What is symbolic computation? -

according wiki:

in mathematics , computer science, computer algebra, called symbolic computation or algebraic computation scientific area refers study , development of algorithms , software manipulating mathematical expressions , other mathematical objects

does symbolic computation focus on symbol manipulation , computation? lisp program written in form of ast atoms leaves. lisp said language symbolic computing. mean in symbolic computation, is:

• all symbols (symbols atoms or non-atom expressions in lisp)
• every symbol assigned semantic
• symbolic computation paradigm orients programmers focus on working symbols , semantics (a semantic can atom or expression something) , relationships between symbols, opposed think data structure , code 2 separated entities.
• program design language design, based on symbol composition/manipulation , semantic assignment.

according this question, opposite of symbolic computation numeric computation. what's primary difference between these two? when work octave (i'm studying it), have work numbers lot , have guess meaning of magic numbers many times. numerical computation focus?

"symbolic computation" computation symbolic expressions.

examples symbolic expressions:

• a mathematic formula. example integral expression
• a logic theorem
• a plan situation

for latter:

• roads a b, b d, c e, e f, b f, ...
• parcels p1 @ a, p2 @ d , p3 @ f
• a truck t1 @ d

now task generate plan picks parcels

1. pick parcel p2 @ d
2. move truck t1 d b
3. move truck t1 b a
4. pick parcel p1 @ a
5. ...

in above examples symbols stand places , things (truck, parcel). symbol expressions describe situation, plan generator return sequence of actions - again described symbolic expressions.