝yx<＝y2(x)；
y1(x)<＝yx<＝y2(x),a<＝x<＝b,f(x,y)；
a<＝x<＝b,y1(x)<＝yx<＝y2(x),f(x,y)。
the integration information equivalent to the second format also has the following 5 cases:
x1(y)<＝xy<＝x2(y),f(x,y),c<＝y<＝d；
f(x,y),c<＝y<＝d,x1(y)<＝xy<＝x2(y)；
c<＝y<＝d,f(x,y),x1(y)<＝xy<＝x2(y)；
x1(y)<＝xy<＝x2(y),c<＝y<＝d,f(x,y)；
c<＝y<＝d,x1(y)<＝xy<＝x2(y),f(x,y)。
the integration information equivalent to the third format also has the following 5 cases:
r1(t)<＝rt<＝r2(t),f(x,y),α<＝t<＝β；
f(x,y),α<＝t<＝β,r1(t)<＝rt<＝r2(t)；
α<＝t<＝β,f(x,y),r1(t)<＝rt<＝r2(t)；
r1(t)<＝rt<＝r2(t),α<＝t<＝β,f(x,y)；
α<＝t<＝β,r1(t)<＝rt<＝r2(t),f(x,y)。
in the prior art, the double integral calculator can only recognize the first, second and third integral input modes, and from the perspective of a user, the double integral calculator should recognize the other 15 modes.
Therefore, in order to make the input requirements of the double-integral computing device on the user more reasonable, the problem of 18 input modes identification needs to be solved, and referring to fig. 2, a flowchart of a first embodiment of a double-integral solving method of the present invention is shown in fig. 2.
In this embodiment, the method for solving the double integral includes the following steps:
step S10: receiving character information input into each text control;
the execution body of the present embodiment is essentially the processor of the apparatus for solving the double integral. Referring to fig. 3, fig. 3 is a schematic diagram of an input interface corresponding to a program loaded in the apparatus for double-integration solution according to the present embodiment, where the program is a double-integration solution program loaded in the apparatus for double-integration solution, and the double-integration solution program may be understood as a dedicated input interface, and in the following description, the present embodiment uses the input interface as an execution subject of the method according to the present embodiment.
In a specific implementation, the user submits the point information through the input interface. In order to enhance the freedom degree of the user, the user only needs to select one or two of the three input boxes to finish input when inputting specifically, and the integral information is not necessarily input in each input box.
Step S20: splicing the character information to obtain target double integral information;
specifically, a preset priority relation among the text controls is obtained; it can be understood that, in this embodiment, the priority of each text control may be set in advance, and this embodiment may use the order of the input boxes from top to bottom in fig. 3 as the preset priority between each text box control (input box).
And splicing the character information according to the preset priority relation to obtain target double integral information.
It will be appreciated that no matter how the user fills in the credit information in the interface of fig. 3, the final submission must be a complete message to calculate the double credit. Thus, receiving user information from the input interface and stitching into a string may provide for subsequent pattern recognition.
Let the string variable corresponding to the first frame be S1S 1 The string variable corresponding to the middle frame is S2S 2 The character string variable corresponding to the lowest frame is S3S 3 The process of splicing the integral information input by the user for the SS by using the character string variable is as follows:
if it is
And->
And->
Then s=s1 ++ ' +. S2+ ' + and ' +S3;
if it is
And->
And s3 noteq 0, then s=s2+.' ++ S3;
if it is
And->
And s3 noteq 0, then s=s1+' ++ S3;
if S1+.0 and
and s3 noteq 0, then s=s1+' ++ S2;
if s1=0 and
and s3+.0, then s=s3;
if s1=0 and s2+.0 and s3=0, then s=s2;
if s1+ 0 and s2=0, s=s1.
