On 12 November 2016 at 22:31, oldk1331 <oldk1...@gmail.com> wrote: > I have a related question: > > Seems your question has something to do with the fact that > in FriCAS Expression is represented by polynomials and > polynomials are always expanded. > > So integrate(1/(x+1)^n,x) will be slow when n is large. > > My question is, is there a domain to express expressions > that are not expanded, for example "a+1/b" will not be > "(a*b+1)/b". >
Domains constructed by Expression(R), provided that R has sufficient algebraic structure, are designed so that evaluation produces a (nearly) canonical representation of an expression. This makes it very efficient for many purposes compared to systems that perform purely symbolic manipulation. This is in keeping with the orientation of FriCAS towards "computer algebra" rather than just "symbolic computatation". But there are situations when the rigorous behavior of the Expression domain does make things awkward and sometimes less efficient. The following is an initial draft of a new domain constructor that implements unevaluated symbolic expressions. https://github.com/billpage/fricas/blob/62cc95b16fb7744700ccb04f16ad9ec9f4c0b95c/src/algebra/symbolic.spad Constructor for unevaluated symbolic expressions Defines symbolic expressions over some domain, e.g. Symbolic Integer and Symbolic Expression Float, etc. These expressions are completely unevaluated with no automatic simplifications. They may be simplified, compared as and/or converted to fully evaluated expressions in the appropriate Expression domain. The underlying representation is InputForm. Example session: (1) -> (a,b):Symbolic Expression Integer Type: Void (2) -> a+1/b 1 (2) a + - b Type: Symbolic(Expression(Integer)) (3) -> simplify % a b + 1 (3) ------- b Type: Symbolic(Expression(Integer)) (4) -> %%(2)=%%(3) 1 a b + 1 (4) a + - = ------- b b Type: Equation(Symbolic(Expression(Integer))) (5) -> test % (5) true (6) -> sin(a)^2+cos(a)^2 = 1 2 2 (6) sin(a) + cos(a) = 1 Type: Equation(Symbolic(Expression(Integer))) (7) -> test map(simplify,%) (7) true Type: Boolean (8) -> x:Symbolic Integer := 1+2+3+4 (8) 1 + 2 + 3 + 4 Type: Symbolic(Integer) (9) -> x::Integer (9) 10 Type: Integer Of course there are more purely symbolic manipulations that could be very useful such as those commonly found in Maple, Mathematica and Sage, for example 'expand', 'combine', 'factor' etc. In many cases these can be implemented utilizing results produce by existing operations in Expression and related domains and packages and then converted to an appropriate InputForm as the internal representation of a purely Symbolic domain. I would be very interested in comments, criticism and suggestions. https://github.com/billpage/fricas/commit/62cc95b16fb7744700ccb04f16ad9ec9f4c0b95c.patch Thanks. Bill Page. -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
