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dispfun-ev-integrate-noundisp-nouns-plot2d-print-ratsimp-rhs-solve-tex-true
plot2d(penum(x), [x, -1, 1]);

noundisp : true;

circ: x^2+y^2=1;

half(x) := rhs(solve(...

Calculate

dispfun-ev-integrate-noundisp-nouns-plot2d-print-rhs-solve-tex-true
plot2d(penum(x), [x, -1, 1]);

noundisp : true;

circ: x^2+y^2=1;

half(x) := rhs(solve(...

Calculate

dispfun-ev-integrate-noundisp-nouns-plot2d-print-rhs-solve-tex-true
plot2d(penum(x), [x, -1, 1]);

noundisp : true;

circ: x^2+y^2=1;

half(x) := rhs(solve(...

Calculate

dispfun-ev-integrate-noundisp-nouns-plot2d-print-ratsimp-rhs-solve-tex-true
plot2d(penum(x), [x, -1, 1]);

noundisp : true;

circ: x^2+y^2=1;

half(x) := rhs(solve(...

Calculate

dispfun-ev-integrate-noundisp-nouns-plot2d-print-ratsimp-rhs-solve-tex-true
plot2d(penum(x), [x, -1, 1]);

noundisp : true;

circ: x^2+y^2=1;

half(x) := rhs(solve(...

Calculate

dispfun

Run Example
(%i1)? dispfun;

 -- Function: dispfun (<f_1>, ..., <f_n>)
 -- Function: dispfun (all)
     Displays the definition of the user-defined functions <f_1>, ...,
     <f_n>.  Each argument may be the name of a macro (defined with
     `::='), an ordinary function (defined with `:=' or `define'), an
     array function (defined with `:=' or `define', but enclosing
     arguments in square brackets `[ ]'), a subscripted function,
     (defined with `:=' or `define', but enclosing some arguments in
     square brackets and others in parentheses `( )') one of a family
     of subscripted functions selected by a particular subscript value,
     or a subscripted function defined with a constant subscript.

     `dispfun (all)' displays all user-defined functions as given by
     the `functions', `arrays', and `macros' lists, omitting
     subscripted functions defined with constant subscripts.

     `dispfun' creates an intermediate expression label (`%t1', `%t2',
     etc.)  for each displayed function, and assigns the function
     definition to the label.  In contrast, `fundef' returns the
     function definition.

     `dispfun' quotes its arguments; the quote-quote operator `'''
     defeats quotation.  `dispfun' returns the list of intermediate
     expression labels corresponding to the displayed functions.

     Examples:

          (%i1) m(x, y) ::= x^(-y);
                                               - y
          (%o1)                   m(x, y) ::= x
          (%i2) f(x, y) :=  x^(-y);
                                               - y
          (%o2)                    f(x, y) := x
          (%i3) g[x, y] :=  x^(-y);
                                              - y
          (%o3)                     g     := x
                                     x, y
          (%i4) h[x](y) :=  x^(-y);
                                              - y
          (%o4)                     h (y) := x
                                     x
          (%i5) i[8](y) :=  8^(-y);
                                              - y
          (%o5)                     i (y) := 8
                                     8
          (%i6) dispfun (m, f, g, h, h[5], h[10], i[8]);
                                               - y
          (%t6)                   m(x, y) ::= x

                                               - y
          (%t7)                    f(x, y) := x

                                              - y
          (%t8)                     g     := x
                                     x, y

                                              - y
          (%t9)                     h (y) := x
                                     x

                                              1
          (%t10)                     h (y) := --
                                      5        y
                                              5

                                               1
          (%t11)                    h  (y) := ---
                                     10         y
                                              10

                                              - y
          (%t12)                    i (y) := 8
                                     8