Step S30: analyzing the target double integral information, extracting an integrated function and upper and lower limits of each function variable from an analysis result, and respectively obtaining position information of the upper and lower limits of each function variable in the target double integral information;
it can be understood that, in order for the processor of the above apparatus for solving double integral to accurately understand the intention of the user, the input information of the user needs to be translated, in a specific implementation, the target double integral information needs to be resolved first, and the upper and lower limits of the integrated function and the two integral variables are obtained from the resolved result. For convenience of description, the following conventions are first made: (setting substring)
(1)f 1 Indicating the presence of substring 'in the information entered by the user'<＝x<Position='s;
(2)f 2 indicating the presence of substring 'in the information entered by the user'<＝y<Position='s;
(3)f 3 indicating the presence of substring 'in the information entered by the user'<＝t<Position='s;
(4)f 4 indicating the presence of substring 'in the information entered by the user'<＝yx<Position='s;
(5)f 5 indicating the presence of substring 'in the information entered by the user'<＝xy<Position='s;
(6)f 6 indicating the presence of substring 'in the information entered by the user'<＝rt<Position='s;
(7) fs1 represents the position of the first comma in the information entered by the user;
(8) fs2fs2 represents the location of the second comma in the information entered by the user;
(9) stage1 represents a variable used to store y1 (x) <=yx < =y2 (x) or x1 (y) <=xy < =x2 (y) or r1 (t) <=rt < =r2 (t);
(10) stage2 represents a variable used to store a < = x < = b or c < = y < = d or α < = t < = β;
(11) func denotes a variable used to store the binary function f (x, y);
step S40: determining an integral input mode corresponding to the target double integral information according to the position information of the upper limit and the lower limit of each function variable in the target double integral information;
specifically, in the process of executing the step S40, the target double integral information is first divided according to the position information of the upper and lower limits of each function variable in the target double integral information;
in the specific implementation, a integrand initial variable stage1 is set, and a function variable upper and lower limit initial variable stage2 is set; setting a binary function initial variable func;
sending the integrated function into an initial variable stage1 of the integrated function to obtain first integrated information; the position information of the upper and lower limits of each function variable in the target double integral information is sent into an initial variable stage2 of the upper and lower limits of the function variable, and second integral information is obtained;
in addition, whether a binary function exists or not is also searched from the analysis result of the target double integral information, and if yes, the binary function is sent into the binary function variable func to obtain third integral information;
and then determining an integral input mode corresponding to the target double integral information according to the segmentation result.
In a specific implementation, the target double integral information is divided based on the first integral information, the second integral information and the third integral information, and an integral input mode corresponding to the target double integral information is determined according to a division result.
For example, let s=s 1 s 2 …s n If the target double integral information is the target double integral information, the segmentation process of the character string S corresponding to the target double integral information is as follows:
step one, if f 1 >0 and f 4 >0, the integrand and integration interval are partitioned as follows:
(1) If f 1 <fs1 and fs1<f 4 <fs2, then stage1=s fs1+1 s fs1+2 …s fs2-1 ，stage2＝s 1 s 2 …s fs1-1 ，func＝s fs2+1 s fs2+2 …s n The method comprises the steps of carrying out a first treatment on the surface of the The integral input mode corresponding to the character information input by the user can be successfully identified, and the integral information according to the integral input mode is as follows:
