Note: Descriptions are shown in the official language in which they were submitted.
CA 02546799 2006-05-15
System and Method for Creating and Presenting Mathematical Documents
FIELD OF THE INVENTION
The invention relates generally to a system and method for creating and
presenting
electronic documents containing mathematical expressions and equations.
BACKGROUND OF THE INVENTION
There are systems for creating documents with mathematical content as well as
systems for performing computations with mathematical expressions and for
displaying
the results of such computations. There are two basic methods of integrating
such
computations into a document. The first method integrates textual commands
into the
document that reference the mathematical algorithm that is to be applied to a
mathematical expression and the result is displayed following this textual
command. This
method has the advantage that it is immediately obvious, from looking at the
document,
what algorithm was applied to an expression and how to reproduce the same
operation
elsewhere in the document or in a new document. The disadvantage is that the
textual
commands are often verbose and distract from the presentation of the document.
The
second method is to display the result, following the input expression and to
display,
between the two, a short text or symbol (e.g., an arrow) that describes the
operation that
was applied. This makes the document visually appealing and close to what one
would
expect to see in a mathematical textbook. There is no textual command or
syntax that
may be a distraction from the actual content that the document is supposed to
convey.
The disadvantage of this method is that, although the exact semantics of the
operation can
be preserved behind the scenes, in order to automatically update results if
the input
changes, the semantics of the operation are not obvious to a reader of the
document.
Because the presentation has to be visually appealing, the description of the
operation has
to be more casual or imprecise.
It is desirable to have a way of producing visually appealing documents that
focus
on the essential mathematical content that is to be conveyed as well as giving
the reader
access to the precise semantics of all the operations that are contained in
the document.
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SUMMARY OF THE INVENTION
A system and method of creating and presenting mathematical documents are
provided. The system and method allow a user to prepare electronic documents
containing mathematical expressions, with a high level of control over how the
document
is formatted. The mathematical expressions contained in a document are live,
in the sense
that changes to one part of the document can affect expressions in a different
part of the
document. Mathematical algorithms that transform one mathematical expression
to
another one are used to capture the relationships between two mathematical
expressions
in a document in order to update one if the other one changes. The user has
control over
how much detail on these mathematical algorithms to expose to a reader of the
document.
In accordance with an embodiment of the invention, there is provided a system
for
creating and presenting mathematical documents. The system comprises an
input/output
component for receiving user input and for displaying a mathematical document
on a
display device, a document repository 104 for storing the mathematical
document and a
mathematical engine for performing computations. The document includes markup
that
specifies display options.
In accordance with another embodiment of the present invention, there is
provided
a method of creating and presenting mathematical documents. The method
comprises the
steps of receiving input data that represent characters, symbols and
mathematical
operations as well as manipulations and presentation control of the
mathematical
document, displaying mathematical expressions or a combination of mathematical
expressions and text in an electronic document, performing computations on the
mathematical expressions contained in the document, and controlling the
formatting and
display of the document.
BRIEF DESCRIPTIONS OF THE DRAWINGS
An embodiment of the invention will now be described by way of example only,
with reference to the following drawings in which:
Figure 1 shows in a component diagram an example of a mathematical document
system for creating and presenting mathematical documents, in accordance with
an
embodiment of the present invention;
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Figure 2 shows in a flowchart an example of a method of creating and
presenting
mathematical documents, in accordance with an embodiment of the mathematical
document system
Figure 3 shows in a diagram an example of a document hierarchy, in accordance
with an embodiment of the mathematical document system;
Figure 4 shows in a screen shot an example of a mathematical document in
Worksheet Mode, in accordance with an embodiment of the mathematical document
system;
Figure 5 shows in a flowchart an example of a method of displaying a
mathematical document in document mode, in accordance with an embodiment of
the
mathematical document system;
Figure 6 shows in a flowchart another example of a method of displaying a
mathematical document in document mode, in accordance with an embodiment of
the
mathematical document system;
Figure 7 shows in a flowchart another example of a method of displaying a
mathematical document in document mode, in accordance with an embodiment of
the
mathematical document system;
Figure 8 shows in a Model-View-Controller framework diagram an example of a
stratification of a document structure, in accordance with an embodiment of
the
mathematical document system;
Figure 9 shows a hierarchal structure of a typical model in the MVC framework;
Figure 10 shows in a screen shot the same document as in Figure 4 that was
modified to display the text "integrates to" between the input expression and
the textual
command representing the operation being applied;
Figure 11 shows in a screen shot the same document as in Figure 10 that is
displayed in an alternate mode, showing only the mathematical expressions and
any
descriptive text, and not the detail of the textual command describing the
operation that
was applied;
Figure 12 shows in a screen shot the same document as in Figure 11 wherein the
input expression was modified;
Figure 13 shows in a screen shot the same document as in Figure 12 displayed
in
the mode shown in Figures 4 and 10, illustrating a toggle between these two
modes of
display;
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Figure 14 shows in a screen shot another example of a document, which was
created by entering an input expression and selecting a mathematical operation
from a list
in a menu; and
Figure 15 shows in a screen shot the same document as in Figure 14 displayed
using an alternate mode, showing that the textual command that connects input
and output
expressions.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
A system and method of creating and presenting mathematical documents are
provided. The system and method allow a user to prepare electronic documents
containing mathematical expressions, with a high level of control over how the
document
is formatted. The mathematical expressions contained in a document are live,
in the sense
that changes to one part of the document can affect expressions in a different
part of the
document. Mathematical algorithms that transform one mathematical expression
to
another one are used to capture the relationships between two mathematical
expressions
in a document in order to update one if the other one changes. The user has
control over
how much detail on these mathematical algorithms (also referred to as
mathematical
operations and computation as described below) to expose to a reader of the
document.
