Sympose It

Sympose It is a straightforward but very unconventional algebra aide, targeted to those who could use a boost in algebraic intuition. I’ve only developed it for iOS so far, and it’s available on the Apple App Store.

Video Tutorial
Watch non-mobile for better video quality.

link to tutorial on YouTube

Text Tutorial
Step 1: enter an equation and hit “Go”
Step 2: select the equals (=) in the diagram by tapping it or an inverse (/ or \) by tapping the node behind it
Step 3: tap a highlighted location in the diagram to move the selected equals or inverse there
Step 4: watch the equation change in the bottom textfield; hit “Use” to copy it to the top
Step 5: hit “Recenter” after moving the equals to redraw the equation with the centered equals
Step 6: hit “Help?” to bring you to this page.

Support
Support is available on Facebook and Twitter.

Notes
1. You can only make levels by interleaving additive nodes and multiplicative nodes.
2. An exception to #1 is by interleaving additive nodes and multiplicative inverses.
3. When you move the equals through a node to one of the node’s branches, all the other branches get inverses of the same type (color coded) as the node.
4. When you move an inverse through a node of the same type to one of the node’s branches, all the other branches get the same inverse.
5. You can’t move a multiplicative inverse through an additive node (this explains #2).
6. You can move an additive inverse through a multiplicative node, but then nothing happens to the other branches.

Questions
1. Is it possible to construct another operator like addition or multiplication, with its own inversing? (hint: commutativity & associativity, hyperoperation)
2. What else can you think of?

The Central Idea
Equations can be represented as trees, and any portion of the equation can be solved for by re-rooting the tree. As simple as the last half of that idea is, I haven’t seen it before, even after scouring the Internet. So I had to make an app. Let me know if you dig anything up!

Further Work
Equations where the same variable appears more than once cannot be represented by a tree. Instead, their graphs are cyclic. As of now, I’m not interested in implementing this on my own, but I am open to offers from anyone who may be interested, especially those who want to buy the app off of me.

P.S. The icon is a color wheel graph of the complex plane.