### Related

##### pred

A( r ) := 2 * %pi * r...

r : 2;

A(r);

Calculate

##### pred

A( r ) := 2 * %pi * r...

r : 2;

res : A(r);

Calculate

x=x,pred;

Calculate

? pred;

Calculate

1<2;

1<2,pred;

Calculate

##### pred

A( r ) := 2 * %pi * r...

r : 2;

A(r);

Calculate

##### pred

A( r ) := 2 * %pi * r...

r : 2;

res : A(r);

Calculate

x=x,pred;

Calculate

? pred;

Calculate

1<2;

1<2,pred;

Calculate

### pred

Run Example
```(%i1)? assume_pos_pred;

-- Option variable: assume_pos_pred
Default value: `false'

When `assume_pos_pred' is assigned the name of a function or a
lambda expression of one argument <x>, that function is called to
determine whether <x> is considered a parameter for the purpose of
`assume_pos'.  `assume_pos_pred' is ignored when `assume_pos' is
`false'.

The `assume_pos_pred' function is called by `sign' and `asksign'
with an argument <x> which is either an atom, a subscripted
variable, or a function call expression.  If the `assume_pos_pred'
function returns `true', <x> is considered a parameter for the
purpose of `assume_pos'.

By default, a parameter is <x> such that `symbolp (<x>)' or
`subvarp (<x>)'.

Examples:

(%i1) assume_pos: true\$
(%i2) assume_pos_pred: symbolp\$
(%i3) sign (a);
(%o3)                          pos
(%i4) sign (a[1]);
(%o4)                          pnz
(%i5) assume_pos_pred: lambda ([x], display (x), true)\$
x = a

(%o6)                          pos
x = a
1

(%o7)                          pos
(%i8) asksign (foo (a));
x = foo(a)

(%o8)                          pos
(%i9) asksign (foo (a) + bar (b));
x = foo(a)

x = bar(b)

(%o9)                          pos
(%i10) asksign (log (a));
x = a

Is  a - 1  positive, negative, or zero?

p;
(%o10)                         pos
(%i11) asksign (a - b);
x = a

x = b

x = a

x = b

Is  b - a  positive, negative, or zero?

p;
(%o11)                         neg

(%o1)                                true
(%i2) ```
Run Example
```A( r ) := 2 * %pi * r^2 + 2 / r;
2   2
(%o1)                        A(r) := 2 %pi r  + -
r
(%i2) define( A1( r ), diff( A( r ), r ) );
2
(%o2)                        A1(r) := 4 %pi r - --
2
r
(%i3) define( A2( r ), diff( A1( r ), r ) );
4
(%o3)                         A2(r) := -- + 4 %pi
3
r
(%i4) result : solve( A1( r ) = 0, r );
sqrt(3) %i - 1        sqrt(3) %i + 1           1
(%o4)     [r = --------------, r = - --------------, r = -----------]
4/3    1/3            4/3    1/3         1/3    1/3
2    %pi              2    %pi           2    %pi
(%i5) atom( result[3] );
(%o5)                                false
(%i6) atom( rhs( result[3] ) );
(%o6)                                false
(%i7) /* only result [3] is a solution with a real number - NOT an imaginary */r_o : rhs( result[3] );
1
(%o7)                             -----------
1/3    1/3
2    %pi
(%i8) atom( r_o );
(%o8)                                false
(%i9) op( r_o );
(%o9)                                  /
(%i10) A2(r_o)>
0, pred;
(%o10)                               true
(%i11) x : rhs( result[3] );
1
(%o11)                            -----------
1/3    1/3
2    %pi
(%i12) res : A2(x);
(%o12)                              12 %pi
(%i13) res, numer;
(%o13)                         37.69911184307752
(%i14) res>
1, pred;
(%o14)                               true
(%i15) ```
Run Example
```sin(x) + cos(y) + (w+1)^2 + 'diff (sin(w), w);
d                    2
(%o1)              cos(y) + sin(x) + -- (sin(w)) + (w + 1)
dw
(%i2)  ev (%, numer, expand, diff, x=2, y=1);
(%o2)              programmode: false;
x+y, x: a+y, y: 2;
(%o3)                                false
(%i4)  2*x - 3*y = 3;
(%o4)                              y + a + 2
(%i5)  -3*x + 2*y = -4;
(%o5)                            2 x - 3 y = 3
(%i6)  solve ([%o5, %o6]);
(%o6)                           2 y - 3 x = - 4
(%i7)  %o6, %o8;

solve: variable list is empty, continuing anyway.
(%o7)                                 []
(%i8)  x + 1/x >
gamma (1/2);
(%o8)             (%i9)  %, numer, x=1/2;
1
(%o9)                          x + - > sqrt(%pi)
x
(%i10) (%i10) (%o10)             %, pred;
```

Help for Pred