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The Maxima on-line user's manual

Algebra Calculator

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At Calculator

At

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

f:2*r*sin(%pi/r)/sqrt(((1+r^2)+(1-r^2)*cos(2*%pi/r-2*phi))*((1+r^2)+(1-r^2)*cos(4*%pi/r-2*phi)));
plot3d(at(f,r=1/rI),[rI,1/4,3],[phi,-%pi,%pi],[grid,110,30]);

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) 

At Example

Related Examples

at-diff-linsolve-pi-plot2d-subst
plot2d(f2,[s,0,1]);

a2: 10;

f: s^2*(a0 + a1*s + a...

c0: at(f,s=1)=%pi;

Calculate

at-mod-rat

rat(0.1234);

rat(0.12345);

rat(0.12345);

Calculate

at-eigenvalues-invert-jacobian

A: jacobian ([a*If*Sh...

B: jacobian ([gh*Ih, ...

C: invert (B);

Calculate

at-eigenvalues-invert-jacobian

A: jacobian ([a*If*Sh...

B: jacobian ([1/r*Ih,...

C: invert (B);

Calculate

at-cos-diff-linsolve-pi-plot2d-quad_qags-sin-subst
plot2d([parametric,x(t),y(t),[t,0,1]]);

sd: 0.6014101289859;

f0: s^2*(a0 + a1*s + ...

c0: at(f0,s=1)=%pi;

Calculate

at-diff-sin

f:x+2*x^3+sin(y)-y^2;

df:diff(f,x);

s:at(df,x=3);

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-eigenvalues-invert-jacobian

A: jacobian ([a*If*Sh...

B: jacobian ([gh*Ih, ...

C: invert (B);

Calculate

at-rat

rat(((x^4-x^3-11*x^2+...

rat((2-x)/(x+1))*((3*...

rat((x^3+2*x^2+4*x)/(...

Calculate

at-rat

rat((x-x^n)/(1-x)-n*x...

Calculate