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maxima

Simplification of rational expressions

I'm struggling with getting maxima to simplify expressions in the way that I want them.

rhs(solve(a*x-3=b*y,x)[1]);

returns

(b*y+3)/3

However, I'm wanting to display the result to students and so I want the output to be

(b*y/3) + 1

Is there some simplification that I can do to a rational expression in this form to get the output I want?

Solution

  • You can undo the effect of ratsimp in this case by dividing each term in the numerator by the denominator. Here is a simple-minded implementation:

    (%i1) unratsimp (e) := 
          block ([foo, bar],
                 [foo, bar]: [num(e), denom(e)],
                 map (lambda ([foo1], foo1/bar), expand (foo))) $
(%i2) 1 + a/b + c*d/3 - %pi*x/y;
                        %pi x    c d   a
(%o2)                (- -----) + --- + - + 1
                          y       3    b
(%i3) ratsimp(%);
                (b c d + 3 b + 3 a) y - 3 %pi b x
(%o3)           ---------------------------------
                              3 b y
(%i4) unratsimp(%);
                        %pi x    c d   a
(%o4)                (- -----) + --- + - + 1
                          y       3    b
(%i5) unratsimp((b*y + 3)/3);
                             b y
(%o5)                        --- + 1
                              3

    I don't know how general that is; it's just the first thing I tried, but maybe it's enough for your purpose. I don't know a built-in function for this.

    The results %o4 and %o5 are maybe not exactly as a human would write them. Convincing Maxima to display the terms in + and * expressions in a different way is not straightforward -- Maxima has strong ideas about how to order terms in an expression which are assumed throughout the code. But I think that others have asked questions, which might have answers, about displaying expressions -- you might search Stackoverflow if you are are interested.