a<＝x<＝b,y1(x)<＝yx<＝y2(x),f(x,y)
the data to the right of the stage1 equal sign is the first integral signal, the data to the right of the stage2 equal sign is the second integral signal, and the data to the right of the func equal sign is the third integral information.
(2) If f 4 <fs1 and fs1<f 1 <fs2, then stage2=s fs1+1 s fs1+2 …s fs2-1 ，stage1＝s 1 s 2 …s fs1-1 ，func＝s fs2+1 s fs2+2 …s n The method comprises the steps of carrying out a first treatment on the surface of the The integral input mode corresponding to the character information input by the user can be successfully identified, and the integral information according to the integral input mode is as follows:
y1(x)<＝yx<＝y2(x),a<＝x<＝b,f(x,y)
(3) If f 1 <fs1 and f 4 >fs2, func=s fs1+1 s fs1+2 …s fs2-1 ，stage2＝s 1 s 2 …s fs1-1 ，stage1＝s fs2+1 s fs2+2 …s n The method comprises the steps of carrying out a first treatment on the surface of the The integral input mode corresponding to the character information input by the user can be successfully identified, and the integral information according to the integral input mode is as follows:
a<＝x<＝b,f(x,y),y1(x)<＝yx<＝y2(x)
(4) If fs1<f 1 <fs2 and f 4 >fs2, then stage2=s fs1+1 s fs1+2 …s fs2-1 ，func＝s 1 s 2 …s fs1-1 ，stage1＝s fs2+1 s fs2+2 …s n The method comprises the steps of carrying out a first treatment on the surface of the The integral input mode corresponding to the character information input by the user can be successfully identified, and the integral information according to the integral input mode is as follows:
f(x,y),a<＝x<＝b,y1(x)<＝yx<＝y2(x)
(5) If f 4 <fs1 and f 1 >fs2, func=s fs1+1 s fs1+2 …s fs2-1 ，stage1＝s 1 s 2 …s fs1-1 ，stage2＝s fs2+1 s fs2+2 …s n The method comprises the steps of carrying out a first treatment on the surface of the The integral input mode corresponding to the character information input by the user can be successfully identified, and the integral information according to the integral input mode is as follows:
y1(x)<＝yx<＝y2(x),f(x,y),a<＝x<＝b
(6) If fs1<f 4 <fs2 and f 1 >fs2, then stage1=s fs1+1 s fs1+2 …s fs2-1 ，func＝s 1 s 2 …s fs1-1 ，stage2＝s fs2+1 s fs2+2 …s n . The integral input mode corresponding to the character information input by the user can be successfully identified, and the integral information according to the integral input mode is as follows:
f(x,y),y1(x)<＝yx<＝y2(x),a<＝x<＝b
step two, if f 2 >0 and f 5 >0, the integrand and integration interval are partitioned as follows:
(1) If f 2 <fs1 and fs1<f 5 <fs2, then stage1=s fs1+1 s fs1+2 …s fs2-1 ，stage2＝s 1 s 2 …s fs1-1 ，func＝s fs2+1 s fs2+2 …s n The method comprises the steps of carrying out a first treatment on the surface of the The integral input mode corresponding to the character information input by the user can be successfully identified, and the integral information according to the integral input mode is as follows:
c<＝y<＝d,x1(y)<＝xy<＝x2(y),f(x,y)
(2) If f 5 <fs1 and fs1<f 2 <fs2, then stage2=s fs1+1 s fs1+2 …s fs2-1 ，stage1＝s 1 s 2 …s fs1-1 ，func＝s fs2+1 s fs2+2 …s n The method comprises the steps of carrying out a first treatment on the surface of the The integral input mode corresponding to the character information input by the user can be successfully identified, and the integral information according to the integral input mode is as follows:
x1(y)<＝xy<＝x2(y),c<＝y<＝d,f(x,y)
(3) If f 2 <fs1 and f 5 >fs2, func=s fs1+1 s fs1+2 …s fs2-1 ，stage2＝s 1 s 2 …s fs1-1 ，stage1＝s fs2+1 s fs2+2 …s n The method comprises the steps of carrying out a first treatment on the surface of the The integral input mode corresponding to the character information input by the user can be successfully identified, and the integral information according to the integral input mode is as follows:
c<＝y<＝d,f(x,y),x1(y)<＝xy<＝x2(y)
(4) If fs1<f 2 <fs2 and f 5 >fs2, then stage2=s fs1+1 s fs1+2 …s fs2-1 ，func＝s 1 s 2 …s fs1-1 ，stage1＝s fs2+1 s fs2+2 …s n The method comprises the steps of carrying out a first treatment on the surface of the The integral input mode corresponding to the character information input by the user can be successfully identified, and the integral information according to the integral input mode is as follows:
