add System (of relations)

[kevinbarabash]

A System node can describe the following things:

• system of equations 2x + y = 10, x - y = 3
• system of inequalities x >= 2 - y, y > 5x

A System can be collapsed, e.g.

• 2x = y + 3 = z - 10
• a < x < b

Certain Systems can be interpreted as bounds, e.g. a < x < b could also be a Bounds node:

{
   type: "Bounds",
   variable: { type: Identifier, name: "x" },
   min: { type: Identifier, name: "a" },
   max: { type: Identifier, name: "b" },
}

[aliang8]

{  type: System, args: [ equation1, inequality2, ... ], collapsed:  }

Example:

// Not collapsed
x + 2 = 1; x = 1 --> { type: System, args: [ { type: Apply, op: 'eq', args: [x + 2 = 1] }, 
{ type: Apply, op: 'eq', args: [x = 1] }, collapsed: false } 

// Collapsed
a < x < b --> { type: System, args: [ { type: Apply, op: 'lt', args: [a < x] }, 
{ type: Apply, op: 'lt', args: [x < b] }, collapsed: true } 

Is the idea of a bounds node supplementary to a system? So a < x < b can be interpreted as both a bound and a system?

[kevinbarabash]

I think we should not parse things like a < x < b or x = y = z as a 'System'. This removes the need for the collapsed flag.

[kevinbarabash]

Right now I believe that a < x < b is parsed as

{
  type: 'Apply',
  op: 'lt',
  args: [ a, x, b ],
}

I need to fix the demo and verify that this is the case. If not, I'll fix it so it is. x = y = z will work similarly.

[aliang8]

I see. a < x < b and x = y = z will be parsed as above. And what do you think of parsing a System as

{  type: System, args: [ equation1, inequality2, ... ] }

[kevinbarabash]

I think that fits a lot better with the existing structure. I need to update the spec.md with the new structure we've been working with.