A system and method of the present patent disclosure will now be described
with
reference to various examples of how the embodiments can best be made and
used. For
convenience, like reference numerals are used throughout the description and
several
views of the drawings to indicate like or corresponding parts, wherein the
various
elements are not necessarily drawn to scale.
A mathematical document is created using a word-processor like software
system,
which allows the combination of text with more complex content such as
mathematical
expressions, graphs and images. A document is a linear sequence of
subcomponents
including Text Paragraphs (which can contain text, two-dimensional
mathematical
expressions, graphs and images) and Execution Groups. An Execution Group is a
linear
sequence of Text Paragraphs, Input Fields and Output Fields. An Input Field
can contain
two-dimensional mathematical expressions mixed with linear text, all
representing either
a mathematical expression or an operation or algorithm to perform or both. An
Output
Field can contain two-dimensional mathematical expressions, linear text,
graphs or a
combination of these.
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Figure 1 shows in a component diagram an example of a mathematical document
system 100 for creating and presenting mathematical documents, in accordance
with an
embodiment of the present invention. The mathematical document system 100
comprises
an input/output component 102 for receiving input data and displaying a
mathematical
document that is created and formatted in response to the input data, a
document
repository 104 for storing the mathematical document and a mathematical engine
106 for
performing mathematical computations. The mathematical document including
markup
that specifies display options. The input/output component 102 includes a
display 108 for
reading document markup and displaying documents having two-dimensional type-
set
mathematical expressions, a keyboard 107 and pointing device 109 that allows a
user to
input characters, symbols and mathematical operations as well as initiate
manipulations of
the mathematical document.
Figure 2 shows in a flowchart an example of a method of creating and
presenting
mathematical documents (110), in accordance with an embodiment of the
mathematical
document system 100. The method begins with receiving input data (112). The
input
data represent characters, symbols and mathematical operations as well as
manipulations
and presentation control of the mathematical document. Next, mathematical
expressions
or a combination of mathematical expressions and text are displayed in an
electronic
document (114). Computations on the mathematical expressions contained in the
document are performed (116) and the formatting and display of the document is
controlled (118) in order to toggle the display of the textual commands
representing the
operations that are performed versus hiding the commands and displaying only
the input,
only the output or both input and output as well as any descriptive text
explicitly added by
the user. In addition controlling whether input and output appears inline,
within
surrounding text or on a separate line may be performed.
Figure 3 shows in a diagram an example of a document hierarchy 120, in
accordance with an embodiment of the mathematical document system 100. The
document hierarchy 120 comprises a document node 122, an execution group node
124, a
text paragraph node 126, an input field node 128 and an output field node 130.
The input
field noted 128 and the output field node 130 include content such as a
mathematical
expression and display markup to indicate that the content is to be displayed
as hidden or
visible, and/or inline with text or on line by itself.
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A document is presented to the user in one of two modes: Worksheet Mode or
Document Mode. In Worksheet Mode, Text paragraphs are displayed with the
content
that they contain. Each Input Field 128 within an Execution Group 124 is
displayed on a
new line, optionally preceded by a prompt symbol (e.g., ">"). Each Output
Field 130
within an Execution Group 124 is displayed on a new line, optionally centered.
Figure 4 shows in a screen shot an example of a mathematical document in
Worksheet Mode, in accordance with an embodiment of the mathematical document
system 100. A mathematical expression was created using the system (1).
Subsequently
a textual command (int((1),x)), referring to a particular mathematical
operation, was
inserted into the document. Execution of this command yielded a result, which
is
displayed as (2).