f(x,y),c<＝y<＝d,x1(y)<＝xy<＝x2(y)
(5) If f 5 <fs1 and f 2 >fs2, func=s fs1+1 s fs1+2 …s fs2-1 ，stage1＝s 1 s 2 …s fs1-1 ，stage2＝s fs2+1 s fs2+2 …s n The method comprises the steps of carrying out a first treatment on the surface of the The integral input mode corresponding to the character information input by the user can be successfully identified, and the integral information according to the integral input mode is as follows:
x1(y)<＝xy<＝x2(y),f(x,y),c<＝y<＝d
(6) If fs1<f 5 <fs2 and f 2 >fs2, then stage1=s fs1+1 s fs1+2 …s fs2-1 ，func＝s 1 s 2 …s fs1-1 ，stage2＝s fs2+1 s fs2+2 …s n . The integral input mode corresponding to the character information input by the user can be successfully identified, and the integral information according to the integral input mode is as follows:
f(x,y),x1(y)<＝xy<＝x2(y),c<＝y<＝d
step three, if f 3 >0 and f 6 >0, the integrand and integration interval are partitioned as follows:
(1) If f 3 <fs1 and fs1<f 6 <fs2, then stage1=s fs1+1 s fs1+2 …s fs2-1 ，stage2＝s 1 s 2 …s fs1-1 ，func＝s fs2+1 s fs2+2 …s n The method comprises the steps of carrying out a first treatment on the surface of the Namely, the integral input mode corresponding to the character information input by the user can be successfully recognized finally, and finallyThe integration information according to the integration input mode is:
α<＝t<＝β,r1(t)<＝rt<＝r2(t),f(x,y)
(2) If f 6 <fs1 and fs1<f 3 <fs2, then stage2=s fs1+1 s fs1+2 …s fs2-1 ，stage1＝s 1 s 2 …s fs1-1 ，func＝s fs2+1 s fs2+2 …s n The method comprises the steps of carrying out a first treatment on the surface of the The integral input mode corresponding to the character information input by the user can be successfully identified, and the integral information according to the integral input mode is as follows:
r1(t)<＝rt<＝r2(t),α<＝t<＝β,f(x,y)
(3) If f 3 <fs1 and f 6 >fs2, func=s fs1+1 s fs1+2 …s fs2-1 ，stage2＝s 1 s 2 …s fs1-1 ，stage1＝s fs2+1 s fs2+2 …s n The method comprises the steps of carrying out a first treatment on the surface of the The integral input mode corresponding to the character information input by the user can be successfully identified, and the integral information according to the integral input mode is as follows:
α<＝t<＝β,f(x,y),r1(t)<＝rt<＝r2(t)
(4) If fs1<f 3 <fs2 and f 6 >fs2, then stage2=s fs1+1 s fs1+2 …s fs2-1 ，func＝s 1 s 2 …s fs1-1 ，stage1＝s fs2+1 s fs2+2 …s n The method comprises the steps of carrying out a first treatment on the surface of the The integral input mode corresponding to the character information input by the user can be successfully identified, and the integral information according to the integral input mode is as follows:
f(x,y),α<＝t<＝β,r1(t)<＝rt<＝r2(t)
(5) If f 6 <fs1 and f 3 >fs2, func=s fs1+1 s fs1+2 …s fs2-1 ，stage1＝s 1 s 2 …s fs1-1 ，stage2＝s fs2+1 s fs2+2 …s n The method comprises the steps of carrying out a first treatment on the surface of the I.e. the integral input mode corresponding to the character information input by the user can be successfully identified finally,and finally, the integral information according to the integral input mode is as follows:
r1(t)<＝rt<＝r2(t),f(x,y),α<＝t<＝β
(6) If fs1<f 6 <fs2 and f 3 >fs2, then stage1=s fs1+1 s fs1+2 …s fs2-1 ，func＝s 1 s 2 …s fs1-1 ，stage2＝s fs2+1 s fs2+2 …s n . The integral input mode corresponding to the character information input by the user can be successfully identified, and the integral information according to the integral input mode is as follows:
f(x,y),r1(t)<＝rt<＝r2(t),α<＝t<＝β
step S50: and solving the target double integral information based on the integral input mode and the integrated function.
Specifically, in executing the step S50, an integration interval corresponding to the target double integration information is first extracted based on the integration input pattern;
and then solving the target double integral information according to the integrated function and the integral interval.
In a specific implementation, the embodiment uses VC6.0 as a test tool, and the test is completed on a personal desktop computer with a CPU of 3.2GHz and a memory of 1.86 GB.
For example, calculating
Double integration on D, where D is represented by x 2 +y 2 The closed area in the first quadrant enclosed by the coordinate axes=1.
