Allow for defining new functions in terms of previously defined functions in graphing mode

SubjunctiveQuaver commented 4 years ago

Problem Statement

A major use in defining functions is for using them to define further functions. This would be useful for visualising, explaining and manipulating composite functions, a major concept in mathematics that spans all disciplines, and is often a barrier for students. Currently, we cannot refer to previously defined functions when defining new ones in graphing mode; the function names are treated as constants.

Evidence or User Insights

Implementing this would enable students and users of the graphing calculator to define functions in terms of other existing functions. This is presently a feature on most, if not all, competitor apps, such as Desmos, GeoGebra and handheld graphing calculators, and is an important way to quickly define families of functions and view them simultaneously.

Currently, if we define the function with rule $f_1(x) = \sin(x)$ and attempt to define $f_2(x) = 3f_1(e^x)$ , we get a slider for "f_1" appearing, set to 1, which means it is treated as a constant, and what is displayed for $f_2$ is really the graph of $f_2(x) = 3f_1 \times e^x = 3e^x$ , where $f_1 = 1$ . This would not be expected behaviour. See this for current behaviour:

Proposal

Say we have defined, as above, the function with rule $f_1(x) = \sin(x)$ . Then if we define $f_2(x) = 3f_1(e^x)$ , the calculator realises that $3f_1(e^x)$ refers to "3 times $f_1$ composed with the exponential function" is the intended interpretation.

Then the result that is graphed is that of $f_2(x) = 3f_1(e^x) = 3\sin(e^x)$ , as one would expect.

To help achieve this, it would also be good to allow for functions to be named something other than just $f_k$ for positive integers k; for instance, the letters f, g, h, p, q, r etc. could be interpreted as function names in the right context, where they haven't been previously assigned as a constant.

Functions could also be renamed by clicking on the function name after entry. (Another wish is that you would be able to save/share a graphing screen for later use to an editable file, but that's for another suggestion.)

Goals

The user should be able to define new functions in terms of existing functions, and they should be treated as function compositions, as expected.
These function names should be treated as such, and not as constants when used in defining new functions. However, existing/new constants should still work when defining functions in this new way, and graphs should update as required.
Allow for usage of different letters for function names, so that it is easier to refer to previously defined functions.
(Eventually, for better sharing capabilities, it should be possible to export a graphing screen to a format that can later be edited again in the Calculator app, so that complicated graph visualisations can be retained, interacted with and shared.)

Low-Fidelity Concept

See the Desmos implementation:

Of course, the existing Calculator UI would be retained, but with the graphing output as in the screenshot. This is a mock-up in the Calculator app, but with the desired output of $f_2$ defined manually in $f_3$ :

Requested Assignment

I'm just suggesting this idea. I don't want to implement it.

MicrosoftIssueBot commented 4 years ago

This is your friendly Microsoft Issue Bot. I've seen this issue come in and have gone to tell a human about it.

ghost commented 4 years ago

This pitch looks like it has everything it needs for review. In the meantime, we'll keep this idea open for discussion so the community has the chance to provide feedback. Check out our New Feedback Process for more info on the user-centered process we follow for new feature development.

ghost commented 4 years ago

We reviewed the pitch and would love to explore this idea further! The pitch is a great start, but there are still some open questions. I am moving this issue into planning to iron out some of those details and I created calculator-specs/graphingFunctions to track progress. A human will follow up with some feedback on your pitch shortly. Keep in mind that not all ideas that make it into the planning phase are guaranteed to make it to release. For more information on next steps, check out our spec workflow.

grochocki commented 4 years ago

@SubjunctiveQuaver Thank you for your detailed submission! We think this is a great idea that adds a lot of value to the new graphing mode. The UI seems like it would be straightforward to implement, but we believe there might be prerequisite work in the graphing engine, and while the UI is part of this repository, the proprietary Microsoft-built graphing engine, which also drives graphing in Microsoft Mathematics and OneNote, is not. We will need to coordinate with our internal partners to investigate how best to incorporate this functionality into the graphing engine before moving forward with implementing this feature.

mattjes commented 7 months ago

bump

Krzycho666 commented 2 months ago

bump

microsoft / calculator

Allow for defining new functions in terms of previously defined functions in graphing mode #1048