Alvigra To Do List

Major Capabilities to Be Added

Right now, Alvigra can only simplify algebraic equations - which is handy in itself and also key to doing pretty much anything else in algebra.  Now that Alvigra is doing that fairly well, I plan to be working on three other more major capabilities soon:

1. Solving equations (not just simplify them) - In particular, my Alvigra development will focus on:
• Solving linear equations.
• Solving quadratic equations (both by factoring and using the quadratic formula)
• Solving inequalities
• Solving equations and inequalities with absolute values.
2. Graphing - In particular, I want to have Alvigra do graphing the way teachers ask students to do graphing - so Alvigra will be able to graph in the following ways (eventually with lots of animation to show exactly how it is done):
• Graphing a linear equation using y-intercept and slope or using x and y intercepts.
• Graphing a quadratic equation by graphing the vertex and using the rule of odds to graph nearby points.
• Graphing using a value table (complete with calculations).
3. Generating Presentations - Finally, I want to allow teachers to be able to use Alvigra to generate teaching presentations that can be used in class or put on line.  This means letting a teacher change the automatically generated solutions (or generate their own) and then save off their work to be displayed later in a classroom or on line by a student.  This will require adding the following capabilities to Alvigra.
• Allow teachers to change comments and choose animation levels for each step.
• Allow teachers to add in pop up dialog boxes during equation solving (for instance, a teacher may have a dialog box pop up saying "What do you think will happen next?" or have a box pop up with a deeper explanation for the next step).
• Allow teachers to add in operations and animations of their own.
• Allow a solution to be saved off for later display (this will actually be the first step in generating presentations).
4. Help Menus and Hints - Right now Alvigra has no help menus, but I would like to add them.  Also, I would like to add a hint button for most operations, so the user can click on the operation and get more information (maybe from a web page) on how that operation works and when it can be used.

This is a lot to add, and it's going to take a lot of time before I'm done.  Mostly I plan to do it in the order shown, but I will probably jump forward sometimes as the previous capability starts to get fairly functional, rather than perfecting each new major capability before going on to the next.

Missing Math Operations to Be Added

There are a few major mathematical capabilities still missing from Alvigra.  I will add them as I get time:

• Decimal numbers - right now Alvigra can only handle integers
• Radicals - Alvigra can't yet handle or display square roots, cube roots, and the like.
• Fractional Exponents - Alvigra can show them, but it can't calculate 8^(1/3) = 2, for instance.
• Expanding binomials - for instance (x + 1)^2 = x^2 + 2x + 1.
• Factoring quadratics
• Absolute values
• Inequalities

Of course, these are only operations one might find in a standard algebra I class.  It will be some time before I add Algebra II capabilities in Alvigra (such as logs, trig functions, etc.).

User Interface Problems

I know that the user interface is still pretty rough, and it will probably take quite a while to smooth it all out.  However, there are some particular problems I plan to address as soon as I have time:

• The cursor does not work smoothly with fractions (you have to click in the fraction to get the cursor to go into the numerator or denominator because using the arrow key will just skip over it).
• Fractions cannot currently be selected for cut and paste.
• Cutting and pasting or selecting text then hitting the divide button causes formatting to be lost.
• Some buttons and menu options should fade or disappear when they are not usable.
• Parentheses should size appropriately.
  

User Interface Additions

There are some minor additions I would like to add to the interface as time permits:

• A regular edit menu with cut and paste, etc.
• If the user clicks on an operation message, display the highlight animations associated with that message.
• Have the ability to back up the animations.
• Have an option to display messages in a pop-up box connected to the animation arrows running between the old equation and the new one.

Minor Bagaboos

These are some minor bugs I've found as I've tested, but haven't quite fixed yet:

• Alvigra handles negative signs correctly in the result, but sometimes does not show the most intuitive intermediate values.
• If a result exceeds a maximum integer, Alvigra returns an erroneous result instead of failing gracefully.  I should also probably change base type from int to long to allow larger numbers.
• There are occasional crashes related to GUI threading issues.
  

Comments

I will be adding to this page as ideas occur to me.  If there are any changes you especially want made, if you've noticed some bugs or limitations that I haven't listed, or if you have any kind of comment at all, send me an email and I will think about adding it to my "To Do" list.

email: john@alvigra.com