The calculation questions are analyzed by human calculation as follows: the user has 18 input modes to calculate the double integral:
(1)sqrt((1-x^2-y^2)/(1+x^2+y^2)),-sqrt(1-x^2)<＝yx<＝sqrt(1-x^2),-1<＝x<＝1；
(2)-sqrt(1-x^2)<＝yx<＝sqrt(1-x^2),sqrt((1-x^2-y^2)/(1+x^2+y^2)),-1<＝x<＝1；
(3)sqrt((1-x^2-y^2)/(1+x^2+y^2)),-1<＝x<＝1,-sqrt(1-x^2)<＝yx<＝sqrt(1-x^2)；
(4)-1<＝x<＝1,sqrt((1-x^2-y^2)/(1+x^2+y^2)),-sqrt(1-x^2)<＝yx<＝sqrt(1-x^2)；
(5)-sqrt(1-x^2)<＝yx<＝sqrt(1-x^2),-1<＝x<＝1,sqrt((1-x^2-y^2)/(1+x^2+y^2))；
(6)-1<＝x<＝1,-sqrt(1-x^2)<＝yx<＝sqrt(1-x^2),sqrt((1-x^2-y^2)/(1+x^2+y^2))；
(7)sqrt((1-x^2-y^2)/(1+x^2+y^2)),-sqrt(1-y^2)<＝xy<＝sqrt(1-y^2),-1<＝y<＝1；
(8)-sqrt(1-y^2)<＝xy<＝sqrt(1-y^2),sqrt((1-x^2-y^2)/(1+x^2+y^2)),-1<＝y<＝1；
(9)sqrt((1-x^2-y^2)/(1+x^2+y^2)),-1<＝y<＝1,-sqrt(1-y^2)<＝xy<＝sqrt(1-y^2)；
(10)-1<＝y<＝1,sqrt((1-x^2-y^2)/(1+x^2+y^2)),-sqrt(1-y^2)<＝xy<＝sqrt(1-y^2)；
(11)-sqrt(1-y^2)<＝xy<＝sqrt(1-y^2),-1<＝y<＝1,sqrt((1-x^2-y^2)/(1+x^2+y^2))；
(12)-1<＝y<＝1,-sqrt(1-y^2)<＝xy<＝sqrt(1-y^2),sqrt((1-x^2-y^2)/(1+x^2+y^2)
(13)sqrt((1-t^2)/(1+t^2)),-sqrt(1-(r*cos(t))^2)<＝rt<＝sqrt(1-(r*sin(t))^2),0<＝t<＝2*pi；
(14)-sqrt(1-(r*cos(t))^2)<＝rt<＝sqrt(1-(r*sin(t))^2),sqrt((1-t^2)/(1+t^2)),0<＝t<＝2*pi；
(15)sqrt((1-t^2)/(1+t^2)),0<＝t<＝2*pi,-sqrt(1-(r*cos(t))^2)<＝rt<＝sqrt(1-(r*sin(t))^2)；
(16)0<＝t<＝2*pi,sqrt((1-t^2)/(1+t^2)),-sqrt(1-(r*cos(t))^2)<＝rt<＝sqrt(1-(r*sin(t))^2)；
(17)-sqrt(1-(r*cos(t))^2)<＝rt<＝sqrt(1-(r*sin(t))^2),0<＝t<＝2*pi,sqrt((1-t^2)/(1+t^2))；
(18)0<＝t<＝2*pi,-sqrt(1-(r*cos(t))^2)<＝rt<＝sqrt(1-(r*sin(t))^2),sqrt((1-t^2)/(1+t^2))。
if the integration mode input by the user is any one of the above (1) to (6), after the processor of the double-integration solving device determines the corresponding integration input mode, the double-integration is calculated by using the following method:
if the integration mode input by the user is any one of the above (7) to (12), after the processor of the double-integration solving device determines the corresponding integration input mode, the double-integration is calculated by using the following method:
if the integration mode input by the user is any one of the above (13) to (18), after the processor of the double-integration solving device determines the corresponding integration input mode, the double-integration is calculated by using the following method:
firstly, receiving character information input into each text control, and splicing each character information to obtain target double integral information; then analyzing the target double integral information, extracting an integrated function and upper and lower limits of each function variable from an analysis result, respectively obtaining the position information of the upper and lower limits of each function variable in the target double integral information, and determining an integral input mode corresponding to the target double integral information according to the position information of the upper and lower limits of each function variable in the target double integral information; and finally solving the target double integral information based on the integral input mode and the integrated function, so that the input modes of various different double integral information can be successfully identified, a more free double integral information input selection mode can be provided for a user, and the double integral computing equipment is more convenient to use.
Namely, the embodiment encapsulates the double integral solving method into an input interface, and can accept various reasonable integral information input by a user to the maximum extent. First, the interface can discern all the correct formats of user input. And secondly, information input by a user can be spliced, so that the interface can conveniently extract the upper and lower limits of the integrated function and the variable. Finally, we have devised that we can extract the integrand and the integration interval from the 18 correct input formats. In a word, through the design of intelligent input interface, can provide the input of the double integral information that is more free for the user, make the use of double integral computing equipment more convenient.
Referring to fig. 4, a second embodiment of a method for solving a double integral of the present invention is presented based on the first embodiment of the method for solving a double integral, and fig. 4 is a schematic flow chart of the second embodiment of the method for solving a double integral of the present invention.
