Algebra in C#

[cbmeeks]

I'm working on a project that deals with some algebra. Or, actually,
just math in general. It could eventually work it's way up to more
advanced math, analytics, etc.

Anyway, I'm looking for ideas on how to store the actual formulas
using classes.

For example:

class X
{
public Value;
}

class Y
{
public Value;
}

X x = new X();
X.Value = 10;

Y y = new Y();
Y.Value = 20;

Now, I want to store this formula:

x.Value + y.Value * 2

Which should give the value of 60.

Hope that makes sense. I thought about having a Formula class with a
List of classes and then build the formula when needed. Taking care
to add special classes like "multiply", etc but I don't think I like
that idea.

I also thought about storing a string somehow and then just parsing
the string and substitute keyword for classes.

Any suggestions?

Thanks

 

[cbmeeks]

Thanks for replying.

Well, it would take a very deep knowledge of exactly how this is going to
be used to provide any really good, specific advice.

However, a reasonably common approach would be to treat your expressions
as a tree graph of operators and operands. An operator instance would
have one or more operands as children. An operand could be a single
value, or the root of a sub-tree that represents a more complex
expression. Both operators and operands would share a base class used as
the fundamental element in the tree; that base class would be simply
something that returns a value.

This sounds like the lines I was thinking of. I like the tree idea.
I will need to think of how to store a formula like:

M1 * 15 + (M2 / M3)

Where Mx = a class that returns a value.

I'm actually doing this in SQL and it works but it seems a little
kludgy. In SQL, I am storing each operator/operand as a row, then
assembling the row as a string and then parse the formula.

My long term goal is to allow a user to type the formula out in a text
box so I guess strings are still in my future.

Operator precedence and explicit precedence (i.e. parentheses) would
control the layout of the graph. The result of any given graph would be
obtained by recursively evaluating the operands for each operator until
you wind back up at the top having evaluated the root operator.

Right. This is what I am going to have to work on.

For added difficulty points, allow your values to take on more than one
actual numeric type, handling type conversion as necessary as you process
the graph.

That is interesting because I've only been working with doubles since
I thought that would allow more than enough precision for most
business related values. Is that wise?

That said, I would guess that there's already some solutions out there.
If you're looking for anything really elaborate, you might find it makes
more sense to search for and use a pre-existing package. I don't know for
sure that any exist, but it seems likely. Google would be helpful there,
obviously.

Pete

Yeah, but this is something I hope to offer as a service one day and I
enjoy the learning experience.

Thanks Pete, you've been a lot of help.

-cecil

 

[Peter Bromberg [C# MVP]]

All mathematical "Formulas" in code eventually get reduced to math operations
on defined types and they return a result of a defined type (it could be a
complex number, matrix, doesn't matter). If you look at some of the
open-source math libraries, this is how they are structured. In other words,
you don't "store a formula", instead you have a method or methods with code
the *performs* the particular mathematical operation and returns it's result.
-- Peter
To be a success, arm yourself with the tools you need and learn how to use
them.

Site: http://www.eggheadcafe.com
http://petesbloggerama.blogspot.com
http://ittyurl.net

 

[cbmeeks]

All mathematical "Formulas" in code eventually get reduced to math operations

on defined types and they return a result of a defined type (it could be a
complex number, matrix, doesn't matter). If you look at some of the
open-source math libraries, this is how they are structured. In other words,
you don't "store a formula", instead you have a method or methods with code
the *performs* the particular mathematical operation and returns it's result.
-- Peter

AH. That makes sense. Right now, I have some methods like that.

For example, I can do something like:

Metric m = new Metric();
m.Sum();
m.Avg();
m.PowSum();
m.MultiplySumBy(15);
etc...

That's working pretty well. So it's easy to do:

double r = m.Sum() + 15;

I will keep chugging along until I find a way to represent these chain
of actions

 

[Ian Semmel]

I think you basicaly need a stack which pushes values and operators,
taking into account operator precedence.

I would find some open source compiler and see how they do it.

 

[Gilles Kohl [MVP]]

On Fri, 25 Apr 2008 11:03:04 -0700, "Peter Duniho"

[...]

That said, I would guess that there's already some solutions out there.
If you're looking for anything really elaborate, you might find it makes
more sense to search for and use a pre-existing package. I don't know for
sure that any exist, but it seems likely. Google would be helpful there,
obviously.

Indeed - one of them confirms a hunch I had: that the solution to the
"representation" and "evaluation" parts of the problem (although not
the parsing) is already built into C# 3.0 in the form of expression
trees. Here's a very nice article that also provides the parsing, by
converting to a postfix representation (as you suggested) before
assembling the tree.

http://www.jot.fm/issues/issue_2008_03/column4/index.html

Regards,
Gilles.

 

[cbmeeks]

Thanks for all of the suggestions guys!! I am going to look into the
RPN....that is very interesting!

Define "business related values". For many business applications, the
"decimal" type is actually more appropriate. Floating point ("double" or
"float") is susceptible to rounding errors. In financial applications,
this is often impermissible. The "decimal" type can suffer rounding
errors (try dividing one dollar into 3 equal parts ) as well depending
on how they are used, but the rules for dealing with rounding are usually
better-defined in that context.

AHH!!! Yeah, I had forgotten about that. hmmm...all of the Math
routines I use use double as input. Wouldn't


You guys have been great. Wish me luck!