In Document Mode, Text Paragraphs 126 are displayed as in Worksheet Mode
and for each Execution Group 124, a user may choose a display of the document
122.
Figure 5 shows in a flowchart an example of a method of displaying a
mathematical
document in document mode (140), in accordance with an embodiment of the
mathematical document system 100. A selection of Output Fields 130 and a
selection of
Input Fields 128 are received as an input (142). For each Execution Group 124
(144),
each Output Field 130 of the selection is displayed on a new line (146). None
of the other
Output Fields 130 (i.e., not in the selection) in that Execution Group 124 are
displayed.
Next, for each Execution Group 124 (148), each Input Field 128 is displayed on
a new
line (150). None of the other Input Fields 128 (i.e., not in the selection) in
that Execution
Group 124 are displayed. Preferably, each visible Input Field 128 or Output
Field 130 in
an Execution Group 124 is displayed on a new line, optionally centered.
Figure 6 shows in a flowchart another example of a method of displaying a
mathematical document in document mode (160), in accordance with an embodiment
of
the mathematical document system 100. A selection of Output Fields 130 and a
selection
of Input Fields 128 are received as an input (142). For each Execution Group
124 (162),
each Output Field 130 of the selection is displayed in a separate line or
inline with any
Text Paragraphs 126 that may precede or follow the Output Field 130 (164).
None of the
other Output Fields 130 (i.e., not in the selection) in that Execution Group
124 are
displayed. Next, for each Execution Group 124 (166), each Input Field 128 is
displayed
(168). None of the other Input Fields 128 (i.e., not in the selection) in that
Execution
Group 124 are displayed. The result is that the contents of the Output Field
130 can
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appear on the same line with surrounding text. Preferably, no space is
inserted between
the text and the contents of the Output Field 130. If spacing is desired, this
spacing is
explicitly inserted into the surrounding text.
Figure 7 shows in a flowchart another example of a method of displaying a
mathematical document in document mode (170), in accordance with an embodiment
of
the mathematical document system 100. A selection of Input Fields 128 are
received as
an input (172). For each Execution Group 130, each Input Field 128 are
displayed on a
separate line or may be displayed inline with any Text Paragraphs 128 that may
precede
or follow the Input Field 128 (174). None of the other Input Fields 128 (i.e.,
not in the
selection) in that Execution Group 124 are displayed. None of the Output
Fields 130 in
that Execution Group 124 are displayed. The result is that the contents of the
Input Fields
128 can appear on the same line with surrounding text and other Input Fields
128. No
space is inserted between the text and the contents of the Input Field 128 or
between Input
Fields 128. If spacing is desired, this spacing is explicitly inserted into
the surrounding
text.
Regardless of whether mathematical evaluations are visible or hidden, they are
still expressed in the structure of the document. This is made possible by
using a Model-
View-Controller (MVC) framework to separate the document's "data" from its
visual
representation. This stratification of the document structure 180 is shown in
Figure 8.
The user interacts with a document via its controller 182. Actions performed
on the
document modify its structure (i.e., modify the model 184), which in turn
notifies the
controller 182 (which implements a model listener interface 186) that the
visual
appearance may have changed. The view structure 188 is automatically updated
in
response to notifications.
Figure 9 shows a hierarchal structure of a typical model in the MVC framework
(190). Each model may be broken down into submodels, and is linked to the top
level
model to facilitate synchronization locking of the document. Furthermore, each
model
contains attributes that may affect the visual appearance of the model, and
which may
store metadata information to enable association between models.
At any time, the user can toggle between viewing a document in Worksheet Mode
or in Document Mode by selecting from a menu or pressing a hot key, or any
other
selection means. The controller will receive this request and perform an
action on the
model as in Figure 8 and update the display. Typically, Document Mode will be
used to
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hide all the commands that specify which mathematical operation is being
applied to an
input expression in order to get the resulting output and to focus the
document on
presenting the intermediate and final results of working through a problem.
Typically,
Worksheet Mode will be used to expose all the commands and display the precise
semantics of what operation is being applied for each of the computations.
Figure 11
shows an example of a document in Document Mode.
In addition to the linear description above, optionally two-dimensional tables
and
collapsible sections can be used to further structure the document. The
behaviour within
such a structure will follow the description above.
Within a mathematical document, a user can perform an action (for example,
pointing the mouse at a mathematical expression and clicking the right button)
that will
cause the display of a list of available operations for a particular
mathematical
expression. This list may be static or it may be constructed based on the
nature of the
expression. Alternatively, an operation can be selected by pressing a key or
key
combination or by clicking on a control. On selecting an expression, the
corresponding
textual command representing this operation will be inserted into a new Input
Field in the
document, the operation will be executed using a mathematical computation
engine and
the result of this computation will be inserted into a new Output Field. If
such an action
occurs in Document Mode, the textual command will by default be hidden, such
that
only the input expression as well as the output expression is visible. In
addition, a Text
Paragraph is inserted with a textual description of the operation performed.