In this embodiment, the step of splicing the character information according to the preset priority relationship to obtain the target double integral information further includes:
substep S201: traversing the character information in each text control, and judging the character information as calculus information when character strings matched with the integrated function format and the parameter format exist in the traversing result;
sub-step S202: searching target symbols in character information in each text control, and counting the number of the searched target symbols;
substep S203: and when the number of the target symbols is a preset number threshold, executing the step of splicing the character information according to the preset priority relation to obtain target double integral information.
In a specific implementation, the target symbol in this embodiment is preferably a comma, or is preferably an operator "<=", and when the number of commas in the integral information input by the user is only 2, the integral information input by the user is considered to be double integral information; or when the number of "<=" substrings in the integral information input by the user reaches 4, the integral information input by the user is recognized as double integral information.
According to the method and the device, the point type corresponding to the character information can be quickly identified to be double-point according to the number of target symbols in the character information input by the user.
In addition, the embodiment of the invention also provides a double integral solving device. As shown in fig. 5, the double integral solving apparatus includes: the system comprises a receiving module 10, a splicing module 20, an analyzing module 30, a determining module 40 and a solving module 50.
The receiving module 10 is used for receiving character information input into each text control;
the splicing module 20 is used for splicing the character information to obtain target double integral information;
the analysis module 30 is configured to analyze the target double integral information, extract an integrated function and upper and lower limits of each function variable from an analysis result, and respectively obtain position information of the upper and lower limits of each function variable in the target double integral information;
a determining module 40, configured to determine an integral input mode corresponding to the target double integral information according to position information of upper and lower limits of each function variable in the target double integral information;
a solving module 50 is configured to solve the target double integral information based on the integral input mode and the integrand.
It is clear from the above description that the double-integral solving apparatus of this embodiment may be understood as a double-integral solving program loaded in the double-integral solving device, and the double-integral solving program may be understood as a dedicated input interface, that is, this embodiment encapsulates the double-integral solving method into one input interface, so as to accept various reasonable integral information input by a user to the maximum extent. First, the interface can discern all the correct formats of user input. And secondly, information input by a user can be spliced, so that the interface can conveniently extract the upper and lower limits of the integrated function and the variable. Finally, we have devised that we can extract the integrand and the integration interval from the 18 correct input formats. In a word, through the design of intelligent input interface, can provide the input of the double integral information that is more free for the user, make the use of double integral computing equipment more convenient.
In addition, it should be noted that the above embodiment of the apparatus is merely illustrative, and does not limit the scope of the present invention, and in practical application, a person skilled in the art may select some or all modules according to actual needs to achieve the purpose of the embodiment, which is not limited herein.
In addition, technical details not described in detail in this embodiment may refer to the double integral solving method embodiment provided in any embodiment of the present invention, which is not described herein.
In addition, the embodiment of the invention also provides a storage medium which is a computer readable storage medium, wherein a double integral solving program is stored on the computer readable storage medium, and the double integral solving program realizes the steps of the double integral solving method when being executed by a processor.
It should be noted that, in this document, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or system 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 system. Without further limitation, an element defined by the phrase "comprising one … …" does not exclude the presence of other like elements in a process, method, article, or system that comprises the element.
The foregoing embodiment numbers of the present invention are merely for the purpose of description, and do not represent the advantages or disadvantages of the embodiments.
From the above description of the embodiments, it will be clear to those skilled in the art that the above-described embodiment method may be implemented by means of software plus a necessary general hardware platform, but of course may also be implemented by means of hardware, but in many cases the former is a preferred embodiment. Based on such understanding, the technical solution of the present invention may be embodied essentially or in a part contributing to the prior art in the form of a software product stored in a storage medium (e.g. read-only memory/random-access memory, magnetic disk, optical disk), comprising instructions for causing a terminal device (which may be a mobile phone, a computer, a server, an air conditioner, or a network device, etc.) to perform the method according to the embodiments of the present invention.
The foregoing description is only of the preferred embodiments of the present invention, and is not intended to limit the scope of the invention, but rather is intended to cover any equivalents of the structures or equivalent processes disclosed herein or in the alternative, which may be employed directly or indirectly in other related arts.
