Program to fiddle with large mathematical equations visually

Question

When working with mathematics or presenting something at math class I often need to work at a whiteboard writing up equations or scribbling equations on a paper.

A considerable time is spent copying the equations again and again. Then manually doing algebraic changes in them which is error prone.

I tried using latex but the problem is that I don't see what I'm doing until I render it, and in huge equations mistakes are hard to spot (eg. missing bracket somewhere). And doesn't look immersive enough for the math class.

I'm looking for a software that makes this fiddling with equations easier to do.

It's important I'm not looking for a CAS to solve the equations - they are not very useful when writing up proofs in a visually appealing manner, instead I'm looking for something that allows me fiddle with and rearrange terms in large equations without making mistakes while seeing what I'm doing.

The requirements:

• Ability to enter equations and math entirely visually (just like you would do it at a whiteboard) without having to enter an expression textually in a secondary text area. Especially when entering fractions and matrices.

• Allow at least basic algebraic manipulations. For example:

  • Rearranging terms using drag and drop. For example in a - b + c. I should be able to pick up -b and drag it around to turn it into a + c - b. Similarly I should be able to pick up a and drag it around to rearrange it to c + a - b (note the plus sign introduced).
  • Allow switching products: turning ab into ba.
  • Allow selecting ax + ay then tell it to factor a out from it to change it to a(x+y). The same operation can be used to turn 2x+3x to 5x and to get rid of cancellations like 2x-2x.
  • Allow selecting a bracket to tell it to expand it (the inverse of the previous).
  • Allow simple substitution of variable: the most likely gesture is selecting a subexpression and dragging it over a variable - all the parenthesization this causes should be done for you.
  • Allow the introduction of cancellations into fractions and equations. eg. multiplying the denomitator and nominator of a fraction with the same term, or doing identical things to both sides of an equation.
• Nice to heave: export the formulas into Latex.