The detail of
this description can vary from a simple equal sign or an arrow symbol to an
arrow
symbol with a stacked piece of text further describing the operation. In
general, the
description can be composed of arbitrary text and mathematical expressions,
arranged in
a two-dimensional fashion. The result of such an action is shown in Figure 11.
It is
important to note that the exact textual command is preserved, even though it
is not
displayed by default and that it can be made visible at any time by the user
by toggling to
Worksheet Mode.
An Output Field can optionally be associated with an Equation Label, which can
be displayed as an equation number next to a mathematical expression. Such
equation
numbers are pervasive in mathematical text books and this allows the
mathematical
document to more closely resemble such a text book. Figure 4 shows two
Equation
Labels, (1) and (2). Equation Labels are automatically numbered using a user-
defined
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numbering scheme that may reflect the structure of the document. For example,
the
Equation Labels can be numbered with consecutive integers starting at one for
the first
Output Field in the document. An Equation Label can be referenced from any
point in
the mathematical document in order to refer to the mathematical expression
that is
associated with the Equation Label. In particular, a reference to an Equation
Label can
be inserted at any point in an Input Field in order to reuse a mathematical
expression that
occurs elsewhere in the document.
The mechanism that automatically inserts textual commands based on a selection
from a list of operations, described above, can optionally take advantage of
Equation
Labels in order to refer to the input expression within the generated textual
command.
This ensures that, if the input expression is modified at any later moment,
the textual
command can be applied to the new input expression automatically and thus user
changes of input in the document can update output expressions as appropriate.
This
process is also shown in the transition from Figure 11 to Figure 12.
Preferably, only
Equation Labels that are displayed based on the current setting of Worksheet
Mode or
Document Mode, will be considered in the numbering scheme. Output Fields that
are
not being displayed can still have Equation Labels and such Equation Labels
can still be
referred to from other parts of the document, without restrictions, even
though these
Equation Labels will not have equation numbers. This is because in addition to
an
equation number, each Equation Label also stores a label that uniquely
identifies this
Equation Label. When a reference to an Equation Label is inserted into the
document,
the user specifies the equation number. Based on this equation number and the
current
numbering scheme, the label for the corresponding Equation Label is looked up
and used
for the reference that will be inserted. This ensures that references remain
consistent if
Output Fields are inserted into the document (causing a, possibly partial,
renumbering of
the Equation Labels) and that references also remain consistent if Output
Fields are no
longer displayed due to a switch from Worksheet Mode to Document Mode or due
to a
change in the display options in Document Mode, causing an Output Field's
Equation
Label to no longer have an equation number.
Figure 10 shows in a screen shot the same document as in Figure 4 that was
modified to display the text "integrates to" between the input expression and
the textual
command representing the operation being applied. Figure 11 shows in a screen
shot the
same document as in Figure 10 that is displayed in an alternate mode, showing
only the
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mathematical expressions and any descriptive text, and not the detail of the
textual
command describing the operation that was applied. Figure 12 shows in a screen
shot the
same document as in Figure 11 wherein the input expression was modified. In
response
to a user request, the result expression was updated to reflect the change in
the input.
Figure 13 shows in a screen shot the same document as in Figure 12 displayed
in the
mode shown in Figures 4 and 10, illustrating that it is possible to toggle
between these
two modes of display.
Figure 14 shows in a screen shot another example of a document, which was
created by entering an input expression and selecting a mathematical operation
from a list
in a menu. The result of the operation is displayed and in between input and
result
automatically appears a textual description of the operation that was
performed (an arrow
with the text "integrate" above it). Figure 15 shows in a screen shot the same
document
as in Figure 14 displayed using an alternate mode, showing that the textual
command that
connects input and output expressions and thus the full semantics of the
operation is
available to a user by toggling between the two modes of display.
The systems and methods according to the present invention may be implemented
by any hardware, software or a combination of hardware and software having the
above
described functions. The software code, either in its entirety or a part
thereof, may be
stored in a computer readable memory. Further, a computer data signal
representing the
software code which may be embedded in a carrier wave may be transmitted via a
communication network. Such a computer readable memory and a computer data
signal
are also within the scope of the present invention, as well as the hardware,
software and
the combination thereof.
While particular embodiments of the present invention have been shown and
described, changes and modifications may be made to such embodiments without
departing from the true scope of the invention.
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