Claims (6)
1. A double-integral solving apparatus, characterized in that the double-integral solving apparatus includes: a memory, a processor, and a double-integral solver stored on the memory and executable on the processor, the double-integral solver configured to implement the steps of:
receiving character information input into each text control;
splicing the character information to obtain target double integral information;
analyzing the target double integral information, and extracting an integrated function and upper and lower limits of each function variable from an analysis result;
respectively acquiring the position information of the upper limit and the lower limit of each function variable in the target double integral information;
determining an integral input mode corresponding to the target double integral information according to the position information of the upper limit and the lower limit of each function variable in the target double integral information;
solving the target double integral information based on the integral input mode and the integrand function;
the determining an integral input mode corresponding to the target double integral information according to the position information of the upper and lower limits of each function variable in the target double integral information specifically comprises the following steps:
dividing the target double integral information according to the position information of the upper limit and the lower limit of each function variable in the target double integral information;
determining an integral input mode corresponding to the target double integral information according to the segmentation result;
the dividing the target double integral information according to the position information of the upper and lower limits of each function variable in the target double integral information specifically comprises the following steps:
setting an initial variable of a function to be integrated, and setting initial variables of upper and lower limits of the function variable;
sending the integrated function into the integrated function initial variable to obtain first integrated information;
the position information of the upper limit and the lower limit of each function variable in the target double integral information is sent into the initial variable of the upper limit and the lower limit of the function variable, and second integral information is obtained;
correspondingly, the step of determining the integral input mode corresponding to the target double integral information according to the segmentation result specifically comprises the following steps:
dividing the target double integral information based on the first integral information and the second integral information, and determining an integral input mode corresponding to the target double integral information according to a dividing result;
after the initial variables of the integrated function are set, and the initial variables of the upper limit and the lower limit of the function variables are set, the double-integral solver is configured to realize the following steps:
setting a binary function initial variable;
searching whether a binary function exists in the analysis result of the target double integral information, and if so, sending the binary function into the binary function variable to obtain third integral information;
accordingly, the step of dividing the target double integral information based on the first integral information and the second integral information, and determining an integral input mode corresponding to the target double integral information according to a division result specifically includes:
dividing the target double integral information based on the first integral information, the second integral information and the third integral information, and determining an integral input mode corresponding to the target double integral information according to a dividing result.
2. The apparatus of claim 1, wherein the solving the target double integral information based on the integral input pattern and the integrand comprises:
extracting an integration interval corresponding to the target double integration information based on the integration input mode;
and solving the target double integral information according to the integrated function and the integral interval.
3. The apparatus according to any one of claims 1-2, wherein the splicing the character information to obtain the target double integral information specifically includes:
acquiring a preset priority relation among the text controls;
and splicing the character information according to the preset priority relation to obtain target double integral information.
4. The apparatus of claim 3, wherein before the splicing the character information according to the preset priority relationship to obtain the target double integral information, the double integral solver is configured to implement the following steps:
traversing the character information in each text control, and judging the character information as calculus information when character strings matched with the integrated function format and the parameter format exist in the traversing result;
searching target symbols in character information in each text control, and counting the number of the searched target symbols;
when the number of the target symbols is a preset number threshold, executing the step of splicing the character information according to the preset priority relation to obtain target double integral information;
the determining an integral input mode corresponding to the target double integral information according to the position information of the upper and lower limits of each function variable in the target double integral information specifically comprises the following steps:
dividing the target double integral information according to the position information of the upper limit and the lower limit of each function variable in the target double integral information;
determining an integral input mode corresponding to the target double integral information according to the segmentation result;
the dividing the target double integral information according to the position information of the upper and lower limits of each function variable in the target double integral information specifically comprises the following steps:
setting an initial variable of a function to be integrated, and setting initial variables of upper and lower limits of the function variable;
sending the integrated function into the integrated function initial variable to obtain first integrated information;
the position information of the upper limit and the lower limit of each function variable in the target double integral information is sent into the initial variable of the upper limit and the lower limit of the function variable, and second integral information is obtained;
correspondingly, the step of determining the integral input mode corresponding to the target double integral information according to the segmentation result specifically comprises the following steps:
dividing the target double integral information based on the first integral information and the second integral information, and determining an integral input mode corresponding to the target double integral information according to a dividing result;
after the initial variables of the integrated function are set, and the initial variables of the upper limit and the lower limit of the function variables are set, the double-integral solver is configured to realize the following steps:
setting a binary function initial variable;
searching whether a binary function exists in the analysis result of the target double integral information, and if so, sending the binary function into the binary function variable to obtain third integral information;
accordingly, the step of dividing the target double integral information based on the first integral information and the second integral information, and determining an integral input mode corresponding to the target double integral information according to a division result specifically includes:
dividing the target double integral information based on the first integral information, the second integral information and the third integral information, and determining an integral input mode corresponding to the target double integral information according to a dividing result.
