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SciMax Toolbox >> multthru

multthru

Maxima Function

Calling Sequence

multthru (expr)
multthru(expr_1,expr_2)

Description

Multiplies a factor (which should be a sum) of expr by the other factors of expr. That is, expr is f_1 f_2 ... f_n where at least one factor, say f_i, is a sum of terms. Each term in that sum is multiplied by the other factors in the product. (Namely all the factors except f_i). multthru does not expand exponentiated sums. This function is the fastest way to distribute products (commutative or noncommutative) over sums. Since quotients are represented as products multthru can be used to divide sums by products as well.

multthru (expr_1, expr_2) multiplies each term in expr_2 (which should be a sum or an equation) by expr_1. If expr_1 is not itself a sum then this form is equivalent to multthru (expr_1*expr_2).

(%i1) x/(x-y)^2 - 1/(x-y) - f(x)/(x-y)^3;
                      1        x         f(x)
(%o1)             - ----- + -------- - --------
                    x - y          2          3
                            (x - y)    (x - y)
(%i2) multthru ((x-y)^3, %);
                           2
(%o2)             - (x - y)  + x (x - y) - f(x)
(%i3) ratexpand (%);
                           2
(%o3)                   - y  + x y - f(x)
(%i4) ((a+b)^10*s^2 + 2*a*b*s + (a*b)^2)/(a*b*s^2);
                        10  2              2  2
                 (b + a)   s  + 2 a b s + a  b
(%o4)            ------------------------------
                                  2
                             a b s
(%i5) multthru (%);  /* note that this does not expand (b+a)^10 */
                                        10
                       2   a b   (b + a)
(%o5)                  - + --- + ---------
                       s    2       a b
                           s
(%i6) multthru (a.(b+c.(d+e)+f));
(%o6)            a . f + a . c . (e + d) + a . b
(%i7) expand (a.(b+c.(d+e)+f));
(%o7)         a . f + a . c . e + a . c . d + a . b
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