### The Maxima on-line user's manual

Algebra Calculator

#### At

Function: at (<expr>, [<eqn_1>, ..., <eqn_n>])

Function: at (<expr>, <eqn>) Evaluates the expression <expr> with the variables assuming the values as specified for them in the list of equations `[<eqn_1>, ..., <eqn_n>]` or the single equation <eqn>.

If a subexpression depends on any of the variables for which a value is specified but there is no atvalue specified and it cant be otherwise evaluated, then a noun form of the `at` is returned which displays in a two-dimensional form.

`at` carries out multiple substitutions in series, not parallel.

See also `atvalue`. For other functions which carry out substitutions, see also `subst` and `ev`.

Examples:

```          (%i1) atvalue (f(x,y), [x = 0, y = 1], a^2);
2
(%o1)                          a
(%i2) atvalue (diff (f(x,y), x), x = 0, 1 + y);
(%o2)                        @2 + 1
(%i3) printprops (all, atvalue);
!
d             !
--- (f(@1, @2))!       = @2 + 1
d@1            !
!@1 = 0```

2 f(0, 1) = a

```          (%o3)                         done
(%i4) diff (4*f(x, y)^2 - u(x, y)^2, x);
d                          d
(%o4)  8 f(x, y) (-- (f(x, y))) - 2 u(x, y) (-- (u(x, y)))
dx                         dx
(%i5) at (%, [x = 0, y = 1]);
!
2              d           !
(%o5)     16 a  - 2 u(0, 1) (-- (u(x, y))!            )
dx          !
!x = 0, y = 1```

There are also some inexact matches for `at`. Try `?? at` to see them.

```(%o1)                                true
(%i2) ```

### Related Examples

f:a0+a1*s^2+a2*s^4;

cond1:at(f,s=1)=0;

cond2:at(diff(f,s),s=...

Calculate

f: a0 + a1*s^2 + a2*s...

cond1: at(f,s=1)=0;

cond2: at(diff(f,s),s...

Calculate

##### at-rectform

at ((1/(c*(x+%i*y) + ...

(1/(c*(x+%i*y) + d)^4...

Calculate

##### at-diff-ratsimp

sn(f,x,g):=g-at(f,x=g...

ratsimp(sn(x^2-a,x,sn...

%,a=3,g=2;

Calculate

##### at-rectform

at ((1/(c*(x+%i*y) + ...

Calculate

##### at-solve

z: V1*p1/T1 = V2*p2/T2;

isop: z, p1=1, p2=1;

isoV: z, V1=1, V2=1;

Calculate

##### at-laplace-sin-solve

inv_laplace(sin(at),t...

solve(%o1);

Calculate

##### at-matrix

mat:matrix([1,2,3],[2...

mat[2,2]: a;

Calculate

f:sin(x)^2+3;

at(f,x=1);

df:diff(f,x);

Calculate

##### at-determinant-matrix-sqrt

mat : 1/3*matrix( [ (...

determinant(mat);

Calculate