5. A double-integral solution system, the double-integral solution system comprising:
the receiving module is used for receiving character information input into each text control;
the splicing module is used for splicing the character information to obtain target double integral information;
the analysis module is used for analyzing the target double integral information, extracting an integrated function and upper and lower limits of each function variable from an analysis result, and respectively acquiring the position information of the upper and lower limits of each function variable in the target double integral information;
the determining module is used for determining an integral input mode corresponding to the target double integral information according to the position information of the upper limit and the lower limit of each function variable in the target double integral information;
the solving module is used for solving the target double integral information based on the integral input mode and the integrand function;
the determining module is further used for dividing the target double integral information according to the position information of the upper limit and the lower limit of each function variable in the target double integral information; determining an integral input mode corresponding to the target double integral information according to the segmentation result;
the determining module is also used for setting initial variables of the integrated function and initial variables of upper and lower limits of the function variables; sending the integrated function into the integrated function initial variable to obtain first integrated information; the position information of the upper limit and the lower limit of each function variable in the target double integral information is sent into the initial variable of the upper limit and the lower limit of the function variable, and second integral information is obtained;
accordingly, the determining the integral input mode corresponding to the target double integral information according to the segmentation result includes: dividing the target double integral information based on the first integral information and the second integral information, and determining an integral input mode corresponding to the target double integral information according to a dividing result;
the determining module is also used for setting binary function initial variables; searching whether a binary function exists in the analysis result of the target double integral information, and if so, sending the binary function into the binary function variable to obtain third integral information;
accordingly, the dividing the target double integral information based on the first integral information and the second integral information, and determining an integral input mode corresponding to the target double integral information according to a division result, includes: dividing the target double integral information based on the first integral information, the second integral information and the third integral information, and determining an integral input mode corresponding to the target double integral information according to a dividing result.
6. A storage medium having stored thereon a double-integral solver, the double-integral solver when executed by a processor performing the steps of:
receiving character information input into each text control;
splicing the character information to obtain target double integral information;
analyzing the target double integral information, extracting an integrated function and upper and lower limits of each function variable from an analysis result, and respectively obtaining position information of the upper and lower limits of each function variable in the target double integral information;
determining an integral input mode corresponding to the target double integral information according to the position information of the upper limit and the lower limit of each function variable in the target double integral information;
solving the target double integral information based on the integral input mode and the integrand function;
the determining an integral input mode corresponding to the target double integral information according to the position information of the upper and lower limits of each function variable in the target double integral information specifically comprises the following steps:
dividing the target double integral information according to the position information of the upper limit and the lower limit of each function variable in the target double integral information;
determining an integral input mode corresponding to the target double integral information according to the segmentation result;
the dividing the target double integral information according to the position information of the upper and lower limits of each function variable in the target double integral information specifically comprises the following steps:
setting an initial variable of a function to be integrated, and setting initial variables of upper and lower limits of the function variable;
sending the integrated function into the integrated function initial variable to obtain first integrated information;
the position information of the upper limit and the lower limit of each function variable in the target double integral information is sent into the initial variable of the upper limit and the lower limit of the function variable, and second integral information is obtained;
correspondingly, the step of determining the integral input mode corresponding to the target double integral information according to the segmentation result specifically comprises the following steps:
dividing the target double integral information based on the first integral information and the second integral information, and determining an integral input mode corresponding to the target double integral information according to a dividing result;
after the initial variables of the integrated function are set, and the initial variables of the upper limit and the lower limit of the function variables are set, the double-integral solver is configured to realize the following steps:
setting a binary function initial variable;
searching whether a binary function exists in the analysis result of the target double integral information, and if so, sending the binary function into the binary function variable to obtain third integral information;
accordingly, the step of dividing the target double integral information based on the first integral information and the second integral information, and determining an integral input mode corresponding to the target double integral information according to a division result specifically includes:
dividing the target double integral information based on the first integral information, the second integral information and the third integral information, and determining an integral input mode corresponding to the target double integral information according to a dividing result.
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