          (%o12)       [%t6, %t7, %t8, %t9, %t10, %t11, %t12]
          (%i12) ''%;
                               - y              - y            - y
          (%o12) [m(x, y) ::= x   , f(x, y) := x   , g     := x   ,
                                                      x, y
                            - y           1              1             - y
                  h (y) := x   , h (y) := --, h  (y) := ---, i (y) := 8   ]
                   x              5        y   10         y   8
                                          5             10


(%o1)                                true
(%i2) 
Run Example
noundisp : true;
(%o1)                                true
(%i2) circ:  x^2+y^2=1;
                                   2    2
(%o2)                             y  + x  = 1
(%i3) half(x) := rhs(solve(circ, y)[2])*2;
(%o3)                  half(x) := rhs(solve(circ, y) ) 2
                                                    2
(%i4) tex(half(x));
$$2\,\sqrt{1-x^2}$$
(%o4)                                false
(%i5) penum(x) := ''(ratsimp(''(integrate(half(x), x))));
                                                       2
(%o5)                penum(x) := asin(x) + x sqrt(1 - x )
(%i6) dispfun(penum);
                                                       2
(%t6)                penum(x) := asin(x) + x sqrt(1 - x )

(%o6)                                [%t6]
(%i7) print(penum(x));
                      2
asin(x) + x sqrt(1 - x ) 
                                                 2
(%o7)                      asin(x) + x sqrt(1 - x )
(%i8) pgrad(x) := 0.5 + (ev(penum(2*x-1), nouns) / (%pi / 2));
                                    ev(penum(2 x - 1), nouns)
(%o8)             pgrad(x) := 0.5 + -------------------------
                                               %pi
                                               ---
                                                2
(%i9) tex(pgrad(x));
$${{2\,\left(\arcsin \left(2\,x-1\right)+\left(2\,x-1\right)\,\sqrt{1
 -\left(2\,x-1\right)^2}\right)}\over{\pi}}+0.5$$
(%o9)                                false
(%i10) plot2d(penum(x), [x, -1, 1]);
plotplot2d(penum(x), [x, -1, 1]);plot2d(''pgrad(x), [x, 0, 1]);
plotplot2d(
Run Example
noundisp : true;
(%o1)                                true
(%i2) circ:  x^2+y^2=1;
                                   2    2
(%o2)                             y  + x  = 1
(%i3) half(x) := rhs(solve(circ, y)[2])*2;
(%o3)                  half(x) := rhs(solve(circ, y) ) 2
                                                    2
(%i4) tex(half(x));
$$2\,\sqrt{1-x^2}$$
(%o4)                                false
(%i5) penum(x) := ''(integrate(half(x), x));
                                                        2
                                  asin(x)   x sqrt(1 - x )
(%o5)              penum(x) := 2 (------- + --------------)
                                     2            2
(%i6) dispfun(penum);
                                                        2
                                  asin(x)   x sqrt(1 - x )
(%t6)              penum(x) := 2 (------- + --------------)
                                     2            2

(%o6)                                [%t6]
(%i7) print(penum(x));
                         2
   asin(x)   x sqrt(1 - x )
2 (------- + --------------) 
      2            2
                                                  2
                            asin(x)   x sqrt(1 - x )
(%o7)                    2 (------- + --------------)
                               2            2
(%i8) pgrad(x) := 0.5 + (ev(penum(2*x-1), nouns) / (%pi / 2));
                                    ev(penum(2 x - 1), nouns)
(%o8)             pgrad(x) := 0.5 + -------------------------
                                               %pi
                                               ---
                                                2
(%i9) tex(pgrad(x));
$${{4\,\left({{\arcsin \left(2\,x-1\right)}\over{2}}+{{\left(2\,x-1
 \right)\,\sqrt{1-\left(2\,x-1\right)^2}}\over{2}}\right)}\over{\pi}}
 +0.5$$
(%o9)                                false
(%i10) plot2d(penum(x), [x, -1, 1]);
plotplot2d(penum(x), [x, -1, 1]);plot2d(''pgrad(x), [x, 0, 1]);
plotplot2d(

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